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My taste in painting runs toward the abstract. Not everyone’s first choice, I understand, but one that never had to be “sold” to me; I seem to have been born with an intuitive appreciation of large-scale gestural expressionism. I see a quality that I would label “beauty” immediately upon viewing certain paintings by Jackson Pollock and Robert Motherwell and Franz Kline. Beyond that, it’s also clear when these painters were striving for the beautiful but failing to reach it, as in Pollock’s early figurative work.

Because of that innate response, the famous “difficulty” of such canvases has never troubled me, and I did not fall into any of the too-easy traps that keep people away from modern art (“Anybody could do that,” “My five-year old could do that,” “He’s laughing all the way to the bank,” and so on). I wouldn’t necessarily want to argue the merits of a Cy Twombly triptych in a formal way – though I think I could -- but fortunately, there’s no need to. When a painting, even a difficult painting, is beautiful, I can just see it.

Not so in mathematics. Thanks to whatever genetic arrangement decides these things, my brain has never been naturally attuned to an appreciation of the logical relationships among numbers. Here, there seems to be an inverse correlation between the difficulty of the subject matter and my recognition of its aesthetic potential. On occasion I suspect I have glimpsed mathematical beauty (my first intuition of what makes certain statements axiomatic within their formal domains, for example) or the beauty of particular scientific theories (the way time dilation can be derived from nothing more than geometry and algebra). These experiences felt, in a particular way, like piercing the veil between suspicion and Truth. But, not being favored with a mathematical mind, this kind of aesthetic is largely beyond my ken.

Yet again and again when interviewing physicists I have heard people use the criterion of Beauty to describe not only what they are seeking, but how they know when they are getting close. Two models equally well describe a certain particle interaction; as yet we can’t achieve high enough energies to disconfirm either one; from a purely theoretical standpoint, either stands as great a chance of being correct. (By “correct” I mean, perhaps naively, that one model accords more closely with the patterns that actually adhere in nature.) But the physicist will tell me he or she is deeply suspicious of model A because it is “ugly”; or much more interested in model B because it shows a certain “beauty.” If you are a physicist, or a mathematician, or spend time around such people, you have heard this said – or you have experienced it yourself.

What could this quality of Beauty possibly be? Can it be quantified in some way, so that objective debate could take place over the merits of competing theories based on their Beauty? Surely not. And yet the invocation of Beauty is no fluke; too many scientists have referred to it, in my experience, for it to be mere shorthand for “personal whim” or “subjective preference.” Yet what else could it be?

Here’s Steven Weinberg from *Dreams of a Final Theory*:

“There is further reason for optimism in the peculiar fact that progress in physics is often guided by judgments that can only be called aesthetic. This is very odd. Why should a physicist’s sense that one theory is more beautiful than another be a useful guide in scientific research? There are several possible reasons for this, but one of them is special to elemental particle physics: the beauty in our present theories may be ‘but a dream’ of the kind of beauty that awaits us in the final theory.”

Could it be . . . to posit an answer to my own rhetorical question . . . that something like Plato’s scheme really does exist in nature, and the True is equivalent to the Beautiful? (Philosophers: I recognize that statement is only “something like” Platonic Realism.) Could it be, that is, that the closer we get to the TOE, the more beautiful our models inevitably become . . . because ultimate Truth is ultimate Beauty?

A final theory that is merely a mathematical curiosity would be a grave disappointment to many. And many more would be deeply suspicious that we really had the TOE if it exhibited not only symmetry but something like a profound excellence, even loveliness. To those who know science deeply, I am persuaded, bland math and cumbersome theorizing just don’t seem *true*.

And yet nature is under no a priori obligation to manifest a single, coherent deep structure -- to say nothing of one that triggers ecstasy in a certain hominid brain at a certain point in its evolution. How can such a criterion as the Beautiful be justified?

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The human mind has evolved an appreciation of and emotional response to the natural environment.Including both the visual forms and their spatial arrangement and other sensory input from the natural environment.Being within nature can be very relaxing and restorative to the stressed mind. I read a recent article about how a walk in the park, rather than walk through urban environment, has a calming effect on children with ADHD allowing them to concentrate better on return to the classroom. So this has measurable effect.

It may be that the mathematically attuned mind can recognise within the mathematics those forms and arrangements that are a natural rather than unnatural likeness. The natural being that which we have evolved to appreciate as beautiful and right and good and the unnatural being ugly, wrong, bad or unpleasant.This does not mean that unnatural objects can not be beautiful, but when they are they in some way reflect some aspect of the natural.It should be possible to test this hypothesis, if it has not already been done.

Incidentally there are also people among the human population without normal emotional responses. Who have little if any appreciation of the difference between beautiful and ugly, natural and unnatural, right and wrong, bad or unpleasant, that other people know innately.

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Being guided only by aesthetic considerations can easily lead one into blind alleys. Kapler devoted considerable time to fitting the orbits or orbs of planets into Platonic solids. It was an idea which was guided by a sense of beauty in the time. The whole thing of course went nowhere, and his later suggestion about orbits are ellipses, equal area & time and frequency squared proportional to cube of semi-major axis worked.

Modern physics may in time become lost as such. This is particularly the case with cosmology, where it appears the universe is a "multiverse ," and may be even far vaster according to Max Tegmark. Our abilities to access empirical data on this may grow very tenuous. Modern science might in the future become mired in the sorts of uncertainties and quibbles which plagued the ancient intellectual tradition. As the late George Harrison put it, "All things must pass."

As for art, I can approciate abstract art. I would say my interest in modern art is mostly with the French impressionists, where in parallel I am a devoted lover of Debussy's music. Though Debussy refused the label "imprssionist." I read some time back that Pollack's paintings had fractal structure. Somebody did a computer scan of the patterns in his painting and found a Hausdorff dimension.

Cheers LC

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I find this subject fascinating. Here's my opinion, I hope it helps:

- In order to anticipate dangers and to find food, humans developed an ability to anticipate the future. This means to guess a regularity, like in an IQ test "find what's next", "guess the rule" etc.

- The brain learned to reward itself when a new unifying rule has been found. The idea was to encourage the mind to...

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I find this subject fascinating. Here's my opinion, I hope it helps:

- In order to anticipate dangers and to find food, humans developed an ability to anticipate the future. This means to guess a regularity, like in an IQ test "find what's next", "guess the rule" etc.

- The brain learned to reward itself when a new unifying rule has been found. The idea was to encourage the mind to find rules, to predict the future. The reward is felt like a "good feeling", a joyful "aha", brain chemistry. And there is no need for the rules to be true, just to be effective.

- This led to the increase in intelligence, and also of the appreciation of art. Both intelligence and art are types of finding regularities. Music is so beautiful because it is an interplay between our expectations of the next note, based on the rules find by our mind, and the actual next note. Appreciation of painting is finding some meaning, not necessarily rational, between parts of an image, based on their shapes, colors, and positions. Take for example the golden rectangle. We tend, automatically, to compare visually the ratios, to estimate positions and distances. We take the short edge of a rectangle, and compare it with the large one. The difference rectangle is then decoded in the same way. If one single rule goes forever to "explain" the rectangle, then the rectangle has the edges in the golden ratio. Plastic art is not just symmetry, nor just reproduction of objects in nature, but induction of feelings, based on the rules our mind learned so far.

- In mathematics, the sense of beauty occurs when we see some relations between things we thought to be different, even incompatible. Think at the beauty of Ceva's theorem, when you see that medians intersect in one point for the same reason the bisectors or the heights do. Think at the beauty of the same theorem, when you understand that Menelaus' theorem is just its projective geometric dual. Think at the feeling Klein had when he realized that all geometries are in fact explainable as groups acting on some spaces.

- In physics, beauty is associated with the moment when Newton realized that the same force which maintains the moon on its orbit is responsible for the falling apple. Or when Maxwell realized the unification between electric and magnetic forces, when Lorentz, Poincare and Einstein related space and time, Einstein related energy and momentum, curvature and gravity etc. Beauty is when many of the problems of the weak force vanish when this is seen as a half of the electro-weak force, or when we see that the gauge theory describes all the three forces.

- Beauty is the mystical feeling of unity, experienced when meditating about the Universe. Perhaps this is why TOE is regarded as the extreme beauty.

- To conclude, I think that the feeling of beauty is associated with the understanding of unity of a great diversity, in a few principles, or a few painted lines, or a haiku, or a unifying theorem. Unifying diverse concepts in a small, preferably simple, set of basic concepts, the infinity in your hand, that's beauty.

Cristi

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I am attracted to the beauty of mathematics. In my essay's conclusion, I talked about the struggle between simplicity and beauty. A good example is the Standard Model of Particle Physics. It seems ugly to me because the couplings are not unified, but it is practical and accurate.

My interpretation of Occam's razor is that simplicity and beauty are often balanced in physics applications. Unfortunately, simplicity and beauty are difficult to define, so this 'balance point' is even more difficult to define. I have found that there is much beauty in mathematics, and it often seems to have no application to a physics problem at hand.

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Congratulations Bill,

You have a knack to pick up interesting topics that stir discussions and we are happy to oblige.

Like a moth attracted to the flame, I too have something to say about this topic.

First, beauty is in the eye of the beholder. I recall this comedy where an Amish guy ventures in the larger world and at some point meets a beautiful girl. He looks at her and starts finding defects: too skinny, cannot have 10 children, etc. I forgot the name of the movie, but the point holds for mathematical beauty as well. Math is often criticized by physicists for being too abstract and hard to understand, like programming the blinking 0:00 on a new VCR. But find a physical application, and the perception changes.

Second, mathematical beauty is necessary, but not sufficient. Laurence’s example with the Platonic solids is an excellent example of why.

Third, used properly, mathematical beauty can tell you if you are on the right track. In research, you spend a lot of time in the land of confusion, and if you are not blinded by bias, when things starts falling into place naturally, then you know you are onto something valuable.

It is not nice to toot your own horn, but my own essay in the contest attempts to solve Hilbert’s sixth problem, a necessary step on the way towards a TOE if it indeed exists. If time will prove my approach right, then I can state that the overall understanding of the universe is indeed beautiful even if we will not solve all the puzzles of nature right away. Each major problem we encountered so far in physics had a beautiful (and unexpected) solution. Solving nature’s puzzles is like taking an onion apart and I am not of the opinion that our universe is this giant monolithic mathematical object that a naïve TOE paradigm entails.

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The movie mentioned by Florin is Kingpin.

From my viewpoint, the beauty of Kepler's laws is superior to the beauty of its Platonic solids approach. Sometimes, it is a thin line between mathematical beauty and "numerology". Newton's theory is even more beautiful, since it concentrates Kepler's laws and gives them an explanation.

I agree with Ray that there is much mathematical beauty...

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The movie mentioned by Florin is Kingpin.

From my viewpoint, the beauty of Kepler's laws is superior to the beauty of its Platonic solids approach. Sometimes, it is a thin line between mathematical beauty and "numerology". Newton's theory is even more beautiful, since it concentrates Kepler's laws and gives them an explanation.

I agree with Ray that there is much mathematical beauty which remains without physical applications. On the other hand, it seems to me that the beauty in Physics is mathematical in origin. Considering the examples I gave in my previous comment, they all are of this kind. When Newton unified the attraction between earth and moon with the attraction of an apple, he showed that it is the same inverse square dependence, which on short distances seems to be constant. So we have a field which in one instance is radial, in another seems constant and parallel, hence the apparent difference. The other examples I gave, and others that come through my mind, are all mathematical. Ray's example with the Standard Model is good. The success of this physical theory is based on mathematical beauty, and its shortcomings (coupling constants, lack of simplicity of the gauge group, unexplained masses, etc) originate in lack of mathematical beauty. I hope that is not a particularity of me to be more sensible to mathematical beauty than to other types of beauty, so if somebody can give examples of non-mathematical beauty in physics, it would be interesting.

I wouldn't identify beauty with simplicity, as repetitive symmetry is not the best example of art. I think that a good approximation of a definition of beauty can be given with the help of Chaitin-Kolmogorov complexity. A theory, or a piece of art, tries to describe some meaningful content. Assume we have a theory which explains a domain of data, and does not make false predictions. To compute its beauty, write down the meaningful content, write down the basic principles from which we can derive the meaningful content, and compute the compression rate. This provides a rough measure of beauty. It said how much meaningful information is contained within a small set of principles. It is rough, because it obviously depends on the language employed. But this is good, because beauty is in a large measure dependent on the language employed too. So perhaps this approximation of a definition of beauty is not that rough.

The same can be said about a piece of art. Beauty is the rate of compression of the meaningful content expressed by that piece of art. When you watch a painting, your senses are invaded by its meaning, and you feel the infinity compressed in the rectangle of the frame. You can write a book describing all the meaning of this painting, but this is explicit description, and it is not art by itself. Of course, the book itself may be a piece of art, if it adds extra meaning beside the description it gaves to the painting. The same is true about a book on popular physics, describing the beauty of Maxwell's equations in a way that adds new meaning to the plain equations.

I don't want to give the impression that beauty is just highly concentrated information. Beauty is unification of many apparent distinct meanings, without sacrificing the simplicity. Beauty is both in the way the meaning is encoded, and in the way it is decoded.

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Cristinel Stoica,

You said "I hope that is not a particularity of me to be more sensible to mathematical beauty than to other types of beauty, so if somebody can give examples of non-mathematical beauty in physics, it would be interesting."

I found your post very interesting because I do not understand the appreciation of beauty in mathematics itself. I can only appreciate beauty in those mathematical forms that I am able to visualise or see represented visually. So symmetry may be beautiful, certain curves can be beautiful and fractals can be beautiful etc. Raw mathematics may be interesting or intriguing or clever but I get no sense of beauty at all. Perhaps because I get no personal pleasure or sense of peace from raw mathematics.

You said "Beauty is the rate of compression of the meaningful content expressed by that piece of art. When you watch a painting, your senses are invaded by its meaning, and you feel the infinity compressed in the rectangle of the frame."

I find your perspective very interesting. I would disagree however. From my personal point of view, beauty is a quality that evokes an enjoyable emotional reaction. Which may be a sense of peace or calm or pleasure. This is different from a good painting, which may or may not be beautiful. I would personally define a good painting as one which captures ones attention and makes one wish to prolong the viewing experience of the work. It may be interesting or intriguing or clever or it may be beautiful.

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Dear Georgina,

You say: "I can only appreciate beauty in those mathematical forms that I am able to visualise or see represented visually."

I can say the same about myself, to some extent. Whenever I studied a mathematical theory, or a physical one, I tried to understand it geometrically, because I always felt comfortable when I could picture myself somehow the ideas. And I can say that, starting from elementary arithmetic, to very difficult mathematics, this can be done. Doing this, I must say, slows down considerably the process of learning math. All examples I gave, I perceive as being geometric. Perhaps before understanding them geometrically, I was less able to see their beauty. One friend, mathematician, is "algebraist", and, as some other "algebraists", despises somehow the "geometrists", because they need to draw pictures for everything. This is somehow beneath the dignity of "algebraists", because they perceive it like counting using fingers. But when he was interested on some topics in group theory (a chapter of algebra), and I provided him some geometric representations, he was very happy, because he understood very fast something he was trying for long time. Yet, it is difficult, and it takes very long time, to build inside your mind geometric structures to picture highly abstract ideas. But I am aware that the mathematicians who don't represent much geometrically the mathematical stuff, are also sensible to the mathematical beauty.

You say: "From my personal point of view, beauty is a quality that evokes an enjoyable emotional reaction."

I agree with you, although you say you disagree with me. My viewpoint is just a viewpoint, subjective and limited. But my words, "Beauty is the rate of compression of the meaningful content expressed by that piece of art", must be taken in conjunction with my previous comment, in which I proposed that there is a chemical reward we get when we "find the rules", when we decode the meaning. In my opinion, it is this chemical reward which we perceive as "enjoyable emotional reaction", and this is why decoding art "captures ones attention and makes one wish to prolong the viewing experience of the work", to use your words. It is the feeling of things coming in one place, of conflict resolution, of unification. Ad extremis, it is the religious experience of unity of the apparent diversity, the experience of encoding the manifested world in the unmanifested Tao.

Best regards,

Cristi

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Beautiful Truth can be experienced directly. When there is no gap between perception and experience we experience Truth. Conscious observer knows the truth, he is truth himself.

In physics we experience via rational mind

perception - mind processing - experience.

Conscious observer experiences directly:

perception - experience.

This "objective experience" is called in zen "Tathagata" - suchness.

yours amrit

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Thanks Cristi,

The movie was indeed Kingpin. Physicists have the same (amish) mentality in the land of math. A mathematician seeks beauty in generalizations and unexpected links between unrelated structures. A physicist has an inward looking perspective and we want to prove uniqueness and applicability of math to the real world. To a mathematician octonions and sedenions are beautiful manifestation of the Cayley Dickson construction, while to physicists they are the crazy old uncle or they are not used at all. I once had a debate with a mathematician about relaxing a common mathematical assumption. To him this looks like the escape from Egypt, to me it looked like the fall from Paradise.

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Cristi,

I very much like your perspective. I was not surprised by your statement that you agreed with Georgina, for that was my original takeaway from the total of what you said.

The beauty in physics is mathematical, since physics is nothing without mathematics. Physics is and should be finding mathematical explanations for our physical reality. So why would the beauty of physics be...

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Hi Rick,

Can you please explain in detail how electrodynamics comes out octonions? If you have a paper about this I would like to read it. Real and complex numbers have well defined derivation operators, but quaternions do not. I am not sure about octonions, but I bet they lack a well defined derivation also. If so, how can you get electrodynamics out if them? (I bet electrodynamics might be expressed in quternionic and even octonionic language, but obtaining electrodynamics and nothing else out of octonions seems hard to believe).

My intuition problem about them is their lack of associativity. Do you have a physical intuition about this?

Thank you,

Florin Moldoveanu

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Hi Rick and Florin,

I have seen Maxwell's Equations cast into one Quaternionic equation (but its buried with all my grad school notes in the garage). That can be done. The six antisymmetric quaternionic tensor components contain the electromagnetic field tensor. Octonions contain 10 symmetric and 10 anti-symmetric tensor components - enough tensor components to contain Einstein's 10 symmetric tensor Field Equations of General Relativity AND the six antisymmetric electromagnetic field tensor components. But an 8-D Octonion TOE doesn't quite work - Lisi's "An Exceptionally Simple Theory of Everything" was a great attempt, but did not properly contain 3 chiral generations of fermions (one, maybe two, but not three). This is why I am playing with 12-D and calling it the union of a Quaternion (with Maxwell's Eq's) and an Octonion (with Einstein's Eq's). Certainly, many details need to be worked out...

Dear Florin,

Details such as associativity need to be worked out. I am neutral towards quantions - they may be a 2-D part of the puzzle in one of Lawrence's 26-D models. But to build everything out of quantions may get cumbersome (especially if we need more than Lisi's 8-D, so we need more than 4 types of interacting quantions), and may lack natural "Beauty".

But how do we define beauty? My wife is an artist. She saw the simplices in my essay and thought it was interesting that physics and math could resemble art.

Have Fun!

Ray Munroe

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Hi Florin and Rick,

Indeed, it is especially beautiful when physical data fit perfectly into a mathematical structure. This is why we tend to prefer math which admits natural geometric or physical interpretations. I need to mobilize much empathy to understand how the purist mathematicians get motivated, and I think that the explanation is this: When we activate in an area, this area is the most natural for us. Then, we try to fit/interpret/connect any new data in that framework. What fits easily seems natural for us, what cannot be easily connected, seems unnatural. The beauty, as Florin said, is in the eye of the beholder, and this is why we have different opinions about beauty in mathematics and physics. But I think that the difference in our appreciation of beauty comes from the basic notions in which we encode the more complex ones. It comes, according to the interpretation I proposed above in terms of Chaitin-Kolmogorov complexity, from the difference between the "compression algorithms" we employ to encode the information. The beauty which moves us more is that which unifies more data, or solves more conflicts, in our subjective "worldview". Therefore, any formula trying to evaluate beauty must include the "beholder".

Best wishes,

Cristi

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Hi all ,

Very interesting .

the complexity returns to the simplicity .....small quantum spheres ...time evolution and codes of becoming ......build cosmological spheres ...complexification in an unique universl sphere .The beauty of our Universe is beautiful indeed .A specific number of spheres exist .

All future extrapolations shall be always correlated with this universal law ,the spherisation ....there is an ultim aim evidently .We are youngs .

The maths are essentials when they are coorrelated with this physicality ,if not it is false .We can imagine but we must rest in the physicality .It is foundamental .

Thanks for your relevant discussions to all .

Best Regards

Steve

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The general concept of "beauty" must have a person specific context to it, since it is more emotional in its realization than factual, tangible, something that can be taught.

We can better define mathematical beauty, especially in the context of physical reality, physics if you will. When simple axiomatic concepts lead to a broad understanding of how things seem to work, we have beauty. To Cristi's point, the beauty is "compression" of the broader applications into a smaller fundamental set of concepts we have the capacity to fully take in and appreciate. We take pleasure in the belief we can apply the crystallized beauty to better understand the details yet unknown in the world about us. When we come across this form of beauty, we smile and say to ourselves, this is good.

Octonions fit my personal definition of beauty in mathematics/physics. The beauty is the marriage of mathematical fact that octonions do not have a singular definition, with axiomatic faith that the difference should not have an effect on the outcome of mathematical application to physical reality. This is a full measure of "compression", and is the beauty I have observed in finding things like octonionic representations of observables like energy, work, force, momentum all by no accident meet the requirements. Better yet, the algebra tells us how they must be, we are not free to choose any of it.

Florin asked if I have a paper on this, anyone interested can go to my website here. There is much work to be done yet. It is a "hobby", not my paying job.

Florin, EM is a subset only of the full presentation. If it only did EM, it would be boring. The EM presentation is not in any way quaternionic, due to the fact that quaternions do not fundamentally cover the multiplication characteristics of the E and B field components. This is why in 4D you must use a tensor to cover the fields. Not so in 8D. There is a quaternionic central force separate from the charge force that IMHO is gravity.

Also Florin, I would like your opinion or a restatement of others on why you believe the concept of derivation is universal and must be part of any proper calculus.

Thanks,

Rick Lockyer

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each person has his point of vue ,and of course some are trues and others are falses.

When a theory is correct we see its applications and adaptations in all centers of interest ,in all foundamentals .

Math ,phys ,chem ,biology ,ecology ,philosophy,astronomy and cosmology ,astrobiology ,evolution....an axiom is an axiom ,and the confusion appears when the imaginaries without borders are inserted ,thus it exists two kinds of roads ,or sciences ,one real and the other imaginary .

All is a question of perception and interpretation like a play between the Copen. Interpret. and the EPR and that and that .....at the unification of course only the physicality and its reals are of course an pragmatic extrapolation ,because it is our physicality simply .A closed system is a closed system and the infinity more the zero and the - needs adaptation with our Universe and its laws ,basics ,logics ,rationals and foundamentals .

Best Regards

Steve

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Octonions ,quaternions ,strings ,branes ,decoherences ,imaginary external particles .....all that is false in the whole ,sorry but it is like that .

The gravity is the gravity and the light is the light ,let's see thus their synchronizations on this line time which is CONSTANT .

Only 3D AND A CONSTANT .it is essential .

Regards

Steve

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Steve said "Octonions ,quaternions ,strings ,branes ,decoherences ,imaginary external particles .....all that is false in the whole ,sorry but it is like that."

They are all used for producing models of reality. In time some will be seen to give a more useful representation than others. All models might be said to be false because they can not be reality itself only a representation. Likewise all art might be said to be false because it can only represent reality or some aspect of reality, it is not reality itself. That inaccuracy does prevent it from being beautiful, worthwhile, or useful as a representation. Although not all models will be equal in their beauty, worth or usefulness.

A bus time table might be considered false because the buses never actually arrive when timetable says they should. That does not stop it from being very useful as a predictive tool. I doubt you would say that bus timetables should not be produced because of their scientifically verifiable falsehood. Bohr's model of the atom might be considered false but it is still very useful for predicting the behaviour of chemicals.

As an analogy. I could, if so motivated, build a sculpture representing a beautiful human form from old aluminium cans. A master stone mason could carve a human form from marble. Both would be representations of a human form not an actual human body. Both might be considered beautiful although one is a more accurate representation (and so more useful for anatomical study) than the other.

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Last post was me.

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Oops In noticed an error in my post.

I said "That inaccuracy does prevent it from being beautiful, worthwhile, or useful as a representation. Although not all models will be equal in their beauty, worth or usefulness."

It should read that inaccuracy does -not- prevent it being beautiful, worthwhile or useful.

An important difference. Sorry I should have checked what i had written more carefully.

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Rick,

Thank you for your link. Derivation is important for various physical and mathematical reasons, but I do not know of an overriding reason overall. Among the usual reasons are: fundamental theorem of algebra, existence of tangent and cotangent linear spaces (or equivalently in physics the Lagrangean and Hamiltonian mechanics, or Schrodinger and Heisenberg pictures), gauge theory of bosons and fermions, perturbation theory.

If I am hard pressed for a universal reason for derivation, I would say that it is important due to the fundamental theorem of algebra in conjunction with the Gelfand and Naimark theorem which identifies locally compact Hausdorff spaces with commutative C*-algebras.

Ray,

I have a vague recollection seeing Maxwell’s equations in quaternionic format a long time ago.

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Dear Rick,

You said "Florin, EM is a subset only of the full presentation. If it only did EM, it would be boring. The EM presentation is not in any way quaternionic, due to the fact that quaternions do not fundamentally cover the multiplication characteristics of the E and B field components. This is why in 4D you must use a tensor to cover the fields. Not so in 8D. There is a quaternionic central force separate from the charge force that IMHO is gravity."

It sounds as if tensor properties disturb you. To the contrary, I think that 10 symmetric and 10 anti-symmetric tensor components are the octonion's signature, and the reason why the octonion might be able to contain the 10 symmetric tensor Einstein Field Equations of General Relativity. You can avoid tensors by using Quantions (like Emile and Florin), but then you will need at least 5 of those. Beauty is in the eye of the beholder - Are 5 quantions more beautiful than an octonion and a quaternion? I can't say without seeing the final product.

I am also a fan of the Octonion and E8, but I haven't yet seen one of these models that incorporates all of particle physics and gravity - Lisi's E8 came close.

I will look up your web site next week.

Have Fun!

Ray Munroe

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Hi all ,

Dear Georgina ,

I liked your point of vue ,it is a beautiful diplomatic analyze .There I agree about the sharing of ideas .

The problem is the actual sciences system and the desire of many to find a TOE .That becomes ironic ,the sister of the individualism thus is a reality for this quest of what......

The truth is not a play ,it is the truth .The ultim equation is in the ubiquity with its codes ,intrinsic in the quantum reality .Nothing causes the gravity from the exterior ,of course the light polarizes with the gravity in an evolution point of vue but the gravity and the time has built the graitational gravity and that continues .I think really what many people doesn't take the right road in their extrapolations .We can superimpose maths ,of course the maths are universals but if and only if the correlation is a pure physical link with its NUMBERS ,specifics furthermore .

The whole can be false but the technic or method can be improved in this physicality like a foundamental superimposing and sorting .

The sciences community has a very big problem with the series and its limits .Always these specifics numbers thus ,viva el prime numbers .....it is the physicality in its fractal ,even the volume of spheres .

Best Regards

Steve

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A derivation ,yes of course but with always a good referential and its Borders .A closed system and its thermodynamical laws are essentials in a perceptible relative analyze.

an we derivate like we want ,I don't think .

Let's take a derivation of a volume or a space ,with their vectors and scalar fields .Let's take now a point and let's integrate with the surface.Now how is the method ,if we tending towards a personal referential .Even for the divergences and rotations .The vectorial field thus must be pragmatic in its numbers it seems to my .

The theorem of Stokes perhaps .....with alwxays the good limits in the serie.It is the same with our coordonates and their calculs .The different operators become relevant ,let's insert thus the Hamiltonian and Laplace systems .

What I maka personaly is the link with spherical coordonates more the rotations ,it is there I return about the correct numbers of spheres and the evolution point of vue with the increase of mass .

The Ostrogradsky gauss theorem is relevant .

What I say is simple in fact ,it is always a qustion of referential ,and an universal referential exists .....thus let's derivate yes but with rationality of course .

Best Regards

Steve

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This is my interpretation of why the particular image accompanying this blog, which is exceptional, has the quality of beauty that perhaps other abstract works do not achieve to the same degree. (I do not usually intellectualise why a particular image is pleasing to me, I just enjoy it.)

Firstly it -is- reminiscent of nature in a number of ways. It could be likened to gossamer threads on dry sticks or a mycelium growing on dry grass. The hues are neutral and natural looking. These are calming rather than stimulating. It is not an alien or artificial looking canvas.

Secondly there appears to be a balance between each of the hues themselves and the background. There appears also to be some discernible order emerging from what might otherwise be random disorder. There is on the one hand great complexity which provides interest but on the other balance and emerging order which is restful and allows one to contemplate the canvas as a whole rather than being lost or disoriented by the disorder. Also the way it does not crowd the edge of the canvas but there is a less dense border defining the boundary of the image inside is helpful in that regard.

The quality of emerging order from complexity does seem to be a natural phenomenon. When contemplation of ideas or application of mathematics discovers order from complex and perhaps unconnected areas of consideration that seems to be natural and therefore beautiful. When the mathematics or ideas fall together easily it seems that that is how it should be. Though it is perhaps mimicking the order of nature without actually being the best description of the natural ordering itself.It could be that a less beautiful path could eventually yield an even more beautiful outcome, when it is fully understood and completed.

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Thanks, Florin -- I'll keep them coming. It's a pleasure to have an online community of thinkers such as we find at the FQX blogs.

Here's Roger Penrose being interviewed in Discover this month:

DISCOVER: "When physicists finally understand the core of quantum physics, what do you think the theory will look like?"

PENROSE: "I think it will be beautiful."

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Thank you Bill,

And happy Thanksgiving. Please, keep them coming.

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Hi all ,

Dear Georgina,

That is a beautiful philosophical interpretation .You have a personal approach of the objectivity and the subjectivity where the philosophy hrmonizes the curves of the balance between them .I think that the personal imaginaries are of course specifics ,thus uniques ....that says the universal objectivity and its specificities in the laws and codes are an evidence and there it doesn't exist subjectivity because the perception is total in this scale of whole with its limits .It is very simple ,a human can say for example what in the future a star will become a sqare ....it is subjectif but of course the universe never will change its spherisation .It is the same with the numbers ,a human can extrapolate a serie but we can't say a error about the real numbers of physical bodies .It is always a balance between the right and left brain .

The complexity is specific and there in this line of evolution ,the actual imaginary of human is young thus the subjectivity is going to evolve too towards thus the universal objectivity .and that due to the complexification .

It is a little like a puzzle ,the time arranges correctly the puzzle .

I consider the sciences like an art ,an all .Even with music or poems ,a certain logic is essential to harmonize the fundamentals .

We can interpret a painting with our dreams but the painting rests like it is.

The maths are fundamentals when the physics are the main piece ,the reals must be the main driving force of the serie in the real referential .In this logic all which is correlated is good and all above the limits must be improved or balanced .

Thanks for your point of vue dear Georgina .

Best Regards

Steve

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Maybe of topic, but it has to do with symmetry, beauty and fundamental questions.

I like symmetry. If there is symmetry between the physical quantities, why is the quantity 'energy' so special among the other quantities? We have the Lagrangian and the Hamiltonian. The classical Lagrangian is kinetic energy minus potential energy. Why two different forms of energy? Why not more? Is there a kind of relation between those different forms of energy? kinetic energy has the term 'velocity squared'. potential energy has the term 'product of acceleration and length'. If we differentiate velocity then we get acceleration. If we differentiate acceleration then we get jerk. So maybe there could be also a quantity in the lagrangian that is the product of 'jerk' and 'lengthtime'. Can we go on forever? Is it a series?

I think that energy must be treated on the same level as the other quantities. So energy is not more special then the other scalar quantities mass, time or gmflux. If we don't tread energy in the same way as mass then we do not understand what is going on. So there must be a kind of lagrangian of mass and a lagrangian of time and a lagrangian of gmflux. And together they form a bigger equation that combines al those lagrangians.

Any thoughts?

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Dear Peter,

One of Lawrence's works in progress is the attempt to develop a quantum time operator. The Heisenberg Uncertainty Principle relates Energy and Time. Fourier transforms also relate these two concepts. And of course, Relativity relates Energy with Mass and Time with Space. I agree that more must be happening here. Perhaps it is hidden in higher dimensions?

Have Fun!

Ray

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I have been working on a problem with the Taub-NUT spacetime. This spacetime turns out to have Killing symmetries on a 7-dimensional space with a G_2 holonomic action. This spacetime is then a “mirror,” of sorts, for the M^{11} = M^4xS^7 superspace, where the G_2 holonomy on the 7-sphere is determined by the structure of this odd spacetime. The G_2 and F_4 as centralizers of the E_8 can be...

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After the TeX'ed equation the in line expression [T_{op}, H} is supposed to be a commutator [T_{op}, H]. This is based on an email to somebody, where I indicated the gravi-magnetic mass of the TN spacetime, called the NUT parameter is tied to magnetic monopoles with GUT (like) Yang Mill gauge theories.

Cheers LC

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Hello Peter and Ray,

Dear Ray ,

I beleive that if a quantum time operator is inserted ,the evolution and its polarisation must be considered ,the codes of informations and activations whre the mass increases on this line time .Thus the time is like an activator of the rotations implying mass with the very weak polarisations of complexification .The the mass ,the energy increase too in the time if we consider the universa phical energy ,different han the unknew unlimited entropy if I can say .Personaly I do't see hidden dimensions ,variables ....just a 3D MORE A CONSTANT and these codes of becoming in time and space .The informations are inttrinsics I think ,the mass and its velocity of rotation more the entangled spheres IN EVOLUTION thus polarisation.Can we consider a time operator different than just a constant ,perhaps the key thus is in the information ,thus the main code ,in conclusion ,too far of us due still to our limits and walls and our young age at the universal scale .

In a fourier analyse and series ,the referential thus becomes important like the topology ,thus the limits must be foundamentals .There the thermodynamics takes all its sense I think with these limits .

What do you think dear Ray ?

Best Regards

Steve

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Oops hello too Lawrence ,

NUT parameters ,I don't know ,could you develop a little please ?

Steve

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Dear Steve,

Your ideas and mine are more similar than you realize. Although I normally refer to my theory as a 'lattice' which implies strings connecting lattice sites, the reality is that these lattice spacings are non-zero which implies spherical packing of non-zero radius. This brings us full-circle to the idea of String/ Sphere duality and its similarities to Wave/ Particle duality. Furthermore, Lawrence and I have discussed scenarios whereby an H4 of Spacetime may decompose into a series of SU(4) tetrahedra (3-dimensional 3-simplices) similar to Pati-Salam theory or a series of SU(5) pentachora (4-dimensional 4-simplices) similar to Georgi-Glashow theory. Although your ideas seem more basic than mine, they could be a representation of a modified Pati-Salam theory.

Lawrence's above post requires a minimum of 11 dimensions: M^4xS^7, 11=4+7. I think 11 dimensions imply at least 12 - perhaps an Imaginary time, and we need to understand where the 12th dimension disappeared to. Add in Supersymmetry, and we need a minimum of 24 dimensions. Add in Lawrence's Jordan transformation, and we need a minimum of 26 dimensions. But it may be that these all decompose into simplex-based branes that can be described in terms of spherical packing in various numbers of dimensions (Space is a 3-brane, so the tetrahedron is a very relevant simplex).

Have Fun!

Ray Munroe

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The problem with time operators in ordinary settings is that a unitary operator formed with a time operator is a sort of "energy development" operator. This has the effect of mapping any Hamiltonian to a continuum of eigenvalues. This poses two problems. The first is the energy spectrum is not bounded below. This means that quantum systems would be inherently unstable, such as how the 1S level in the hydrogen atom prevents a run away collapse and radiation production. The other is that discrete eigenvalues for energy are not supported. If an initial Hamiltonian has a discrete eigenspectrum the time operator T|t> = t|t> a unitary map U = exp(ieT} maps this to a continuum. Since U is 1-1 this prevents any Hamiltonian from having a discrete eigenspectrum, as there would be no unique inverse U^{-1}. This is the essence of Pauli's theorem against the existence of a time operator.

In what I am doing the time operator is defined in a very specialized manner with a discrete set of points on patches of the TN spacetime. The nonHausdorff condition on the spacetime then permits this time operator on a measure zero Hilbert space. So this is not a quantum time operator which obtains in a universal sense.

Cheers LC

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Hello Ray ,Lawrence ,all ,

You know Ray ,I think that all roads go towards the same aim .Thus the superimposings and smilarities indeed are a evidence .I like the complemetarity ,it is better than the individualism .

I like your idea about this new duality ,I must admit what at the Planck scale ,the vibration of the spherical membran before the code is unknew for me .Probably what this main central sphere ,and its main code of informations (or others specific entangled spheres,)is the real key about the ultim frequence and sense.The contact between spheres seem interesting too about waves .

SU 5 I don't know dear Ray ,I have difficulties to extrapolate in several dimensions above the planck limits and above 3D .GG theory ,PT theory ,I don't know .Could you explain me please .

If your extra dimensions were after the planck scale ,I could understand but in our 3D system ,I can't arrive to encircle it .11D OR 24 D ??

About SUSY ,I am not a supporter o this symetry just because the entangled spheres seem specifics thus the symmetry globaly can be understood but localy that becomes confusings ,thus implying a global confusion too .

I like crystals and the beauty of our nature ,but is it sufficient to extrapolate with these crystals adding with some imaginaries like the tetrahedron ? If the evolution is a key ,thus can we consider these crystals like the rel architecture .It seems to me that the cosmological spheres are more interestings .It exists only one cosmological architecture ,on the other side it exists many crystals ,pyroxens ,carbons ,tetrah,....

What do you think Dr Cosmic Ray ?

Regards

Steve

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The NUT parameter is the gravitational analogue of the magnetic monopole. I have written up a rather extensive post here which illustrates how the Taub-NUT spacetime is connected with the excetional Jordan algebra. This is not complete, and requires my writing up a fairly lengthy paper. However, this might be the start of such. The business of time operators with TN spacetime is also an...

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The second paragraph got nixed because I goofed a tex command. I suppose you might say this post is a disconnected topological set

--------------

\For a spacetime which has a static electromagnetic field there is the vector

potential A_e that determines a field two form F_e

$ A_e~=~{q\over r}dt~\rightarrow~F_e{{q\over{r^2}}dt\wedge dr $

which has a Hodge star duality to a magnetic monopole field

$ F_m~=~*F_e~=~qsin(\theta)d\theta\wedge d\phi~\rightarrow~A_m~=~qcos(\theta)d\phi $

which indicates how in a pure dual setting for the EM field the electric potential is associated with a magnetic monopole A_m. The duality involves the exchange of the electric vector along the time direction with a magnetic potential along the azimuthal angle. A similar situation exists for general relativity. The Schwarzschild black hole, or spacetime, is dual to a spacetime where the radial direction for the field is replaced by time. We consider the Schwarzschild metric

ds^2 = Adt^2 + A^{-1}dr^2 + r^2(dθ^2 + sin^2θdφ^2), A = 1 – 2M/r

Just as we took the Hodge star of the field two-form for the electric field we take the Hodge star of the Riemann curvature tensor

$ *R_{abcd}~=~{\tilde R}_{abcd}~=~{1\over 2}\epsilon_{abef}{R^{ef}}_{cd} $

where the dual metric is then --- continue on original page

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Dear Steve,

We only observe 3+1 dimensions, and any successful model must explain why the Universe collapsed from 26 to 24 to 12 to 11 to 4 dimensions. String theory proposes that these other dimensions are in a compact hyperspace - perhaps hyperspace never experienced Inflation as did Spacetime. Conversations with Jason and Lawrence have led me to believe that if Spacetime and Hyperspace interact, then it must be a Quantum Gravity interaction - being a quantum interaction prevents the two different branes from merging into a new equilibrium, and being a gravitationally weak interaction implies that the strongest effects of overlapping branes will occur in the regions of highest gravity - Black Holes.

You say you do not believe in Supersymmetry. Supersymmetry is a symmetry between particles of different intrinsic spin. Your spheres can have spin and can thus represent intrinsic spin. Why does it seem unnatural to you?

Dear Lawrence,

I enjoy reading your posts. I wish I understood more than half of your mathematics. I'm sorry, I guess I'm just slow...

Your Friend,

Dr. Cosmic Ray

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This establishes the role of G_2 in supersymmetry. This is all a rather interesting development. It is a new insight into how 26 and 11 dimensions are related to each other.

Since this blog thread is largely about art, I attach a rendering I did last year (about this time in fact) on the evolution of the universe.

Cheers LC

attachments: desitter10.gif, desitter20.gif

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It was more like that I wondered about the origin of the lagrangian L.

L = E_kin - E_pot.

So we can write the classical Lagrangian like (a = acceleration, h is length):

E = 1/2mv^2 - m a h.

E/m = 1/2v^2 - a h.

c^2 = 1/2v^2 - a h.

The derivate of velocity is acceleration.

The integral of velocity is position (length).

a h = derivate * integral.

Can we expand c^2 = 1/2v^2 - a h to a series?

Peter van Gaalen

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Hi all ,

Dear Lawrence ,thanks a lot for this super explaination .

Dear Ray,

"You say you do not believe in Supersymmetry. Supersymmetry is a symmetry between particles of different intrinsic spin. Your spheres can have spin and can thus represent intrinsic spin. Why does it seem unnatural to you?"

In fact I like the symmetry and I think it is foundamental evidently .But the specificities of entangled spheres of the quantum system imply a neccessity to adapt the globality and the locality .The steps of mass/energy/fields seem in a SUSY but these specificities must be inserted .Can we say that a galaxy is perfectly symmetric with an other ? The intrinsic spin is so complex, if like in my model I insert the number of spheres ,probably a serie of primes numbers .

Thanks to both of you the two mavericks ,dear Lawrence ,I am always impressed by your maths and methods .

Best Regards

Steve

Best Regards

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@Peter van Gaalen: Your Lagrangian argument mixes relativistic an nonrelativistic aspects of physics. Secondly, to do physics you might take the equation

c^2 = 1/2v^2 - a h.

and sau the speed of light is an invariant, and a variation on this is zero. The calculus of variations is the basis for Lagrangian dynamics. From that you would just get a Newton's law for a body moving near the Earth.

The variantion of the speed of light to derive motion in relativity is a standard tool. The invariant interval ds^2 = g_{ab}dx^adx^b, defines an action principle as

$ \delta s~=~\delta\int\sqrt{ds^2}~=~0. $

This is a general version of Fermat's principle of least time in optics. If you crank through this (about a page or two of calculations) you derive the geodesic equations in general relativity.

Cheers LC

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Dear Steve,

I overlooked part of your earlier question.

Tetrahedra are not 'imaginaries'. If we stack spherical fruit on a grocery shelf, we build a Face Centered Cubic (FCC) Close Packing Lattice. The underlying basis vectors are tetrahedral. Thus tetrahedral symmetries arise naturally in the spherical packing of 3-spheres. There is nothing strange about it - it is as natural as any other part of your ideas.

A "3-dimensional" SU(4) contains the translational symmetries of the tetrahedron. A "4-dimensional" SU(5) contains both the translational and rotational symmetries of the tetrahedron. If you insist on a 3-dimensional model, then you need SU(4). If we use two SU(4)'s, we obtain enough degrees of freedom to represent the translational and rotational symmetries of the tetrahedron, but the underlying symmetries seem messed up. You may say that you do not have six dimensions, but if you are using spinning spheres, you may have more "effective" dimensions than you realize. One 3-dimensional tetrahedron represents an Electro-Color of SU(4) -> G2 x U(1) -> SU(3)_c x U(1)_Y + 3 + 3-bar. The other 3-dimensional tetrahedron represents a broken Hyperflavor-Weak (similar to Pati-Salam theory) of SU(4) -> SU(2,2) -> SU(2)_L x SU(2)_R + 4 + 4-bar + 1. It is tempting to call that last "1" a U(1) of Gravity (and use Lisi's Gravi-Weak model as your second tetrahedron), but the symmetries seem wrong for that. It is similar to Lisi's model in that essential components may fit, but the symmetries are slightly wrong.

This six-dimensional dual-tetrahedral Pati-Salam-like model is about half of my model, and about a quarter of Lawrence's model. Unfortunately, those respective expanded theories do add in many 'imaginary' particles that may be Kaluza-Klein particles that exist at the Planck scale.

Have Fun!

Dr. Cosmic Ray

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Dear Ray ,

Thanks for this explaination .Indeed the FCC seems very relevant if and only if we insert the real number and their specificities .Even the volume is very importaznt correlated with the rotational effect implying mass .At the Planck scale I imagine this ultim coded sphere and its membran like the limit between the physicality and the intrinsic code of informations for others entangled spheres .

The only problem for me with extra dimensions id their definitions in fact .I can't imagine the rule of these dimensions .If these dimensions are in the physicality ,thus it exists only 3D ,even if some locality seems to appear .The laws in this scale of perception are the same with their relativistic adaptability .

If the cosmological link and the quantum world are in a pure universal link with the number of spheres ,thus we can superimpose the real symmetry and its fields of energy and their rotations of mass .There the volume coming from the ultim main coded sphere and its specifics fractals ,probably correlated with prime numbers ,becomes very relevant in this division .It is just a question of good referential with its closed system and of good number ,the serie becomes very relevant in an universal point of vue .

You know Dr Cosmic Ray ,I like your extrapolations ,Lawrence ideas ,....what I find important is these imaginaries particles that the probability of maths tools implies.For me the elemenatry particles are in the same dynamic,thus of course we are going to find many new particles before this scale, like a division of mass and fields ,but these particles are not stranges or in hidden variables ,just different in their specificities .It is the same with HIGGS ,they don't exist for me ,I beleive strongly that the mass has an intrinsic cause.I agree about the complexity by weak polarisations ,there the evolution and the increasing of mass seem very essential .We can say thus about the mass what the gravity polarises the electro magnetism due to this ultim code in the main central sphere at the Planck scale .The senses of rotations imply thus an evolutive synchronisation .I am persuaded about the potential of this gravity ,the gravitational system can change the sense thus the plarity thus the mass ,the evolution point of vue is essential I think to encircle the real polarity and the real rule of the mass .

In conclusion I don't see FCC like strange ,but only not sufficient ,it lacks an global point of vue .

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In all case your ideas are very interstings .The future is like a synchronization in optimization ....

Best Regards

Steve

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Dear Dr Cosmic Ray ,

Have you already thought about a superimposing of all crystal systems discovered at this moment on Earth and in our solar system .What I find interesting with these crystals is their properties .Like all is complementary thus has a rule .These crystals are there for something but can we consider their architectures like fondamental towards the Planck scale .I don't think .Let's take for exemple a big passion for me ,the botany and the plants ,and flowers too .The form of the flower diagram is spherical too and a symmetric system appears naturally in many biological (an or veg) systems like in the mineral world .Is it a reason to extrapolate these architectures with the real cosmological and quantum numbers .I beleive that the evolution still seems a main part of the puzzle about too the consciousness and the complementarity ,even technologic .There thus we can consider our systems around us ,sphericals like still youngs and correlated and that to be adapted .

Thus our quantum and cosmological dimensions are not finished .All is relative in fact ,even our step of evolution and its limits .

Sure the ultim superimposing will imply the ultim sphere thus we can't superimpose for several reasons of time and perception.Just that to say thus that all superimposing thus will be not sufficient because they are limited in all referentials at this moment .This line of reasoning implies thus a real necessity to have the good topology in a closed system where the numbers ,physicals are considered .All superimposings if they are universaly linked in their constants can be inserted in the ultim equation if the pure physicality and the thermodynamics are unified .The time operator is a limit due to the evolution .An other important thing too is the utilisation of the math tools ,the balance between imaginaries and reals thus is always a real actual problem implying a lot of confusions for me .It is probably the reason why the experiments of the sciences community imply a big lost of money due to some parameters like in the LHC experiments .

Best Regards

Steve

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Dear Steve,

You mention superimposing all crystalline structures. this idea may be relevant.

In my essay, I built up SU(5), SU(7) and SU(11) GUT's out of various crystalline symmetries: Tetrahedral Conjugacy classes (order 24 like SU(5)), Octahedral Conjugacy classes (order 48 like SU(7)) and Icosahedral Conjugacy classes (order 120 like SU(11)). I then built up a K12' 'Super-Lattice' out of multiples of Simplices. Jonathan Dickau said the following insightful comments about my essay,"It seems you are trying to connect the limits of complexity with the corresponding simplicities afforded by geometry, and I like that idea. You have made some complicated ideas simple, or should I say simplicial?"

Coincidentally, M. El Naschie used a different (but possibly related) approach. He summed/ superimposed all of the two and three Stein spaces to create E-Infinity. K12' has an order of 684. E-Infinity has an order of 685 plus a fractal (alpha-bar times five in MEN's ideas). I think there are more similarities than differences here. It is a shame that Physicists are so quick to discard new ideas that they do not fully understand. I found a sponsor for my paper on arXiv (I have a Doctorate in HEP-PH and friends in the profession, why is it so hard to publish?), but then had the paper kicked back about an hour later. Does Jacques Distler (the HEP-TH arXiv editor) object to Lisi's ideas so strongly that he opposes efforts to correct Lisi's ideas? I would prefer to be Distler's friend. He and I are probably cheering for the same team in the National College Football Championship - Hook 'EM Horns! I agree with Distler that Lisi's symmetries are messed up. However, it is interesting that everything seems to fit into Lisi's theory, and SOMEONE should try to correct it.

Have Fun!

Ray Munroe

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One problem is that SU(4) does not decompose into G_2xU(1) in quite this way. You have two ways to get SU(3). One is through spin(7) ---> G_2 ---> SU(3) and the other is through SU(4) ---> SU(3). The role of G_2 is as a holonomy which is associated with the F_4. These are of course the centralizers of the E_8. The G_2 has a duality with the action of the B_4 < F_4, which is supersymmetric and due to the duality between the mass and NUT parameters. The NUT-parameter is analogous to the magnetic monopole, which is dual to the mass. The symmetries of the Taub-NUT spacetime are equivalent to the 7 elements of G_2.

This is more in the say that I tend to proceed here. The G_2 is then a QCD-like holonomy, similar to a gauge field, which may then of course have elementary particle representations. The only thing which I can see with respect to SU(3) is that the two decompositions might in some way be similar to a double fibrations. So the G_2 holonomy on the 7-sphere and the SU(4) embedding coexist in some manner. The only way in which I can presume this is so is that the G_2 holonomy is given by a two-tangent planet on a C^5. This in some way determines the AdS/CFT, which includes the SU(4). At this point I have not ferreted this out in great detail.

Cheers LC

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Dear Lawrence,

Is it OK to say SU(4) -> SU(3) x U(1) + 3 + 3-bar? If so, this has significant similarities with G2 -> SU(3) + 3 + 3-bar.

Ray

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I will hazard a guess that since SU(4) \superset SU(3)xU(1), and since SU(4) has 15 dimensions, with SU(3) 8 dimensions and U(1) one, that 3 + bar-3 might then take up the remaining 6. There is in this a double system of the sort

SU(4) --> SU(3)xU(1)

G_2 --> SU(3) + 3 + bar-3,

where at a minimum the two overlap on the SU(3)

Cheers LC

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Hi all ,

Dear Ray ,

Perhaps Lisi ,you ,Lawrence and others shall win the Nobel price for this incredible and splendid discvery about our Universe .

My spheres and the theory of spherisation seems so far of this truth .I congratulate you all for this ultim discovery in sciences .

Lisi is on Facebook ,me too ,I am going to contact him ,If he speaks there ,he can come here .The complemenatrity is the key towards the best discoveries .I invite you to work in team ,personaly my model is too different .But in the future I suppose what some superimposings can be inserted with pragmatism and rationality .

But pay attention dear Ray ,you know the business and this sad society .The sciences are not a play but must be foundamentals .At this moment for me ,the model of Lisi is false ,and the title is arrogant .Mr Lisi please come on FQXi ,it is more foundamental than Facebook .There we shall see all in total transparence if your E8 is correct .

Best Regards

Steve

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Why I disagree about these extrapolations .

1 The E infinity is false ,the limit of the referential is essential .

2 The mass is not linked universaly

3 The imaginaries tools become more important than the reals

4 The system is not applicable in all centers of interest(math,chem,phys,biol,astronomy,cosmology,universe)

PS
..."Does Jacques Distler (the HEP-TH arXiv editor) object to Lisi's ideas so strongly that he opposes efforts to correct Lisi's ideas?"

My answer is the same ,it is a lost of time because the road is false.Thus is it importnt to correct it ,personaly no .I agree thus with Mr Distler.

5 The higgs ,hidden variabes ,extradimensions,strange external particles ,all that is false for me

6 The distorsion of the space time is too a lost of time ,lease let's accept the real relativity and our limits and walls of perception and understanding .

The Copenhagen Interpretation seems still in a desesperated paradox.

7 The referential and thus the thermodynamic laws disappear .The mass ,the gravity ,the energy are not the main driving force of these extrapolations .How can we arrive to a correct analyze if the closed system with its volumes and pression are not inserted like an universal gauge with the numbers in the good serie.

8 The Gosset systems exist since the utilisation by Gosset .Is it foundamental in our quantum adimesions ,no evidently and still less for our Universe .

....I stop here .

I have nothing against these works and the people who work about it ,I just say my opinion about this lost of time .I think you and Lawrence are so competents and creatives ,like Jason too but I am frank ,I don't understand why you focus on these extrapolations .You are ,the 3 ,so competents ,I imagine your extrapolations if you focus on a rationality .

I have already tried to change your points of vue but I don't arrive grrrrr hihihi lol it is the life .In all case When the center will be created it will be a honor to can work with you ,Lawrence and Jason ,and our others friends to help the difficult local places .We can invent many concrete and pragmatic system on ground for our fellow man .I am not a a kind of crazzy or a illuminated prophet ,no just a human ,a scientist who think that it is possible to act by adapted sciences in an universal optic .It is possibe to invent concrete systems and simply more we are more the results and inventions shall be better .

Take care all

Steve

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Dear Steve,

Yes, Lisi is on Facebook occasionally (he is one of my Facebook friends, certainly he would add you as well), and has been on FQXi a lot in the past. He travels the world and seems to enjoy his youth (he will be 42 in January). The odds are that he will be somewhere near Belgium (Steve) or Florida (Ray) or New Mexico (Lawrence) or Oregon (Jason) sometime in the next year. I just missed him in Jackson Hole, Wyoming this past Summer.

I understand that you are searching for a simple and universal theory. A relatively simple theory, a rank-4 (4-dimensional) SU(5) does not contain gravity. Thus, we must find something more complex. I personally liked Lisi's theory. It seems to contain all of the known fermions and bosons in an interesting E8 Gosset lattice. But I could not find an anticipated 5-fold pentality symmetry in Lisi's E8 model. I agree that "Theory of Everything" or TOE is an obnoxious name, but Lisi and I are simply following pre-existing nomenclature, we did not invent the word TOE.

Only time will tell if El Naschie is right or wrong about E-Infinity. Lawrence has found some soliton solutions in his model. The extrapolation to fractals is not 'crazy'.

Does your model reflect Lie algebra symmetries, or is it a pictoral representation of GUT/ TOE? I would like to analyze your symmetries - I am guessing that you are working with Pati-Salam SU(4)'s or Georgi-Glashow SU(5)'s and do not recognize it.

Have Fun!

Ray Munroe

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Dear Ray ,

Don't complicate the simplicity .I don't search dear Ray ,I have found and I have still many to find in complementarity with pragmatic scientists .

I have already explained my point of vue about these extrapolations what I think totaly falses .Why I must to read works what I find not relevants in an universal point of vue about the rotation of quantum and cosmologic...

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Dear Steve,

We both continue to search for a universal truth. I understand that some people publish 'crazy' ideas to make money or keep their position. To date, I have invested more money into my ideas than I have made from them. If you add in the value of my time, then I am at a definite loss. I continue because I love the search for truth.

Perhaps my ideas are complex. Perhaps spinning spheres adds enough new degrees of freedom that your ideas are more complex than they seem at first glance.

Gravity and mass are both mysteries. You say you do not believe in a Higgs, but you have Gravity. What is your origin of mass? Spinning Spheres? What is the origin of your spinning spheres? If there was a GUT or TOE at the Big Bang, then SOMETHING had to break that symmetry.

Have Fun!

Dr. Cosmic Ray

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There are deep principles at work here, which motivate the mathematics of exceptional groups and ultimately sporadic groups. At the end it requires that certain ideas we have had about classical events in space, trajectories and causality are being deformed. Relativity has changed our notion of how space and time are related to each other, where the two are transformable into each other by the...

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There are deep principles at work here, which motivate the mathematics of exceptional groups and ultimately sporadic groups. At the end it requires that certain ideas we have had about classical events in space, trajectories and causality are being deformed. Relativity has changed our notion of how space and time are related to each other, where the two are transformable into each other by the Lorentz group. Quantum mechanics has changed our notion of what it means to specify the variables which describe the dynamics of a system on the atomic scale or smaller.

Configuration space is just multiple copies of space for each particle. So for N particles each exists in an R^3 space and the total system is described in an R^{3N} dimensional space with the set of coordinates {q}. This turns out to be half of the phase space which includes a momentum configuration space of R^{3N} dimensions, with the momentum coordinates {p}, so the phase space is R^{6N} dimensional. The Hamiltonian then tells us that H({q},{p}) = E and is a constraint which reduces the system to dynamics on R^{6N-1} dimensions.

The relationship between the coordinate configuration space and momentum space is the Fourier transform of course. In quantum mechanics we can't describe dynamics with perfect accuracy in both sides of the phase space. To compute processes the Lagrangian configuration space system is transformed to momentum space, or represented according to integrals which sum over momentum. These compute channel amplitudes for processes at high energy. Yet these tell us nothing about the configuration of these interactions. This is why you must have a beam with many particles which collide, for in those statistics you are likely to get the configuration space of particle necessary for the process to happen.

This funny situation is extended of course in quantum gravity. We have the fact that a vacuum description according to one observer is a vacuum plus particles according to another. The transformations are based on the noncompact Lorentz group, which are quantum mechanically the Bogoliubov transformations of quantum operators. In another perspective the time variable for quantum theory is dependent upon a coordinate condition in spacetime. It is not the invariant proper time of relativity. Thus the description of particles or quantum fields according to different observers are incommensurate if the spacetime is curved. This is particularly the case if there is an event horizon. The event horizon is a fundamental barrier which prevents the two descriptions from having a single S-matrix basis of description. An observer who witnesses a string approach a black hole horizon detects very different physics from an observer who commoves with the string into the black hole. So the concept of well defined trajectories or configurations is further adulterated, which is a likely feature of quantum gravity. This is one aspect of the so called black hole complementarity principle or holography.

The observer watching a string approach a black hole will observe it increase its transverse length as it covers the event horizon. This is comparable to the increase in the scattering cross section of a particle at higher energy. The longitudinal modes of the string Lorentz contract until they approach the Planck length. The string according to an infalling observer exhibits completely different physics. There is not of the transverse expansion or the longitudinal contraction, and the string remains relatively constant in is geometry or dynamics until the center of the black hole is reached. There the string exhibits extreme tidal forces which distend it enormously.

This is discussed in my essay at Can we see into a black hole? .

The role of the exceptional groups, in particular the automorphism of G_2 in J^3(O) is to define a triality between the vector basis of an octonion and the spinor plus hermitian conjugate V, θ, bar-θ, as well as a duality system that is supersymmetric and intertwines the mass-parameter with the gravi-magnetic dual NUT parameter. In the Taub-NUT spacetime the nonHausdorff manifold condition across the three regions (Penrose diagram patches etc) is such that a time operator may be constructed. The time operator is expended around energy eigenvalues which correspond to the discrete symmetry of the TN spacetime. By the nonHausdorff condition there exist non-separable discrete elements which can define an energy spectrum and a time operator. This time operator does however not correspond to a spacetime in the usual sense of the term, but is rather an artifact of the G_2 holonomy and 7 Killing spinors.

The notions we have about space, time and the existence of events therein is adjusted further away from our classical reasoning. This is what motivates the mathematics of exceptional groups, and eventually sporadic groups. The final synthesis on this I think is the 26-dimensional Lorentz group and AdS group for holographic quantum amplitudes, which is decomposed into the Leech lattice plus two additional dimensions which serve as time-space or time-time depending upon whether this is Lorentzian or AdS.

Cheers LC

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Dear Ray ,

I know you are a real searcher of truth and what you ,you make the difference between sciences and the economy or the business ,but all is not like that ,unfortunaly .We return to a simple reality ,the individualism or the complemenatrity of course if the road is synchronized in an universal link .

About the complexity of my model ,indeed it is simple and complex ,simple in the whole ,complex in the details and localities .It is logic if we link all with the rotating spheres implying mass and universaly linked .Indeed the rotating of quantum spheres is the cause of the mass ,and the effect of an intrinsic coded in the main central sphere .The number and volumes of spheres becomes essentials ,thus we can imagine indeed a big complexity with all these rotating entangled spheres implying the specifity and the rule of becoming if I can say .Thus about this ultim information at this scale ,it is out of our actual perception and understanding .I don't understand why some people wants fire some steps .Let's admit our walls and our young age .

The symetry since the hypothesis Big Bang evolves and changes thus can we accept a symmetry or it is better to calculate the correct number of spheres implying a symmetry in evolution .It is a little different I think .

The pression ,volume ,mass ,rotations seems in the same dynamic with the specific serie of numbers ....It is simple but complex if we want know this number and volumes more the velocities of rot more the synchronization in an evolution point of vue.The frequences of this universal music towards the harmony are robably in contact by these quantum spheres with or without rotation ,there the intrinsic code is a kind of activation on this line time .The Dark matter seems a main part of this evolution ,if the mass increases thus the code implying the rotation thus the mass has many codes ,Time code ,space code (sense ,angle,direction ,spinal ,orbitals ....the polarity seems linked in this logic )the evolutive polarisation thus is a pure synchronization of these rotating spheres .Let's imagine the real number of cosmological spheres ,let's admit it is complex .The quantum number is the same .

I have a question

The Higgs are intrinsics?

Best Regards

Steve

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Dear Steve,

You ask if the Higgs is intrinsic. The answer is not that simple. On one hand, we need something like a Higgs scalar multiplet to break our initial symmetry. On the other hand, without knowing the exact TOE group, we do not know how many Higgs or Higgs-like particles should be inserted into our symmetry-breaking mechanism, and thus confusion abounds.

The Standard Model (SM) inserts a complex scalar doublet (4=2x2 degrees of freedom (dgf's)). Three of these four dgf's become the required longitudinal modes (spin-0 projection) of the W+, W-, and Z. The fourth dgf becomes a physical Higgs boson of spin-0. This is the minimalist example of Higgs theory.

The Minimal Supersymmetric Standard Model (MSSM) requires two complex scalar doublets (8=2x2x2 dgf's). This yields a Light Higgs (relatively lesser mass), a Heavy Higgs (relatively larger mass), two Charged Higgs H+ and H-, a pseudoscalar Higgs (imaginary-like symmetries) and the required longitudinal modes of the W+, W-, and Z. If the LHC discovers the Light Higgs of the MSSM, its properties should be slightly different from the Higgs of the SM.

In my models, the number of Higgs-like dgf's is given by the difference between the SO(8) (of order 28) and SU(5) (of order 24) algebras for an answer of 4, or by the difference between the SO(12) (of order 66) and SU(7) (of order 48) algebras for an answer of 18, or etc... As you can see - it is not simple, nor does this calculation seem particularly fundamental.

Still, we need a symmetry-breaking mechanism. If you object to the Higgs theory, then you should study some symmetry-breaking mechanisms from Solid State Physics, and see which is better suited to your specific model.

Have Fun!

Dr. Cosmic Ray

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Steve,

You asked if the Higgs is intrinsic. I think that the broken symmetry is intrinsic but the Higgs is an array of imaginary interpretations. The standard model has grown buy adding more and more particles to explain observation. To my mind non of the bosons are particles but effects of the dynamics within a medium that transfer forces. These disturbances of the medium are interpreted as particles but do not have independent existence from the medium. The particle interpretation works from a mathematical accounting perspective. The accounting will work just the same if the boson is recognised as an amount of force transferred via other means.

It seems to me that the dynamic change that gives rise to the asymmetry that physicists wish to account for with the Higgs is the loss of Universal potential energy, which is change in position of matter along the scalar dimension. According to the model I have been explaining this spatio-energetic change gives rise to the mass of particle and matter. It is not due to yet another particle to further bloat the standard model. Which is already overstuffed with particles.

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Dear Georgina,

Second Quantization allows us to treat intermediate bosons like particles. They carry intrinsic spin, momentum, energy, various 'colors' and/or charges, and some (such as the W and Z) even carry properties of mass. The LHC will not find a 'Higgs' boson - it should discover decay particles that are characteristic of a Higgs having existed - even if only for the briefest of moments.

In my opinion, the Standard Model is anorexic, and needs to be bloated.

You and Steve may be able to describe your respective asymmetries, but what caused those asymmetries? If we had a GUT/TOE - even if only for 10^-40 of a second - then we must explain how it broke. This is what the Higgs is about. Perhaps you have another mechanism for spontaneous symmetry breaking, but I am dissatisfied with the idea that there never was a GUT/TOE and the symmetries have always been broken. I guess we take the idea of a GUT/TOE or non-GUT/TOE on faith. I doubt science will ever be able to prove it one way or another.

Have Fun!

Ray

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Ray,

Why are you dissatisfied with the idea that there has always been asymmetry?

A process of perpetual motion and recycling within energy-space(or alternatively a perpetuating sequence of big bangs followed by contraction along the scalar dimension), without objective time, seems far more satisfactory to my mind than a single big bang out of a mysterious singularity and then cold death within space-time.

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Quantum mechanics has operators which correspond to things we observe. A classic case is the commutator [q, p] = iħ, which determines the Heisnberg uncertainty principle between position and momentum, q and p respectively, as ΔqΔp >= ħ. Second quantization in effect undoes this and considers the wave functions as due to the action of field amplitudes φ on a Fock space, or a sort of bookkeeping space. The field amplitudes now obey the commutators [φ, φ^*] = 1, and we drop the commutation between the old q and p. An elementary example of this is the a and a^dagger approach to the harmonic oscillator. It is called second quantization because the old observables which are quantized in quantum mechanics are replaced by a new set of quantized observables.

Ray is right about the LHC finding the Higgs particle. Particle physics has not been about detecting particles directly since the 1960 to early 1970 days of bubble chambers. We now detect particles more indirectly by knowing what their lower energy decay products should be.

Cheers LC

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Dear Georgina,

I admit that my view is a matter of faith. We can be content that the Universe is the way it always was, or we can say that this scenario is 'ugly' and a more beautiful TOE must have existed prior to the existence we see. If a TOE existed, then SOMETHING broke that symmetry. In the case of Steve's theory, SOMETHING created rotating spheres. In the case of your theory, SOMETHING caused spatial and scalar (time) dimensions to behave differently. It disturbs me that people call the Higgs the "God Particle". But in the sense that the Higgs broke the original symmetry, it could be considered an important part of the First Cause.

Our best data still implies a Big Bang and the possibility that our Universe did have a different configuration in the past.

The cold death you refer to is billions of years in the future. Humanity will not still exist then. We will have died off, or evolved thousands of levels by then.

Have Fun!

Dr. Cosmic Ray

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Ray,

thank you for your reply. I am glad you had the courage to admit that your scientific position on symmetry is based on faith. I do not think that the current scenario playing out in the universe is ugly, I think it is misunderstood.I do not think it is broken either.

If there is perpetual motion in the Megauniverse hypersphere all spatial and energetic change is conserved. If there is flow of the matter of the universe towards the centre of the Megauniverse hypersphere there must be a balancing flow back to the exterior region of the hypersphere completing the symmetry. This would have to be the medium of space incorporating disintegrated former universe.

Alternatively if the material universe is coming together in 3D space as it progresses towards the centre of the hypersphere following a big bang scenario, then on reaching the centre it must be destroyed again causing a new inflation. So there is perfect oscillation and conservation of spatial and energetic change over the complete "life cycle". Both scenarios are beautiful not ugly and posses symmetry. The first scenario has integral symmetry ( but requires a medium of space) and the other sequential symmetry whereby it is completion of the "life cycle" that gives overall symmetry.

There has to be coming together of matter within space as movement along the scalar dimension progresses not expansion of 3D space. This change in position along the scalar dimension is the loss of Universal potential energy. If the matter of the universe alone is considered it does appear asymmetric, though this is not necessarily so, as I explained above. It may appear, due to interpretation of red shift, that the whole universe is moving away from the earth. However it is far more likely in my opinion that the telescopes on the earth or the Hubble telescope are moving away from the original position of the source of the EM radiation along the scalar dimension giving the red shift effect. Erroneously interpreted as evidence of universal expansion. IMO.

Universal expansion will lead to cold and final death. That scenario is asymmetric and ugly.

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The expanding universe does indicate that 13.7 billion years ago the universe was much hotter and at higher energy. At higher energy symmetry is likely recovered, and near the few Planck units of time complete symmetry of the universe obtained. The heat from the big bang is similar to a latent heat of fusion. In inflationary models there is a period called reheating, which is basically a thermal distribution similar to latent heat production.

The complexity of the universe in its current state is likely a manifestation of this thermalization. The universe started out at much lower entropy, and the higher entropy of its current state is a manifestation of how complex configurations have come into existence. There are many ways in which microstates can be shuffled around to create the generic appearance we observe, including the complexity of things here on Earth --- such as life and conscious beings.

Cheers LC

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Lawrence,

How do you relate to that story?

It is an assumption that the universe began from a singularity and continues to expand outwards. If there was an inflation phase the universe must now be contracting not continuing to expand.IMO.It can be hypothesised that the universe formed from the outer region of the hypersphere and is contracting back towards the centre, following on from an inflationary phase of a perpetual cycle.

It is the misinterpretation of red shift and the fixing of the cosmological constant to comply with expansion that causes this belief in universal expansion not the scientific evidence itself.

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I would recommend spending time with Ned Wright's Cosmology Tutorial to get a better idea of these things. There is a lot more there than what I can write in a blog post.

Cheers LC

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Dear Lawrence,

I've been playing around with Spin algebras and wondered if a 12-dimensional (rank 6+6) Spin(12) of order 132 might decompose into a 4-dimensional (rank 2+2) Spin(5) of order 20 and a 6-dimensional (rank 3+3) Spin(7) of order 42 plus a 35-plet and a 35-bar-plet. These Spin(N) algebras are also related to the SU(N) algebras.

Some of these symmetries are important. I'm not sure they are all important. What do you think?

Dear Georgina,

I recently had a conversation with Frank about the redshift on my essay blog site. Please read it. It is OK to question Modern Physics, but it would take a 'Super-Einstein' to rewrite ALL of Modern Physics. Choose your battles wisely.

Have Fun!

Ray Munroe

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The CL_{16} takes us up to SO(32) ~ E_8xE_8, so there is considerable space here.

I can comment more tomorrow. I am for various reasons a bit tied up this evening.

Cheers LC

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Ray,

you said,"It is OK to question Modern Physics, but it would take a 'Super-Einstein' to rewrite ALL of Modern Physics."

I do not believe that is the case. A slight adjustment of the current perspective is required and then all of the pieces fall naturally into place. A single person can not rewrite the whole of modern physics, I agree. Some of it is just fine as it is. Some of it just needs reinterpreting and some of it could benefit from being rewritten in quaternion mathematics. I envision this as an enterprise undertaken by the scientific community as a whole, not a single individual. Once the framework and meaning has been properly ascertained, which has been the major stumbling block for 50+ years, the rest is comparatively easy to adjust to fit with that model and its meaning.

Time has always been the problem. That is why Godel and Einstein spent a considerable amount of time concentrating on this issue when the rest of mainstream science was off on its own quest having decided that space-time was the answer, there was no problem with time and it was all now about quantum physics. It is well past time to question why Einstein and Godel were so concerned and where physics went wrong.IMO.

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Ray,

I have taken a look at your discussions with Frank. I admire your steadfast patience and tolerance. Although it will be detrimental to your own sanity if you continue with such conversations indefinitely.IMO. I do not need to be reminded of the interpretation of red shift. Though I thank you for your attempt to better educate me.

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Dear Georgina,

I understand. Frank tries my patience, but I have seen enough insanity that I would have lost it long ago if so inclined. I should ignore him...

I agree that there are serious issues with time. This is why it made such an interesting FQXi contest. In my models, I keep coming up with what appears to be a second time, perhaps imaginary time. What is your opinion of the meaning of this?

Have Fun!

Ray

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Hi all ,

Dear Dr Cosmic Ray ,

First of all ,thanks for this development .Like I said I have nothing against these Higgs .But My perception is like that ,I can't consider them like axioms .

Now of course ,if experiments proof their existences ,I will accept them like all proofs .

Dear Georgina,

Thanks a lot too .

You say

"It seems to me that the dynamic change that gives rise to the asymmetry that physicists wish to account for with the Higgs is the loss of Universal potential energy"

It is relevant ,the intrinsic potential energy seems essential ,if we link with mass and evolution thus increase of polarisations .The Higgs in this point of vue seems confusings .

Dear Ray ,Lawrence and Georgina,

Could you explain me why the time of life is so short for the Higgs ,that has no sense for my mind in a gravitational point of vue and its stability in imporvement and complexification.

The balance between Ec and Ep seems imply a logic in the time evolution ,thus why a short time of life ,it is not possible .If the Ec is correlated with the increase of mass and thus the rotation and the time ,why this comportment for a particle ,the relation Ec/Ep looses all its sense I think .

Best Regards

Steve

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A particle is stable when there is no decay channel available to it. It there exists some quantum state with a lower energy available the system can decay into it. A proton as an arrangement of (uud) quarks has no decay channel open to it. High mass quarks, such as the strange quark, can decay. Another way of looking at it is that the up quark and down quark are the lowest mass quarks and represent the bottom of the energy well. So the SU(3) of quantum chromodynamics has a maximal subgroup SU(2), which is satisfied by the two state system of the proton and neutron. The electric field breaks the symmetry of the proton and neutron state, with the proton being the lower mass state.

The Higgs is similar. It is a ~ 150 GeV mass particle and unstable, so it may quantum transition into eigenstates for lower mass particles. Our lower energy universe is largely defined by such.

Cheers LC

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Dear Lawrence,

I only need Cl(12) to get Spin(12). It looks like a 12-dimensional Spin(12) prefers decomposing into a 4-dimensional Spin(5) and a 6-dimensional Spin(7) versus decomposing into two 6-dimensional Spin(6)'s. But what happens to the other two dimensions? Is one dimension removed by the light cone constraint, and the second dimension an unobservable Imaginary Time?

Dear Steve,

Lawrence described the unstable nature of the Higgs accurately. The Higgs mass determines which decay channels are available, but likely decay channels include Higgs -> bottom + bottom-bar and Higgs -> tau + tau-bar, which are themselves unstable.

Have Fun!

Ray

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Representations of thought as sensory experience are basically beautiful, powerful, and/or captivating -- this is the connection with art, TV, truth, physics, and power. To the extent that the truth mirrors the integrated extensiveness of nature/the natural, these ideas are held to be more

beautiful/desirable -- although they can be shocking. The deepest truths require the greatest/deepest strength. Dreams represent thought as sensory experience IN GENERAL -- so this may be held to be an experience of excessive or extreme genius, thereby (in this meaniningful sense) making dream experience generally less desirable than waking experience.

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The highest thoughts of genius and the best theory of physics necessarily involve/pertain to past/present/future extensiveness of experience.

This is a fact of great significance.

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"The search for truth and knowledge is one of the finest attributes of any man, though often it is most loudly voiced by those who strive for it the least." --- Albert Einstein

Cheers LC

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Since astronomical/telescopic observations are already, to a significant extent, an interactive creation of thought, the ability to comprehend them is necessarily diminished; for it is in the description of what is the integrated and natural extensiveness of experience (past, present, and future) that our greatest, most beautiful, and daring theories are found.

It is so much easier to be critical than correct, and so easy to attempt to detract from a discussion than it is to add to it. Maturity and seriousness matter alot.

Television may be seen as an accelerated experience of art. TV is a creation of generalized thought. TV is even more similar to thought than in the case

of dream vision/experience. This is why the visual images in TV become even more shifting and variable than those of the dream. (Thoughts are relatively shifting and variable).

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Dr. Crowell,

Would you please give data, perhaps temperatures, or polar bear statistics, or whatever to support your opinion? What was in the emails?

James

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I am trying to think about spin(12). It is spin(12) ~ SO(12) which contains an SU(6). SU(6) theories of QCD were seriously considered back in the 1960-70 time frame. That all seemed to have ended for the most part. The AdS/CFT holds for SU(4) ~ SU(2,2), which is contained in SO(8) in N = 4 supersymmetry. I don't know what a higher dimensional AdS SU(4,2) would buy us. There is a decomposition here to SU(2,2)xSU(2). I will have to think about this some.

Cheers LC

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Hi all ,

Thanks dear Ray and Lawrence .I understand better these decays correlated with fields .

I think that a decay is different than a desintegration ,there like in the oxydo reduction equation ,the coherence appears .The time can't be inserted with variables and limits I think but it is personal of course .The mass don't disappear ,cahang yes but don't disapear ,there the linearity of the particles after the changement ,intrinsic must be well in its referential .If the rotations of quantum spheres with their specifics numbers imply mass ,thus a desintegration is just a division of mass but this mass don't disappear .The stability of the gravitational system thus seems very important if we link the 4 interactions with the evolution .We can use indeed the polarity and the + and - but in accepting our limits and walls of perception and analyzes.I think still strongly that the thermodynamic is essential in a closed or local or global system.

Can we derivate like we want with the specific architecture if the math tools are not balanced with the universal referential .That will imply probably a big confusion before the synchronization .

In all case thanks to both of you for your ideas and extrapolations .

Best Regards

Steve

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Ray,

The issue with g_2 and spin groups is likely to have the greatest bearing on QCD and black holes. With the LHC up and running we might produce amplitudes for the production of black hole physics. The G_2 group is contained in SO(8) which decomposes into SU(3) with a 3 and bar-3. We can also extract SU(3) from the SU(4), which is also a subgroup of SO(8). The G_2 group is then a holonomy defined by the spin(7) in SO(O), which fixes a basis in S^7 sphere. The low energy decomposition of AdS/CFT with the AdS group SU(4)  SU(3)xU(1) should connect with QCD on the CFT end of the correspondence. The parton configurations are QCD ~ AdS_3 amplitudes for black hole (like) amplitudes which might occur. Above the TeV, or Higgs domain, there should be some partial recovery of the conformal renormalization group flow. At this energy scale there is expected to be some small amplitude or channel productions corresponding to quantum (super) gravity. Hence parton systems of quarks will have amplitudes for quantum black holes.

Quantum black holes as the AdS_3 ~ SU(3)xU(1) have color and electromagnetic charges, and can be classified according to their SU(3)_c and U(1)_em representations. In proton-proton collisions the allowed particles which can form the black hole are quarks, antiquarks, and gluons. There are then nine electric charge states which may exist ±4/3,±1,±2/3,±1/3, 0. The ±4/3 and ±1 charge states can only be formed by quark pairs, the charge states ±2/3 and ±1/3 can be formed by either two quarks, or a quark and a gluon, while the 0 charge state can be formed by either a quark-antiquark or pair of gluons. The possible color states in a two parton scattering are

3x3 = 8+1 -> g_2 irrep of states

3x3 = 6+3

3x3 = 6+3

3x8 = 3+6+15

3x3 8 = 3+6+15

8x8 = 1+8+8+10+10+27S

Since black holes form representations of SU(3)c, they are predominantly colored, but can occur as colorless singlets. The four color scheme corresponding to SU(4) is then at lower energy the SU(3) color and the U(1) hypercharge or em charge.

I think that given the LHC has started up this might be the most fruitful approach towards finding representations of particle states with respect to the 7 and 14-fold systems with respect to G_2 and the Klein 7-fold function.

Cheers LC

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Dear Lawrence,

I read this few days ago. I'm sorry I didn't respond. Parts of this still confuse me. However, you have convinced me that I need to focus on G2 as opposed to I(2)_7 - both could be relevant to Klein's Chi(7). I still think this G2 is related to, but more complicated than, Color Theory. The Spacetime models that appeal to me are H4, Spin(5), SU(5) and SU(4). I'll be glad to go off-line with these ideas.

Have Fun!

Ray

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I have been thinking about circles and spheres. I am not a mathematician. I do not have background knowledge of the complexities and theories of numbers. However I have read that all real numbers can be thought of as complex numbers with zero for the imaginary part and all imaginary numbers as numbers that have zero for the real part. If the 3 dimensions of space are represented by the real numbers and the 4th dimension by imaginary numbers as described by Hamilton this makes physical spheres and circles interesting structures.

Taking a material sphere, rather than a mathematical object, the centre of the sphere is ahead along the 4th dimension compared to the exterior surface of the sphere, that is there is time dilation. There is the Swartzchild metric maths to show this. So the radius of the sphere is a measurement in part along the 4th dimension because there is time dilation and one end of the radius would thus have to exist at a different time to the other end of the radius. If the 4th dimension is actually time.( I think it is not time itself and that that is a misinterpretation but that is another matter.) The radius is measured with a real number but if it is in part a measurement along the 4th dimension it should be a complex number because it has both 3D space real component and 4th dimensional imaginary component. Not a zero imaginary component of a normal (I mean by that just another everyday number nothing technical) real number.I say it has a 4th dimensional component and not that it is the 4th dimension because it is not possible to give the orientation of the 4th dimension from 3D space it is not a single direction but will pass from every point on the surface of the sphere through to the centre of gravity of it. So the radius is running through 3D space but also aligned with the 4th dimension.

Since a circle is just a slice through a sphere the same applies. I mean the relationship of ratio of circumference to radius is the same if it is a material slice of a real object rather than a mathematical object. So should the radius not be a complex number with a non zero imaginary component not a real number in this case also? Is this something elementary? Does this explain why pi is an unusual transcendental number or is this completely unrelated? Am I talking nonsense?

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I meant could it be that pi is irrational and transcendental because it is an approximate representation of a complex number with its imaginary component missing?

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I still don't think I said that precisely enough. I meant, could it be that pi is irrational and transcendental because it is an approximate representation of a complex number, written as an irrational real number because the imaginary part of the complex number has not been taken into account.

Am I saying something sensible and possibly elementary and obvious or nonsense? It seems quite sensible to me at the moment but I am not a mathematician. If nonsense can someone please attempt to explain the error to me? Does anyone know?

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Hi Dear Georgina,

Indeed pi or the golden number or others are irrationals, your idea about the synchronization of the objectivity and subjectivity(reals or irrationals) is relevant.

I beleive the referential becomes an important piece of the puzzle because in the physicality we need limits.

Best Regards

Steve

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Hi Georgina

Still me about the irrational numbres like pi or the gold number,they can't be wrote in fact like a fraction of the entires, thus you can understand what thoses numbers are NOT PERDIODICS.It is very important.

On the other side you have the reals and the rationals which are very very important to encircle the physicality in its pure laws of divisibility.

When Pythagore has found a ratio between the diagonal and the sides, the rational appears inside a system of reals, it is thus the explaination of the real complexification inside a referential in 3D.

Thus like Cantor said the reals are more numerous than the rationals but this point of vue implies confusions in the serie of the physicality.The reals, the rationals,the irrationals, the complexs have a specific serie.

In fact dear Georgina, it is the real big question about the infinity and thus our referential.Even the numbers are on the equation in the same logic than our physical dynamic in building.Where is the irrationality when we multiplicate we have a rational.Thus how can we interpret this divisibility or ratio.In fact, the superimposing is specific for the physicality and different in the maths tools.

If for exemple you take a real and you insert the imaginary part thus you have a complex but if already the reals has a irrationality in the serie, thus that becomes confusings, why let's imagine this function (-i)² = (-1 x i)²=(-1)² x(i)²=-1 thus we see already what a (-) exists here and thus can't be inserted for the physical serie.The fact to be irrational because the racine ² is inserted for the entires for exemple is a big problem of interpretation about our limits and walls.Only a reasonment by absurdity is possible to solve the irrationality, is it physical, I don't think personaly.

In fact the most important is the intrinsic laws of diffusion if I can say and their properties in a finite system in evolution.The rationalization thus is specific with its time sequence too.It is exactly the same with the infinity and these irrationals ratios.There the utilization of primes becomes relevant in its fractal and its distribution.

Sincerely

Steve

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Ray Munroe replied on Feb. 3, 2010 @ 13:37 GMT

Dear Steve,

The prime numbers are relevant. If you study a 5-fold (5 is a good prime number) 'pentality' symmetry, then you find many multiples of the Golden Ratio (see attached file). If this 'pentality' symmetry is related to the origin of mass, then we should expect the golden ratio to reappear in mass ratios.

Have Fun!

Dr. Cosmic Ray

attachments: 2_goldenratio.pdf

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Steve Dufourny replied on Feb. 3, 2010 @ 13:45 GMT

Thanks dear Dr Cosmic Ray,

I am going to read it and more about the golden ratio. It is indeed relevant.

Regards

Steve

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Steve Dufourny replied on Feb. 3, 2010 @ 14:28 GMT

If we take several serie like Fibonacci and phi, it is logic to tend towards this irrational where appears the infinity.

This ratio is universal and like a gauge, where we can't perceive its serie in fact in its fractalization.Phi-1=1/phi or x²-x-1=0...We can just appoach some steps of this continu fraction.If we increase the numbers in the ratio, we approach the infinity which is not infinite in fact like pi, in fact this complexification is always in 3D.In all sense the system will give the same result due to this constant irrational because not perceptible.

I can understand dear Ray what the pentagon has the ratio like all in fact, in all forms the ratio appears but the system is different in its pure physicality in my humble opinion.

If we can't write the fraction,it is irrational but if can understand this ratio, thus that becomes rational hihihih

An important point is this one it seems to me, if this ratio is everywhere, thus there is a reason, it is like a balance correlated with the intrinsic codes of building, thus inside the finite system that facilitates many things simply like the foundamentals.The building whith irrationals is reals and it is the sphere, pi and phi shall be happy about this realism ....hihih and even always this ratio will be in 3D.The evolution becomes a math tools to encircle thus this irrationality becoming a rationality due to this evolution.

We can approach but we can't see it , but we can imagine it fortunally, is it a reason to change the referential and its pure divisibility and fractalisation , it is the question for a better rationality.

It is fascianting all that in fact those numbers, these constants irrationals and infinities, it is the pure proof of the evolution, each day the decimals can be improved, but is it essential when we understand the real sense of the evolution.

Friendly

Steve

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LC, Please forgive me. I feel the box symbol rather than SO(n) theories beautiful. When I looked for those who Columbus trusted in, I found besides Aristoteles and Pierre d'Ailly's book Imagio Mundi also Paolo Toscanelli who on his part was influenced by Nicolaus Cusanus, born in Kues/Mosel 1401. Cusanus considered the universe infinite, homogeneuous, with isotropy, and without a center. Interestingly, with respect to infinity, Cusanus did not share the logic approach by Albert of Saxony. He understood: As long mathematics is rigorously derived from what is valid for finite quantities, and it obeys in particular the sentence the whole is larger than its parts, as long there are paradoxes of infinity, which were listed much later by Bolzano in 1848.

I consider Cusanus still correct when he wrote: Every mathematics is finite. And I would like to add: Infinity complements mathematics in so far as it is a beautiful self-contradiction unless we admit incomparability.

Physics is punished by the sins of those who tried to give mathematics a rigorous foundation by force. Resulting transfinite cardinality is ugly, useless, and misleading.

Much worse is the mistake to confuse general mathematical solutions with the more restricted reality. To me, detours, arbitrariness, and redundancies rarely deserve to be considered beautiful, no matter how exciting string theories might be. In the end nature has the last word, maybe already via experiments with LHC.

Eckard Blumschein

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Dear Eckard,

You addressed my friend Lawrence, but this comment strikes close to me.

There is nothing special about the box operator. In 3-D space, the grad-dot operator represents divergence, and the grad-cross operator represents circulation. The box operator or D'Alembertian is simply (grad-dot)^2 in a proper 4-D Spacetime metric. Any calculus-based/ change-based view of reality would require a box-like operator. If we were deriving Physics in 12-dimensions, we would need a 12-D box-like operator (should we call it the Lawrencian or does that sound too much like Lawrencium?).

I am partial to SU(N) algebras. If you read my essay (topic 520) and the more in-depth "A Case Study..." paper posted on that topic's first blog, you will find many applications of SU(N) algebras. Chapter 4 of the "A Case Study.." paper describes why Simplices are relevant, and shows the relationship between an (N-1)-Simplex and SO(N), Spin(N) and SU(N) algebras.

Have Fun!

Dr. Cosmic Ray

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Eckard Blumschein replied on Feb. 3, 2010 @ 19:39 GMT

Dear Ray, a 12_D box is less familiar and therefore less beautiful to me. Moreover, the risk to confuse the symbol "box" that has 12 edges with an other one that has a few more or less seems to be high.

In general, I doubt that the most general expression, e.g. SU(N), is always the best one. I vote for simplicity and realism. A lot of experts are considering me unqualified if I am arguing that the simpler cosine transform can in virtually all cases of real world replace the complex Fourier transform without loss of any essential information. Even those of moving pictures expert group (MPEG), who are clever enough to prefer the cosine transform for coding because it is superior, tend to do so with distrust. They wrongly consider the complex Fourier transform the strictly speaking more correct one. I am arguing: It was for Heisenberg and Schroedinger, and it is still more likely to make mistakes with the redundant and in my eyes less beautiful complex Fourier transform. My basic point is: Future does not matter at all.

I will read your 520, and I guess: You considered time from -infinity to +infinity. Cosi fan tutte. This might seemingly look beautiful. It ignores our limitation to reality alias causality. The future cannot influence the past.

If you read 527, what do you consider questionable?

Regards,

Eckard

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Ray Munroe replied on Feb. 3, 2010 @ 20:45 GMT

Dear Eckard,

The 12-D box operator was just an example. Perhaps we need another symbol...

Technically, all I have built into my model thus far is CPT symmetry - I have not defined a 12-D box operator, a Delta_t, etc.

We had discussions from November 2nd - 7th. I understand your approach towards realism. What does negative time in a Fourier transform imply? My best guess (and it is only a guess) is that 'negative' time may represent waves that reflect off of the ear drum and subsequently travel away from the ear. Have we ignored anything substantial if we throw away those 'solutions'? Probably not.

Have Fun!

Ray Munroe

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Eckard Blumschein replied on Feb. 4, 2010 @ 05:41 GMT

Dear Ray,

“Plurality ought never be posited without necessity.” Doesn't PCT tacitly include the redundant future?

I am ashamed because I did share, decades ago, the wrong idea that the ear throws away phase information. I did not yet understand what is apparently too trivial as to be accepted: The complex representation in terms of magnitude and phase is redundant since reality is one-sided, not symmetrical or asymmetrical but exactly one-sided. PCT is also subject to this one-sidedness and consequently redundant. The complex wave function is redundant. Nonetheless, one must not throw away any redundant part because the one-sidedness is coded in the apparent symmetry.

Even good experts tend to fail comprehending that Hermitian symmetry means the originally unilateral and real function of time is replaced not just by two but by four complete copies.

Regards,

Eckard

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Steve thank you very much for your replies.

It is rather difficult to understand them entirely. Along with much enthusiasm for the golden ratio etc, I think you are saying that you do not think that the irrationality of pi has anything to do with physical cause. I think you are also saying that there is a problem with different kinds of mathematics being incompatible? It would not surprise me if that is correct even though it is a little disappointing.

What about time dilation within a spherical object? This has been proven mathematically. Does it not imply that there must be a time difference along the radius of a material sphere? Is it just ignored because it is so minute? But this seems to imply a 4th dimensional thickness, the difference between time position of exterior and centre of object. It seems to me that that time difference is not to do with duration of the object but a measure of the distribution of the object itself along the 4th dimension. So the objects "present" existence is not a point in time but spread within a band of time. Furthermore if the 4th dimension is thought of a spatial like the others but also scalar and giving rise to changes perceived as passage of time, because of its relationship to the other 3, then the so called 3 dimensional object has an addition dimension of material existence.

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Ray Munroe replied on Feb. 3, 2010 @ 21:49 GMT

Dear Georgina,

You make a good point. Further, spinning spheres also imply a 4th dimension, time. If we consider Hilbert space and the properties of fundamental particles, then this also implies more dimensions.

Have Fun!

Dr. Cosmic Ray

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Steve Dufourny replied on Feb. 4, 2010 @ 10:09 GMT

Hi Dear Georgina,

You are welcome, with pleasure.

In fact it is very simple, the pi or phi appears irrationals due to our young age of evolution at the universal scale.

Thus they are rationals in their whole, like a finite serie.

Thus the infinity is a subjective analyze where the objectivity is not a reality, because the evolution is an important point of vue about the finality and the building of the universal equation.

A little if I said, the irrationals are rationals for the Universe, and the irrationals are irrationals for humans.That resumes all in fact.

About the dilatation of the time, I think the time is irreversible because we can't change the mass which has evolved, thus the proportion of the rotating spheres is different.The density could be a problem thus for the check of the space time.

In logic when we increase the speed of a mass, we increase its mass, all that in a linear velocity, thus we can decrease the duration in logic ,thus we can go in the future because we can decrease our duration during a big speed linear, thus when we return at home, we are in the future because the duration is different for the two people.But the problem is this one, we can't return at home(our past and its story), thus how can we interpret this reality about the time.The question id there in fact.

we can't invent this machine, we can't return, we can't check the mass and its increasing, ....thus is it important for the physicality, I don't know.

Best Regards

Steve

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Hi Ray,

Re. Hilbert space. I think that the various abstract mathematical spaces are different from the physical reality of how matter is distributed within actual space, space-time or energy space. I do not know if that kind of abstract description and analysis is actually really helpful.It does allow things to be calculated but then the calculation must be interpreted and related back to the different physical reality. You feel at home in those mathematical spaces, I don't.

When I finally grasped the effect of the 4th dimension I realised that one dimension was all that was necessary, not 3 of time superimposed, to account for time experienced through out the 3 dimensions of space. Motion of matter along that dimension would give changes interpreted as the the effect of the passage of time everywhere. If the 4th dimension is another spatial dimension not time itself likewise its effect is everywhere. It is not necessary to have lots of additional physical spatial dimensions. A mathematical description involving lots of additional dimensions need then only be an alternative way of describing events within the space defined by the 4.

As I understand it, space-time is currently viewed as a static manifold and time has been made into another vector. However to give the passage of time and arrow of time effect I think there must be progression of all matter along the 4th dimension. This can be visualised as a series of 3D space only manifolds stacked on top of each other, through which the object "falls" disturbing and distorting the medium around it,identified as curvature of space. It is not actually necessary to describe a medium, as alternatively the variation in potential energy gradient can be used. So not a single flexible sheet in which an impression is made. The individual "space sheets" of the stack I have described are just a way of describing space and time in comparison to the single sheet description used for Einstein's model.They have no actual physical existence.

The 4th dimension is the direction of "fall", which is perpendicular to the stacked 3D space manifolds or sheets. That direction can not be given from within 3D space. However as the centre of the object will be further ahead along the 4th dimension than the exterior (as shown by time dilation within a spherical object maths), the closest we can give for the orientation of the 4th dimension, from within 3D space, is towards the centre of gravity of the object from the whole of the exterior of it. The centre of the object is itself progressing along the 4th dimension, it is not ever a static point.It can be seen from this description that the 4th dimension, time and gravity are all inter-related. The best description of orientation of the 4th dimension from within 3D space and the direction of the force of gravity (towards the centre of the attracting body) are the same.

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Eckard,

I am aware that you have some personal mission to see the foundations of mathematics rescripted. I frankly think this is about like King K'nut (Canute) putting his throne by the sea shore and trying to command the incoming tide back out. Conversely I don't have the time to write on the axiomatic foundations of pont-set topology. The box operator is just a form of a Laplacian, or a Laplace-Beltrami operator. These exist for problems involving higher gauge groups --- such as SU(N).

Cheers LC

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Eckard Blumschein replied on Feb. 4, 2010 @ 06:27 GMT

Lawrence, Steve wrote: "Thus like Cantor said the reals are more numerous than the rationals". It is indeed tempting to conclude that there are e.g. more numbers as compared to just the positive ones. Cantor wrote: "Je le vois, mais je ne le crois pas" (I see it but I cannot believe it). He seemingly solved the problem by declaring something countable on condition it can be put into bijection to the natural numbers. While this is not wrong, it merely substituted Euclid's definitions 1 and 2 in book 7 according to which all rational numbers are based on the same unity. Dedekind is to blame for changing the meaning of numbers from a representation of measures to a representation of points. I found out that this has serious consequences not just in physics but to a lesser extent in mathematics itself.

Perhaps the first one who uttered that the relations smaller, equal to, and larger are not valid for infinite quantities but only for finite ones was Salviati(Galilei). Actually, only the rationals are countable with respect to the unit one, and there are no limitations for choosing a different basis for counting. It is also reasonable to imagine fictitious limits for all irrational (not exactly commensureable) measures. I dealt with the question whether we have therefore to accept Cantor's idea of transfinite numbers. The most easy way to decide is to look for applications to aleph_2, etc. Result: no use in more than 100 years. Cantor's original text nurtures doubts, and his seemingly compelling proofs were based on lacking awareness for the fact that one cannot rigorously treat something infinite as if it was finite. Continuity and discreteness mutually exclude and complement each other.

Regards,

Eckard

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Steve Dufourny replied on Feb. 4, 2010 @ 11:32 GMT

Hi dear Eckard, dear Lawrence, all,

Dear Eckard, it is so important what you say, all is there indeed about the interpretation of the infinity.

Aleph 0...the cantor infinity of the entires.and Aleph 1 for our curves.

Dear Eckard do you know a big thinker, Blaise Pascal, his analyze is relevant about the two systems, the quantum and the cosmos ....the war between Gauss and Bolzano after that continues with Cantor and Poincarré..etc etc...what I find relevant is the utilisation of this infinity due to our evolution.

Indeed the artistic point of vue seems more reasonable about the capacity to perceive this infinity.

At this scale of perception, the reasonability is important in my humble opinion.

The infinity or the transfinity take a main rule for a better understanding, like a taxonomy of this logic of distributions of numbers.

Aleph 0(N Q)entires, fractions...Aleph 1(R)lines, ² and cubic Aleph 2 is relevant about the whole of the curvatures there the spherization is important with a center and a finite system for the universal sphere.

In fact we can resume like a balance between the physicl universe and the unknown, one is finite and the other infinite, it is there it is essential to encircle the difference when we calculate inside this finite Universe.

Transfinites, infinites, finites....the status is relative.

For exemple when Lemaître and Friedmann said the dilatation is infinite, that has no sense.

I prefer the physical finite system and it is more rational in my opinion.

Thales could help in this point of vue and Aristote too, even if I agree with all their ideas.The difference between the unknown and the physicality is essential.Kepler too was pragmatic about this subject.And Gallileo and Descarted were in the doubt or understood the meaning of this foundamental.

In fact it is the real problem about the understanding of the works of Eisntein, many confound unfortunally this interpretation of the infinity and finite system in the physicality.

Bolzano, Cantor, Hubble, Eisntein imply confusions for the people who don't make the differerence between them.

Best Regards

Steve

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Lawrence B. Crowell replied on Feb. 4, 2010 @ 13:29 GMT

Attempts to derive a finite mathematics run into its problems. The simple fact is that even with integers, if you have the integer n then you have n+1 and so forth. This is why mathematics includes this additional set or class called “infinity.” It is not a number, but rather a set included in mathematics to make sequences and inductive processes complete. Cantor found that there must exist different categories of infinity and the situation is more subtle than previously thought. I can’t write up any extensive set of essays here on the foundations of mathematics, for time is limited and I have other matters to attend to. I do think that trying to rewrite the foundations of mathematics is not likely to capture the mathematical world out there.

Cheers LC

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Eckard,

You said "Even good experts tend to fail comprehending that Hermitian symmetry means the originally unilateral and real function of time is replaced not just by two but by four complete copies."

I think it is such an important point that it was worth saying again. The mathematics used for analysis distorts the view of the physical reality under analysis.

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Eckard Blumschein replied on Feb. 4, 2010 @ 16:18 GMT

Georgina,

Why does Fourier transform create four copies? I see two splits of the original.

1) Any transform into complex domain omits half of the original. E.g. cos(x) = cos(x) + i sin(x) - i sin(x) gets replaced by cos(x) + i sin(x). In other words: There are always two conjugate complex planes. Already Bombelli (1526-1572) understood: A complex number always occurs together with its conjugate.

It was an arbitrary choice to omit either the positive or the negative imaginary part or positive or negative phase, respectively. In order to get more meaningful components of complex power, electrical engineers decided to correct the old preference made by physicists. When Gauss in his theory of biquadratic residua 1831 introduced just one complex plane he hided this ambiguity maybe deliberately. It is known how arrogantly the gifted Gauss treated his teachers and the dummies which he called Booeter. Made his pupil Riemann the necessary distinction? Anyway, we merely have to use and keep on mind always the same agreed variant and correspondingly to return into the original domain.

2) The second split is the result of analytic continuation for an one-sided function, which is a prerequisite for application of Fourier transform. Following Heaviside, the values of the function are first assumed to be zero along the missing half-line. Then an even and an odd component are build by splitting the zeros into mutually annihilating values. The sign of the imaginary part indicates whether the original function was located to the left or to the right.

As a result of these two splits Hermitian symmetry means symmetrical real parts and anti-symmetrical imaginary parts, and an entanglement of real part with imaginary part or magnitude and phase, respectively: Except for an arbitrarily chosen point of reference, one can calculate the imaginary part from the real part or vice versa.

Someone who desires a better explanation or additional aspects may look into my essays 369 and 527 including attachments to the discussion or into the revised version of my IEEE paper, available at http://home.arcor.de/eckard.blumschein/ M283.html .

Regards,

Eckard

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Eckard,

thank you. It is good to have someone who understands the mathematics well to explain the inherent problems clearly. As I said I think it is such an important point. The history is fascinating.

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Eckard Blumschein replied on Feb. 4, 2010 @ 20:21 GMT

Georgina,

Thank you for encouragement. Let me tell you some sources I have presently at hand: Oskar Becker: Grundlagen der Mathematik in geschichtlicher Entwicklung. Helmuth Gericke: Geschichte des Zahlbegriffs, and Mathematik im Abendland. Mueckenheim: Die Geschichte des Unendlichen. Anglin: Mathematics A Concise History and Philosophy. I also prefer Ebbinghaus et al.: Numbers.

While there is a lot of literature on the history of mathematics, I looked in vain for books or at least articles that dealt with the discrepancy between mathematics and its application in particular in physics.

Regards,

Eckard

this post was moved here from a different topic

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Eckard Blumschein replied on Feb. 5, 2010 @ 03:55 GMT

Dear Georgina,

Someone mentioned the matrix representation of complex numbers. It is likewise subject to the arbitrarily agreed choice of the sign for the imaginary part or clockwise/anti-clockwise rotation, respectively. I see it a pity that Wikipedia does not mention what already undersood the engineer Bombelli who was the first one who used complex numbers: They occur always together with its conjugate: piu di meno and meno di meno. To me this omission indicates a perhaps serious mistake suggested by Wessel and by Gauss which eventually mislead in particular the fathers of quantum mechanics. Actually one needs the apparently symmetrical couple of complex numbers and the entangled conjugates as to correctly reflect reality.

Please find my reply with sources elsewhere on this topic. I did not find an option for reply at the due place.

Regards,

Eckard

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Lawrence,

You said "I do think that trying to rewrite the foundations of mathematics is not likely to capture the mathematical world out there."

With respect, I do not think it is about capturing the mathematical world. It is about having a mathematical system that is fully compatible with physical reality rather than the abstract mathematical world.If using mathematics to gain understanding of physical processes, those numbers must mean what we intend them to mean. Otherwise it could be misleading. This clarification of the foundations of mathematics used by physicists is quite possibly necessary to fully address the foundational questions of physics. It should then be pursued by those with the inclination and ability for that purpose, which is reason enough in itself. Whatever the "mathematical world" cares to think.IMO

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Eckard Blumschein replied on Feb. 5, 2010 @ 10:24 GMT

"clarification of the foundations of mathematics used by physicists is quite possibly necessary to fully address the foundational questions of physics."

Yes. Georgina. Let's reveal the decisive mistakes.

Eckard

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Lawrence B. Crowell replied on Feb. 5, 2010 @ 15:47 GMT

Mathematics has a connection with physics and astronomy back to the ancient world. Trigonometry was developed fist by Arabs and later in the west so that the position of stars and planets could be computed by sextant and theodolite measurements. From then on what we observe in the world is understood if these observables have properties similar to categories or objects in mathematics, or a mathematical system. The issue of infinities in physical theories means that a working physical theory which produces them is incomplete in some manner. This is the case of course with general relativity, where singularities in black holes must have some description within a more generalized physics --- quantum gravity etc. So far physics has proceeded this way when ever infinities show up.

This is different from saying that we should abandon several centuries of mathematical foundations so as to abolish infinity. In one perspective these infinities are our friends in a sense. They are telling us something: We need to rethink physical foundations! Changing mathematical foundations in order to change this might be misguided. Further, the foundations of mathematics, particularly since the 18th century, constitute a vast area. Trying to rewrite this would be a monumental task. There have been some attempts within some areas of mathematics to do just this, but largely they failed to materialize into a mathematical system that was more powerful.

Cheers LC

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Eckard Blumschein replied on Feb. 5, 2010 @ 21:40 GMT

Lawrence, You might read books on the history of mathematics in order to slightly correct your statement.I mentioned six of them. Why do you think we need to rethink physical foundations and abstain from any doubt in correctness and appropriateness of something that is considered basic to it?

Well, the murky issue of transfinite numbers, *IR, and the like has obviously no bearing for...

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Lawrence, You might read books on the history of mathematics in order to slightly correct your statement.I mentioned six of them. Why do you think we need to rethink physical foundations and abstain from any doubt in correctness and appropriateness of something that is considered basic to it?

Well, the murky issue of transfinite numbers, *IR, and the like has obviously no bearing for physics and it seems therefore to be harmless. However, if I recall correctly, Einstein belittled unresolved mathematical disputes as fight between frogs and mice. It was the same Einstein who could not accept a seeming contradiction, which is expressed in the EPR paper and led to the theory of entanglement.

You hopefully realized that I found mounting evidence confirming my suspicion: The apparent time symmetry which is assumed to distinguish the micro-world from the usual physics can be explained as simply a mistake, an inappropriate application of the complex ansatz without the due care. While nobody can deny that there are no physical influences from expected future into the past, what Wikipedia tells about use of complex numbers and what physicists have to learn about them does not suffice to understand the flaw.

I see it a bad practice to circumvent paradoxes and evade problems by fabricating more and more sophisticated, less and less understandable, in the end not even verifiable twists instead of nor shying back from possibly unwelcome basic corrections.

I see it an even worse behavior to blame those incompetent who are putting in question what we in former GDR called "the party is always correct"i and Catholics call the pope is infallible. For mathematicians there is no doubt in the existence of singularities. They are even familiar with a variety of them. Ergo they must play a role in nature too. Really?

Let me try to mediate. I have been using singularities for nearly half a century as I am likewise using lines and points for instance when I describe a crossroad where it does not make sense to exactly locate the lines and the point.

A related problem was among the first ones that puzzled me. A a piece X of a line is included between a first point A to the left and a second point B to the right. Does it include these points? I know, it is considered rigorous to distinguish between open and closed intervals. Let's attribute a value one to all points between A and B and a value two to an adjacent piece Y of the same line. What value is valid for the "common" point B? It is lazy practice to arbitrary attribute the singular value 1.5 to B.

Meanwhile I prefer a solution that I consider the only natural one. A point has no parts. Therefore it can cut a line but it must not be seen as an element of a piece of line, neither included nor excluded. Instead of insisting of the value f(B) we should remember that the piece is endlessly splittable. Nothing is wrong if we restrict the piece X to the limit -->B from the left. Provided the line is continuous, then any value of f exactly at B is irrelevant in any application since the difference measure B minus measure -->B is the measure zero. Brouwer was correct in that. I agree with you: Revisionism is not powerful and I add, it is no final solution. A spade is a spade. Not just aleph_2 does no longer deserve defense if we ignore questionable mathematical gospels for the sake of realistic physics. I do not expect harm for any valuable work.

Eckard

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Georgina

"I think that the various abstract mathematical spaces are different from the physical reality of how matter is distributed within actual space, space-time or energy space."

I agree. But perhaps not quite so different as we may have thought. In fact it appears that if we can find a real physical connection with mathematical spaces, or sets of co-ordinates, it may solve some important issues. It may also give us an arbitration on how central the math is compared to intuition and how important it is to keep it grounded in reality. I posted a belated response to you in the Forum under 'Hunting for theories of (not) everything.' Which I hope you may consider and respond to.

Best wishes

Peter

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Thank you Peter,

it was nice to read your reply to my post in "Hunting for theories of (not) everything." Glad someone actually read it. Positive feedback is always very nice too.

I will most certainly find the time to read your essay and respond. Don't hold your breath though, as it may take me a while. It is certainly encouraging if a model is able to explain anomalies, especially if those anomalies were not known about at the time the model was constructed. I am intrigued.

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Thanks Georgina

The Essay itself was more about the essay subject, and the postulate that - It doesn't matter if anyone finds the real answer to life, the universe, and everything that's possible in physics as we're now in a state where no-one will even notice it!

In a way it was a test to see if the assessors proved it's own postulate. It was proven. Some (you can see in the posts) saw through the thin veil, but very few.

I hope it will resonate with you, but this is also perhaps a test, to evalute where I'm currently going wrong in communicating it. Your opinion will be valued.

Peter

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Dear James Putnam, I looked at 364 and 490. Thank you. We used "absolute time" in different meaning. My approach is so fundamentally different from all theory so far that most experts reject it while my argument seems to be not refutable: Future is not yet real. Consequently there is a natural zero to all influences.

You are criticizing that physics is inanimate. To me as an engineer, even the function of the organ of Corti invites to be well understood like something inanimate.

You are also criticizing artificial limitations. I am rather complaining about the loss of natural restrictions by abstraction. This opinion of mine is also well founded but highly unwelcome to those who built a lot of speculative theory on the idea that anything what mathematics provides has a physical correlate.

Let me quote Albert Einstein: "as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality" (Einsteins Ideas and Opinions: Crow Publishers NY 1954, p. 233).

My critique goes further: I do not consider differential equations like f=ma the primary relationships in reality, but I argue reality is something that integrates an infinite diversity of influences. We may abstract those that are decisive and reproducible. Nonetheless, we have to check whether or not the general solution to DEQs are reasonable and exclude for instance nonsensical advanced ones.

Also, old engineers like me learned to use ideal mathematical tools like point, line, negative, imaginary, and irrational numbers, singularities, evanescent modes, etc. without leaving the awareness that they must not confused with reality. A point charge, a line current, etv. are fine but do not exactly reflect reality. If I am unable to express my view, I beg your pardon. English is my fourth language after German, Russian, and Latin.

I am pretty sure having found a few benign mistakes and a hurting one in basics.

Regards,

Eckard

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Steve Dufourny replied on Feb. 8, 2010 @ 10:35 GMT

Fourth language, fourth language, you you speak well english, have you seen mine hihiih the languages are really the thing I dislike studying.

Steve Repeat after me ... my tailor is rich, steve: mi taylor is rich , still my teilor is rich, it is better steve still one..... my tailor is rich, ahhahah like what all evolves and our numbers too hihi

Dear Eckard, There I need explainations about that...you say I do not consider differential equations like f=ma the primary relationships in reality, but I argue reality is something that integrates an infinite diversity of influences.

What are these influences?

Why do you consider F=ma like that?

Regards

Steve

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James Putnam replied on Feb. 8, 2010 @ 19:54 GMT

Dear Eckard Blumschein,

I am re-reading your essays. This time I will make sure I understand what you are saying. We have a tendency to see things through our own perspective even when that perspective is distortional. By the way, it was very diplomatic of you to reply to differences in our approaches while avoiding challenging the most contentious, some others might say silly, parts of what I wrote in my two essays. Because of your courtesy, it will be easier to keep the emphasis on your ideas. Those are the ones that I am interested in understanding.

James

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James Putnam replied on Feb. 13, 2010 @ 00:17 GMT

Dear Eckard Blumschein,

I, in the past, read your essays, but, I recognize now that I was merely skimming through them. I know that I did not understand them then, because, I am struggling to understand them now. I will keep at it as time permits. There are some other essays and books that I am also reading in my spare time. I saw that you had conversations with others about your ideas. I am wondering if anyone else has a recent opinion that they may be willing to express. It helps to read discussions, especially by mathematically skilled reviewers.

One point of clarification about my own viewpoint with regard to what I called absolute time. I do not insist that arbitrary zero points in time are necessary. I limit my concern about time to two points. One is that: Time is not affected by activity in the universe. The second is that there is a natural timing device always present in the activities of the universe. That timing device keeps absolutely perfect time. I say this so that you understand why I titled my first essay 'The Absoluteness of Time'.

It is your ideas that show your depth of thought, and, that I think deserve thoughtful evaluation by qualified others. So, disregarding what I think for now, I am wondering if anyone else has something helpful to say about your essays. Especially the second one.

James

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Why we must not consider differential equations like f=ma the primary relationships in reality?

Acceleration a is the second temporal derivative of distance x. Velocity v is the first derivative. Let's assume f given as a cause the value of which does not depend on t. Then integrating once over a dt yields v=at. This means, velocity is influenced by the sum of infinitesimal influences f dt. The symbol for an integral is a stretched "S" for sum. In order to get x one has to integrate once again over v dt. Usually one has additionally to consider influencing constants of integration. While the law f=ma is invariant against shifting or even flipping time, the influences all relate to the past and end at the zero of (elapsed) time.

Consider laws like naked bones and reality the whole animal.

Eckard

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Steve Dufourny replied on Feb. 8, 2010 @ 17:13 GMT

Thus dear Eckard you consider an infinity in the physicality, if yes, you are false simply, a derivation or an integral are just tools to extrapolate towards 2 limits, in 2 sense,....you know ax²...2ax for the derivation and a cubic for the other sense , but I don't see an infinity dear Eckard.

The universe is finite, the space too even with our adds or multiplication.And if the add or the multiplication are too important thus it is not necessary.

The influences are correlated in this finite system.All derivations or integration shall give the same results.

If not it is false in a whole point of vue.

Could you explain me the difference between the physicality and the unknew, after we shall speak about this infinity better I think.

Regards

Steve

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Eckard Blumschein replied on Feb. 8, 2010 @ 23:09 GMT

Steve,

Let me add: While it is common practice to abstract previously unknown laws, in particular differential equations, which ascribe results to observed data that might be causal influences, one cannot deduce the results just from the laws without knowing for sure all essential influences. Causality is directed from cause to effect, not vice versa. Therefore knowledge of particular cases is a precondition of any generalization. The opposite does not hold.

I will tell to those who are not yet old enough as to have experience with analog computers: Analog computers were based in integrators only. The could not directly perform differentiation. Why? Because differential equations are not the primary ones in physics.

Now to your arguments. Admittedly I do not always clearly understand your English. I understood: You consider the universe finite. To me this question of belief does not matter. At least from a practical point of view there is no absolutely closed system in physical reality. If something is so large that no boundary is known then I consider it reasonable considering it unbounded.

You might suspect me wrong but hopefully not false.

If I understood you correctly, you are misled by Laurent Schwartz or André Weil who introduced generalized functions as to allow differentiation without restriction. In the reality of engineers it is plausibly possible to integrate e.g. a triangular pulse as often as you like. However, repeated differentiation yields first already somewhat unrealistic rectangular pulses, then fictitious while still reasonable Dirac impulses, finally doublets which can be interpreted as dipoles but then nothing useful.

Only for sinusoidal functions the operations integration and differentiation can be interpreted as shift to the left or to the right, respectively. Notice: One cannot shift reality into the future. Reality cannot be shifted at all.

Sinusoidal functions that range from minus infinity to plus infinity do merely fit to closed loops or unrealistic cavities between ideal mirrors, not to typical cases of the real world.

Eckard

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Steve Dufourny replied on Feb. 9, 2010 @ 10:24 GMT

Dear Eckard,

First of all, thanks for this answer, I see better your gauge in the physicality and thus I understand your understanding about the infinity.

I beleive you confound the unknew and the physicality.

About Mr Schwartz, he is competent but his arrogance is not a good road.That's why afetr a message, I have answered, it is logic no ?

In fat you know it is not important for me, I am laughing in fact.Some people invents and the others try to create , it is like that.

For an animal, all is composed by quantum spheres and it doesn't exist an infinity there.The mass is finite and evolves furthemore.

In these lines of reasoning, thus you can't find the truth dear Eckard, I beleive too you confound the spirituality and the universality with the human inventions like religions, it is totaly different and it is well like that.

Best Regards

Steve

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Eckard Blumschein replied on Feb. 9, 2010 @ 13:32 GMT

Steve, Laurent S. competent but arrogant? I rather suspect we should ask whether his line of mathematics can provide an appropriate tool for physics.

I realized fruitless efforts to apply pertaining generalizations in technology.

While I accept that some mathematicians consider unrestricted possibilities and also symmetries like beautiful and true creations, to me it is reality that counts.

I am distinguishing between two gauges that are permanently sliding relatively to each other:

- Reality includes anything that left traces that are observable in principle. It is assumed to exist independent of us while restricted to the past.

- Theory additionally includes prediction and the possibility to influence the future. It is however restricted to determinism, i.e., it cannot grasp the whole reality.

You wrote: "I beleive you confound the unknew and the physicality." If something confounds me, it makes me feel confused or surprised. The word "unknew" is indeed confusing to me because I have to guess whether you meant unknown or unknowable. Maybe instead of "confound" you meant "confused". I also do not understand and I do not intend understanding what you meant with physicality. Physical things can be touched or seen like a human body, or at least they relate to physics.

Eckard

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Anonymous replied on Feb. 9, 2010 @ 14:02 GMT

Dear Eckard,

Each people is free and equal.

Each people has its point of vue about the physicality and the unknown, perhaps this definition is better.

What I say is very simple, it exists a difference between this system behind our walls and the physical universe.

The difference beteen these 2 points is so so so important for a real application of the tools in this finite system which evolves, this sphere and its spheres.

The determinism and the realism is like that.

It exists a difference too about two points.The fact to have limits due to our step of evolution and thus our analyzes about the physical matters and the infinity, all that implies confusions.

In the physicality, the infinity is not an infinity , it is just a lack of whole point of vue due to our age.

If people doesn't understand the difference about the physicality and the infinity behind the walls , there that becomes ironic and bizare.

Thus it is a lost of time for me to explain that because I have already explained in several posts even with my english.

A scientist must be an universalist and must respect this building.

Sincerely ,humbly and respectfully

Steve

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Steve Dufourny replied on Feb. 9, 2010 @ 14:04 GMT

OOPS sorry it was mine the last post

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Eckard you said "Consider laws like naked bones and reality the whole animal."

So well put. I shall. Thank you for that.

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Re. Fibonacci series, golden spiral and circles or spheres

To Steve and whoever else it may interest.

It seems to me that the golden spiral or something approximating to it can be constructed in the following way. Take spheres or circles each with a radius equal to a number in the Fibonacci series.For concise explanation I will say circle but it could also apply to...

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I did say that the two circles of diameter 1 are superimposed. I did not mention that the second one will be rotated 90 degrees however. Also if the two equidistant lengths of the triangles are divided by the base distance between the two centres it gives a number approximate to the golden ratio, alternating higher and lower for adjacent triangles, probably approaching the golden ratio as the size of the triangles increase as is the case when rectangles are used to produce such a spiral.

I did not take into account the circle of diameter 0. I took it to be non existent. Is that correct or should it be represented as a point superimposed on the centre of circles of diameter 1? If there is such a point for circle diameter 0 then perhaps the spiral should begin at the centre of circle diameter 1 as it needs to start at the mid point between centre of circle of diameter 0 and diameter 1 which is still the centre point. Which ever gives the best golden spiral is probably the correct solution.

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There is another clear pattern here in that the larger circle only intersects those circles of diameters that will add to give the diameter of that larger circle.

Looking at how each circle intersects the circles of smaller size. Circle diameter 21 only intersects circles of diameter 13 and 8. Adding their diameters gives 21. Circle 13 only intersects circles of diameter 8 and 5. Adding these diameters gives 13. Circle 8 only intersects circles of diameter 5 and 3. Adding these diameters gives 8. Circle 5 intersects circles of diameter 3 and 2 only. Adding these diameters gives 5. Circle of diameter 3 intersects circle of diameter 2 and 1 and 0. Adding these values gives 3. Circle of diameter 2 intersects circle of diameter 1 twice as there are two circles of diameter 1 superimposed but rotated 90 degrees and circle of diameter 0. Adding these two diameters of 1 and 0 gives 2.

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Ray Munroe replied on Feb. 15, 2010 @ 13:48 GMT

Dear Georgina,

This sequence of 3, 5, 8, 13, 21 is obviously ratios of the Golden Ratio phi = (1+SQRT(5))/2 =1.618~5/3~8/5~13/8~21/13. El Naschie makes heavy use of double this sequence: 6, 10, 16, 26, 42 and relates it to String Theory dimensions - which may just be an incredible coincidence that 10 and 26 dimensions are so relevant to String Theories.

The origin of the Golden Ratio is rooted in the geometry of the pentagon. Draw a pentagon. Inscribe a 5-pointed star inside the pentagon's vertices. Now take ratios of various line segments. You will find ratios of phi=1.618, (phi)^(-1)=0.618, (phi)^2=2.618, etc.

A year ago, I suggested that Steve might want to look at fractal kissing spheres. That involves Fibonacci's sequence and could be the key to understanding El Naschie's E-Infinity (if we can ever derive a good proof of E-Infinity).

Have Fun!

Ray

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You need to view my last 3 posts in chronological order or they get muddled up with other things.

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The spiral I have described does seem to me to be perhaps the kind that might be produced by swirling weather system or cosmic dynamic systems.

There is another spiral that can be drawn with the same circles put together in the same way. To draw this one start from the point at the centre of circles of diameter 1 ( Circle diameter 0), then move through 90 degrees to the right hand edge of circle 1 so that the point is on the end of a horizontal diameter line. This is the first of the two circles of diameter 1. Then move through 90 degrees to the bottom of the circles of diameter 1 and make a point on the bottom of the circumference where it meets a vertical diameter line. This is the second circle of diameter 1.

Move clockwise to a point on the circumference of circle of diameter 2 where it meets a horizontal diameter, then to the top of circle diameter 3 where it meets the vertical diameter. The next point is right hand side of the circumference of circle diameter 5 where it meets the horizontal diameter, then the bottom of circle diameter 8, then the left hand side of circumference of circle diameter 3 and finally top of circle diameter 21 where circumference meets vertical diameter. These points can be joined with a smooth spiral. This demonstrates the formation of another spiral pattern.

This seems to me more like the kind of growth spiral one would find in shells for example where there is rotation combined with increase in size as more material is added.

I think it is interesting that this arrangement of circles produces these two spirals which are similar but not identical.What do you think?

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Is the first spiral called a Fibonacci spiral and the second just called a logarithmic type of spiral? It seems that the golden spiral is just one particular form of a logarithmic spiral. Which I probably haven't drawn. Is it common knowledge among mathematicians that these two different spirals can be made from the Fibonacci radius circles? Its all new to me.

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Should have said Fibonacci diameter circles, oops.

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Hi Ray,

did you take a look at the whole of the first post about the spirals? It describes how to construct a particular spiral, using circles with Fibonacci numbers for diameters arranged in increasing size of diameter with 90 degree rotation. I thought the pattern in the intersections of the spheres themselves was very interesting as well as the triangles formed by the drawing of the spiral equidistant from the centres of the circles.The triangles have circumferences equal to the diameter of the largest circle whose centre forms a corner point of the triangle. I am interested to know what is already known about this particular spiral and whether the observations I have made are common knowledge among mathematicians. What is this particular spiral known as? and the other one? Which is less interesting to me but still nice in its own right.

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Ray Munroe replied on Feb. 15, 2010 @ 19:55 GMT

Dear Georgina,

I'm not a mathematician, but check out this reference:

http://en.wikipedia.org/wiki/Golden_spiral

It sounds like the golden spiral is a special case of a logarithmic spiral, and the Fibonacci spiral is a good approximation of the golden spiral (and becomes a better approximation for larger numbers in the sequence).

Much of El Naschie's research sounds like a reapplication of Fibonacci's ideas.

Have Fun!

Ray

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Hi Ray ,

thank you for your prompt reply. I have already had a look on the Wikipedia page. I am not sure what I have drawn. I didn't construct the two spirals with rectangles as is shown there, or use logarithms but just circles with Fibonacci number diameters.In response to Steve's question. (He was asking about a connection between the Fibonacci sequence and spheres".)

The reason I think the first spiral might be relevant to topology, chaos theory and cosmology is because the spiral seems to flow directly between the "disturbance" caused by the circles. Like the path of least resistance followed by a stream for example.It could be that the centres of the circles are the point of rotation of air in the atmosphere or cosmic dust or other matter in space. As the size of the disturbance (circle) grows so does the spiral. Following a particular path in relationship to the circle of disturbance. The first spiral takes the path of least resistance between the circles of disturbance and in the second case follows the surface of the circle as it rotates and grows. The second one seems more like the growth of something like a snail shell to me.

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Ray Munroe replied on Feb. 15, 2010 @ 21:08 GMT

Dear Georgina,

My approach is that 5-fold 'pentality' symmetries are relevant to the origin of mass. Five-fold symmetries appear in groups such as the Icosahedron, H4 and E8. The Golden Ratio (1+SQRT(5))/2 = 1.618... arises from 5-fold pentagonal geometries. The Petrie Pentagon is a 2-D diagram for a 4-D 4-simplex. If you have insight into the relevance of the Golden Spiral, then that may be interesting.

Have Fun!

Ray

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Steve Dufourny replied on Feb. 16, 2010 @ 10:32 GMT

Hello dear Georgina and Dr Cosmic Ray,

Dear Georgina,

Thanks.

It is very interesting that georgina.The superimposings can give many intresting ideas.

Dear Ray,Yes indeed we discussed about that, you know, the fractal makes me crazzy , I search the divibility, the serie, the number and their volumes and really that takes all my mind at this moment.Dear Dr Cosmic Ray I think my mathematical method is false or not complete for this number and fractal of the ultim sphere.I don't know in fact how I must divide this central sphere like our universal center or our central quantum sphere.The serie is specific but how is this specificity.I need cosmological datas to find that.Alone it is impossible I think, my series and maths methods make me crazzy.hihihi furtermore with all the ideas of FQi , you imagine my confusions Ray hihi I must reread my taxonomy and classment because I confound a little there.

The entanglement like a kind of Bose Einstein condensate seems interesting for the quantization of our mass.If the rotation is correlated with the mass and the volume, that becomes very relevant in my humble opinion.

The temperature is correlated too with the fields and the energy.Thus the rotating spheres too, dear Ray like in an evolutive point of vue, the lattices, these spaces between spheres , change due to parameters.The tempeature and the time are correlated thus for the specificty of the entanglement it seems to me.

Friendly

Steve

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Steev Dufourny replied on Feb. 16, 2010 @ 11:21 GMT

Hello dear Georgina and Dr Cosmic Ray,

Dear Georgina,

Thanks.

It is very interesting that georgina.The superimpo

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Ray Munroe replied on Feb. 16, 2010 @ 14:08 GMT

Dear Steve,

You said "Dear Dr Cosmic Ray I think my mathematical method is false or not complete for this number and fractal of the ultim(ate) sphere.I don't know in fact how I must divide this central sphere like our universal center or our central quantum sphere.The serie(s) is specific but how is this specificity."

I am not certain if the answer to your problems is the soccer ball or fractal kissing spheres, or some 'crazzy' combination of those ideas. The soccer ball introduces pentagons and hexagons, and thus naturally introduces several important prime numbers (2, 3 and 5) and the Golden Ratio (via pentagonal symmetries). I think these prime numbers tie back into Clifford algebras. Fractal Kissing spheres introduces Fibonacci's sequence, and thus introduces the Golden Ratio 3/2~5/3~8/5~13/8~21/13 ... -> 1.618 and the Golden Spiral (similar to a snail's shell).

Go study a soccer ball and HAVE FUN! Do Europeans celebrate Mardi Gras the way that French-American Catholics celebrate in New Orleans?

Ray

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Steve Dufourny replied on Feb. 16, 2010 @ 14:52 GMT

Hi dr Cosmic Ray,

Yes indeed in Europe we celebrate that too, and even now Halloween .You are everywhere you the americans hihihi even a Mc Donald near my home hihihi

About the number ,This architecture is so far for me.These spheres are specifics and in motion.The soccer ball is just when I play soccer in fact, it is all hihii.

Penta hexa etc etc no no I speak about the real number of spheres, limited furthermore.The golden ratio is not sufficient like the serie of Fibonacci.The golden ratio is like pi, phi and pi are just irrationals and for me an irrational needs rationality and the only thing which is evident in this line of reasoning is the evolution of the irrationality.Thus we perceive just a step.

It is the same with the infinity.

Friendly

Steve

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PhysOrg - May 1, 2007

"While the aesthetics and symmetry of Fibonacci spiral patterns has often attracted scientists, a mathematical or physical explanation for their common occurrence in nature is yet to be discovered.".......

...Zexian Cao said "The least energy configuration for particles is dependent on the geometry of the space in which the particles are confined....."I only know that the Fibonacci spiral patterns are not the least energy pattern for a sphere (try to imagine a football) or flat plane (we can make Fibonacci spirals on street pavement, but it is not self-assembled)......Cao explained why this proof is so difficult. "The patterns on a sphere are now referred to as the Thomson problem, which has been generalized as the Generalized Riesz Problem. There is no general method to find the least energy configuration for a given confining geometry, and the numerical solution costs enormous time of both the computers and the scientists. Even worse, it is difficult to make oneself believe that the least energy solution he finds is really the global minimum. And numerical solutions would never be accepted as proof. There are many similar embarrassments in physics."

Taking the first spiral pattern that I described. It is equidistant from the circle centres which could be taken to represent physical peaks of a material barrier (like the tops of hills or centre of a disturbance or force that prevents entry of the spiral into that region or makes it less probable. The second spiral appears to follow the surface of the circle as it grows perhaps forming and growing onto an existing expanding circular or conical surface.

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Perhaps I should have said expanding circular, spherical or conical surface.

The first spiral seems to form as the size of the excluding force or material barrier increases and there is rotation of the spiral flow around it.

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Actually the first spiral probably forms the other way around in nature too. So it would be decreasing in circumference of spiral path as it flows around a barrier, material or energetic, of decreasing magnitude. Or increasing in circumference of spiral path if flowing around a barrier of increasing magnitude.

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So sorry, I just noticed to my annoyance an error in my first post about the spirals.

I said "Take spheres or circles each with a radius equal to a number in the Fibonacci series." I meant to say diameter. This may have become clear as later on I mentioned diameter a number of times. Just take it that each of the circles has a diameter that is a Fibonacci number. Then it will all work as explained. Anywhere else I have mentioned radius I also meant diameter.

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Error correction from me.

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Steve,

I'm glad you find it very interesting. I find it absolutely amazing, fascinating and exciting. Thank you for asking the original question.

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FQXi members,

It is in my opinion a beautiful geometric truth that....

the intersection of circles, with Fibonacci number diameter arranged in size order, with centres separated by a value that is the increase in diameter and rotated 90 degrees always in the same direction ,clockwise or anticlockwise, is an ordered pattern such that a circle only intersects with smaller circles whose diameters add to give the diameter of that larger circle.

It is also in my opinion a beautiful geometric truth that when a spiral is drawn around the circles arranged as described above and its path intersects a circle at a point equidistant from the centres of two circles, then the circumference of that triangle thus created will be equal to the diameter of the largest circle who's centre forms one point of the triangle.

It is in my opinion a beautiful geometric truth that two different spirals may be drawn using the Fibonacci diameter circles arranged as described. The first following a path of points that are equidistant from the circle centres and the second following a path of points on the surfaces of the circles rotated 90 degrees, always in the same direction, clockwise or anticlockwise for each change in size of Fibonacci diameter circle.

These observations can be replicated by anyone with pencil, paper, pair of compasses and ruler.

Does this not suggest that the self assembly of Fibonacci spirals in nature may be due to a comprehensible underlying geometry. Is it not therefore reasonable to use relatively simple geometry rather than complex arithmetic to ascertain the path of least energy and so interpret the spirals?

Where are you?

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Ray Munroe replied on Feb. 16, 2010 @ 20:37 GMT

Dear Georgina,

The Fibonacci Spiral based on the Fibonacci sequence is an approximation of the Golden Spiral based on the Golden Ratio. If we look at ratios of the Fibonacci sequence, we have 3/2~5/3~8/5~13/8~21/13~...-> 1.618... the Golden Ratio. The Golden Ratio arises from pentagonal symmetries (see attached 'golden' file). Recent experimental work by Coldea et al (you should be able to download a personal copy of the Jan 8, 2010 article from www.sciencemag.org) implies that the golden ratio may be relevant to certain quasiparticle mass ratios. I think that the origin of the Golden Ratio and pentagonal symmetries is the Petrie Pentagon - which is a 2-D representation of the 4-D 4-simplex. In my models, a broken 4-simplex ~ (3+1)-simplex represents Spacetime. I know you don't like extra dimensions - my model has extra dimensions...

El Naschie uses double (part of) the Fibonacci sequence: 4, 6, 10, 16, 26, 42 in many of his papers. His critics consider it all 'numerology', but what if it is indication of an underlying pentagonal mass symmetry?

Have Fun!

Ray

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Ray Munroe replied on Feb. 16, 2010 @ 20:38 GMT

Oops! I forgot the attachment!

attachments: golden.pdf

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Dear Georgina,

I've replied to your comments, but you never responded back to mine. I didn't know if you were intentionally ignoring me (like you would Frank - I hope I'm not in the same category...) or if your web browser is so messed up that you are losing all of the reply threads. So I decided to repost my prior comments.

The Fibonacci Spiral based on the Fibonacci sequence is an approximation of the Golden Spiral based on the Golden Ratio. If we look at ratios of the Fibonacci sequence, we have 3/2~5/3~8/5~13/8~21/13~...-> 1.618... the Golden Ratio. The Golden Ratio arises from pentagonal symmetries (see attached 'golden' file). Recent experimental work by Coldea et al (you should be able to download a personal copy of the Jan 8, 2010 article from www.sciencemag.org) implies that the golden ratio may be relevant to certain quasiparticle mass ratios. I think that the origin of the Golden Ratio and pentagonal symmetries is the Petrie Pentagon - which is a 2-D representation of the 4-D 4-simplex. In my models, a broken 4-simplex ~ (3+1)-simplex represents Spacetime. I know you don't like extra dimensions - my model has extra dimensions...

El Naschie uses double (part of) the Fibonacci sequence: 4, 6, 10, 16, 26, 42 in many of his papers. His critics consider it all 'numerology', but what if it is indication of an underlying pentagonal mass symmetry?

Have Fun!

Ray

attachments: 1_golden.pdf

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Ray,

I just happened to wander in here, and this caught my eye. I haven't read El Naschie's papers; however, I note that the difference in terms up to 26 is the sequence 2, 4, 6, 10, which corresponds to cardinal points of dimensions 1, 2, 3, 4 (allowing 10 as the number of non-redundant points of the 16-member matrix of the 4-dimension tensor field). Numerology?--maybe, but quite an interesting correspondence to proposed string theory dimensions, even if only coincidence.

http://home.comcast.net/~thomasray1209/site/

See ICCS2006

Cheers,

Tom

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The potential (i.e., what can be), actual, and theoretical have to all be merged in order to achieve a relatively unified understanding of physics.

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Ray,

thank you for the information. The golden spiral may hold a clue or not, I just don't know right now. What if...? So tired.I now understand the reason for the mathematical use of dimensions for numerous variables by the way, but that's not how I like to think. It all gets so complicated.

Everyone,

I do not know if the 2 spirals I drew are either a one golden spiral or even Fibonacci spirals. They may just be logarithmic type spirals of no particular significance. I am not a mathematician. I was hoping someone would recognise them and tell me what they are. The only way I can think to determine this is to draw them out carefully again and then copy some examples of the golden spiral and Fibonacci spiral and see if they can be superimposed.

I have browsed the net and can find no answer to that question there. However it does seem that many of the spirals found in nature are not actually golden spirals or Fibonacci spirals but just very rough approximations, being logarithmic type spirals. That does mean perhaps that the Fibonacci numbers and spiral produced from it may not be so very special after all.

A repeating geometric pattern has been produced which has a changing scale. Therefore it should not be surprising that there are other repeating patterns to be found within that geometric pattern, such as the triangles. However -the significance seems to be - that when spatial change is investigated it is considered more often in terms of linear changes and may involve unvarying barriers or forces rather than rotations and changes of scale in the barriers or forces constraining the change. From this investigation it can be seen that it is the combination of rotation and underlying change of scale that produces the particular morphology, in this case a spiral pattern. In nature, rather than on paper, this could be either increase or decrease of a material barrier or force that would require energy to overcome. The morphology observed is in part a result of the varying magnitude of the material barriers or forces that constrain that growth. The orientation of change in position in relationship to it also being of importance.

Perhaps there is a glimmer of hope here that further investigation of simple geometric relationships, combined with rotation over changing scales, could help us to elucidate how various material forms arise by self assembly.

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Ray,

I certainly do not compare you to Frank. You are never rude or abusive and show great patience, tolerance and understanding. Respect.I am not ignoring you. However several things may conspire to make it appear so.

I have read your posts with interest. I realise that you see some possible correspondence of the golden spiral with your own work and that of El Naschie and others. That is interesting in its own right. However I do not think that I can even begin to understand what you or they do. Therefore I do not think that anything I would have to say in relationship to your work or that of the other gentlemen would be helpful to you. Likewise I can not really converse with Lawrence about his work. It is not that I do not wish to reciprocate and be helpful.

I am openly sharing what I understand about these spirals. It is all new to me.

I am very focussed on their significance right now. I am also very tired because I have been spending far too long writing about them here and trying to find out about them on the net.I apologise for seeming inconsiderate. I really need more sleep.

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Ray,

I still can't reply to threads only submit new post. So if you are expecting a reply on a particular thread it won't necessarily be there. The web master hasn't been in touch to offer any suggestions. The "conversation" should still work in chronological order though.

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Dear Georgina,

If you are in Britain, then it is bed time. I'm in Florida - 5 hours behind your time zone.

Have you tried navigating with a different web browser? I usually use Internet Explorer at work and Mozilla Firefox at home. When I noticed Firefox wasn't working with the reply threads, I changed to Explorer, and that solved my problem.

My 'excuse' for using extra dimensions is that extra information is present. How does an electron 'know' its properties? Where is Hilbert space? Mainstream physics uses these concepts all of the time without seriously asking where that information is stored.

I don't always understand Lawrence either (his math is a little ahead of mine), but I hope that our correspondances can lead to something productive.

The snail shell is an example of a general logarithmic spiral. The Golden Spiral is a particularly 'beautiful' logarithmic spiral. And I think you actually drew a Fibonacci Spiral with your radii of 1, 1, 2, 3, 5, 8, 13, etc.

Good luck in your research.

Dear Tom,

I'll check out your website tomorrow. Yes, El Naschie likens the 4, 6, 10, 16, 26, 42 part of the sequence to String Theory dimensions. He seems to have more critics than supporters these days, although that is difficult to determine because both sides may use 'sock-puppets' (web pseudo-names). I have chosen to keep my mind open until I can prove or dis-prove his ideas. That puts me in a dangerous position - in the 'middle of the road' - where I can get hit by traffic coming from both directions.

Have Fun!

Ray Munroe

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Anonymous, You said "The potential (i.e., what can be), actual, and theoretical have to all be merged in order to achieve a relatively unified understanding of physics."

I am proposing the hypothesis that (Potential)- Simple geometric analysis, including rotation and change of scale of underlying physical barriers, energetic or material (as well as magnitude and rate of flow or change), will allow the -actual- observed morphology of material substance to be better understood and allow a -theoretical- explanation for the formation of that observed morphology.

This will be more effective than relying upon complex arithmetic analysis of changes within fixed landscape, fixed magnitudes of barriers energetic and-or material and fixed flow.

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Hi all,

The title is relevant, the beautiful truth, like a harmony of thje building.

When I invented the spherisation , I was so excited about this reality ,this universal sphere and its spheres build by quantum spheres.It is a beautiful, even this word is not sufficient, this truth is the truth in fact.

Let's imagine this universal sphere and its center where all began.Let's imagine all these spheres(cosmologics) which turn around tyhis center and continue their dance of evolution of the mass.The light becomes mass due to the intrinsic gravitational codes of these quantum spheres and their specific number, rotations, volumes, mass....the gravity is like a modulator of evolution and the light becomes mass and this gravity, these quantum spheres polarise and shall continue to polarise to optimize the spheres, physicals and their rules.All has a rule of complemenatrity in this sphere.We are spheres, we live on a sphere, we turn around a sphere, we' turn all times, we are inside a sphere and there is an ultim aim between all these spheres.

This truth is so beauuuuuuuutiful , it is the reality of all things, everywhere in this sphere.We are a pat of this sphere like catalyzers of this truth.

It was evident in fact.The spherization is the harmonization of the spheres in the spheres.

Spherically yours

Steve

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Thanks, Ray.

Yes, I noticed after I read back in the thread that you had said El Naschie made the connection between his sequence and string theory dimensions. I should have known; the correspondence--or coincidence--is quite apparent.

I wouldn't worry about being in the middle of the road. There doesn't seem to be too much traffic there these days. :-( I am old enough to remember when reserving one's opinion was a mark of intellectual integrity. It is sad, I think, that I only know of El Naschie because of the criticism. Now I've got to make a point of reading the papers.

Tom

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Dear Tom,

Your website's ICCS2006 link doesn't seem to work. Can you post it on one of these blogs?

El Naschie was very prolific, although many of his publications sound like short 'weekend project' papers.

In my opinion, some of his most relevant papers to the Golden Ratio are (all in Chaos, Solitons & Fractals):

CS&F 30 (2006) pp 579-605

CS&F 36 (2008) pp 1121-1125

CS&F 41 (2009) pp 1263-1265

CS&F 12 (2001) pp 1361-1368

CS&F 14 (2002) pp. 369-376

and International Journal of Nonlinear Sciences and Numerical Simulation, 8(4), pp. 469-474, 2007.

Dear Georgina,

You might want to check out Leonard Malinowski's work. He had a website last year - I'm not sure what happened to it. Len is a Chemist in Pennsylvania. He took 3-1/2 years off to write his theory, got it published in CS&F just as he was running out of money, and then went to work for BASF. A couple of Chaos, Solitons & Fractals references are:

CS&F 42 (2009) pp. 1396-1405

CS&F 42 (2009) pp. 3130-3131

Have Fun!

Ray

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Thanks again, Ray.

The address is correct. I just forgot to follow link protocol:

Tom's site

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Dear Tom,

The sub-link from your home page down to the ICCS2006 link doesn't seem to work. I googled you to see if I could find this proceeding and I saw that the mathematicians are giving you a hard time about "6th grade math" at the Math Forum @ Drexel. You might want to check out my paper. It touches on Geometric Algebra, but needs more development. Lawrence Crowell and I are combining ideas and efforts.

Have Fun!

Ray

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T H Ray replied on Feb. 17, 2010 @ 19:48 GMT

Ray,

The online proceedings are no longer linked to full texts of papers, though abstracts remain, and the Interjournal will only link you to my Comcast home page, which is the link I posted here. You have to copy and paste into your browser to retrieve the pdf files. There's probably a way to make a live link, but I am ignorant of so many of these computer based processes.

The MathForum colloquy saddens me. It's absolutely uncalled for, and distressing on many levels. I can't understand why some people calling themselves professionals feel they must denigrate others to elevate themselves. The individual who claimed that I "randomly strung together" some technical terms and hung the "crank" label around my neck must have gotten this knowledge by divine revelation--how would he know such relations are random, in the absence of an explanation for the connections? I am just staying away from the nonsense, for now. Waste of time.

I share your and Lawrence's enthusiasm for geometry and number theory. Perhaps we could all share some Email correspondence? I have some unpublished results I'd like to get both your opinions on. I promise to give your paper a careful read.

Thanks.

Tom

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Ray Munroe replied on Feb. 18, 2010 @ 13:48 GMT

Dear Tom,

I finally pulled up your "Self Organization in Real & Complex Analysis" paper. I tried pasting the address into my browser at home, and it didn't work. But my browser at work did work.

In some ways, we are asking similar questions. As you ask "If nature appears to be self-organized, and mathematics appears to be the language of nature, what can we mean when we suggest that mathematics is itself organized?"

You, Steve Dufourny and I are all looking at the relevance of prime numbers. I have not seen Steve's full-blown theory, but I understand that prime numbers are relevant to his work. My own work includes some of the small prime numbers, and I think this ties back into Clifford Algebra. My current models are buckyballs. The Carbon-60 buckyball has pentagonal and hexagonal symmetries which decompose into 2x3x5=30, which is a relevant sub-component of some symmetries that Lawrence Crowell and I have been playing with: icosahedron (order 120), H4 (order 120), and E8 (order 240). The Boron-80 buckyball also has face-centered hexagons which could be interpreted as 2-fold, 3-fold, or 7-fold symmetries (along with the 5-fold pentagonal symmetries). Some of my larger models included 7-fold symmetries.

In Section 3.1 and Table *, you list cardinal points and their sums. I see some similarities between these numbers and Clifford algebras, but I'm not sure of the interpretation:

Clifford Algebras

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

You have a sequence of 1, 2, 4, 6, 10 from the sum of cardinal points, whereas Clifford algebras might give a sequence of 1, 2, 3, 6, 10. You know as well as I that such a 'minor' difference messes up prime sums.

I am not a mathematician. I have a tendancy to read too many proofs too quickly, and it just goes in one ear and out the other. I need to mull on papers such as this for several days. Lawrence Crowell is a more experienced mathematician than me - you might ask for his opinions.

Good Luck & Have Fun!

Ray

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Georgina Parry replied on Feb. 18, 2010 @ 22:29 GMT

Observations.

Doubling the fibonacci diameters will still produce the same pattern of perfect intersection of the circles when separated by increasing diameter and rotated 90 degrees. 4 will intersect with the two 2s. 6 intersects 4 and 2 , 10 intersects 6 and 4, 16 intersects 10 and 16, 26 intersects 16 and 10. Same pattern of increase in scale and rotation so as expected.

Some other number sequences show some similarity of pattern of intersection but it is imperfect. 1113591731 for example 3 intersects the 1s, 5 intersects the 3 and the 1s Possily making 4 5 or 6. 9 intersects 5 and 3 which makes 8 , so that is 1 too low. But 17 intersects 9,5 and 3 which makes 17. 31 intersects 17 and 9 but near misses 5. Making 26 but with the extra 5 it would have been 31.

13471118. 3 intersects the 1s, 4 intersects the 3s and 1 ( but should that count as 2 1s which would make 5 not 4?, 7 intersects 4 and 3 making 7, 11 intersects 7 and 3 though just slightly missing intersection with 4 instead. That would have been 11 rather than 10 if it hadn't just missed, 18 intersects with 11 and 7 making 18.

The sequence 2,4, 6 , 10 shows a good pattern of intersection. 4 intersects 2,

6 intersects 4 and 2 ,10 intersecrts 6 and 4 ,16 intersects 10 and 6. The sequence 123610 however does not show a similar clear patern.

It seems that perhaps the Fibonnacci sequence matches exacctly the scale of increase in magnitude of circle, (which could represent a physical barrier material or energetic to growth and development of observed morphology), to rotation of 90 degrees for each addition of the golden ratio phi.

Perhaps some other sequences giving different scales of increase in magnitude might be linked to other angles of rotation or other patterns of seperation. The exponential increase does not work with this pattern of separation and 90 degree rotation. Nor doe the sequence of prime numbers.

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Ray,

not ignoring you. Thanks for all the reference material. Thats plenty to contemplate.

William Orem,

well there you have it. I have just given you the perfect demonstration of the beautiful truth in action. Mathematics won't do for me because I can't "see it". Geometry however I can see in my mind and then draw on paper and it represents something real to me.

A least two factor make up the psychological hit. First is the neatness of it. Second the suprise. I suspect it is a dopamine rush, similar to winning unexpectedly at gambling or getting an unexpected great bargain at the shops. That would also explain the sense of excitement and inability to sleep well.

It would be interesting to have a blood test now and then compare in a few days to see how the dopamine level has fallen. As I come to realise that nobody else is equally interested in the geometrical relationships I have found. That is understandable because they have not experienced the same dopamine rush. They have already been told what to expect, so the suprise is gone. If they do choose to take a look themselves only the neatness remains. They will therefore not feel the same level of excitement and enthusiasm.

The way the geometry falls together is just amazing to me in itself. I had no idea it would do that until I began to think about it. Because geometry represents real shapes It is hard not to think that this must have some relevance to the physics of the material world. However the beautiful truth is in the geometry itself not necessarily in the interpretation of it. That is the problem. The excitement and enthusiasm( dopamine enhanced emotion) needs to be tempered with cool, calm logic...but ...Must draw more circles!

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Steve Dufourny replied on Feb. 18, 2010 @ 11:40 GMT

hihihi and of course a star will become a triangle, the planets shall become sqares and of course the geometry is an illusion, yes indeed nothing has a form in fact....when I see with my string eye, and I analyze with my rectangular brain due to my penta form glands, yes indeed the fruits are future sqares like a water drop , when you take some water, it doesn't exist spheres, no no no any form ....Thus in conclusion the universe has no form evidently and the galaxies are going to the infinity,.....laugh is good for health hiihihi

Regards

Steve

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Georgina Parry replied on Feb. 18, 2010 @ 23:24 GMT

Steve,

When you have regained your composure, may I ask -have you even looked at the pattern? You asked the question "what is the relationship?" I have found very clear relationships in the geometry. What did you expected the outcome to be? Does this fit your expectations or were you hoping for something entirely different to be revealed?

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Georgina Parry replied on Feb. 19, 2010 @ 00:29 GMT

William Orem,

The geometric relationships I have shown are very neat, you must admit. They will still be neat when they are old and boring. I appreciate them even if no one else will.

Finding them beautiful (amazing, fascinating, captivating )rather than just midly interesting and satisfactory is definitly an emotional response. Interestingly I have read that people in love experience a drop in serotonin level. Serotonin and dopamine are balanced so rise in one leads to fall in the other. Hence the feelings of heightened interest and enthusiasm for the other person and other symptoms of love sickness.

How fascinating that a biochemical change, inducing quite extreme physiological changes, can be induced by the sensory input of novel but very simple geometry produced from a few numbers. Unfortunately it seems it is not possible to determine dopamine levels by simple blood test but Cerebro-spinal fluid would be required. Don't fancy that!

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Dear Georgina,

I understand the dopamine rush. I have also stayed up into the middle of the night when I was so excited with a mathematical or physical idea that I couldn't sleep. My TOE approach was geometrical. The problem is that it is a 12-D geometry that no one can imagine. In the longer paper, "A Case Study...", I broke the symmetries down into Petrie polygons that can be imagined....

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Hi all,

Let's be pragmatic and realist about our physicality.

The sciences are everywhere in a flower, in a water drop.....the best to understand the sciences is to study what we see really.

An extrapolation can be rational.

The problem is the understanding of our mass around us in 3D which evolves in the time.

Let's take the H or He....the secret of the fractalisation, finite is there in all gravitational system.

The evolution and the increasing of mass like a foundamental inside a finite spherical system in optimization.

If I take the He for exemple , thus it is on 3D and the datas are reals like with the ideas of Landau ,London or Feynman.The divisibility of the mass on the line of evolution must be well understood for a good model.

It is like a Bose Einstein condensate, thetre you shall understand my relation with the rotating spheres, the moments and their proportionalities.

The superfluidity takes all its sense but to understand this beautiful truth, he 3D and a duration constant of evolution is necessary.

TEMPERATURE DENSITY MASS MOMENT VOLUMES....it is essential dear Friends really .There you can use maths tools correctly to impriove the extrapolations with the good finite serie of the fratlisation of the sphere.The entanglment is specific and always in 3D , the energy is correlated too with the fields towards the Planck scale.The time in these experiments is constant .IOf it exist variations dear fRIENDS THEY ARE INTRINSIC WITH THE GRAVITATIONAL CODES and with exterior parameters like pression, rays, temperature , the mass thus takes its rule of understanding with its synchronization with the light.

When you divide mass, you separate simply the light, thus the fractal is better understood.For all universal dynamics, this foundamental of 3d in a duration locally harmonized is essential in my humble opinion.If not the mass is not encircled.

All experiments are in this thermodynamical correlation.

And if we want understand the quantum architecture like the cosmological sphere, thus the analyzes must be synchronized with this evidence which is the evolution of the mass .

I invite you to see the apparatus of Ambler for exemple with the Co 60 for the Beta emission with N2, have you seen the time in these results, ands what do you think about ther principle of conservation of parity? there the answer isz in 3D still.

What do you think too about the energy and the entropy of a system of partyicles for exemple?

If I take for exemple the Boltzman equation and an infinite number of levels of energy, where is the rationality about this?

Thus the finite system is relevant for an understanding of the number of spheres and I repeat all that is in 3D.

Regards

Steve

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Steve,

the spirals are seen self constructed in nature. Geometry represents real shapes. I could cut out a cardboard circle and throw it at you! Custard pie would do.

We can not look at the underlying geometry that constrains morphological development but we can look at geometric models.

I notice that the use of rotation translation and scaling transformation is widesprerad but using mathematical technique not drawing. Perhaps it is not so obvious using mathematics, that only particular sequences of numbers give the perfect intersection of circles.

It does concern me that this is a flat 2d piece of paper but in the real world it would be 3d space. If some circles are on top of others it might mean that there is no intersection with circles lower in the sequence because there is seperation along another spatial dimension. Such as in the sequence 1,3,4,7,11,18,29 where 4 would be higher than 3.It might then prevent intersection of 11 with 3 and so intersection with 4 would occur instead, which would give the neat pattern, as 7+4 =11.

The sequence 1,3,4,7,11,18,29 allows the 2 spirals to be constructed .It appears to show the pattern that... a triangle constructed using the centerpoints of two adjacent circles in the sequence and a nearest point equidistant from them on the circumference of the smallest circle whose centre point was used, has a triangle circumference equal to the radius of the largest circle whose centre point was used. That's neat.Using the equidistant points a less obvious spiral can be constructed, as well as the one formed by rotation on the surface of the circles.

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Georgina Parry replied on Feb. 19, 2010 @ 20:28 GMT

Actually I must correct my previous statement... It is not always a point on the circumference of the smallest circle whose centre was used but a handy nearby cirumfernce, which in some cases in this particular example is that of the smallest circle.

The triangle made using the centre points of circles with diameter 1 and 3 has an equidistant point on circumference of circle 7, that will give the triangle circumference matching that of diameter of circle 4, not diameter 3 .But that made from centre points of 3 and 4 has an equidistant point on circumference of 7 which appears to give a triangle circumference of 2 not 4 or 3. So this is not a perfect patttern as in the case of the Fibonnacci sequence circle diameters. That imperfection is interesting in itself.

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Georgina Parry replied on Feb. 19, 2010 @ 21:21 GMT

Scale increase of Pi gives an interesting pattern with 90 degree rotation and translation of pi. Circle circumferences intersect so that the addition product of the diameters of the circles intersected equals the diameter of the larger intersecting circle.

Also the circumference of the triangles formed from centre points and nearest equidistant point on a circle circumference does seem to approximate the diameter of the largest circle whose centre point was used in the triangle. The first one being less accurate though. I think it may be becoming closer with each rotation. (It is difficult to be sure without drawing it on a much larger scale though.) The interesting feature is that the equidistant triangle points are getting further away from the centres with each rotation so the triangles are getting more and more elongated.I don't know the significance of this but it looks neat.

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Georgina Parry replied on Feb. 19, 2010 @ 21:42 GMT

Cynthia wrote on Apr. 22, 2008 19:47 GMT FQXi

"The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed." Albert Einstein

How appropriate. I'm glad Cynthia shared that quote.

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Now you can rest assured that E8 and the golden mean are real physics. The Helmholtz Inst. in Germany in cooperation with the University of Oxford and the Bristol University as well as Appleton Laboratory found experimentally the golden mean in quantum mechanics. Long ago El Naschie married E8 and the golden mean into the transfinite E8 exceptional Lie group. To obtain the dimension you simply multiply the exact theoretical inverse fine structure constant with three plus phi where phi is the golden mean 0.618033989. You divide the result with two and you get the dimension which is slightly le