Does mathematics has anything to do with physics?

[1x0]

Does mathematical operations has to follow the observed reality?

 

 

[ajb]

Does mathematical operations has to follow the observed reality?

There is no rule that says that mathematics has to say anything about the real world. However, it seems that just about every branch of mathematics can find an application in physics. It is true that not every result is of importance in physics, but generally every branch seems to say something.

 

It was also said to me that every important result in mathematics was either motivated by physics or quickly found application in physics. This seems to be generally true in my opinion.

[1x0]

There is no rule that says that mathematics has to say anything about the real world. However, it seems that just about every branch of mathematics can find an application in physics. It is true that not every result is of importance in physics, but generally every branch seems to say something.

 

It was also said to me that every important result in mathematics was either motivated by physics or quickly found application in physics. This seems to be generally true in my opinion.

Could mathematics exist without the physical reality?

 

Could our mathematical understanding exist without physical reality?

 

I mean: Our brain processing the information we gain from the observed reality and related to that information we determined the axioms of the mathematical tool we use. Without a physical tool as our brain and without the observed physical reality we live in mathematics would not exist. Or?

Edited May 19, 2015 by 1x0

[studiot]

 

Could our mathematical understanding exist without physical reality?

 

What do you really mean?

[mathematic]

There is no rule that says that mathematics has to say anything about the real world. However, it seems that just about every branch of mathematics can find an application in physics. It is true that not every result is of importance in physics, but generally every branch seems to say something.

 

It was also said to me that every important result in mathematics was either motivated by physics or quickly found application in physics. This seems to be generally true in my opinion.

As a mathematician I have to disagree. Number theory has nothing to do with physics. In addition there are many esoteric branches of mathematics such as algebraic geometry, category theory, etc. which also have nothing to do with physics.

[Acme]

As a mathematician I have to disagree. Number theory has nothing to do with physics. In addition there are many esoteric branches of mathematics such as algebraic geometry, category theory, etc. which also have nothing to do with physics.

Erhm...nothing?

 

NUMBER THEORY IN PHYSICS

In describing significant occurrences of number theory in physics, we will, on the

one hand, restrict our attention to quantum physics, while, on the other hand, we

will assume a somewhat extensive definition of number theory, that will allow us

to include arithmetic algebraic geometry. The territory is vast and an extensive

treatment would go beyond the size limits imposed by the encyclopaedia. The

choice of topics represented here inevitably reflects the limited knowledge, particular

interests and bias of the author. Very useful references, collecting a lot of material

on Number Theory and Physics, are the proceedings of the Les Houches conferences

[1], [2], [3]. A Number Theory and Physics database is presently maintained

online by Matthew R. Watkins. ...

number theory and physics archive

 

 

The idea of this website is to document all known research which in some way links number theory and physics. Although there have been a few conferences and subsequently published proceedings on this topic, these have only been able to touch on a small part of the overall body of work which has gone on.

 

The contents of the site should be of interest to both number theorists and physicists. In recent times we have seen, somewhat unexpectedly, number theory being applied by physicists to solve physical problems and, perhaps even more unexpectedly, techniques developed by physicists applied to problems in number theory. Material relevant to all such developments is archived in the sections linked from the upper part of the front page. ...

[ajb]

Could mathematics exist without the physical reality?

This is the question of if we create mathematics or discover it. I tend to side with discover, but as this cannot be tested I do not think it is an important difference.

 

As a mathematician I have to disagree. Number theory has nothing to do with physics. In addition there are many esoteric branches of mathematics such as algebraic geometry, category theory, etc. which also have nothing to do with physics.

 

 

But all have found applications of some form in physics. It is true that the original motivations were not physics directed, you can find examples of applications of all three subjects you state. In fact I use methods form algebraic geometry and category theory all the time, though I work in mathematical physics which is closer to mathematics than physics.

 

I am surprised a mathematician would disagree.

Edited May 20, 2015 by ajb

[1x0]

This is the question of if we create mathematics or discover it. I tend to side with discover, but as this cannot be tested I do not think it is an important difference.

 

 

 

 

But all have found applications of some form in physics. It is true that the original motivations were not physics directed, you can find examples of applications of all three subjects you state. In fact I use methods form algebraic geometry and category theory all the time, though I work in mathematical physics which is closer to mathematics than physics.

 

I am surprised a mathematician would disagree.

I would say that we discover as our complete mathematical understanding originates from the observed physical reality. It can be tested I think as we can inspect the physical operations and we can set mathematical values and axioms basically to anything we would like to (binary system?)

 

The question is: Does mathematical operations clearly follow the observed physical reality?

 

If not what is the reason that we use the mathematical tool as we do?

 

Do we understand and exploit the mathematical tool 100%?

 

Can some of the disturbances(undertermined axioms) depend on that we do not adjust the mathematical tool to the observed evolving reality?

Edited May 20, 2015 by 1x0

[Strange]

The question is: Does mathematical operations clearly follow the observed physical reality?

 

Much mathematics is developed without any relation to physics or physical reality. Some of it may turn out to be useful to describe the world, some probably wont.

[ajb]

The question is: Does mathematical operations clearly follow the observed physical reality?

I am not sure what this means. Many mathematical constructions are motivated by physical reality and others not. Are you asking if it is always possible to find a physical system that 'models' the mathematics? If so, we just don't know. This is part of Tegmark's mathematical universe hypothesis.

 

If not what is the reason that we use the mathematical tool as we do?

Because in general it is the best language to describe nature and other things.

 

Do we understand and exploit the mathematical tool 100%?

I don't know what this means.

 

Can some of the disturbances(undertermined axioms) depend on that we do not adjust the mathematical tool to the observed evolving reality?

I am not sure what you are asking.

[Acme]

 

... Do we understand and exploit the mathematical tool 100%?...

I don't know what this means.

 

I don't quite get it either and we can hope 1x0 clarifies this question, but my inclination is to answer no as I think of Gödel's incompleteness theorems.

[Strange]

Do we understand and exploit the mathematical tool 100%?

 

I don't know what this is supposed to mean, either. But one possible answer is no; there is probably a lot of work done in mathematics, and theorems proven, which are never referred to again. So those "tools" are never used.

[Acme]

 

Do we understand and exploit the mathematical tool 100%?

I don't know what this is supposed to mean, either. But one possible answer is no; there is probably a lot of work done in mathematics, and theorems proven, which are never referred to again. So those "tools" are never used.

 

I would take exception to saying "never" as it seemingly implies no such use is possible. Even if the use is not immediately in physics, one cannot say such tools won't in the future find utility in other -possibly equally arcane- proofs.

[Strange]

I would take exception to saying "never" as it seemingly implies no such use is possible. Even if the use is not immediately in physics, one cannot say such tools won't in the future find utility in other -possibly equally arcane- proofs.

 

Fair comment: I suppose I meant "have never" rather than "are never". But that is still a possible answer to the question, which was in the present tense: i.e. what we have done so far.

[Acme]

Fair comment: I suppose I meant "have never" rather than "are never". But that is still a possible answer to the question, which was in the present tense: i.e. what we have done so far.

A fair comment to my fair comment. If 1x0's question means 'have we discovered all there is to discover in mathematics?', then the answer is an obvious and resounding no. Moreover, Gödel's proofs inform us that even for some things already discovered which appear to be true (because no exceptions have been found) are in fact true, no proof may ever be given. In this we can say never, i.e. consistent systems of axioms can never be complete and any complete system can never be consistent. Edited May 20, 2015 by Acme

[mathematic]

This is the question of if we create mathematics or discover it. I tend to side with discover, but as this cannot be tested I do not think it is an important difference.

 

 

 

 

But all have found applications of some form in physics. It is true that the original motivations were not physics directed, you can find examples of applications of all three subjects you state. In fact I use methods form algebraic geometry and category theory all the time, though I work in mathematical physics which is closer to mathematics than physics.

 

I am surprised a mathematician would disagree.

I disagreed with the original assertion that all mathematics development was motivated by physics. You are describing the reverse, where existing mathematics has found application.

[ajb]

I disagreed with the original assertion that all mathematics development was motivated by physics.

But I did not assert that, you have misunderstood my meaning.

 

My point was generally, in my opinion, most of the important and far reaching ideas in mathematics come from physics or quickly find application there. That is not to say that all mathematical ideas were original developed with physics in mind. It is also very interesting that all branches of mathematics can be applied in physics in some form or another.

[Belcher]

Does mathematical operations has to follow the observed reality?

 

 

That is a silly question from you, Every calculation has math in it and the physics is all about calculation of terms and that is only possible with mathematics latest concepts and implementations.

[swansont]

That is a silly question from you, Every calculation has math in it and the physics is all about calculation of terms and that is only possible with mathematics latest concepts and implementations.

 

Not really a silly question. There is no inherent reason that science has to use all that math has to offer.

[MountainGuardian]

Math is simply an idea that we use to interpret the world around us, the universe itself is not a mathematical concept, the mathematical "concept" is what we use to describe and predict the universe.

.

Math as we know it, is our limited form of understanding and is ever changing, our current ability to predict outcomes using our current understanding of math and physics begins to fall apart at the subatomic scale. This does not mean that subatomic particles are inherantly unpredictable, it simply means that the tool that we use to make this prediction understandable to us does not work properly in this scale.

.

Physics is a combination of direct scientific observation and mathematical prediction, again physics is simply an idea or tool used by us to help us understand and predict the universe around us. Math and physcs are not exactly some hidden function of the universe around us, but a way and means that we employ in interpreting and predicting the universe around us. Much of what we know is actually wrong, we have disproven many ideas and theories that we have used in the past with further observation and discovery. Math and physics is the current culmination of what has been observed, theorized and hypothesized about the universe around us.

Edited January 27, 2016 by MountainGuardian

[studiot]

Math is simply an idea that we use to interpret the world around us, the universe itself is not a mathematical concept, the mathematical "concept" is what we use to describe and predict the universe.

.

Math as we know it, is our limited form of understanding and is ever changing, our current ability to predict outcomes using our current understanding of math and physics begins to fall apart at the subatomic scale. This does not mean that subatomic particles are inherantly unpredictable, it simply means that the tool that we use to make this prediction understandable to us does not work properly in this scale.

.

Physics is a combination of direct scientific observation and mathematical prediction, again physics is simply an idea or tool used by us to help us understand and predict the universe around us. Math and physcs are not exactly some hidden function of the universe around us, but a way and means that we employ in interpreting and predicting the universe around us. Much of what we know is actually wrong, we have disproven many ideas and theories that we have used in the past with further observation and discovery. Math and physics is the current culmination of what has been observed, theorized and hypothesized about the universe around us.

 

Mathematics is not always about the real world at all.

 

When spreadsheets first came in they were welcomed because they allowed quick and easy access to the "What if " game.

 

What if the price of oil doubles / halves ?

 

What if the electronegativity of copper was 1.6 or 2.1 instead of 1.9?

 

What could I spend a lottery win of £100,000 on?

 

None of this actually happens but mathematics allows us to speculate.

Edited January 27, 2016 by studiot

[TakenItSeriously]

I had brothers that taught me about QM, GR, and cosmology at the age of 7 and I understood it though I probably didn't know much beyond simple arithmetic at that age.

 

I think my age actually made it easier to understand before life experiences had biased my intuition too much against accepting the unintuitive. I'm still not very good at math though.

 

An open mind is the biggest hurdle for understanding science IMO, and math is mostly useful for proofs or sometimes problem solving.

 

In college, there was a non-math physics class for all majors that weren't technical in nature and they even used the same text.