Does mathematics really exist in nature or not?

[seriously disabled]

I searched everywhere on the Internet but couldn't find a conclusive answer.

 

My question is: Do mathematical entities (like numbers or probability distributions for example) really exist in the universe or are mathematical entities just a human invention?

 

In other words, is mathematics really out there in the universe or is mathematics just a tool that humans invented in order to describe the universe?

Edited November 11, 2015 by seriously disabled

[Klaynos]

Can you please define a test for "really exists".

[seriously disabled]

No I cannot because I'm not a certified physicist in profession.

[DrP]

Nature is pretty quantised - so yes maths applies... you can count and add things (exact numbers of molecules in systems).. things decay at certain rates which obey or follow mathematical forms. Maths is everywhere and I do not have time to list some of the many many examples of maths being found in nature, but look around and you will see examples.

[seriously disabled]

So do mathematical probabilities as described by the wave function squared in quantum mechanics, for example, really have a physical existence in nature?

[Strange]

No I cannot because I'm not a certified physicist in profession.

 

I don't think you need to be: what do you mean by "really exist"? How would you tell if something really exists or is just a concept?

 

Do dreams really exist? Do photons really exist? Do electrons really exist? Do atoms really exist? Do tables really exist?

 

For all of these, for suitable definitions of "exist" the answer could be yes or no.

 

This is not really a physics question (because numbers are abstract concepts and don't have measurable properties - which may answer your question). It is philosophy, and there has been a debate among mathematicians and philosophers about this ever since mathematics was invented. Or do I mean discovered.

 

My impression is that most mathematicians think that mathematics (and therefore numbers) exists as a concept that we discover. But there are many who think it is purely an invention of the human mind. And some who would say there is no difference between these two positions.

[DrP]

That is a specific question that QM experts should answer... I personally do not know but would assume that it is a pretty good model.

 

We can mathematically model almost anything... standing waves on a string, for example, or the depletion rate of a chemical during a reaction over time. Real maths accurately describing or modelling real life physical observations.

[Phi for All]

I think mathematical relationships exist everywhere in the universe, and our mathematics is the system we invented to analyze the properties of reality here. But numbers aren't real things, they aren't physical in nature. You can't eat pi, but pi can help tell you how much pie you've eaten.

[Strange]

So do mathematical probabilities as described by the wave function squared in quantum mechanics, for example, really have a physical existence in nature?

 

I would guess that most physicists just consider it a good model; an accurate description of behaviour. But some claim it has some physical reality. Wikipedia has a good article on different interpretations of quantum mechanics, with a handy table summarising which consider the wave function to be real:

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Tabular_comparison

 

 

Of course, that depends on what "real" means:

https://en.wikipedia.org/wiki/Wave_function#Ontology

Edited November 11, 2015 by Strange

[studiot]

 

certified physicist

 

Yes, you have to be at least a little bit mad to be one.

 

[Klaynos]

 

I don't think you need to be: what do you mean by "really exist"? How would you tell if something really exists or is just a concept?

 

Do dreams really exist? Do photons really exist? Do electrons really exist? Do atoms really exist? Do tables really exist?

 

For all of these, for suitable definitions of "exist" the answer could be yes or no.

 

This is not really a physics question (because numbers are abstract concepts and don't have measurable properties - which may answer your question). It is philosophy, and there has been a debate among mathematicians and philosophers about this ever since mathematics was invented. Or do I mean discovered.

 

My impression is that most mathematicians think that mathematics (and therefore numbers) exists as a concept that we discover. But there are many who think it is purely an invention of the human mind. And some who would say there is no difference between these two positions.

This really is what I was getting at. It's not really a well defined question.

[kisai]

No, mathematics does not exist. It acts as a consistent and precise language, which is useful for describing universal phenomena, for these are also usually consistent and precise.

[Klaynos]

No, mathematics does not exist. It acts as a consistent and precise language, which is useful for describing universal phenomena, for these are also usually consistent and precise.

So you have done the test I asked about above? If not how can you be so sure? What's your evidence?

 

I'm not taking any side, I think people need to think very carefully about what they mean with their questions and how you can make any definitive answer which can be backed by evidence.

[andrewcellini]

No, mathematics does not exist. It acts as a consistent and precise language, which is useful for describing universal phenomena, for these are also usually consistent and precise.

what do you mean by exist?

[DevilSolution]

No, mathematics does not exist. It acts as a consistent and precise language, which is useful for describing universal phenomena, for these are also usually consistent and precise.

 

Everythings a concept darling. Sofa's dont actually exist there just extremely useful for resting on after a long days work,,,,,,,,,,

I searched everywhere on the Internet but couldn't find a conclusive answer.

 

My question is: Do mathematical entities (like numbers or probability distributions for example) really exist in the universe or are mathematical entities just a human invention?

 

In other words, is mathematics really out there in the universe or is mathematics just a tool that humans invented in order to describe the universe?

 

Is your username an irony? Anything with purpose exists.....and humans didnt discover or invent maths.....it invented us.

Edited November 12, 2015 by DevilSolution

[seriously disabled]

Physics is too difficult for me and I think for the majority of people also.

 

You need to be extremely intelligent to understand quantum mechanics, special relativity, general relativity, thermodynamics, statistical mechanics, dynamical systems, chaos theory, quantum field theory, particle physics, the Standard model, supersymmetry, loop quantum gravity, supergravity, and string theory/superstring theory/M-theory because all these are very difficult subjects to understand and those who study these subjects in university and succeed at them must be extremely intelligent in my opinion (above average intelligent).

 

Not to mention all the difficult mathematical topics you need to be able to understand and memorize like college algebra, calculus, multivariable calculus, vector calculus, linear algebra, calculus of variations, functional analysis, operator theory, real and complex analysis, measure theory, probability and statistics, abstract algebra (also called modern algebra), tensor calculus, topology, lie groups, lie algebras, differential geometry, differential topology, algebraic topology, set theory, category theory and many others extremely complicated mathematical subjects.

 

Most people cannot understand these highly technical physics and mathematics subjects.

 

In order to succeed at physics you must work extremely hard and have extremely good memory because you need to be able to remember and connect between a lot of things.

 

But the drawback to all of this is that the pay is not so good. Physicists must work extremely hard but the pay is not so good. Many other professions pay more than physics and they are also less difficult.

Edited November 12, 2015 by seriously disabled

[studiot]

 

Many other professions pay more than physics and they are also less difficult.

 

 

Those 'professionals' closest to the money somehow see the most of it.

[cladking]

Math isn't "real" nor are numbers or the way math is applied.

 

But logic is real and any system founded on a logical framework will yield consistent answers. While brains operate on a logical system modern language does not. Instead we operate on constructs with which we create paradigms and models. Since math is at the heart of many of these models they will always appear to be true to the observer. The closer you look at natural forces stripped to their basics as in the lab then observation will almost always match models perfectly. When they don't a new model is invented based on new experiment.

[Acme]

No, mathematics does not exist. It acts as a consistent and precise language, which is useful for describing universal phenomena, for these are also usually consistent and precise.

To what does the highlighted pronoun 'It' refer?

 

Anyone who denies the law of noncontradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned. ~Avicenna

[Klaynos]

Math isn't "real" nor are numbers or the way math is applied.

 

But logic is real and any system founded on a logical framework will yield consistent answers. While brains operate on a logical system modern language does not. Instead we operate on constructs with which we create paradigms and models. Since math is at the heart of many of these models they will always appear to be true to the observer. The closer you look at natural forces stripped to their basics as in the lab then observation will almost always match models perfectly. When they don't a new model is invented based on new experiment.

I'd love to see any definitive evidence you have for any of those statements.

[Strange]

Math isn't "real" nor are numbers or the way math is applied.

 

But logic is real ...

 

Logic is a branch of mathematics. So it isn't real (according to you).

[Klaynos]

 

Logic is a branch of mathematics. So it isn't real (according to you).

Unless we're using the "what makes sense to me" definition of logic, which we all know doesn't match the universe.

[Gees]

Seriously Disabled;

 

I searched everywhere on the Internet but couldn't find a conclusive answer.

 

My question is: Do mathematical entities (like numbers or probability distributions for example) really exist in the universe or are mathematical entities just a human invention?

 

In other words, is mathematics really out there in the universe or is mathematics just a tool that humans invented in order to describe the universe?

 

It is very difficult to get a conclusive answer regarding all of nature, no matter the source, but I think that philosophy may have the best answer to your question. In studies of nature, many different things have been learned, but through all of this knowledge there is one consistency, and that consistency is balance.

 

Science confirms this and can show the balance in matter, whether it be an atom or a solar system. We know that life is self balancing whether we are talking about an ecosystem or a body, and we know that there must be a balance in governments, societies, and economies in order for them to maintain themselves. There is also balance in the mental; the rational conscious mind works off of logic, which is a form of math, and the unconscious mind possesses an innate understanding of more and less, and of self and other. The "more and less" is obviously about math and the "self and other" can be looked at as being similar to a simple binary code, like the "1" and "0" used in computer coding. So it seems that balance is everywhere.

 

Can balance exist without math? Without some kind of measure? Without some kind of "equal"? I don't see how. So I think that math is something that we discovered, not something that we created.

 

Gee

[cladking]

I'd love to see any definitive evidence you have for any of those statements.

 

I've been trying very hard to show this evidence for a long time now but it requires a completely different way of thinking apparently. It requires a whole new perspective at the very least. From the prerspective of the way we think we see what we know and we know that four is more than two. If I ask whether you want two big piles of something you desire or four tiny piles you'll take the two big ones and then claim the question was some sort of trick instead of a representation of the reality that no two of anything actually exists so that numbers are a construct. What makes the person choose the two big piles is simple logic; he can see that two is greater than four in this instance.

 

By the same token there are many ways to skin a cat and any system that works will be repeatable. If you apply logic to a system and define the terms such as math it will simply be repeatable. If we strip nature down to something that works in the lab then this too will be repeatable. Every time we slide a weight down an inclined plane it will never accelerate at 32' per sec ^ 2. It will always be dependent on the specific angle and friction. But this doesn't mean we've invented gravity but merely that we've identified a force that always acts the same and that can be quantified.

 

Yes, everything is in perfect balance and this was called "maat" in ancient science. It is the balance of logic and nature which gives rise to it. We didn't invent it but merely quantified it. We typically don't see this balance and we don't see the reality directly but rather we see the models that derive from experiment and definition. We see the world as an extension of our knowledge, we see the world in terms of our knowledge never realizing the nature of knowledge is distinct from reality because of definitions and perspectives. Our understanding is derived from the effect of reality on experiment.

Edited November 13, 2015 by cladking

[Klaynos]

 

I've been trying very hard to show this evidence for a long time now but it requires a completely different way of thinking apparently. It requires a whole new perspective at the very least. From the prerspective of the way we think we see what we know and we know that four is more than two. If I ask whether you want two big piles of something you desire or four tiny piles you'll take the two big ones and then claim the question was some sort of trick instead of a representation of the reality that no two of anything actually exists so that numbers are a construct. What makes the person choose the two big piles is simple logic; he can see that two is greater than four in this instance.

 

By the same token there are many ways to skin a cat and any system that works will be repeatable. If you apply logic to a system and define the terms such as math it will simply be repeatable. If we strip nature down to something that works in the lab then this too will be repeatable. Every time we slide a weight down an inclined plane it will never accelerate at 32' per sec ^ 2. It will always be dependent on the specific angle and friction. But this doesn't mean we've invented gravity but merely that we've identified a force that always acts the same and that can be quantified.

 

Yes, everything is in perfect balance and this was called "maat" in ancient science. It is the balance of logic and nature which gives rise to it. We didn't invent it but merely quantified it. We typically don't see this balance and we don't see the reality directly but rather we see the models that derive from experiment and definition. We see the world as an extension of our knowledge, we see the world in terms of our knowledge never realizing the nature of knowledge is distinct from reality because of definitions and perspectives. Our understanding is derived from the effect of reality on experiment.

No evidence then.