Lets assume if two integers collide their values combine and gain different properties, however collisions become exponentially(?) harder as the size gets bigger. — Ben Ngai

I think your intuition has some validity, But, in what sense could "two integers collide"? In order to literally bump into each other, mathematical values (quanta) would have to possess material properties (qualia) That's why it's always hard to discuss metaphysics without using physical metaphors.

Values are subjective & relative evaluations from some perspective. Even mathematical "values" are assigned in the context of their relationship to subjective human observers. Nevertheless, my intuition is that ultimately "objective" mathematical & logical values & functions must be assigned relative to an observer outside the system : the universe. So, when universal or abstract values are added or subtracted (due to "collisions" or inter-relationships) the computation would be in a Mind of some kind, not in "empty space". Does that make any sense? :smile:

so think of numbers as "piles of sets identical objects". Properties of piles change as it gets bigger. Think a puddle vs an ocean. you don't have waves in puddles or vast temperature changes or other stuff.

If two piles get close they become one bigger pile.

In mathematics there are operations that come in inverse pairs. think addition/subtraction multiplication/division integral/derivative. The list goes on.

Now there are two forces in physics: attractions and repulsion. PIles collide due to attraction. But some piles also repel.

my intuition is if they are far away from a natural number maybe the ideal number is say 6 and all numbers work towards that. (random number and all natural numbers are a steady state.

Lets say number 1 hits number .4 if they collide they would make 1.4, but since 1 is more stable, then they repel. if .4 collide with .4 they make .8 which is closer to 1 so they collide.

But if we are dealing with integers, two opposite signed integers would always collide and annihilate.

Sorry for the multiple comments, but so lets say natural numbers are the building blocks of the universe. and attraction and repulsion are addition and subtraction (or an analogous operation.)

The best theories of physics we currently have represent the universe as set of overlapping kinds of mathematical spaces (differentiable manifolds) that obey certain rules that make them count also as mathematical objects called groups, where every point in the space is a specially symmetric square matrix of complex numbers, a different size of square for each of the different spaces.

We know already that that is not a perfectly accurate model, but it’s somewhere in the ballpark, and whatever the correct mathematical model of reality is, there’s no reason to think that there is anything more to reality itself than just exactly that math.

as every number has a unique property — Ben Ngai

Haven't read the rest of the thread but his phrase jumped out at me, as it's false.

Almost all real numbers are neither computable nor definable. If a "property" is a predicate, a finite-length string of symbols drawn from some finite or countably infinite language. then there are only countably many properties. The set of real numbers that are characterized by a unique property has measure zero and is countably infinite. All the rest of them are noncomputable and nondefinable, and have measure 1 in the unit interval or measure infinity in the extended real numbers. So this technical point you made is wrong. As I say I don't know how that relates to the rest of your argument or whether it's materially important, but I did not want to let it pass.

FWIW the real numbers are very strange and are an abstract construction. It's extremely unlikely the universe is like the real numbers. For one thing, if they were, you'd immediately turn all highly technical mysteries of set theory, such as large cardinal axioms, into experimentally-verifiable matters of physics. For example the Continuum hypothesis would be subject to experimental verification. That seems very implausible to me.

Of course this is not a proof, only a plausibility argument. If the standard mathematical real numbers are actually physically realized in the world, that would be front-page news. For one thing it would blow all the constructivists and computationalists out of the water. It would show that the world is not a computation, and that constructive math is wrong.

Of course I could ask you, which model of the real numbers do you mean? The constructivists would complain that their model is just as good and even better, since everything is computable. And the nonstandard analysis folks would complain that you left out all the infinitesimals. These are murky waters. There's more than one model of the first-order axioms of the real numbers.

I should add that there's a subtlety here. It's true that most real numbers can NOT be characterized by any property. However, any two real numbers can indeed be distinguished by a first-order definable property. If you have two real numbers x and y, then the statement x < y is either true or false. That's the case even though we have no way of characterizing the individual numbers by properties. This shows that even the undefinable real numbers are nevertheless subject to Leibniz's identity of indiscernibles. Given any two distinct real numbers, they are always distinguishable by a first-order property.

https://en.wikipedia.org/wiki/Definable_real_number

https://en.wikipedia.org/wiki/Computable_number

https://en.wikipedia.org/wiki/Large_cardinal

https://en.wikipedia.org/wiki/Identity_of_indiscernibles

ps -- If you think the physical universe is accurately modeled by the mathematical real numbers, do you think that the Banach-Tarski paradox is physically realizable? I hope you can see that the idea that the real numbers are physical is highly problematic.

Mathematical Universe

This might be of interest. I'm doubtful, myself.

I made a typo... ssssh I ment to say. Every natural number has unique properties at the very least.

I've heard of the Mathematical Universe. This is pure intuition, can be made rigorous.

I went on a walk and I just thought of this idea.

1) Lets say the universe has the initial condition it is uniformly 0 every. and and say 0 can seperate itself into two infinitesimally small numbers say alpha and -alpha. now we know infinity times any positive number is infinity. So that means that the sum of finite alphas is infinite. that means there is a number x such that the sum of x alphas is 1.

So it's possible that natural numbers can spontaneously emerge in a from a non-euclidean space (NES) with zero energy with sufficient time.

2) Now lets assume that positive numbers have an attractive force on the NES based on their numerical value and negative numbers have a repulsive force based on their numerical value.

Implication. Give my assumption that the universe started uniformly at a zero energy space, as natural numbers pop into existence, since the natural numbers are positive, the rest of the NES becomes ever slightly negative with positive points that are slight attractive wells. This implies that the NES expands faster over time as there is more and more average negativity in the NES almost everywhere.

I use the term real numbers in the mathematical sense. https://en.wikipedia.org/wiki/Real_number.

I'm doing something right now, let me read what you posted a bit later and i'll address your point. If that's okay.

I ment to say. Every natural number has unique properties at the very least. — Ben Ngai

Oh well nevermind then! It was a highly nontrivial typo but if you meant natural numbers then you are right.

I use the term real numbers in the mathematical sense. https://en.wikipedia.org/wiki/Real_number. — Ben Ngai

As do I. The notion that the real numbers are physically instantiated is highly problematic. Most are not first-order definable, which means most are not characterized by any finite-length string of symbols. Secondly, you'd then turn every abstract set-theoretical puzzle into a question experimental verification. Can you imagine a physics postdoc applying for a grant to count the number of zero-dimensional points in a meter of space in order to see of the Continuum hypothesis is true? I can't either.

Besides, your idea violates the Planck length, the length below which contemporary physics ceases to be meaningful.

0 can seperate itself into two infinitesimally small numbers say alpha and -alpha. — Ben Ngai

Well now you have another problem, which is that there are no infinitesimals in the real numbers. You could invoke the hyperreals of nonstandard analysis, but then you'll have other anomolies to deal with.

https://en.wikipedia.org/wiki/Hyperreal_number

now we know infinity times any positive number is infinity. — Ben Ngai

In the extended real numbers, yes.

So that means that the sum of finite alphas is infinite. — Ben Ngai

No, you said alpha is infinitesimal, so you are now working in the hyperreals, where "infinity times an infinitesimal" may be finite.

Your mathematical ideas are unclear, you keep bouncing around from the reals to the extended reals to the hyperreals without realizing it.

2) Now lets assume that positive numbers have an attractive force on the NES based on their numerical value and negative numbers have a repulsive force based on their numerical value.

Implication. Give my assumption that the universe started uniformly at a zero energy space, as natural numbers pop into existence, since the natural numbers are positive, the rest of the NES becomes ever slightly negative with positive points that are slight attractive wells. This implies that the NES expands faster over time as there is more and more average negativity in the NES almost everywhere. — Ben Ngai

This is all a little convoluted. The positive and negative integers are what they are, they're not charged particles.

That's an interesting point but I think it might be an non sequitur. Because I can just define zero to have the ability to create two numbers size alpha and -alpha which is exactly whatever the smallest size plank length (I want to call it a pixel) allows.

Also I would argue that even though a pixel exists it's irrelevant because it's so small that we might as well approximate the universe with a continuous non-euclidean space for simplification.

Before we rigorize it anyways.

I also know this is irrelevant because I only judge based on the merit of your ideas, not your formal education. But out of curiosity what did you study and how far did you get? I have a BS in mathematics and a small amount of graduate training. But I'm mostly an autodidact.

non formal argument (intuition)

as integers get bigger in the NES, it goes from being more energy to more matter. So Dark matter might just be lots of big integers in the universe.

I also made a argument that dark energy is NES space being turned slightly negative overtime. (But I know you got that)

I also know this is irrelevant because I only judge based on the merit of your ideas, not your formal education. But out of curiosity what did you study and how far did you get? I have a BS in mathematics and a small amount of graduate training. — Ben Ngai

You're right, it's irrelevant. You seem confused about infinitesimals, infinity, the real numbers, and a number of other things. How'd you get through real analysis?

Real analysis was the easiest subject in undergrad for me. Went to class. didn't study got A+ from chancellor professor. Made me consider grad school seriously. I skipped to measure theory my senior year and took some grad econ and stat. That was really hard and I realized grad school wasn't for me. To put it bluntly.

Real analysis was the easiest subject in undergrad for me. Went to class. didn't study got A+ from chancellor professor. Made me consider grad school seriously. I skipped to measure theory my senior year and took some grad econ and stat. That was really hard and I realized grad school wasn't for me. To put it bluntly. — Ben Ngai

I notice you've changed the subject. Your ideas are muddled. Your credentials mean nothing.

Also it's been like 9 yeas since i took real analysis so... i might be confused. — Ben Ngai

Well you know there are no infinitesimals in the real numbers, right? An infinitesimal by definition is a quantity that is strictly between 0 and 1/n for any natural number n. Clearly if you claim something's an infinitesimal, I can choose n large enough to falsify your claim. There are no infinitesimals in the real numbers.

But this is less important than your speculative idea that the physical universe models the standard mathematical real numbers. I think that idea has many problems. Not that it's wrong, necessarily, but it would be a heck of a scientific revolution that would revolutionize math and physics.

Okay I'm using alpha in a nontraditional way. but tangentially relevant to real analysis.

Also it's been like 9 yeas since i took real analysis so... i might be confused.

Sorry Fish I misread your post. I read it as "How did you do in real analysis not how did you get past."

Sorry Fish I misread your post. — Ben Ngai

You're replying before I'm finished typing. I'm out of breath! I don't mean to be at odds. I think the idea that the physical world is the same as the mathematical real numbers is highly unlikely, but if it ultimately turns out to be true it will be one hell of a revolution in both math and physics. Do you think the Banach-Tarski paradox would become a physical reality? Or would you reject the axiom of choice? You'd have many conceptual problems along these lines.

In any event I only popped in to point out that the statement that each real number is characterized by a property, is false. It's not right. But if you meant the natural numbers, you're right and it was only a typo.

To be honest I really need to think about this. This is just an idea i came up with today. So can you bare with me, but i realize I do not now know to solve the infamous Banach-Tarski paradox. I would need to do research. I have gaps in my knowledge in math and especially physics.

Fish, I don't think you're at odds I just presented the most crazy, outlandish idea that exists at the moment on a metaphysics forum.

Of course you would question me and my idea. If it was true, the implications would be insane. I would have my name etched everywhere in math and physics overnight and win all the awards in math and physics. Which would be a ridiculous idea.

I'm just here for a good time.

So can you bare with me, — Ben Ngai

I will keep my clothes on if that's ok :-)

Fish, I don't think you're at odds I just presented the most crazy, outlandish idea that exists at the moment on a metaphysics forum. — Ben Ngai

Like I say, I only jumped in to correct the claim that each real number is characterized by a property. Other than that, I took no stand.

I agree with you that the idea that the real numbers might be physically real is an interesting one, full of wild implications. Sometimes I'm too picky for my own good.

Fish, thanks for help me bounce this outlandish idea. I was looking for someone that would help and reddit was no help. If this forum didn't exist i probably would have wrote a first draft and published a book that nobody would read then be sad and stop sharing my wild ideas due to being frustrated from being ignored.

Fish, thanks for help me bounce this outlandish idea. I was looking for someone that would help and reddit was no help. If this forum didn't exist i probably would have wrote a first draft and published a book that nobody would read then be sad and stop sharing my wild ideas due to being frustrated from being ignored. — Ben Ngai

You're welcome. I'm very happy to know that my pedantic pickiness has been useful for a change.

But you know philosophically, the idea that the physical universe is modeled by the real numbers is very common. For example in physics, time is modeled by the real numbers, even though this is very unlikely to be literally true. I don't think the physicists give this much thought, but it's an important philosophical issue.

Wow, so i might have accidentally come up with the idea of the century if it turns out to be true at least even in some way or leads to an explosion of new ideas?

That's what I'm hearing? But i know that's not what you're saying.

I won't get my hopes up.

Before someone else tries to name it. I want to call this the Mathematical Theory of the Universe. if it becomes scientific cannon.

Wow, so i might have accidentally come up with the idea of the century if it turns out to be true at least even in some way or leads to an explosion of new ideas?

That's what I'm hearing? But i know that's not what you're saying.

I won't get my hopes up.

Before someone else tries to name it. I want to call this the Mathematical Theory of the Universe. if it becomes scientific cannon. — Ben Ngai

If you tag my handle I will be notified of your reply. That is, you can highlight some of my text and hit Quote, or you can simply type in an '@' sign followed by my (or anyone else's) handle in double quotes. Or you can hit the @ button above the edit window and find the handle in the search bar. This will trigger a notification to me that someone's talking to me or about me. Otherwise I might miss your reply.

Now the idea that the world is accurately modeled by the real numbers is not new, but if it someday turns out to be true it will most definitely be the idea of the century. It would be a massive mathematical and scientific revolution. As I've noted, if nothing else it would turn set theory into an experimental science. I find this most unlikely.

The idea of the mathematical universe is due to Max Tegmark. He argues that the universe is not only modeled by mathematics, but that it actually "is" mathematics. That is, the universe is literally a mathematical structure. Many people take this idea seriously; while others, myself included, regard this as a massive elementary category error that is so obviously wrong that he must be trolling.

Yeah, im aware of the concept. But i don't think he broke it down like i did. Obviously though science and philosophy is built on itself. So. This is a continuation of the Mathematical universe idea.

@fishfry

sorry let me learn this forum. it'll take me a maybe like 1 more hour...

I really hope this is true now, because set theory is among the coolest pure math subject. And it could have vast physical applications potential?

But I think we're looking at it the wrong way. Instead of saying Math and physics are the same. We can say This universe is one of the many universes with unique properties that math can completely be derived by just a space and numbers.

sorry let me learn this forum. it'll take me a maybe like 1 more hour... — Ben Ngai

No prob it took me years to figure out the @ sign!

I really hope this is true now, because set theory is among the coolest pure math subject. And it could have vast physical applications potential? — Ben Ngai

Well in my opinion no, because it's not likely to be true that the mathematical real numbers are physical. But yes if they are, it would be a huge deal. But again, think what it would mean for the Continuum hypothesis to become a problem of physics. "Let's write a grant application to count the number of points in a meter of space and see which Aleph that is." Very unlikely. Unless some genius yet unborn figures it out.

But I think we're looking at it the wrong way. Instead of saying Math and physics are the same. We can say This universe is one of the many universes with unique properties that math can completely be derived by just a space and numbers. — Ben Ngai

Could be.

This is just an idea i came up with today — Ben Ngai

Check out https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis