If you have an idea for a blog post or a new forum thread, then please contact us at forums@fqxi.org, with a summary of the topic and its source (e.g., an academic paper, conference talk, external blog post or news item).
Current Essay Contest
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
Previous Contests
Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discuss • winners
Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discuss • winners
What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discuss • winners
The Nature of Time
August - December 2008
read/discuss • winners
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
Previous Contests
Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discuss • winners
Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discuss • winners
What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discuss • winners
The Nature of Time
August - December 2008
read/discuss • winners
Forum Home
Introduction
Terms of Use
RSS feed | RSS help
Introduction
Terms of Use
Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.
By using the FQXi Forum, you acknowledge reading and agree to abide by the Terms of Use RSS feed | RSS help
FQXi FORUM
June 19, 2013
CATEGORY:
FQXi Essay Contest - Spring, 2012
[back]
TOPIC: Questions for Physics and the Physics Community by Joseph Leonard McCord [refresh]
TOPIC: Questions for Physics and the Physics Community by Joseph Leonard McCord [refresh]
Essay Abstract
What is the relationship between the mathematical abstractions of the theories of physics and the world of perceptual experience? How might a reconception of this relationship generate questions of theoretical interest to physics?
Author Bio
Too many questions, not enough time. Living, breathing, bipedal tetrapod.
Download Essay PDF File
report post as inappropriate
What is the relationship between the mathematical abstractions of the theories of physics and the world of perceptual experience? How might a reconception of this relationship generate questions of theoretical interest to physics?
Author Bio
Too many questions, not enough time. Living, breathing, bipedal tetrapod.
Download Essay PDF File
report post as inappropriate
"The question that I want to pose is of a slightly different nature; it is whether or not, to what degree or within what limits, everything that is real is mathematizable. ... It is possible that mathematization has its limits."
Strong fermionic interaction in QFT, which gives rise to the fermion minus-sign problem (aka the Sign Problem, the N-Body Problem, the Many-Body Problem etc.) is an excellent possible example and/or case in point.
Perhaps the main go-to people regarding this are Jan Zaanen and Matthias Troyer. Zaanen has this specifically to say:
"We have in fact no understanding at all of what is going on in space-time, because we need mathematics to look around and the sign problem is 'NP hard', meaning that the problem is mathematically unsolvable."
Then he cites Troyer and Wiese. Speaking of cites I can provide several.
report post as inappropriate
Strong fermionic interaction in QFT, which gives rise to the fermion minus-sign problem (aka the Sign Problem, the N-Body Problem, the Many-Body Problem etc.) is an excellent possible example and/or case in point.
Perhaps the main go-to people regarding this are Jan Zaanen and Matthias Troyer. Zaanen has this specifically to say:
"We have in fact no understanding at all of what is going on in space-time, because we need mathematics to look around and the sign problem is 'NP hard', meaning that the problem is mathematically unsolvable."
Then he cites Troyer and Wiese. Speaking of cites I can provide several.
report post as inappropriate
Thank you for the references. It's exciting to me to find this agreement!
report post as inappropriate
report post as inappropriate
Joseph,
" ... whether or not, to what degree or within what limits, everything that is real is mathematizable."
Of course, one must define "real" and "limit." You are correct that there are no numbers nor ideal geometrical obects in nature. OTOH, does one think that the symbols C-A-T are real objects in nature?
If you pop over to my essay, "The Perfect First Question," I'd like to convince you that you have unlimited time to ask unlimited questions. :-)
Thanks for some stimulating reading.
Tom
report post as inappropriate
" ... whether or not, to what degree or within what limits, everything that is real is mathematizable."
Of course, one must define "real" and "limit." You are correct that there are no numbers nor ideal geometrical obects in nature. OTOH, does one think that the symbols C-A-T are real objects in nature?
If you pop over to my essay, "The Perfect First Question," I'd like to convince you that you have unlimited time to ask unlimited questions. :-)
Thanks for some stimulating reading.
Tom
report post as inappropriate
One must distinguish between signifier and signified.
The terminology is from Saussure, who distinguished both signifier and signified from the referent object.
The signifier "C-A-T", whether as a sound or as a written expression, is of course a real object in the physical world (maybe only in the form of bits and bytes, but nevertheless physically real).
The referent object, a cat or the set of all cats in general, is also something physically real.
In between the two, however, is the signified - the concept, rather than the object or objects, to which the signifier refers.
To switch to an example which I can more easily defend - one cannot, upon hearing or reading the signifier "table", locate a "table" in the physical world, without first making recourse to a generalized concept (whether consciously articulated or not) of what a "table" is.
I think it is empirically true that we do have such concepts, which we use, even before we have begun to analyze or define them. The process of making definitions is itself more complex and more problematic than we might immediately assume. It would be easy for instance to include in the definition of table that it has legs; but I could then show examples of unusual tables that do not have legs, which most people would nevertheless accept as being tables. Definitions of the "signified" of signs (the concepts to which signifiers refer) are, in general, also subject to revision for reasons such as this. The signified or concept, that is to say, is in some way prior to our making of specific attempts at definition, and should not be confused with a definition.
The crucial point is that the signifiers of mathematics which we handle very readily seem to have "signifieds" - to refer to concepts - which are not things in the physical world, and which cannot actually (it would seem) be derived from things that exist in the physical world. It seems more appropriate to say that some things or phenomena in the physical world approximate the nature of mathematical (geometrical, arithmetic, algrebraic, etc.) "objects", than to say that the mathematical concepts are actually derived empirically from our experience of the physical world.
Mathematical concepts or objects and our empirical experience of the physical world are related in intriguing ways. It does not seem immediately obvious that either is reducible to the other.
Thank you for your comment!
report post as inappropriate
The terminology is from Saussure, who distinguished both signifier and signified from the referent object.
The signifier "C-A-T", whether as a sound or as a written expression, is of course a real object in the physical world (maybe only in the form of bits and bytes, but nevertheless physically real).
The referent object, a cat or the set of all cats in general, is also something physically real.
In between the two, however, is the signified - the concept, rather than the object or objects, to which the signifier refers.
To switch to an example which I can more easily defend - one cannot, upon hearing or reading the signifier "table", locate a "table" in the physical world, without first making recourse to a generalized concept (whether consciously articulated or not) of what a "table" is.
I think it is empirically true that we do have such concepts, which we use, even before we have begun to analyze or define them. The process of making definitions is itself more complex and more problematic than we might immediately assume. It would be easy for instance to include in the definition of table that it has legs; but I could then show examples of unusual tables that do not have legs, which most people would nevertheless accept as being tables. Definitions of the "signified" of signs (the concepts to which signifiers refer) are, in general, also subject to revision for reasons such as this. The signified or concept, that is to say, is in some way prior to our making of specific attempts at definition, and should not be confused with a definition.
The crucial point is that the signifiers of mathematics which we handle very readily seem to have "signifieds" - to refer to concepts - which are not things in the physical world, and which cannot actually (it would seem) be derived from things that exist in the physical world. It seems more appropriate to say that some things or phenomena in the physical world approximate the nature of mathematical (geometrical, arithmetic, algrebraic, etc.) "objects", than to say that the mathematical concepts are actually derived empirically from our experience of the physical world.
Mathematical concepts or objects and our empirical experience of the physical world are related in intriguing ways. It does not seem immediately obvious that either is reducible to the other.
Thank you for your comment!
report post as inappropriate
Mathematics is a language. It simply quantifies stuff in the world and constructs narratives based on those quantifications (including geometric abstractions) instead of naming things and constructing narratives on that basis in the manner of verbal language(s).
What it all has in common is that the human species evolved in a general environment which allows for and gives a certain adaptive advantage to quantification, naming and discerning relationships. And we have bodies with fronts, backs and two sides, kind of rectangular when you think about it. On the savannas our ancestors saw the circular horizon, the circular moon and sun. Triangles probably came more serendipitously, but once invented they caught on.
Logic is physical. Formal logic and formal mathematics devolve from physical experience in the world. All mathematics is an extrapolation from natural numbers, natural sets of objects and shapes encountered in ordinary life. Verbal language, based on named things and relationships between named things, besides being useful in a practical sense as well as inseparable from the whole semiotic structure of human culture, adds to life a dimension of poetry and narrative just for the sake of narrative and poetry. Advanced apes like us are easily bored.
A caveat. For example, Bell's inequality is a statement of pure mathematical logic that can be used as the basis of physical experiment here in the macroworld using arbitrary sets of separable objects. Just define three physical features, applicable to all objects in the set, which the objects either possess or do not. Longer than, yes or no. This color, yes or no. Animate, yes or no. Unlike in the quantum realm you'll never violate the inequality. It's both logical and physical here where we live. The point: we evolved in a world with physical characteristics which are always present whether or not we consciously formulate them as abstract rules. But at some level we've internalized them. The problem (not a problem in the case of Bell) is that the languages we employ to consciously effect the abstractions and formalize the rules can take on lives of their own. Then we may mislead ourselves.
report post as inappropriate
What it all has in common is that the human species evolved in a general environment which allows for and gives a certain adaptive advantage to quantification, naming and discerning relationships. And we have bodies with fronts, backs and two sides, kind of rectangular when you think about it. On the savannas our ancestors saw the circular horizon, the circular moon and sun. Triangles probably came more serendipitously, but once invented they caught on.
Logic is physical. Formal logic and formal mathematics devolve from physical experience in the world. All mathematics is an extrapolation from natural numbers, natural sets of objects and shapes encountered in ordinary life. Verbal language, based on named things and relationships between named things, besides being useful in a practical sense as well as inseparable from the whole semiotic structure of human culture, adds to life a dimension of poetry and narrative just for the sake of narrative and poetry. Advanced apes like us are easily bored.
A caveat. For example, Bell's inequality is a statement of pure mathematical logic that can be used as the basis of physical experiment here in the macroworld using arbitrary sets of separable objects. Just define three physical features, applicable to all objects in the set, which the objects either possess or do not. Longer than, yes or no. This color, yes or no. Animate, yes or no. Unlike in the quantum realm you'll never violate the inequality. It's both logical and physical here where we live. The point: we evolved in a world with physical characteristics which are always present whether or not we consciously formulate them as abstract rules. But at some level we've internalized them. The problem (not a problem in the case of Bell) is that the languages we employ to consciously effect the abstractions and formalize the rules can take on lives of their own. Then we may mislead ourselves.
report post as inappropriate
Joseph,
Thank you for the well written and focused essay. Not only do I agree that math is not foundational to reality and is only a tool to describe it, but would go even further and say it can be quite haphazard and misleading on occasion. It is essentially various methods of reductionism, more than a primary ordering principle. Math is no more the essence of reality, than the calcium in the bottom of a tea kettle is the essence of water.
Physics treats measurement as an absolute, when it is anything but. When we measure space, whether lines, planes or volume, we are measuring aspects of space, but when we measure time, we are measuring rates of change, as effected by action. Temperature Is another measure of action, the scalar of activity and if we increase the level of activity, we speed up the rate of change. Since gravity and velocity serve to slow the levels of atomic activity in a given frame, it slows the rate of change. That is why clock rates vary, not because they travel different time vectors. We could use ideal gas laws to correlate temperature and volume, much as the velocity of light is used to correlate distance and duration, but no one talks about "spacetemperature," because we better understand the nature of temperature than we do of time, which is the subject of my essay.
Space is foundational, as an infinite equilibrium state. You make the point that with only one object, it would be impossible to deduce space, but that overlooks centrifugal force. Say you are on an astroid in the deepest regions of intergalactic space and had poor eyesight. Would you then be safe from spinning off, because there are no outside references, but if you were to pull out your glasses and see other galaxies moving, would that then put you in danger?
At its most fundamental level, reality is action in space. The fluctuating vacuum.
Regards,
John
( Hope this posts. I had to rewrite it after the first version disappeared into the void.)
report post as inappropriate
Thank you for the well written and focused essay. Not only do I agree that math is not foundational to reality and is only a tool to describe it, but would go even further and say it can be quite haphazard and misleading on occasion. It is essentially various methods of reductionism, more than a primary ordering principle. Math is no more the essence of reality, than the calcium in the bottom of a tea kettle is the essence of water.
Physics treats measurement as an absolute, when it is anything but. When we measure space, whether lines, planes or volume, we are measuring aspects of space, but when we measure time, we are measuring rates of change, as effected by action. Temperature Is another measure of action, the scalar of activity and if we increase the level of activity, we speed up the rate of change. Since gravity and velocity serve to slow the levels of atomic activity in a given frame, it slows the rate of change. That is why clock rates vary, not because they travel different time vectors. We could use ideal gas laws to correlate temperature and volume, much as the velocity of light is used to correlate distance and duration, but no one talks about "spacetemperature," because we better understand the nature of temperature than we do of time, which is the subject of my essay.
Space is foundational, as an infinite equilibrium state. You make the point that with only one object, it would be impossible to deduce space, but that overlooks centrifugal force. Say you are on an astroid in the deepest regions of intergalactic space and had poor eyesight. Would you then be safe from spinning off, because there are no outside references, but if you were to pull out your glasses and see other galaxies moving, would that then put you in danger?
At its most fundamental level, reality is action in space. The fluctuating vacuum.
Regards,
John
( Hope this posts. I had to rewrite it after the first version disappeared into the void.)
report post as inappropriate
Dear Mr. McCord,
I have concluded that my reading of your exceptionally well written essay was one of the most instructive experiences I have enjoyed in a very long time. I had, I must regretfully admit to begin to suspect that Mathematics could well be the abstract equivalent of crack cocaine for the intelligentsia, and your reasoned essay has certainly tempered that over harsh and probably erroneous assessment on my part.
As far as I can tell, there is only one real Universe once. That one real Universe once has three visual aspects once, only a part of one of which has possibly been observed from one earth once. There is only one of each and every real and imagined thing once in the one real Universe once. Each and every one of these singular occurring things and fancies has three aspects only one of which can ever be evaluated once.
Although you sagely pointed out the fact that actual perfect spheres and cubes and pyramids cannot exist, you failed to point out that the basic shape of all creation, the egg does indubitably exist once.
report post as inappropriate
I have concluded that my reading of your exceptionally well written essay was one of the most instructive experiences I have enjoyed in a very long time. I had, I must regretfully admit to begin to suspect that Mathematics could well be the abstract equivalent of crack cocaine for the intelligentsia, and your reasoned essay has certainly tempered that over harsh and probably erroneous assessment on my part.
As far as I can tell, there is only one real Universe once. That one real Universe once has three visual aspects once, only a part of one of which has possibly been observed from one earth once. There is only one of each and every real and imagined thing once in the one real Universe once. Each and every one of these singular occurring things and fancies has three aspects only one of which can ever be evaluated once.
Although you sagely pointed out the fact that actual perfect spheres and cubes and pyramids cannot exist, you failed to point out that the basic shape of all creation, the egg does indubitably exist once.
report post as inappropriate
Joseph,
Thank you for an interesting essay. Following are some insightful comments on this topic written by a prominent theoretical physicist:
"It is mathematics, more than anything else, that is responsible for the obscurity that surrounds the creative process of theoretical physics. Perhaps the strangest moment in the life of a theoretical physicist is that in which one realizes, all of a sudden, that one's life is being spent in pursuit of a kind of mystical experience that few of one's fellow humans share. I'm sure that most scientists of all kinds are inspired by a kind of worship of nature, but what makes theoretical physicists peculiar is that our sense of connection with nature has nothing to do with any direct encounter with it. Unlike biologists or experimental physicists, what we confront in our daily work is not usually any concrete phenomena. Most of the time we wrestle not with reality but with mathematical representations of it." (Lee Smolin, 'The Life of the Cosmos.')
In my essay Rethinking a Key Assumption About the Nature of Time I address a glaring disconnect between our most primitive empirical observations about objective reality and conclusions about the nature of reality which are believed by mainstream physicists to flow logically from mathematical descriptions of reality. Should you find time to read it I'd welcome your thoughts.
jcns
report post as inappropriate
Thank you for an interesting essay. Following are some insightful comments on this topic written by a prominent theoretical physicist:
"It is mathematics, more than anything else, that is responsible for the obscurity that surrounds the creative process of theoretical physics. Perhaps the strangest moment in the life of a theoretical physicist is that in which one realizes, all of a sudden, that one's life is being spent in pursuit of a kind of mystical experience that few of one's fellow humans share. I'm sure that most scientists of all kinds are inspired by a kind of worship of nature, but what makes theoretical physicists peculiar is that our sense of connection with nature has nothing to do with any direct encounter with it. Unlike biologists or experimental physicists, what we confront in our daily work is not usually any concrete phenomena. Most of the time we wrestle not with reality but with mathematical representations of it." (Lee Smolin, 'The Life of the Cosmos.')
In my essay Rethinking a Key Assumption About the Nature of Time I address a glaring disconnect between our most primitive empirical observations about objective reality and conclusions about the nature of reality which are believed by mainstream physicists to flow logically from mathematical descriptions of reality. Should you find time to read it I'd welcome your thoughts.
jcns
report post as inappropriate
Joseph
I found your essay very intuitive and relevant. I too believe in reality and indeed am convinced I've now found the issue(s) with maths, and the underlying consistent logical reality it hides. I hope you'll read and consider my essay.
It suggests our current maths is woefully inadequate to describe nature, and that maths is essentially just quantified of logic.
After exploring the path it seems that to answers to your questions may be;
1. Yes. A final theory would be possible. (the track is identified once you're ready)
2. Wrong pretext.
3. Mathematizability is theoretically possible but not with current maths or 'computability.' Time stepping maths needs to be better developed to describe interaction evolution, and better logical structures such as PDL (see essay). Use of the simple structure of Truth Propositional Logic also works perfectly for a kinetic unification theory.
4. Answered above.
I hope you are able to glean the explanations of the above from the dense and complex kinetic relationships underlying the metaphores I present. Do please then give me your views.
Very best wishes.
Peter
report post as inappropriate
I found your essay very intuitive and relevant. I too believe in reality and indeed am convinced I've now found the issue(s) with maths, and the underlying consistent logical reality it hides. I hope you'll read and consider my essay.
It suggests our current maths is woefully inadequate to describe nature, and that maths is essentially just quantified of logic.
After exploring the path it seems that to answers to your questions may be;
1. Yes. A final theory would be possible. (the track is identified once you're ready)
2. Wrong pretext.
3. Mathematizability is theoretically possible but not with current maths or 'computability.' Time stepping maths needs to be better developed to describe interaction evolution, and better logical structures such as PDL (see essay). Use of the simple structure of Truth Propositional Logic also works perfectly for a kinetic unification theory.
4. Answered above.
I hope you are able to glean the explanations of the above from the dense and complex kinetic relationships underlying the metaphores I present. Do please then give me your views.
Very best wishes.
Peter
report post as inappropriate
Joseph,
Some intriguing concepts and questions. For a mathematician math is an easier, more exacting, more flexible, and more efficient way of describing reality than creating a word image or drawing an image. Models can come in both. After all, aren't we speaking of models?
My essay deals with conclusions -- a model w/o math -- based on observations and theory.
Jim
report post as inappropriate
Some intriguing concepts and questions. For a mathematician math is an easier, more exacting, more flexible, and more efficient way of describing reality than creating a word image or drawing an image. Models can come in both. After all, aren't we speaking of models?
My essay deals with conclusions -- a model w/o math -- based on observations and theory.
Jim
report post as inappropriate
Dear Joseph,
You have written a very thoughtful essay about very deep questions, and I suspect that the answer to most of them is that no one can answer them adequately, at least, not at the present time!
However, since you focus partly on the role of mathematics in the description of physical reality, and since I happen to be a mathematician preoccupied with my own meager efforts to...
view entire post
You have written a very thoughtful essay about very deep questions, and I suspect that the answer to most of them is that no one can answer them adequately, at least, not at the present time!
However, since you focus partly on the role of mathematics in the description of physical reality, and since I happen to be a mathematician preoccupied with my own meager efforts to...
view entire post
report post as inappropriate
Dear Joseph Leonard McCord
It is true that you too stressed,so arguing too loose,let relax and then posting a more specific supplement.
Kind Regards !
Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY
August 23, 2012 - 11:51 GMT on this essay contest.
report post as inappropriate
It is true that you too stressed,so arguing too loose,let relax and then posting a more specific supplement.
Kind Regards !
Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY
August 23, 2012 - 11:51 GMT on this essay contest.
report post as inappropriate
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is 
and 
was the quantity of people which gave you ratings. Then you have 
of points. After it anyone give you 
of points so you have 
of points and 
is the common quantity of the people which gave you ratings. At the same time you will have 
of points. From here, if you want to be R2 > R1 there must be: 
or  / (N_1+1) >S_1/ N_1)
or 
In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.
Sergey Fedosin
report post as inappropriate
Sergey Fedosin
report post as inappropriate