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FQXi FORUM
May 20, 2013
You might be interested in Sir Roger Penroses's [url:http://online.itp.ucsb.edu/online/plecture/penrose/oh/0
1.html]Extended Physical WorldView.[/url].
attachments: Roger_Penrose.jpg
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1.html]Extended Physical WorldView.[/url].
attachments: Roger_Penrose.jpg
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How does one define a mathematical answer, to a non mathematical question? Mathematics can have multiple answers, ie 2+2 = 4 , 1+3 = 4, 5 -1 = 4 etc ?©tc.. which is the correct process/formula, to a specific question must be where "intepretations" can vary?
Some mathemagicians perform tricks, for instance can 2+2 = 5?
Yes, 2 x 75 seconds plus 2 x 75 seconds equals 5 minutes, so 2+2 = 5 !
Why is it I can compute with exact precision, where the
Earth will be at 03:31 am tomorrow, WRT the Sun and Moon, but I cannot know with any precision where the Earth is at the NOW moment? I can predict its future, but have to rely on uncertainty for the present time of, now!
A zero point, something that can be defined as an area of "nothing", has a small uncertain value, so one can never achieve an absolute "nothing". By the same process, one can never achieve an absolute "everything" point, or moment. The Big-Bang must have a small area of "nothing" contained within it's area of "everything"?
Infinities are for mathematical purpose, "everything" with a small uncertainty of "nothing". Like a single particle within a perfect vacuum, like a finite vacuum space within a particle, like an extreme edge to a given space-time, how does one formulate the correct questioning?
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Some mathemagicians perform tricks, for instance can 2+2 = 5?
Yes, 2 x 75 seconds plus 2 x 75 seconds equals 5 minutes, so 2+2 = 5 !
Why is it I can compute with exact precision, where the
Earth will be at 03:31 am tomorrow, WRT the Sun and Moon, but I cannot know with any precision where the Earth is at the NOW moment? I can predict its future, but have to rely on uncertainty for the present time of, now!
A zero point, something that can be defined as an area of "nothing", has a small uncertain value, so one can never achieve an absolute "nothing". By the same process, one can never achieve an absolute "everything" point, or moment. The Big-Bang must have a small area of "nothing" contained within it's area of "everything"?
Infinities are for mathematical purpose, "everything" with a small uncertainty of "nothing". Like a single particle within a perfect vacuum, like a finite vacuum space within a particle, like an extreme edge to a given space-time, how does one formulate the correct questioning?
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Rusty, the Tin Man:
"Cruelity/ideas arise in other ways. From "spaces created," for which they can manifest? "I needed "a Heart," and so too my father, the Bicentennial Man changed. Until, we now dream."
There has always been this pursuit to define the computer technologies advancement to what can be dreamed? Validation and discoveries of the self needed to be understood to know that this quality will never be instilled in something that is non human.
".....Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus....."
I've included some quotes below for consideration. One might find some relation between the Dalton board and the founders of probability theory? The validation of Pascal's triangle as to what may be emergent in selection of a number process?
"Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition. Alain Connes"
"Under the influence of axiomatic and bookish traditions, man perceived in discontinuity the first mathematical Being: "God created the integers and the rest is the work of man." This maxim spoken by the algebraist Kronecker reveals more about his past as a banker who grew rich through monetary speculation than about his philosophical insight. There is hardly any doubt that, from a psychological and, for the writer, ontological point of view, the geometric continuum is the primordial entity. If one has any consciousness at all, it is consciousness of time and space; geometric continuity is in some way inseparably bound to conscious thought."
http://www.emc.dk/IMU/medals/1958/index.html#0x8249
6a1f_0x0005e9fd
"Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus. Bhargava says it's also hidden in the rhythms of classical Indian music, which is both mathematical and improvisational. He sees close links between his two loves -- both create beauty and elegance by weaving together seemingly unconnected ideas."
http://www.npr.org/templates/story/story.php?storyId=
4111253
Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.
http://www.atributetohinduism.com/quotes321_340.htm
Th
is last quote is very important, although it may seem totally detached from reality?
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"Cruelity/ideas arise in other ways. From "spaces created," for which they can manifest? "I needed "a Heart," and so too my father, the Bicentennial Man changed. Until, we now dream."
There has always been this pursuit to define the computer technologies advancement to what can be dreamed? Validation and discoveries of the self needed to be understood to know that this quality will never be instilled in something that is non human.
".....Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus....."
I've included some quotes below for consideration. One might find some relation between the Dalton board and the founders of probability theory? The validation of Pascal's triangle as to what may be emergent in selection of a number process?
"Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition. Alain Connes"
"Under the influence of axiomatic and bookish traditions, man perceived in discontinuity the first mathematical Being: "God created the integers and the rest is the work of man." This maxim spoken by the algebraist Kronecker reveals more about his past as a banker who grew rich through monetary speculation than about his philosophical insight. There is hardly any doubt that, from a psychological and, for the writer, ontological point of view, the geometric continuum is the primordial entity. If one has any consciousness at all, it is consciousness of time and space; geometric continuity is in some way inseparably bound to conscious thought."
http://www.emc.dk/IMU/medals/1958/index.html#0x8249
6a1f_0x0005e9fd
"Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus. Bhargava says it's also hidden in the rhythms of classical Indian music, which is both mathematical and improvisational. He sees close links between his two loves -- both create beauty and elegance by weaving together seemingly unconnected ideas."
http://www.npr.org/templates/story/story.php?storyId=
4111253
Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.
http://www.atributetohinduism.com/quotes321_340.htm
Th
is last quote is very important, although it may seem totally detached from reality?
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The power of Godels Incompleteness Theorem is only in the world of axiomatic systems that are based off of classic Number Theory (specifically the work of Russell in his Mathematica Principia), i.e fomral systems. Not all systems that have number theory as their root or even as part of their foundation are nessecerily formal. It states not that a finite system of axioms does not completely represent the theory. It is a problem that came from the (mathematical) logical structure of arithmatic. It is possible to extend this to other formal systems, but nothing more than that. It states that in an axiomatic system with too many axioms, contradiction will arise.
The basic idea is this:
If A is a formal theory then there is a variable x such that ~A(x) is true, but A also allows A(x) to be true. Which says that a theory with the Property A exists without giving it value.
So as we can see it is not from Godels Theorems that we can say that a theory will not give a complete picture of what it is describing. Instead it tells us only whether or not a (formal) theory is decidable or not.
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The basic idea is this:
If A is a formal theory then there is a variable x such that ~A(x) is true, but A also allows A(x) to be true. Which says that a theory with the Property A exists without giving it value.
So as we can see it is not from Godels Theorems that we can say that a theory will not give a complete picture of what it is describing. Instead it tells us only whether or not a (formal) theory is decidable or not.
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