The Universe Is Made of Mathematics • Hacker News Board

Re: The Universe Is Made of Mathematics

#41

Post by jameshart » Thu, Sep 03, 2015, 10:27 PM UTC

nemo1618 wrote: post #35

outofcuriosity wrote: post #25

If the universe was "made of mathematics," then there would necessarily exist a Grand Unified Theory. But, Hawking asserts that Gödel's Theorems imply that not only does a Grand Unified Theory not exist, but that the formulation of one is impossible ( http://www.hawking.org.uk/godel-and-the-end-of-physics.html ). The author stresses that all of reality is mathematical in structure, but this is at odds with the fact t…

Hmm. That's an interesting counterpoint. Suppose we discover our universe is a simulation. This would imply that the universe is Turing-computable. Would there not therefore exist a "Grand Unified Theory" that simply described, with absolute precision, the operation of the simulator? Or would it be impossible to produce such a specification?

So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state was possible or not?

Then all you have to do is demonstrate that we live in such a universe, and all the philosophers can retire because we've found the ultimate answer to the ultimate question.

I think we all know exactly what the Gödel number for our universe would be...

Re: The Universe Is Made of Mathematics

#42

Post by DCKing » Thu, Sep 03, 2015, 10:28 PM UTC

goldenkey wrote: post #36

DCKing wrote: post #26

Earlier quoted context omitted.

I'd love to have some evidence that such things as 'concepts' and 'ideas' can exist independent of brains. You can't just assert it and make it so. All concepts and ideas I've ever heard of were the results of brains attempting to model or describe. By the way, I'm not talking about physical human brains. I'm talking about any brain, which includes human brains, dolphin brains, computers, and whatever other modeling…

The thing is, the definition of a concept, is the axiom that it exists outside of human understanding. Concepts are informational objects. Anyhow, the question you really ask, is does information exist outside of conscious humanity. And it might not. It might just be an interpretation.

> The thing is, the definition of a concept, is the axiom that it exists outside of human understanding.

I don't agree with that definition of a concept.

Idea = mental representation of an object, or a set of objects and their interactions.

Concept = generalization of an idea.

wherein 'mental' justifiably implicates the working of a brain. It is very much tied to what we call brain understanding. Sorry for taking this discussion to the definition of words.

Re: The Universe Is Made of Mathematics

#43

Post by jameshart » Thu, Sep 03, 2015, 10:34 PM UTC

Strilanc wrote: post #18

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 hypo…

The problem with these kinds of arguments-from-probability is that they are valid arguments even in highly improbable universes. So yes, maybe on average, most sentient life forms that ponder these questions are living inside tiny simulated universes created as undergraduate term projects for passing credit. But we happen to be in a really big universe. Maybe ours is a grad student lab project. Or an exhibit in a museum. Or maybe we hit the jackpot and ours is real. Point of such arguments is you can't really tell from a sample size of one.

Re: The Universe Is Made of Mathematics

#44

Post by zbyte64 » Thu, Sep 03, 2015, 10:34 PM UTC

westoncb wrote: post #38

zbyte64 wrote: post #33

Earlier quoted context omitted.

Put both in separate rooms you cannot observe and equip them with a two way mic/speaker. Would you be able to determine which was a meat bag and the other was a simulation? If you can then we know the description is inaccurate. If you can't then not only is the description accurate but the substrate that the computation occurs in is not equivalent to what defines the person as a particular agent.

Two things: 1) The A.I is not just a set of symbols, it's a physical machine, which means you're answering a different question. 2) The structure of the test means that you have stripped down the objects to be compared to the sounds they produce, and yet a person is more than sounds, as is the computer. Whenever we use the relation 'X is a Y' there is an implicit definition of the identities of X and Y; the more abst…

1) You need something to compute the outcome of the symbols in order to test the accuracy of those symbols. I am not sure how to experimentally test your point without doing so. Perhaps that is the crux of the issue, we can't test symbols without tying them to a "physical medium".

2) We can introduce more communication layers as you desire and still keep in the spirit of the experiment. I opted for the strip down version due to simplicity of describing the experiment and the similarity it has to the turing test.

Re: The Universe Is Made of Mathematics

#45

Post by DCKing » Thu, Sep 03, 2015, 10:38 PM UTC

zbyte64 wrote: post #40

DCKing wrote: post #34

Earlier quoted context omitted.

> I don't think the author is arguing that mathematics allows for creating reality from nothing but that anything that resembles reality behaves mathematically and thus can transform into new situations with new mechanics (or realities). I'm not sure I follow. What does "transform into new situations" really mean? > We can construct an infinite number of consistent mathematical realities but only by comparing their p…

>I'm not sure I follow. What does "transform into new situations" really mean? Emergence as a side-effect. >If this is really what he meant, I appreciate the correction. If it would have been clear from the text, I would have proceeded with pointing out with pointing out the dodgy assumptions that underly the finetuning problem, but that would be even more like arguing against a deist/theist. Yes, I am probably putti…

Talking about "side effects", "transformation" or "emergence" seems to assign properties to mathematics that I can't really wrap my head around. I thought that all we could be certain of when it comes to math is that it is a self-consistent set of axioms and rules. A set, of infinite size or not, that would be static and fixed.

Re: The Universe Is Made of Mathematics

#46

Post by DCKing » Thu, Sep 03, 2015, 10:51 PM UTC

kazinator wrote: post #12

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 migh…

> The territory is never observed other than through maps, and the maps are all math.

Be careful with words here. The universe is observed through other means than maps all the time. In fact, it is what everyone is doing all the time.

The universe is described using maths. It is also often described by neuron firing patterns in brains or less accurately using English or Russian. Just like territories are described by maps or less accurately using English or Russian.

> 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.)

That doesn't follow. At the limit to infinity, the description is the perfect description. There is no reason to believe it becomes the thing itself.

The line segment representing the radius of a circle perfectly describes a circle. That does not mean a line segment is the same as a circle.

Re: The Universe Is Made of Mathematics

#47

Post by eellpp » Thu, Sep 03, 2015, 10:53 PM UTC

xlm1717 wrote: post #19

kazinator wrote: post #11

Earlier quoted context omitted.

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 possib…

Thanks for the reference. From the essay:

1.In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time.

2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.

Re: The Universe Is Made of Mathematics

#48

Post by kazinator » Thu, Sep 03, 2015, 11:03 PM UTC

thaumasiotes wrote: post #17

kazinator wrote: post #10

Earlier quoted context omitted.

> 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 def…

You're right in that evenness is divisibility by two by definition. For any P which is prime, P is the smallest divisible by P.

It is probably that divisibility by two (evenness) is interesting.

For example, it has the property that if we know the evenness of two integers, then we know the evenness of their sum or product.

Division of cases by even versus odd occurs regularly; in few circumstances do you have to separately reason about cases corresponding somehow to the elements of the congruence modulo 37.

Re: The Universe Is Made of Mathematics

#49

Post by kazinator » Thu, Sep 03, 2015, 11:09 PM UTC

DCKing wrote: post #46

kazinator wrote: post #12

Earlier quoted context omitted.

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 migh…

> The territory is never observed other than through maps, and the maps are all math. Be careful with words here. The universe is observed through other means than maps all the time. In fact, it is what everyone is doing all the time. The universe is described using maths. It is also often described by neuron firing patterns in brains or less accurately using English or Russian. Just like territories are described by…

The line segment representing the radius of a circle perfectly describes a circle. That does not mean a line segment is the same as a circle.

Aha, but there is a territory here: the abstract circle. Now suppose we equate that territory with another territory: something in the real world. Then we have a description of a circle (the map), but two different territories. If we say those are the same, it's not a map/territory confusion. At best it is a territory/territory confusion.

The description of the math will never be the math; but the correct math may in fact coincide with reality.

If a mathematical model of the world is completely accurate, then the math which it describes is the world. The world doesn't have any properties which the math doesn't and vice versa; it doesn't "do" anything which the math doesn't.

Re: The Universe Is Made of Mathematics

#50

Post by kazinator » Thu, Sep 03, 2015, 11:12 PM UTC

eellpp wrote: post #47

xlm1717 wrote: post #19

Earlier quoted context omitted.

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 possib…

Thanks for the reference. From the essay: 1.In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time. 2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.

> In the real universe it is always some present moment

That is rather naive. The entire succession of moments can be described as one object, in which time is a dimension. The unfolding through time is just the subjective experience of the human consciousness.

Some H.264 video also appears to unfold, presenting a depiction of events frame by frame. Yet, at the same time, it's also just a 1.2 gigabyte file: a giant integer.