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RECENT POSTS IN THIS TOPIC

Brain Wave: on 12/6/17 at 4:23am UTC, wrote Auto Lock Boxes Straight Tuck Boxes Reverse Tuck Boxes Seal End Boxes ...

Darius M: on 6/22/14 at 9:45am UTC, wrote I think maths just describes the structure of transcendentally ideal space...

Erickson Tjoa: on 11/16/12 at 11:50am UTC, wrote In my opinion, it is a very hard choice to make between perceiving...

Louis Brassard: on 10/28/12 at 18:30pm UTC, wrote Since the beginning of human language and civilisation we have gradually...

STEVE JEFFREY: on 7/8/10 at 10:59am UTC, wrote Here is my program for odd and even numbers

STEVE JEFFREY: on 7/8/10 at 10:55am UTC, wrote I have a provisional patent on this vrtual time TM clock and Casio R&RD UK...

STEVE JEFFREY: on 7/8/10 at 10:53am UTC, wrote There is something that smells in Denmark when it comes to adding QM and GR...

dan burton: on 6/16/10 at 21:39pm UTC, wrote The human term ‘number’ and the concepts of a counting system are...



FQXi FORUM
June 27, 2019

CATEGORY: Ultimate Reality [back]
TOPIC: Does Math Evolve? [refresh]
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William Orem wrote on May. 27, 2008 @ 18:16 GMT
image: fdecomite


Here’s what I’m wondering: At Plank Density or greater, distinctions such as “here” and “there” have no operational meaning. When the universe was at this density, were simple arithmetical operations true?

If we say yes, we are agreeing that a binary operation, such as addition, has meaning *when it has no referent*. This would be a foundational assertion of the first order. At Plank density there is no “this (object)” plus “that (object),” even in principle; nor is there a “before” or “after,” which are at least implied by the two sides of an equivalence.

If we say the operation is still true, it seems there are only two interpretations. One is that mathematics is supra-natural, existing outside spacetime; though, despite its philosophical popularity, it’s hard to see what this could actually mean.

The other option is that math evolves, so that certain statements become true as they become operationally possible. Or do they become true as they become computationally possible . . .?

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dan burton replied on Jun. 16, 2010 @ 20:52 GMT
The human term ‘number’ and the concepts of a counting system are descriptions of difference between topologically whole areas. ‘Two fish’ decribes two discreet entities within a set ‘fish’. What we call number theory is the detailed analysis of how areas of difference within topologically whole entities organise efficiently within that entity.

The differences described however...

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Anonymous wrote on Jul. 28, 2008 @ 08:40 GMT
There are three fundamental and interrelated relationships of reference for perspective. The three fundamental relationships of reference for perspective are the relationship of the dimensions of Cartesian coordinates with the dimensions of polar coordinates, the relationship of finite with the infinite, and the relationship of 'still' with motion (or constant motion with accelerated motion). Each...

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paull valletta wrote on Aug. 4, 2008 @ 10:18 GMT
Very interesting, of course one can define a "perspective" space, relative to observation?..and thus: space is continuous if matter is absent, and discrete if matter is present. The appearence of matter are the "bits" of non continuous space!

Introduce matter to space and Time appears into the equation, a "bit" of matter creates a "length" of time?

Now mathematically one can relate certain number partitions with parity of ODD + EVEN in congrugences:

10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 >0

EVEN-ODD-EVEN-ODD... down to an EVEN zero, and of coure any even number can be partitioned, or halved!...

add two odd numbers you get an even number result, add two even numbers together and you still get an even result?..now add odd + even numbers, you get odd result!

In measure terms it can be related to space being "even" added with matter "odd" and the rusulting spacetime comes out at '3'..related to of course 3-D!

At the planck scale there must be partitioning of space dimensions, and the appearence of little string "bits" are a virtual quantity, born out of trying to continue a path of matter within a constrained path of continuous space, a "zero" patch of space without matter can be sliced in "two", and you end up with a (string) quantity that is increasing, at least in energy terms, of into theorized "extra-dimensional arena's" ?..by the way the matter "time", componant is obviously planck "odd" or 1, and cannot be halved, or broken down any further than three "bits" or fractional quarks.

Down at the string scale, there is a doubling of string energy, as you calculate the energies exponentially gat greater, "strings" shoulkd really be thought of links in a chain, break one and another two takes it place, not in another dimensions, but literally in a certain scale, or to be correct density!

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STEVE JEFFREY replied on Jul. 8, 2010 @ 10:59 GMT
Here is my program for odd and even numbers

attachments: general_and_special_relativity_calculator.zip.zip

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atomiton1 wrote on Jan. 25, 2009 @ 02:54 GMT
Yes, math evolves. It evens itself out. Here becomes there and there becomes here, but in doing so. A new equation is created

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Anonymous wrote on Oct. 1, 2009 @ 07:16 GMT
Thanks

Ashu

www.ashiyana-yoga-goa.com

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Max™ wrote on Nov. 1, 2009 @ 22:59 GMT
I think the Universe, and the ability to understand both it, and the principles of mathematics through study of it, speaks towards this idea being apt.

I do not think it a coincidence that our formulations of physical laws are so naturally expressed mathematically, I think it means we need to consider the possibility that the laws of physics themselves are an extension of mathematics.

Not just philosophically, but in the literal sense, as I learned has been fleshed out fascinatingly by a fellow Max, Tegmark in this case. Whether string theory proves to be a useful theory for this Universe, the landscape of possible Universes it suggested is what I think will be it's most important contribution to knowledge.

If a theory constructed using mathematics suggested by one Universe can suggest a multitude of other Universes, then the idea that math is something we produced, or that it is immanent only in our Universe seems faulty at best.

If you can have math that describes Universes, yet you can not have a Universe without math, then mathematics is more fundamental. So our intuitions about mathematics point to it existing not just as concepts, but as reality.

If math can exist without a Universe, but not vice versa, then as Tegmark displays wonderfully, and many of our intuitions suggest, there is no reason to try to distinguish the type of reality we seem to experience as being different from the broader reality of mathematical possibilities.

From there the MUH is a natural conclusion, but that in itself asks the question why we seem to be experiencing reality the way we do, if the Universe is just a set of appropriately complex mathematics, where does time emerge, for example?

Which goes back to the topic, if the Universe is a portion of mathematics. Then it should be expressing itself in a manner Godel would have approved of. From the initial set of statements describing the possible Universe before the "big bang", it generated a new set of statements describing the observed Universe we are a part of, and the new states seem to influence the original states, allowing a deep type of feedback, and thus an evolution of states and information beyond a simple abstraction of the original.

I think anyway... I could be wrong.

Max Morriss

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cyna avidinis wrote on Nov. 11, 2009 @ 18:19 GMT
If Math has an existence beyond or 'above' the physical universe, then maybe we should be able to find evidence for enrything that is not forbidden by its laws, and so, mathematical, rather than physical limits should become the boundaries of all observation we ever make.

The answer to such ideas could, in my opinion, lie in observations needing an extremely large (or small, for that matter, but there have been a great deal of research into it) range of time and/or space. We have made such scientific observations only for the past few centuries, but maybe a study on the evolution of math needs a great deal of patience! Is it not possible that, say, a million years in time produces a change of only the tiniest amount of possible change in mathematics, if at all (something like a planck unit limiting the range of mathematical possibility)? Even if all our physics is correct, we have not yet put both-side-caps on many of the physical laws, and that means there could be an infinitum of information revealing itslef at much different rates than the human species have had time.

Yet in a different line of thought, the evolution of math seems to be a funtion of consciousness. A migratory bird, for example, does not need direction numbers to chart its regular flight, but depends on its extra ordinary senses. We, on the other hand, need to learn a few tricks to be able to do the same. It is possible that an alien civilisation could have senses of such measure that it can assimilate all its observations of the physical world as 'natural' and obvious phenomena. Math, in that case, may not even be invented, and so, it is our consciousness that allows us to develop new mathematical tricks. Isn't this is in a sense the 'evolution' of maths? If tomorrow we find a particular geometry of space time that allows one plus one to always be one, and we happen to find some matter in it, the thing that looks most probable at this moment is that we will come up with a new set of rules based on those particular observations, and apply those rules to any future such situations. And if they do not work, we revise and tweak them a bit. So are we ourselves 'evolving' maths just for our own sake?

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GF wrote on Dec. 22, 2009 @ 17:24 GMT
Yes I feel math evolves.

In the spirit of Marshal McLuhan I'll say, "The equation is the message".

I feel this topic is on par with the concept of a perfect Singularity, Zero-Point, a perfect Vacuum, an Isometric and Symmetrical Dimension, etc. etc. Things which can only exist in our minds or Cyberspace. It is our concepts and ideas expressed through writing and math which are not...

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GF wrote on Dec. 22, 2009 @ 18:26 GMT
awwwwww crud I posted "Technicolor requires a Higgs Boson" but IT DOES NOT REQUIRE A HIGGS BOSON

what a bad typo

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GF wrote on Dec. 23, 2009 @ 19:36 GMT
I have added a Part 3.

I also did not mean to put in my comment that I think Garret Lisi's attempt at mapping the E8 is futile. I had copy/pasted my paper from an email I sent and I meant to remove that comment in the post here. If he can realize that there may be one particle path that looks very arbitrary (every particle but one would look Symmetric or "one of the gang" .... perhaps just...

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Member Ian Durham wrote on Jan. 22, 2010 @ 21:50 GMT
> I do not think it a coincidence that our formulations of physical laws are so

> naturally expressed mathematically, I think it means we need to consider the

> possibility that the laws of physics themselves are an extension of

> mathematics.

I'm not sure I agree with that. As a colleague of mine noted recently, while physical laws are continually being adjusted, tweaked, expanded, or sometimes even overturned, properly proven mathematical laws (theorems) have never had this occur (certainly, some conjectures have been disproven, but no properly accepted and rigorously proven theorem has as far as my mathematician colleague is aware). He added that, to him, pure mathematics was as close to the Platonic ideal as one could get.

But let me give you an actual example as well that came up during a conference that just ended. It's a rough description, but it will suffice for what I'm trying to say.

An open question in quantum information theory relates to something known as quantum channels. Pretty generally, these are communication channels and could be just about anything. But some of them have non-unitary behavior meaning we can't approximate them using a bunch of unitary operators. It has been conjectured that if we take more and more copies of one of these channels, we might be able to get closer to an actual unitary representation. Specifically, in the asymptotic limit, the conjecture assumes it is possible.

Now let's put on our experiment's hat. As useful as this conjecture sounds, it means to get a perfect unitary representation we'd need an infinite number of copies of this channel. But this makes no physical sense. No experimenter can ever physically achieve this. Nevertheless, the conjecture exists and may end up being proven.

Another way to put it is that we have plenty of mathematical statements and proofs for situations that are completely unphysical.

Now consider that many - if not most - physical laws can be modeled in multiple ways mathematically, i.e. it is possible to model some physical laws using two seemingly unrelated mathematical procedures. Which procedure would the physical law be extending? In non-relativistic classical theories, there are two types of physical laws: laws of coexistence and laws of succession. In quantum mechanics these become selection and superselection rules. But this puts a serious limitation on mathematics if it is an extension of it since, for example, the former would imply that non-relativistic classical theories are only describable by equations and inequalities and yet there are so many other mathematical structures that can be used to describe even the simplest things in nature, not to mention the fact that mathematics itself has further generalizations for equations and inequalities that work in classical situations (groups, categories, etc.).

I hope that made sense. It's past my bed time.

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Bubba Gump wrote on Mar. 1, 2010 @ 18:56 GMT
Some random thoughts on this issue of the place of mathematics in physical realism.

IMO, a rudimentary system of numbers and basic arithmetic to relate these numbers to one another were formed as a tool that helped us with our survival. Those who could make sense of a number system were in a better position to plan and make predictions which were of benefit to individuals and...

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T H Ray wrote on Mar. 3, 2010 @ 17:37 GMT
William,

I am glad to have stumbled upon this most interesting and well-formed question.

Just recently, I had an exchange with Ian Durham over the nature of mathematics in which we agree that mathematics is a language. If language is independent of meaning, however (and I think it is) then the mapping of linguistic symbols to physical phenomena is a process of evolution, as you...

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dan burton replied on Jun. 16, 2010 @ 21:39 GMT
The human term ‘number’ and the concepts of a counting system are descriptions of difference between topologically whole areas. ‘Two fish’ decribes two discreet entities within a set ‘fish’. What we call number theory is the detailed analysis of how areas of difference within topologically whole entities organise efficiently within that entity.

The differences described however...

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gf wrote on Mar. 21, 2010 @ 06:17 GMT
Tom, I just popped into here to tell you your last post was bang on its good to see someone with some fundamental understanding of key philosophical ideals such as infinity, zero, one , momnotheism/monism etc. that are paradoxial and relative and problematic. I am Agnostic and so Im a Deist and any discussion involving the combination of math or philosophy topics will always fascinate me.

Bubba Gump, also your post was excellent and I agree that , in the end, religion and math and philosophy and science and numerology and chemistry and astrology and biology and even history may well all inevitably be the same thing hhehehehe. It truly is esoteric and too deep to grasp when looking for absolute answers.

Seriously though, I am soon to write a 4th installment to my paper about paradox and what can and cannot be officially stated when it comes to proving which branch of math is more accurate than the other. It's most likely a tie and relative like Celsus vs Fahrenheit or geocentricism vs heliocentricism.

Excellent posts

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gf wrote on Mar. 21, 2010 @ 06:21 GMT
I really should spellcheck first hehe. I meant to type monotheism...

anyways, astrology, for all intents and purposes, may aswell be astronomy or math or science or biology or chemistry etc . etc .etc Seems we are obbsessed with patterns and we seem to think we can completely know these patterns and thus become like gods with predictions and knowledge ... but we can't ... we are only human.

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gf wrote on Mar. 21, 2010 @ 06:41 GMT
Some of you may think I went overboard and too deep with my relative thoughts about how everything is all part of a universal and fundamental pattern ... well this may help you see the universal patterns and connections that all these have with eachother;

http://www.hiddenmeanings.com/body.html

Too many questions, too many topics ... but still all fun to discuss

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STEVE JEFFREY wrote on Jul. 8, 2010 @ 10:53 GMT
There is something that smells in Denmark when it comes to adding QM and GR 2+2=4 In tandem.

Just look at what happens when we add another drug to paracetomal to enhance it's effects.

It results in halucinations.................

Maybe the same thing results when we are doublemnined about physics insisting that both QM and Einstein are right and they can be combined...........

Would appreciate your feedback guys you seem much more rational than the guys on the Hawking forum

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STEVE JEFFREY wrote on Jul. 8, 2010 @ 10:55 GMT
I have a provisional patent on this vrtual time TM clock and Casio R&RD UK are looking at basing a new product on it.

attachments: clock2.zip.zip

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Louis Brassard wrote on Oct. 28, 2012 @ 18:30 GMT
Since the beginning of human language and civilisation we have gradually developed a formal language called mathematics. All human natural languages are intimatly coupled with our sophisticated imagination. They only have a limited self-contained logics. Mathematics has gradually been simplified and formalized. It is a language that has been optimized to expressed relations in the simplest...

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Erickson Tjoa wrote on Nov. 16, 2012 @ 11:50 GMT
In my opinion, it is a very hard choice to make between perceiving mathematics as evolving along with the universe and perceiving mathematics as what you called "supranatural" or beyond spacetime.

To stand by the former would mean that we see mathematics as inherently part of the universe - that is, universe somehow has a mathematical and physical side at the same time. They are dual in the...

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Darius M wrote on Jun. 22, 2014 @ 09:45 GMT
I think maths just describes the structure of transcendentally ideal space and time in which all phenomena appear.

https://www.academia.edu/7347240/Our_Cognitive_Framew
ork_as_Quantum_Computer_Leibnizs_Theory_of_Monads_under_Kant
s_Epistemology_and_Hegelian_Dialectic

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