Why does math work in our reality?

[vectorcube]

Physical laws are mathematical in my opinion. So math is not a tool only. It is the law.

Physical laws does not have to be mathematical, and math is a tool, because there are infinite many mathematical results that do not have any applications to physical world.

 

[Pythagorean]

Physical laws are mathematical in my opinion. So math is not a tool only. It is the law.

Your argument is rather meaningless:

premise 1: physical laws are mathematical
premise 2: (not stated, but implied... not sure I know what it is)

conclusion: It (presumably math) is the law.

In every case, your argument is vague. Premis 1 doesn't really say anything:

"Physical laws are mathematical". In what sense? Surely not in every sense, or it would just be mathematics! Physics is conceptual too, it has quality, not just quantity.

Premise 2: Your still have to tell us your second premise. You have to tell us why you think that Premise 1 leads to your conclusion.

Conclusion. "It is the law" This is meaningless. Is the law of what? Of the whole universe? That's quite a claim.

Come back with a more descriptive argument that can actually be argued.

 

[wofsy]

Physical laws does not have to be mathematical, and math is a tool, because there are infinite many mathematical results that do not have any applications to physical world.

I agree that math is a tool but to say that there is more math than physical laws and more than one mathematical description does not change what i am saying. Kepler thought of physics as a process of ever better approximation to truth. Intermediate theories reflect and guide us towards this truth even though they may be incomplete and non-unique for the set of phenomena that they predict.

To think that mathematics is somehow separate from reality seems to me to be an arbitrary hypothesis and also seems to contradict all of experience.

 

[WaveJumper]

Your argument is rather meaningless:

premise 1: physical laws are mathematical
premise 2: (not stated, but implied... not sure I know what it is)

conclusion: It (presumably math) is the law.

In every case, your argument is vague. Premis 1 doesn't really say anything:

"Physical laws are mathematical". In what sense? Surely not in every sense, or it would just be mathematics! Physics is conceptual too, it has quality, not just quantity.

Premise 2: Your still have to tell us your second premise. You have to tell us why you think that Premise 1 leads to your conclusion.

Conclusion. "It is the law" This is meaningless. Is the law of what? Of the whole universe? That's quite a claim.

Come back with a more descriptive argument that can actually be argued.

He probably read somewhere about the mathematical universe. While i am not a proponent of the theory, it's been a deep conceptual problem in physics to identify and conceptualise the basic constituents of matter in a non-mathematical way. All efforts so far have proved contradictory and incomplete. The basic building blocks of the material universe(electrons, quarks, quanta in general) cannot be unambiguously described without resorting to maths. They are not 'material' in any of the traditional ways that we are accustomed to dealing with. What is an electron? What is a quark? As i am certain you are aware, those are not easy questions to answer. At all.

It takes a leap of faith to jump from "Matter can only be described through mathematics" to "Matter is pure mathematics", though.

 

[vectorcube]

I agree that math is a tool but to say that there is more math than physical laws and more than one mathematical description does not change what i am saying. Kepler thought of physics as a process of ever better approximation to truth. Intermediate theories reflect and guide us towards this truth even though they may be incomplete and non-unique for the set of phenomena that they predict.

To think that mathematics is somehow separate from reality seems to me to be an arbitrary hypothesis and also seems to contradict all of experience.

Contradict all experience my ***. Math is a internally consistent thing don` t need the physical world to make it`s statements true. Physics is about the world! There is a unlimited number of physical realities we can imagine up, and describe with math. Why do we live in a world without jelly monsters? We just don` t! There is no mathematically reasons why things are the way they are. They just are. Case closed.

 

[wofsy]

Contradict all experience my ***. Math is a internally consistent thing don` t need the physical world to make it`s statements true. Physics is about the world! There is a unlimited number of physical realities we can imagine up, and describe with math. Why do we live in a world without jelly monsters? We just don` t! There is no mathematically reasons why things are the way they are. They just are. Case closed.

I understood your point before you responded. I am not saying something superficial as you seem to think.

Theorem proving makes math internally consistent but that just means that there is something internally consistent about the universe. If it did not mean that then you would not even be able to talk.

 

[Pythagorean]

He probably read somewhere about the mathematical universe. While i am not a proponent of the theory, it's been a deep conceptual problem in physics to identify and conceptualise the basic constituents of matter in a non-mathematical way. All efforts so far have proved contradictory and incomplete. The basic building blocks of the material universe(electrons, quarks, quanta in general) cannot be unambiguously described without resorting to maths. They are not 'material' in any of the traditional ways that we are accustomed to dealing with. What is an electron? What is a quark? As i am certain you are aware, those are not easy questions to answer. At all.

It takes a leap of faith to jump from "Matter can only be described through mathematics" to "Matter is pure mathematics", though.

Quite. That leap of faith would be his premise 2. I'm not sure if you could even prove premise 1 in the absolute sense. Physics is mathematical in some sense, but it's not 100% mathematical. Even in the case of leptons (electrons) and quarks. I do agree that these aren't easy questions to answer, but we have gained both a conceptual and mathematical understanding of them as a community. If the unnamed premise 2 were graspable, why would one pick mathematical over conceptual?

To inject my obvious opinion:
I think people have a blind respect and fear for mathematics. Mathematics is like dynamite: it's definitely a tool to respect for its power... but it's still a tool.

 

[wofsy]

Quite. That leap of faith would be his premise 2. I'm not sure if you could even prove premise 1 in the absolute sense. Physics is mathematical in some sense, but it's not 100% mathematical. Even in the case of leptons (electrons) and quarks. I do agree that these aren't easy questions to answer, but we have gained both a conceptual and mathematical understanding of them as a community. If the unnamed premise 2 were graspable, why would one pick mathematical over conceptual?

To inject my obvious opinion:
I think people have a blind respect and fear for mathematics. Mathematics is like dynamite: it's definitely a tool to respect for its power... but it's still a tool.

I never said the universe is only a mathematical theorem. I said physical law is mathematical and thereby is intrinsic to the universe. If you think mathematics is only a tool, I would say that that is a leap of blind faith. why do you use it at all?

 

[Pythagorean]

I never said the universe is only a mathematical theorem. I said physical law is mathematical and thereby is intrinsic to the universe. If you think mathematics is only a tool, I would say that that is a leap of blind faith. why do you use it at all?

This argument is still not sound.

"Why do we use it at all" seems to be your argument for it being more than a tool.

We could apply the same logic to a hammer and the fact that we us a hammer it all is not a sufficient argument for it having some deep, universal meaning.

Mathematics is a much bigger, diverse tool, and I'm not arguing that it's as simple as a hammer, it's not even the same kind of tool. I'm just pointing out that you still haven't made an argument. I invite you to think about it more and develop a better argument, though. I'm willing to listen.

 

[wofsy]

This argument is still not sound.

"Why do we use it at all" seems to be your argument for it being more than a tool.

We could apply the same logic to a hammer and the fact that we us a hammer it all is not a sufficient argument for it having some deep, universal meaning.

Mathematics is a much bigger, diverse tool, and I'm not arguing that it's as simple as a hammer, it's not even the same kind of tool. I'm just pointing out that you still haven't made an argument. I invite you to think about it more and develop a better argument, though. I'm willing to listen.

In fact the ability to predict the outcome of the use of a hammer does have some deep universal meaning.

 

[SixNein]

He probably read somewhere about the mathematical universe. While i am not a proponent of the theory, it's been a deep conceptual problem in physics to identify and conceptualise the basic constituents of matter in a non-mathematical way. All efforts so far have proved contradictory and incomplete. The basic building blocks of the material universe(electrons, quarks, quanta in general) cannot be unambiguously described without resorting to maths. They are not 'material' in any of the traditional ways that we are accustomed to dealing with. What is an electron? What is a quark? As i am certain you are aware, those are not easy questions to answer. At all.

It takes a leap of faith to jump from "Matter can only be described through mathematics" to "Matter is pure mathematics", though.

I think people misunderstand the role of mathematics or physics in general. So I'm going to make a chart to explain it better...

======Formal System=====|====Physical System====
------- Mathematics -----<Observation>----- Stars --------
------- Physical Theories -<Observation>---- Planets -------
===========================================
---- Formal Description <Observation> Event

Physical theories are very formal. They do not have the ability to describe the universe; instead, they can only model it using mathematics. The goal of physics is to place limitations on mathematical equations that are validated through observation. Mathematics does the same thing in a sense, but it works without physical imitations.

I think; therefore, I am.

The above statement is the only thing people can know for sure.

 

[vectorcube]

I understood your point before you responded. I am not saying something superficial as you seem to think.

Theorem proving makes math internally consistent but that just means that there is something internally consistent about the universe. If it did not mean that then you would not even be able to talk.

Wrong in some many levels.

1: The notion that you could make a math theorm true by proving it is a very constructivistic approach to math. It is also a deeply misguided one. Why? Intuitively, A theorm is true independent of anyone. fermat ` s theorm would be true even if that some guy did not prove it.

2. Because math is an internally consistent system. This follows that it is also independent from contingent nature of the world.

_____________________________________________________________

The world is contingent. That is, the world, being made of constitutes, and laws that governs those constitutes need not be the way they are for any mathematical reasons. As such, there could be different physical realities with different constitutes, and dynamical laws. This is as oppose to math propositions which needs to be the case in all possible worlds.

So:

For P, such that P is a law of nature, then there is a possible W, such that -P hold in W.

For P, such that P is a matheamatical proposition, then P is ture in all possible worlds.

 

[wofsy]

Wrong in some many levels.

1: The notion that you could make a math theorm true by proving it is a very constructivistic approach to math. It is also a deeply misguided one. Why? Intuitively, A theorm is true independent of anyone. fermat ` s theorm would be true even if that some guy did not prove it.

2. Because math is an internally consistent system. This follows that it is also independent from contingent nature of the world.

_____________________________________________________________

The world is contingent. That is, the world, being made of constitutes, and laws that governs those constitutes need not be the way they are for any mathematical reasons. As such, there could be different physical realities with different constitutes, and dynamical laws. This is as oppose to math propositions which needs to be the case in all possible worlds.

So:

For P, such that P is a law of nature, then there is a possible W, such that -P hold in W.

For P, such that P is a matheamatical proposition, then P is ture in all possible worlds.

you also did not get what I was saying.

math is not separate from the world and the world is not contingent. Only knowledge from sense experience is contingent.

I am not sure what you mean by mathematical reasons or why reasons at all have anything to do with math or physics.

 

[arithmetix]

My answer:
Maths is a language in which true things can be said, so that the consequences of these truths are implied in the grammar of the statement. I declare that any such careful grammar partakes of whatever spirit is in formally recognised mathematics, and that for the purposes of your question, all statements purporting to be absolute truth are mathematics-like statements.
For me even such simple statements as "it is there" and "it is not there" comprise mathematics-like truths.
Then although I know this answer is scarcely an answer at all, maths works because it is a formalisation of our practical, day-to-day experience.

Is this answer to your point?

 

[wofsy]

My answer:
Maths is a language in which true things can be said, so that the consequences of these truths are implied in the grammar of the statement. I declare that any such careful grammar partakes of whatever spirit is in formally recognised mathematics, and that for the purposes of your question, all statements purporting to be absolute truth are mathematics-like statements.
For me even such simple statements as "it is there" and "it is not there" comprise mathematics-like truths.
Then although I know this answer is scarcely an answer at all, maths works because it is a formalisation of our practical, day-to-day experience.

Is this answer to your point?

yes - but I do not agree that math is a language - i agree that we can talk about it and think about it - to say that a 4 dimensional projective space is just just a word in a language with some grammar is just like saying that a tree is just part of a language.

Mathematical objects are perceived just as trees or cars.

 

[vectorcube]

you also did not get what I was saying.

math is not separate from the world and the world is not contingent. Only knowledge from sense experience is contingent.

I am not sure what you mean by mathematical reasons or why reasons at all have anything to do with math or physics.

Wrong. I do get what you are saying, and i can tell you that you are no different that what the ancient greeks, kelper, rationalist and common people think about the relationship between math& physics. Namely, there is no difference whatsoever. The Ideas that one could make some equations up because it is beautiful, and that it would apply to the real world is extremaly misguided.

In reality, people go on in the real world, makes observations, and described the regularities they see using math, and tease out the consequence of the mathematical description.

math is not separate from the world and the world is not contingent.


Tell me how? Give me a single example, and i will shut the hell up. What you are saying here is no different as saying that the laws of physics is logically necessary, but that is the same as saying it is logically impossible to have a world in which E=Mc^3.

There are infinite many ways which reality could be different. It is entire possible that there is a world govern by a 2-d cellular automata. I suppose the people in such a world could easily figure out the symmetries, and laws. Still, it would be a world.

 

[wofsy]

Wrong. I do get what you are saying, and i can tell you that you are no different that what the ancient greeks, kelper, rationalist and common people think about the relationship between math& physics. Namely, there is no difference whatsoever. The Ideas that one could make some equations up because it is beautiful, and that it would apply to the real world is extremaly misguided.

In reality, people go on in the real world, makes observations, and described the regularities they see using math, and tease out the consequence of the mathematical description.

math is not separate from the world and the world is not contingent. Tell me how? Give me a single example, and i will shut the hell up. What you are saying here is no different as saying that the laws of physics is logically necessary, but that is the same as saying it is logically impossible to have a world in which E=Mc^3.There are infinite many ways which reality could be different. It is entire possible that there is a world govern by a 2-d cellular automata. I suppose the people in such a world could easily figure out the symmetries, and laws. Still, it would be a world.

I do not think that math and physics are identical. But to say that math is just a tool is a blind assumption. I do not view ideas and sense data as existing in two different worlds as say Plato did. That is the whole point that I am making.

You say there are many possible universes. Well that is not a contingent statement and I don't think that you know that.

That there are many possibilities that we can conceive of does not mean that there are actually many possibilities. And even if there were, they would all be distinguished in their intrinsic mathematical laws.

Further the many possibilities would have to be connected through a universal law.

 

[vectorcube]

You say there are many possible universes. Well that is not a contingent statement and I don't think that you know that.

I am saying that there infinite many ways things could be for the universe, and that is what makes it contingent. There could be a universe described by cellular automata, but we do not happen to live in such a world. Mathematical propositions are true in all possible worlds, and that is what makes it necessary.

That there are many possibilities that we can conceive of does not mean that there are actually many possibilities.

I do believe some form of modal realism. You are correct that possibilities only exist if something actually exist. My point that is that there on logical reasons for excluding these worlds based on logic, and logic alone.

And even if there were, they would all be distinguished in their intrinsic mathematical laws.

Something like every possible world corresponds to a fundamental equation of some specific form. I am sure if you open yourself, you see that the world of "harry potter" is logically possible, but there is no governing dymanical law.

Further the many possibilities would have to be connected through a universal law.

Not so. Suppose for a contradiction that such a law exist that govern the entire ensemble of universes. Say law U. But U and -U is also logically possible. Thus, -U would govern it `s own possible ensenble. contradiction.

Here is the thing you need to know. For a law of nature L, -L is a logically possibility.
For a mathematical proposition P, -P is logically impossible.


You benefit greatly by reading Nozick ` s principle of fecundity.

 

[arithmetix]

Some few hours ago, from a distant time zone, I stated that math is a language and met with disagreement.
I have found that until a student understands that 'divided by' (maths) translates to 'per' or 'for every' (english) he will make no progress, but that to show a student that equivalence is to set his feet on the road of understanding the process of division.
Given that the four arithmetical operations are the foundations of the most popular mathematical truths, and that they are explicable in English, it seems to me that the mathematical representation of those truths is no different to the English exposition of them.
Hence mathematics is a language.

 

[Pythagorean]

yes - but I do not agree that math is a language - i agree that we can talk about it and think about it - to say that a 4 dimensional projective space is just just a word in a language with some grammar is just like saying that a tree is just part of a language.

Mathematical objects are perceived just as trees or cars.

Perhaps you underestimate language. Check out linguistic relativity. The wiki on it has some notes on the empirical research involved.

Also, out of curiosity, what is your academic standing in mathematics?

 

[wofsy]

Perhaps you underestimate language. Check out linguistic relativity. The wiki on it has some notes on the empirical research involved.

Also, out of curiosity, what is your academic standing in mathematics?

no academic standing - been reading on my own and sitting in on classes. Great fun.

 

[Pythagorean]

no academic standing

I'm probably not the first to tell you, but as someone who does have an academic standing in physics, I can tell you that mathematics doesn't perfectly describe things in physics. It describes things much better than traditional language does, it's more descriptive in terms of quantification and it's more complex, allowing it to be used to discuss a lot of different situations, but it's still very much a language.

The real universe, however, is very stochastic, and we generally take advantage of the convenience of approximations and where we can, waving our arms about and saying "this mathematical relationship is only good in this situation and only to this accuracy."

Even in quantum mechanics, after the initial groundwork is laid down... it's approximation after approximation after approximation to get to a model of real world applications.

 

[wofsy]

I'm probably not the first to tell you, but as someone who does have an academic standing in physics, I can tell you that mathematics doesn't perfectly describe things in physics. It describes things much better than traditional language does, it's more descriptive in terms of quantification and it's more complex, allowing it to be used to discuss a lot of different situations, but it's still very much a language.

The real universe, however, is very stochastic, and we generally take advantage of the convenience of approximations and where we can, waving our arms about and saying "this mathematical relationship is only good in this situation and only to this accuracy."

Even in quantum mechanics, after the initial groundwork is laid down... it's approximation after approximation after approximation to get to a model of real world applications.

Approximations do not mean that there isn't a mathematical underpinning to the universe. Quite the contrary. By the way, pulling academic rank is in my view inappropriate to this conversation. Do you just want me to stop thinking and take your word for it?

A physicist once told me that rather than physics and mathematics being approximations to observed phenomena, the opposite is true. Observed phenomena and their explanations are approximations to the correct physics/reality.

 

[Pythagorean]

Approximations do not mean that there isn't a mathematical underpinning to the universe. Quite the contrary. By the way, pulling academic rank is in my view inappropriate to this conversation. Do you just want me to stop thinking and take your word for it?

A physicist once told me that rather than physics and mathematics being approximations to observed phenomena, the opposite is true. Observed phenomena and their explanations are approximations to the correct physics/reality.

no, I want you to take some classes and think about it for yourself after you've had some exposure to it.

Your last sentence in your last paragraph, I agree with, by the way. But in my case, it contributes to my point. I don't see it as an "opposite".

 

[wofsy]

no, I want you to take some classes and think about it for yourself after you've had some exposure to it.

Your last sentence in your last paragraph, I agree with, by the way. But in my case, it contributes to my point. I don't see it as an "opposite".

What classes do you suggest. I have taken a course in Quantum Mechanics, General realtivity, have read Feynmann's Lectures on Physics.

BTW On a Riemannian manifold with a potential function the metric can be modified so that the paths of particles in the presence of the potential are geodesics. Why can't this be done with the gravitational potential and give another way to do GR?

 

[arithmetix]

I reply to this message:
[yes - but I do not agree that math is a language - i agree that we can talk about it and think about it - to say that a 4 dimensional projective space is just just a word in a language with some grammar is just like saying that a tree is just part of a language.
Mathematical objects are perceived just as trees or cars.]

My answer:
I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

 

[wofsy]

I reply to this message:
[yes - but I do not agree that math is a language - i agree that we can talk about it and think about it - to say that a 4 dimensional projective space is just just a word in a language with some grammar is just like saying that a tree is just part of a language.
Mathematical objects are perceived just as trees or cars.]

My answer:
I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

Why isn't everything in principle known about the tree? Or why isn't there anything about the tree which is in principle knowable? Or if there is nothing in principal that is knowable about the tree then how can we form a theory about it? Or isn't any theory that successfully predicts new experiments just a theorem and in principal knowable?

 

[vectorcube]

Approximations do not mean that there isn't a mathematical underpinning to the universe. Quite the contrary. By the way, pulling academic rank is in my view inappropriate to this conversation. Do you just want me to stop thinking and take your word for it?

A physicist once told me that rather than physics and mathematics being approximations to observed phenomena, the opposite is true. Observed phenomena and their explanations are approximations to the correct physics/reality.

You should reply to me in what i said on post 138.

 

[vectorcube]

Perhaps you underestimate language. Check out linguistic relativity. The wiki on it has some notes on the empirical research involved.

Also, out of curiosity, what is your academic standing in mathematics?

It is not necessary falses. Mathematical platonism do see mathematical proposition as being descriptive. There is nothing incoherent about this idea.

 

[vectorcube]

My answer:
I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

This makes no sense to me. If math is a map, then it is a composite of many maps of which one correponds to reality. That is to say, our universe is a mathematical structure describle captured by some axioms.