The Universe Is Made of Mathematics • Hacker News Board

Re: The Universe Is Made of Mathematics

#11

Post by kazinator » Thu, Sep 03, 2015, 8:54 PM UTC

xlm1717 wrote: post #7

ccvannorman wrote: post #4

1) All mathematical objects exist abstractly and independently of minds (mathematical Platonism) Without a mind to understand, interpret, and define mathematics, does it exist? This is a core philosophical problem at the intersection of science and feeling. Without observation, no mathematics exists (for the observer). By proving it exists, you must also have an implicit observer. 2) The mind is a computational proce…

With regards to 1), I remember reading a paper I found on HN not too long ago trying to argue that no, it does not exist. To generalize, any piece of knowledge only exists after it is discovered. Can't remember what it is at the moment, maybe someone else knows what I'm talking about. With regards to 3), I would assume Tegmark means laws of physics which we have not yet discovered, but nevertheless govern what occurs…

So before pi was discovered, circles didn't have a ratio of circumference to radius? Or did have one, but a value other than 3.14159...?

Re: The Universe Is Made of Mathematics

#12

Post by kazinator » Thu, Sep 03, 2015, 8:58 PM UTC

eludwig wrote: post #5

"A map is not the territory"

In this case, it may be. The territory is never observed other than through maps, and the maps are all math. That is to say, the maps may be of the same "stuff" as the territory, and as the differences between the maps and the territory are erased, eventually you arrive at the map being the territory.

At least, they are all math beyond those subjective observations that are possible through the human senses. You might think that some hot gas is "glowing blue", and that this is not "math" to you in any sense, but a more advanced understanding of the light emanating from it gives us a spectrum, and that is just a math function.

Of course when we look at an actual map of some place, we know that the place isn't a picture with symbols denoting its features. It's not so clear for features of the universe. When you're far from the bottom, the descriptions look like maps. The mass and acceleration arrows on a free body diagram of an automobile aren't the automobile; it's all just a diagram.

But the more detailed you make the description of something, the less of a distinction there is between the description and the thing! At some point, the description must be the thing. (If it isn't then just alter whatever is different between the two and patch the description; then repeat.)

Another thing to keep in mind is that math itself has map/territory descriptions. The formula or graph representing a mathematical object isn't that object.

When we say that the universe may just be math, we don't mean that the written math is the universe, but rather that the abstract math described by those representations is identifiable with what is real: the map isn't the territory, but those two territories are identifiable with each other!

Re: The Universe Is Made of Mathematics

#13

Post by [deleted] » Thu, Sep 03, 2015, 9:04 PM UTC

kazinator wrote: post #11

xlm1717 wrote: post #7

Earlier quoted context omitted.

With regards to 1), I remember reading a paper I found on HN not too long ago trying to argue that no, it does not exist. To generalize, any piece of knowledge only exists after it is discovered. Can't remember what it is at the moment, maybe someone else knows what I'm talking about. With regards to 3), I would assume Tegmark means laws of physics which we have not yet discovered, but nevertheless govern what occurs…

So before pi was discovered, circles didn't have a ratio of circumference to radius? Or did have one, but a value other than 3.14159...?

[deleted]

Re: The Universe Is Made of Mathematics

#14

Post by ching_wow_ka » Thu, Sep 03, 2015, 9:04 PM UTC

I'm not much of a mathematician, but I found "Mathematics: The Loss of Certainty" by Morris Kline (http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Pape...) very insightful in regards to the development and current state of mathematics. A brief synopsis:

From Amazon: "This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century."

From goodreads.com: "Most intelligent people today still believe that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. Mathematics: The Loss of Certainty refutes that myth."

Edit: This was also interesting: https://www.youtube.com/watch?v=RlMMeqO7wOI , a video by Stephen Wolfram. I know he is often criticized for various reasons, but much of what he says makes intuitive sense.

Re: The Universe Is Made of Mathematics

#15

Post by westoncb » Thu, Sep 03, 2015, 9:09 PM UTC

Lets say you select all the aspects of a person's life that you consider to have any relevance to anyone and write down a description of every one of them—is that person now 'made' of words? That's how ridiculous this is.

I think what this is missing is a justification for thinking the universe somehow 'uses' mathematics in this sense; being /describable/ by it, is not at all the same as actually being generated by it.

There is a mistaken assumptions here that consistent rules from /within/ the universe would apply to its own operation. It's like assuming that because some rules must always hold when Monopoly is played, that the rules governing its physical constitution must be drawn from the same set.

"Confusing the moon with the finger pointing at it" —is a simple concept to understand, but seeing all the subtle places where we actually make the mistake in our mental lives requires another level of effort.

Re: The Universe Is Made of Mathematics

#16

Post by DCKing » Thu, Sep 03, 2015, 9:10 PM UTC

kazinator wrote: post #2

Every result in physics hitherto has been some sort of mathematics: an equation or a constant (measured or otherwise established to some digits of precision). What is a particle? A collection of mathematical properties. So is a wave. If we extrapolate from the past to the future, we can expect more of the same: no "non-mathematical bottom" will be found. Nobody is even looking; the researchers expect all new results…

You're just describing the fact that we can make up descriptions of physics all the way down. If current mathematics is unable to describe physics, then new mathematics is invented [1]. Just because the descriptions work rather well does not mean that those descriptions are somehow more than mere descriptions. It just means that they are very good descriptions.

You're making the same category error as mentioned in the blog post.

[1] https://en.wikipedia.org/wiki/Mathematical_physics

Re: The Universe Is Made of Mathematics

#17

Post by thaumasiotes » Thu, Sep 03, 2015, 9:17 PM UTC

kazinator wrote: post #10

ccvannorman wrote: post #4

1) All mathematical objects exist abstractly and independently of minds (mathematical Platonism) Without a mind to understand, interpret, and define mathematics, does it exist? This is a core philosophical problem at the intersection of science and feeling. Without observation, no mathematics exists (for the observer). By proving it exists, you must also have an implicit observer. 2) The mind is a computational proce…

> Without a mind to understand, interpret, and define mathematics, does it exist? Unquestioningly so. For instance, there is a number 2 and a number pi which are not caused by thinking. Beings which evolve on separate planets (or whatever) in separate universes have to to come to the conclusion that the ratio between the diameter and circumference of a circle is a certain number. Those numbers will be found to agree,…

> facts like that two is the smallest prime and the only even one

I see the fact that two is the only even prime brought up from time to time as if it's inherently interesting. Why is it more interesting than the identical observation that 37 is the only prime which is a multiple of 37?

I guess this bothers me because 2 being the only even prime isn't a consequence of the definition of "prime"... it's part of the definition.

Re: The Universe Is Made of Mathematics

#18

Post by Strilanc » Thu, Sep 03, 2015, 9:25 PM UTC

If the universe we find ourselves in is a result of post-selecting for mathematical models where life can exist (i.e. by the anthropic principle), why is the universe so large and so rich in neg-entropy? Shouldn't minimally-viable-habitat universes be vastly, vastly more numerous (and don't forget about Boltzmann brains!)? Shouldn't we expect to be in one of those, instead of here, and be forced to penalize the hypothesis by a corresponding amount? [1]

> So, as cosmologists, we have an issue to address — why was the entropy of our early universe so small? If high-entropy states are “natural,” why don’t we live in one? You might think to appeal to the dreaded anthropic principle, and argue that life couldn’t exist in a state with really high entropy. But that turns out not to be good enough; the entropy of our universe is much much lower than it needs to be to support the existence of life. So we are faced with the “arrow of time problem.”

1: http://www.preposterousuniverse.com/blog/2004/10/27/the-arro...

Re: The Universe Is Made of Mathematics

#19

Post by xlm1717 » Thu, Sep 03, 2015, 9:27 PM UTC

kazinator wrote: post #11

xlm1717 wrote: post #7

Earlier quoted context omitted.

With regards to 1), I remember reading a paper I found on HN not too long ago trying to argue that no, it does not exist. To generalize, any piece of knowledge only exists after it is discovered. Can't remember what it is at the moment, maybe someone else knows what I'm talking about. With regards to 3), I would assume Tegmark means laws of physics which we have not yet discovered, but nevertheless govern what occurs…

So before pi was discovered, circles didn't have a ratio of circumference to radius? Or did have one, but a value other than 3.14159...?

My mistake, I was remembering it incorrectly. Edited my previous reply to include a link to this:

http://arxiv.org/abs/1506.03733

Lee Smolin discusses a class of facts that are evoked:

"I would like to propose that there is a class of facts about the world, which concerns structures and objects which come to exist at specific moments, which, nevertheless, have rigid properties once they exist. Let us call this possibility evoked."

====

He provides a table of how a fact and it's existence can be described:

Has rigid properties and existed prior? The fact was discovered

Has rigid properties and did not exist prior? The fact was evoked

Has no rigid properties but did exist prior? The fact was fantasized (Smolin does not elaborate on this in the paper)

Has no rigid properties and did not exist prior? The fact was invented

====

Roberto Mangabeira Unger and Smolin hypothesize two principles to describe Smolin's view, temporal naturalism:

The singlular universe, all that exists is part of one singular universe

The reality of time, as in reality is not timeless

====

With all this in mind, yes circles always did have a ratio of circumference to radius of pi. This is a property of the singular universe, and is a fact that was thus discovered.

The universe of mathematical possibilities that does not describe the universe was not discovered, it was evoked.

P.S. Please forgive the formatting of this response!

Re: The Universe Is Made of Mathematics

#20

Post by pera » Thu, Sep 03, 2015, 9:29 PM UTC

kazinator wrote: post #11

xlm1717 wrote: post #7

Earlier quoted context omitted.

With regards to 1), I remember reading a paper I found on HN not too long ago trying to argue that no, it does not exist. To generalize, any piece of knowledge only exists after it is discovered. Can't remember what it is at the moment, maybe someone else knows what I'm talking about. With regards to 3), I would assume Tegmark means laws of physics which we have not yet discovered, but nevertheless govern what occurs…

So before pi was discovered, circles didn't have a ratio of circumference to radius? Or did have one, but a value other than 3.14159...?

A ratio doesn't exist outside of the human mind. The same goes for circles.