Is Mathematics Truly Limited by Physics?

[Gjmdp]

Note I'm not talking about Mathematical Physics. This is a Physical concept not a Mathematical concept.

Speed of light is less than 300000000m/s. Physically, 300000001 (+1) m/s does not exist, but mathematically, this isn't impossible. So Physics is limited by our universe, but Mathematics is only limited by our imagination. Some ago I read Einstein said in its Relativity that Geometry(, Mathematics) can be considered as a branch of Physics. But, if as I said, Mathematics is less limited than Physics, how can it be considered as a branch of Physics?

Then, how is Mathematics limited? Well, first of all, if Physics it's limited by our universe while Mathematics isn't, its perfectly possible the existence of other universes that can have different rules of physics (the speed of light may be higher or lower), because they don't break any rule of mathematics. Then the limit of Mathematics; Mathematics is limited by our imagination, Is our imagination limited? Well, as Mathematics is created by the human mind, it must have a limit. Universes with different physical or mathematical rules? To organize this, it may be sets of universes: In each set are universes with different rules of physics but with the same mathematical logic. Each set has a different mathematical logic (please correct me if Mathematics isn't really limited by anything anything anything).

So, as Mathematics and Physics are separating (many people think they are the same thing!), I'm asking about a branch that connects physics and mathematics: Mathematics that are limited by physics, by our universe. This is a concept of Einstein's Geometry, Geometry limited by the rules of our universe (but in fact, Geometry is only limited by our universe), but as Einstein thought, it isn't the whole Geometry branch, it's only the Geometry limited by our universe. In this concept, a speed of 300000001 (+1) m/s does not exits. So, does this branch have a name? Abstract: Einstein's Geometry.

 

[Calaver]

This is what Einstein said in Relativity, The Special and General Theory (page 4 of the first chapter in the edition that I'm looking at):

"Geometry which has been supplanted in this way is then to be treated as a branch of physics."

Earlier, he talks about that geometry is derived from our intuition of the stuff around us, which he claims is just statics, a branch of physics. With the above statement, he is leading to a further statement where he says that we can determine with experiments whether or not there are other possible postulates to base geometry on instead of our intuition, i.e., the test of whether or not space is Euclidean is an experimental one. Thus, at least it seems to me, his point is not to say geometry in its entirety is a branch of physics, but to justify to the average reader the concepts of non-Euclidean geometry by experimental results.

So no, mathematics is not a branch of physics, but the mathematics which comes from our intuition about the physical world (such as geometry) may be seen as having experimental proof or disproof in it's validity for the explanation of nature.

 

[FactChecker]

This may be the quote that you are referring to, from http://www-history.mcs.st-and.ac.uk/Extras/Einstein_geometry.html

Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only. We will call this completed geometry "practical geometry," and shall distinguish it in what follows from "purely axiomatic geometry."

I don't think this quote should be interpreted as a statement about all mathematics, just early Euclidean geometry.

 

[Gjmdp]

This may be the quote that you are referring to, from http://www-history.mcs.st-and.ac.uk/Extras/Einstein_geometry.html

I don't think this quote should be interpreted as a statement about all mathematics, just early Euclidean geometry.

No, it wasn't that quote; look up to FactChecker

 

[Gjmdp]

This may be the quote that you are referring to, from http://www-history.mcs.st-and.ac.uk/Extras/Einstein_geometry.html

I don't think this quote should be interpreted as a statement about all mathematics, just early Euclidean geometry.

Yes I really know, Geometry isn't a branch of Physics. The question is what branch of physics studies Geometry, Mathematics limited by our universe, Physics. This idea was proposed by Einstein in that quote: Geometry limited by our intuition, Physics.

 

[FactChecker]

No, it wasn't that quote; look up to FactChecker

I see. That was posted after I started writing. Both quotes make the same point. Mathematics is much more than simple Euclidean geometry, so I think we should not read more into those quotes than Einstein intended.

 

[BvU]

Hello GJ,

I almost put a after that hello, but I suppose you've been welcomed already. Read your post with interest. Read it again, and again. Stared at it for a while, pondering if I should answer, comment, challenge, or whatever else. Nice activity, on a Sunday after Christmas.

No answer from my end: no idea if a branch as you describe exists, or what its name would be. Can't imagine that it's a good branch to earn a living -- especially when compared to your mainstream activity as mentioned in your profile.

So you hobby in philosophy of science. Commendable ! Let me make some challenging comments (settles my considerations in the first paragraph..):

You have a tendency to jump in your logic, take things out of context and make something that isn't really connected look like genuine steps in a kind of logical proof.

Then the limit of Mathematics; Mathematics is limited by our imagination, Is our imagination limited? Well, as Mathematics is created by the human mind, it must have a limit

A whole truckload of assumptions is hiding under this preudo-logic. Makes me raise an eyebrow and then a few more hairs. Dominating thought: "Says who?" - in repetition.

Physics is limited by our universe

Not really. What makes you claim such a thing ? I grant you that a lot of what keeps physicists busy is completeley within our universe, but I don't see why your claim should be true.

As a side note: re speed of light

..there is a wave equation featuring permeability and permittivity. Speed is inversely proportional to the square root of each of these:$$c={1\over \sqrt{\epsilon\mu}}$$See also Maxwell equations. Physics with a capital P !--

Those are permeability and permittivity of the vacuum (in our universe, you might say...). So reasoning about other universes is one thing. Reasoning about other vacua (with differrent permittivity and/or permeability) is something else! I'm having a good time imagining discussions like "my nothing is diifferent from your nothing in that ..."

I could go on with my "says who" and comparable comments, but that shouldn't be necessary. Main conclusion: even if I wanted to agree with your facts and proofs, I could not. It rattles.

But I sure liked reading it and thinking about it.

--

 

[BvU]

Hey, what happened to posts 2, 3, and 4 ? [edit] -- weird ! I do see them now. Will read them first, of course...

Factchecker lives up to his/her name. An effective approach, but GJ quickly dodges and repeats the question - leaving us to yes or no take with us all the other stuff in post #1.

By the way, I now have an answer: It's called mainstream physics. Generally abbreviated to "physics". Thereby banning the other stuff to 'esoterics' .

--

 

[Gjmdp]

Hey, what happened to posts 2, 3, and 4 ? [edit] -- weird ! I do see them now. Will read them first, of course...

Factchecker lives up to his/her name. An effective approach, but GJ quickly dodges and repeats the question - leaving us to yes or no take with us all the other stuff in post #1.

By the way, I now have an answer: It's called mainstream physics. Generally abbreviated to "physics". Thereby banning the other stuff to 'esoterics' .

--

Hi Bvu, thanks for paying attention to my post. I'm a 15 year old with a lot of curious. You criticize my argumenys and I know they could be better, but, I'm Spanish (I'm sorry for that, I would want to be American). When I read your answers and notice you're answer another else of what I'm asking, I ask the same again.

Physics has a limit that it's our universe. I know it's a big assumption, but look: Speed of light is less than 300000000m/s, and physically, it isn't possible higher speeds. But mathematically? Why isn't possible? Says who?
Then, Physics it's limited by the universe (the only way we can put it limits), but Mathematics isn't limited by that: there are concepts impossible for Physics but possible for Mathematics.
Then, Physics is limited by the universe,but Mathematics isn't limited by that. Is that an illogical argument? So when we put to Mathematics the limits of Physics we get Mainstream Physics?? What is thaat? How can it be esoteric?

 

[mathman]

Euclidean geometry is a very small part of the subject called mathematics. Non-Euclidean geometry as used in relativity is somewhat bigger. Mathematics itself contains much more, ranging over such subjects as number theory, algebraic geometry, and many other fields.

 

[BvU]

I'm in the same time zone as you are, and intend to go to work tomorrow -- so almost bedtime.
My sincere compliments for your venturing into these areas, really (at 15, a very long time ago, I was fully occupied with a lot of interests, but not something like this!). Do keep up this curiosity and you'll go far !

There is no mathematical speed of light. No point in asking about its possibility. Says me. I know I'm not an authority, but it's really true.

Physics is not limited to the universe. Simple corroboration: we can do physics on the diameter of the universe. But I grant you we can't do much physics any 'further'. (Perhaps we mean the same thing here ?)

.. but Mathematics isn't limited by that: there are concepts impossible for Physics but possible for Mathematics.

I don't see anything wrong with these statements.
Then,

Physics is limited by the universe,but Mathematics isn't limited by that. Is that an illogical argument?

Here I don't see an argument, just the two previous statements with a "but" in between that suggests a contraposition which I don't think is there. Also, no contraposition is there in the (reverse?) sentence; something like
"Physics is NOT limited by the universe, but Mathematics isn't limited by that either"

So, as Mathematics and Physics are separating (many people think they are the same thing!), I'm asking about a branch that connects physics and mathematics: Mathematics that are limited by physics, by our universe. This is a concept of Einstein's Geometry, Geometry limited by the rules of our universe (but in fact, Geometry is only limited by our universe), but as Einstein thought, it isn't the whole Geometry branch, it's only the Geometry limited by our universe. In this concept, a speed of 300000001 (+1) m/s does not exits. So, does this branch have a name? Abstract: Einstein's Geometry.

In the first phrase, you are asking about a branch that connects physics and mathematics. My answer "mainstream physics" is not to your liking. Why not ? (by the way: what do you mean with "are separating" ?)

Then "This is a concept of Einstein's Geometry" -- what is a concept of Einstein's Geometry ? Einstein had a problem involving metric and needed some not-everyday-math to describe the not-flat universe. Most of that math was already there, but Alberts genius was to put things in the right order.

"but in fact, Geometry is only limited by our universe" First you firmly stated as a fact that it explicitly was not :

Mathematics is only limited by our imagination

What, now, is the branch you want a name for ? We really need clear formulations in order not to end up in a mist of confusion !

hasta manana ! buenas noches and such

---

 

[Gjmdp]

I'm in the same time zone as you are, and intend to go to work tomorrow -- so almost bedtime.
My sincere compliments for your venturing into these areas, really (at 15, a very long time ago, I was fully occupied with a lot of interests, but not something like this!). Do keep up this curiosity and you'll go far !

There is no mathematical speed of light. No point in asking about its possibility. Says me. I know I'm not an authority, but it's really true.

Physics is not limited to the universe. Simple corroboration: we can do physics on the diameter of the universe. But I grant you we can't do much physics any 'further'. (Perhaps we mean the same thing here ?)
I don't see anything wrong with these statements.
Then, Here I don't see an argument, just the two previous statements with a "but" in between that suggests a contraposition which I don't think is there. Also, no contraposition is there in the (reverse?) sentence; something like
"Physics is NOT limited by the universe, but Mathematics isn't limited by that either"

In the first phrase, you are asking about a branch that connects physics and mathematics. My answer "mainstream physics" is not to your liking. Why not ? (by the way: what do you mean with "are separating" ?)

Then "This is a concept of Einstein's Geometry" -- what is a concept of Einstein's Geometry ? Einstein had a problem involving metric and needed some not-everyday-math to describe the not-flat universe. Most of that math was already there, but Alberts genius was to put things in the right order.

"but in fact, Geometry is only limited by our universe" First you firmly stated as a fact that it explicitly was not :What, now, is the branch you want a name for ? We really need clear formulations in order not to end up in a mist of confusion !

hasta manana ! buenas noches and such

---

I'm really grateful for your attention.
I don't agree with you: Physics is limited by the universe by definition: Physics is a branch of Science, and Science is a systematic enterprise that creates, builds and organizes knowledge in the form of testable explanations and predictions about the UNIVERSE, no far from that (Wikipedia). Also, physicist can't study matter out of the universe. So, then, by this 2 arguments, Physics is limited by the universe. Mathematics, as you agree, is only limited by our imagination. So Physics is limited by the universe while Mathematics isn't?

Ok, now, Maintream Physics seems esoteric, so how can be that branch the connection between Mathematics and Physics? Where is the esoterics in those 2 branchs? What is Maintream Physics? I can find out what it is, I'm looking on google and I don't find anything more than a discussion if Mainstream Physics can be considered Physics? So what it's that branch?

 

[Gjmdp]

Ok sorry, I've seen what its Mainstream Physics. So, why do you say that Mainstream Physics is Mathematics limited by the universe?

 

[ZapperZ]

Note I'm not talking about Mathematical Physics. This is a Physical concept not a Mathematical concept.

Speed of light is less than 300000000m/s. Physically, 300000001 (+1) m/s does not exist, but mathematically, this isn't impossible. So Physics is limited by our universe, but Mathematics is only limited by our imagination. Some ago I read Einstein said in its Relativity that Geometry(, Mathematics) can be considered as a branch of Physics. But, if as I said, Mathematics is less limited than Physics, how can it be considered as a branch of Physics?

Then, how is Mathematics limited? Well, first of all, if Physics it's limited by our universe while Mathematics isn't, its perfectly possible the existence of other universes that can have different rules of physics (the speed of light may be higher or lower), because they don't break any rule of mathematics. Then the limit of Mathematics; Mathematics is limited by our imagination, Is our imagination limited? Well, as Mathematics is created by the human mind, it must have a limit. Universes with different physical or mathematical rules? To organize this, it may be sets of universes: In each set are universes with different rules of physics but with the same mathematical logic. Each set has a different mathematical logic (please correct me if Mathematics isn't really limited by anything anything anything).

So, as Mathematics and Physics are separating (many people think they are the same thing!), I'm asking about a branch that connects physics and mathematics: Mathematics that are limited by physics, by our universe. This is a concept of Einstein's Geometry, Geometry limited by the rules of our universe (but in fact, Geometry is only limited by our universe), but as Einstein thought, it isn't the whole Geometry branch, it's only the Geometry limited by our universe. In this concept, a speed of 300000001 (+1) m/s does not exits. So, does this branch have a name? Abstract: Einstein's Geometry.

There is a little bit of misunderstanding of the role of mathematics here in physics.

As an analogy, let's say that I have a tool such as a nail gun. I can connect and nail together as many pieces of wood as I want and make as long of a length as I want. The nail gun doesn't care. It will only do what I want. However, if I say that I want to make a ladder using the nail gun that is long enough to go from Earth to the moon, then SOMETHING ELSE comes into play, which is the physics of the material and the FEASIBILITY of making such a contraption. Yet, the nail gun, in principal, can still do it because all it is is a "tool". What you do with the tool and what your goal is with the tool will have external factors that will dictate if it is realistic or not.

I can add 10+10+10... to infinity. However, if these numbers are assigned to a PHYSICAL quality, such as, say, velocity, then the physical properties of that quality comes into play, and it is external and not taken into account by the the simple mathematics of addition. I cannot just add velocity of frames to infinity. It doesn't match the physics that we know of. But this is NOT a sign that physics impose a limit on mathematics, the same way that just because I can't make the ladder from Earth to the moon, it doesn't mean that there is a limit to the nail gun. This is because I STILL use math to arrive at the physical description of Special Relativity/Lorentz transformation, etc. that imposed a limit on how large a velocity that I can get.

So the answer to your question in the topic: No.

Zz.

 

[Gjmdp]

There is a little bit of misunderstanding of the role of mathematics here in physics.

As an analogy, let's say that I have a tool such as a nail gun. I can connect and nail together as many pieces of wood as I want and make as long of a length as I want. The nail gun doesn't care. It will only do what I want. However, if I say that I want to make a ladder using the nail gun that is long enough to go from Earth to the moon, then SOMETHING ELSE comes into play, which is the physics of the material and the FEASIBILITY of making such a contraption. Yet, the nail gun, in principal, can still do it because all it is is a "tool". What you do with the tool and what your goal is with the tool will have external factors that will dictate if it is realistic or not.

I can add 10+10+10... to infinity. However, if these numbers are assigned to a PHYSICAL quality, such as, say, velocity, then the physical properties of that quality comes into play, and it is external and not taken into account by the the simple mathematics of addition. I cannot just add velocity of frames to infinity. It doesn't match the physics that we now of. But this is NOT a sign that physics impose a limit on mathematics, the same way that just because I can't make the ladder from Earth to the moon, it doesn't mean that there is a limit to the nail gun. This is because I STILL use math to arrive at the physical description of Special Relativity/Lorentz transformation, etc. that imposed a limit on how large a velocity that I can get.
i
So the answer to your question in the topic: No.

Zz.

That is true, at least in physical terms. When you are talking about addition of physical units, you are considering the physical properties of THIS UNIVERSE. In mathematics, all is possible when it has logic: So speed is sightly different when we talk about Mathematics or Physics; In Physics, speed has the properties of the universe, but in Mathematics the concept of speed is not limited by the universe. So, in Mathematics it only has the properties of its definition, and it isn't limited by the universe: you can't figure it out that speed has a limit on the UNIVERSE by its definition: Only by studying the universe. In Physics, speed has a limit, in Mathematics it hasn't. The concept of higher speeds than the light is only true for Mathematics. Isn't that true?

 

[ZapperZ]

That is true, at least in physical terms. When you are talking about addition of physical units, you are considering the physical properties of THIS UNIVERSE. In mathematics, all is possible when it has logic: So speed is sightly different when we talk about Mathematics or Physics; In Physics, speed has the properties of the universe, but in Mathematics the concept of speed is not limited by the universe. So, in Mathematics it only has the properties of its definition, and it isn't limited by the universe: you can't figure it out that speed has a limit on the UNIVERSE by its definition: Only by studying the universe. In Physics, speed has a limit, in Mathematics it hasn't. The concept of higher speeds than the light is only true for Mathematics. Isn't that true?

You still don't get it.

"Speed" is not a mathematical concept. It is a physics concept. There is no "speed" in math.

Math is independent of its use. You sometime see the same form of differential equation in an area in physics and in financial derivative market. Mathematics doesn't care where it is used. It is up to that specific area to figure out what and how to use the mathematics.

Is your original question still unanswered?

Zz.

 

[BvU]

Let me put in another one. In this universe we have a speed of light. Fixed value, pretty big. Hard to imagine. The very smart boys and girls at MIT came up with a nice game where the speed of light is reduced more and more as you gather brownie points. Great fun and very educative; highly recommended.

I put it to you they are doing physics. In a universe that is clearly not ours -- even there you can't exceed the speed of light, after all there are certain laws that have to be obeyed.

 

[Calaver]

The very smart boys and girls at MIT came up with a nice game where the speed of light is reduced more and more as you gather brownie points. Great fun and very educative; highly recommended.

Whoah...I've always wondered if there were such a simulator out there, but never really taken the time to look for it. I have just completed my first run through...it's so cool to see many of the principles which I've learned about played out right before my eyes! I was wondering throughout the game "Where's the length dilation?" and then at the end they removed the Doppler effect so that it became very obvious! Thanks for sharing this game!

 

[Fancybio]

Maybe it will take some time to figure out if Math is a branch of Physics. But one thing I'm sure is that things can be seem in different ways. From the angle of philosophy, Math and Physics can be seem as two different angles of one thing. It's just like people use Math and Physics as tools to demonstrate one thing, or we can call it truth in philosophy, to help us learn and understand this universe. Also, the limits of Math and Physics is really hard to define, but at least we know that they are created for a same purpose.

 

[ZapperZ]

Maybe it will take some time to figure out if Math is a branch of Physics. But one thing I'm sure is that things can be seem in different ways. From the angle of philosophy, Math and Physics can be seem as two different angles of one thing. It's just like people use Math and Physics as tools to demonstrate one thing, or we can call it truth in philosophy, to help us learn and understand this universe. Also, the limits of Math and Physics is really hard to define, but at least we know that they are created for a same purpose.

I disagree. There is no question that mathematics is NOT a part of physics. Why not say mathematics is a part of economics? Of actuarial science? After all, it is extensively used in those areas as well! The screw driver that I used to build my vacuum chamber is not part of the vacuum chamber, even though I used it in the chamber's construction. It is a TOOL.

Maybe you and the OP should read Wigner's excellent article on this already:
https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Zz.

 

[BvU]

I also disagree, but first I want to Fancy !

And: thanks for the link, zZ ! Good reading, indeed.

 

[Calaver]

I disagree. There is no question that mathematics is NOT a part of physics. Why not say mathematics is a part of economics? Of actuarial science? After all, it is extensively used in those areas as well! The screw driver that I used to build my vacuum chamber is not part of the vacuum chamber, even though I used it in the chamber's construction. It is a TOOL.

Maybe you and the OP should read Wigner's excellent article on this already:
https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Zz.

I agree that mathematics isn't a part of physics, but I struggle on whether or not to agree with you that mathematics is merely a tool. Perhaps the best way of looking at things is simply to see mathematics as the " wonderful gift which we neither understand nor deserve" that Wigner mentions at the end of the paper.

On a similar note, here is a link to a talk which may interest a few of you, given (what I think to be) the inappropriate title of "How Much Mathematics Does a Theoretical Physicist Need to Know?" It isn't about a list of subjects, as the speaker points out at the beginning, but about the relation of mathematics to discoveries. Here's the link:
http://online.itp.ucsb.edu/online/colloq/morrison1/options.html
(By the way, if the video doesn't work, I found the audio file to be completely sufficient as he does little to no critical writing on the board.)

 

[NihalRi]

Hello people, this conversation is great!
I agree with everything you said right at the beginning Gjmdp. But I think I disagree with Einstein (don't kil me), when he said math is a branch of physics. I think that if anything physics is a branch of math because math as you have said is infinite. Mathematics knows no bounds but physics is mathematics governed by certain rules that make up our universe. Non euclidian geometry sure helps us understand our universe but as a branch of mathematics it goes far beyond this and helps us imagine a universe that has different rules. Yeah, so geometry isn't limited by our universe, our universe limits the application of the geometry (they're different). And since I believe this is true for all of physics I think that a name for the overlap of math and physics is already given, "physics."
People can argue that it's the other way around but doesn't that depend on your definition of physics, to me physics is just within our universe, the limit on the speed of light only exists here. All of physics is some form of math. If the part of physics that interrelated with just geometry had a name (I'm thinking cosmology is pretty close), there should probably be a name for the interelatons with other parts of math, coordinate physics, vector physics, trigonometric physics, endless. Physics makes use of every branch of math, some argue that all of math can be explained geometrically which brings me right back to the branch we call, "physics. "
I'm terrible with words so i can only hope this made sense. If it doesn't feel free to ask me about anything I've stated.

 

[Gjmdp]

You still don't get it.

"Speed" is not a mathematical concept. It is a physics concept. There is no "speed" in math.

Math is independent of its use. You sometime see the same form of differential equation in an area in physics and in financial derivative market. Mathematics doesn't care where it is used. It is up to that specific area to figure out what and how to use the mathematics.

Is your original question still unanswered?

Zz.

Of course I know Mathematics isn't a branch of Physics. It's a tool to make Physics work, like the battery of Physics. Without the battery (Mathematics), Physics can't work. But, as you know, Mathematics is less limited than Physics, so... In this case Mathematics, the battery, must be equal limited as Physics, because if is less, then is Physics its limited by Mathematics! But in this universe that hasn't sense, Physics is more limited than Physics! So, this Battery (Mathematics) is limited by Physics.
Is that a correct description of the branch I'm talking? Is this branch useful? Is this branch a part of Mathematics or Physics?

 

[BvU]

@sophiecentaur has a very nice signature in this context .

 

[ZapperZ]

Of course I know Mathematics isn't a branch of Physics. It's a tool to make Physics work, like the battery of Physics. Without the battery (Mathematics), Physics can't work. But, as you know, Mathematics is less limited than Physics, so... In this case Mathematics, the battery, must be equal limited as Physics, because if is less, then is Physics its limited by Mathematics! But in this universe that hasn't sense, Physics is more limited than Physics! So, this Battery (Mathematics) is limited by Physics.
Is that a correct description of the branch I'm talking? Is this branch useful? Is this branch a part of Mathematics or Physics?

I give up! This thread is meaningless and makes no sense.

Zz.

 

[Hornbein]

Physics has a limit that it's our universe.
?

It used to be that way.

I think the OP's argument is:

Mathematics is limited by the capabilities of mathematicians.
Mathematicians are physical objects.
Physical objects are limited by physics.

-> Mathematicians are limited by physics.
-> Mathematics is limited by physics.

I find nothing wrong with this. It is impossible to conceive of that which is impossible to conceive. Note also that replacing mathematicians with computers or mystics or whatever makes no difference to the argument. It applies to everything within our Universe.

 

[ZapperZ]

It used to be that way.

I think the OP's argument is:

Mathematics is limited by the capabilities of mathematicians.
Mathematicians are physical objects.
Physical objects are limited by physics.

-> Mathematicians are limited by physics.
-> Mathematics is limited by physics.

I find nothing wrong with this. It is impossible to conceive of that which is impossible to conceive. Note also that replacing mathematicians with computers or mystics or whatever makes no difference to the argument. It applies to everything within our Universe.

But that is where the critical FLAW in the logic is. Mathematics is NOT limited by physics. The physical description is the one being limited by physics. Mathematics can describe anything it wants. WHEN IT IS USED IN PHYSICS, then that description must describe the physics!

Musical notes are NOT restricted to pop music, just because that is the only type of music that you listen to. I can write musical notes for the Javanese Gamelan music that has structure that is very different than pop and western classical music. In fact, I can use the musical notes to write any kind of tunes that I wish, without paying attention to the "rules" of western music.

But using the above logic, you'd claim that the musical notes have an inherent restriction because it has to follow the way how western music is written.

Is this rational?

This topic has become something based on a matter of taste, i.e. philosophy. I find no value in this discussion (i.e. what is the usefulness of it?). So I'm out.

Zz.

 

[Hornbein]

In my post "physics" means the physical nature of our Universe.

In your post "physics" means the study of the physical nature of our Universe. IMO.

 

[ZapperZ]

In my post "physics" means the physical nature of our Universe.

In your post "physics" means the study of the physical nature of our Universe. IMO.

And I can show you many aspects of the principles used in Economics that have no resemblance with the "physical laws of the universe". Yet, they also use mathematics!

Zz.

 

[Hornbein]

And I can show you many aspects of the principles used in Economics that have no resemblance with the "physical laws of the universe". Yet, they also use mathematics!

Zz.

I suggest you take a break and look at this again in an hour or day or so.

 

[ZapperZ]

I suggest you take a break and look at this again in an hour or day or so.

Why? It tastes better after it has been fermented?

Zz.

 

[TeethWhitener]

It used to be that way.

I think the OP's argument is:

Mathematics is limited by the capabilities of mathematicians.
Mathematicians are physical objects.
Physical objects are limited by physics.

-> Mathematicians are limited by physics.
-> Mathematics is limited by physics.

I find nothing wrong with this. It is impossible to conceive of that which is impossible to conceive. Note also that replacing mathematicians with computers or mystics or whatever makes no difference to the argument. It applies to everything within our Universe.

This is similar to the argument put forth by early detractors of computer-aided proofs in math. The thinking goes thus:

A valid proof of X requires verification of X.
Let's say we use a computer to prove X.
Computers are physical objects.
The behavior of physical objects is governed by the inductive (in the common non-mathematical sense of the word) laws of physics, rather than the deductive laws of logic.
The laws of physics cannot be verified absolutely like the laws of logic can.
Therefore, the computer proof of X cannot be verified absolutely.
Therefore the computer proof of X is not a proof of X.

Essentially, the detractors claimed that a computer can never prove a statement because we have no way of knowing in general with absolute confidence that the computer didn't go wrong (i.e., behaved in a way contrary to what we expected). Of course, this problem extends to the fact that our brains (the classic theorem proving tool) are also physical objects, which has led into discussion in the philosophy of mathematics about what exactly a proof is.

 

[Hornbein]

Essentially, the detractors claimed that a computer can never prove a statement because we have no way of knowing in general with absolute confidence that the computer didn't go wrong (i.e., behaved in a way contrary to what we expected). Of course, this problem extends to the fact that our brains (the classic theorem proving tool) are also physical objects, which has led into discussion in the philosophy of mathematics about what exactly a proof is.

IMO a proof is an exercise in persuasion. There is a definite element of psychology and (dare I say it) marketing. I'm not being critical, the proof acceptance process is pragmatic, a system to make best use of finite resources.

About twenty years ago there was a movement toward automated verification of proofs. It was abruptly abandoned. I think automated proof is a worthy goal, but beyond what can be done at this time. I guess what they discovered is that it was far too much work to prove anything to a computer. If proving to a computer were a requirement, all mathematical progress would halt. First it would be necessary to enter all the basic proofs, a Herculean and entirely impractical effort. So the current methods of proof must suffice until artificial intelligence technology improves.

Kurt Godel proved that there is no limit to the minimum length of a proof. Starting with a simple proof it is possible to construct a proposition with a proof that must be longer than the first, and so on. So it is practically impossible to prove certain things.

There is a proposed proof of the abc conjecture. The claimant has excellent credentials and reputation. But the proof is so long and complicated that no movement has arisen to verify the alleged proof. If no group will make the effort then we may never know whether or not this is a proof. If a computer ever verifies a proof like that, or a proof with that complexity raised to a power of one thousand, then humans would have no other criteria than trust or lack thereof.

I think that quite often the proposition to be proved is of little importance. What really matters is the discovery of a fresh approach or insight in the course of the proof. It would seem to me that a proof of the Goldbach conjecture that occupies a centillion terabytes would be utterly useless.

There was the controversial computerized proof of the 4-color conjecture. It was useful in the sense that mathematicians (and cranks) could then stop wasting their time on attempted proofs. An expert (Gerhard Ringel) told me that he felt there was no other way to prove it, so good riddance. But it could very well be in some cases that an impenetrable computerized proof would discourage the discovery of a simple, worthwhile proof. In that case the computerized proof would serve the function of inhibiting progress. But probably not. I bet there are a thousand cranks right now trying to come up with a one-page proof of Fermat's last theorem.

IMO automated and natural methods of proof verification are complementary. It would be nice to have both. What's the problem?

 

[Gjmdp]

The rules of Physics, and the rules for studying Physics are different. You are mixing this terms.
To study Physics or whatever we need Mathematics, and this is like a computer program: there is syntax (logical and organized methods) but not semantics (rules or concepts of Physics).
The rules of Physics, the concepts, or the "semantics" are expressed with help of Mathematics, but NOT only with Mathematics (speed is not a mathematical concept).
All this concepts are limited by Physics.

With Mathematics:
The rules of Mathematics are expressed by itself, Mathematics. You can't explain 1+1=2 by anything that isn't Mathematics.
Now, are the rules for studying Mathematics limited by Physics?
Well, the environment for studying Mathematics in this universe is completely physical, not mathematical.
The speed of light is limited on this universe, and for some of you this seems to be a random rule. But how do we know is a random rule? How do we know there could be an universe with no limit on the speed of light? We don't know, we haven't been on that universe and we can't have a proof of the possibility of such universe never.

Maybe (I don't know), the speed of light has to be limited Mathematically.
So this makes me ask: May Physics be as limited as Mathematics? Is that a possibility? I'm not saying anything is a branch of anything, there are things equal limited (Physics and Chemistry are limited by the universe) but there aren't the same thing (Physics and Chemistry aren't the same thing by definition)