Is Maths an underlying principle of nature or did it originate from our brain?

[deltabourne]

Why separate nature from man? What confuses me is terms such as "man-made" (well yes, I know the connotation they have). Isn't man part of nature? Even if math originated solely from our brain it would still remain an underlying principle of nature.

 

[Organic]

Even if math originated solely from our brain it would still remain an underlying principle of nature.

Do you think that our brain totally-included, half-included or totally not-included to the underlying principle of nature?

Can you demonstrate an abstract thought which is totally not influenced by reality?

Do you think that professional mathematicians can develop Math in one hand but on the other hand they say: "We don't care about reality when we develop our definitions"?

For example:

Speaking up for (some of ) the mathematicians: we don't care. If we did we'd be doing philosophy. Would the martians have derived that equation? Perhaps, perhaps not - they almost certianly wouldn't have devised the same way of presenting it, and we couldn't tell if they'd picked i or -i as their square root of -1, which they may have called something else anyway. That answer has a superficial and a non-superficial part to it.

There is a "philosophy" section to Physics forum and this probably belongs there.

Can we ignore our abilities to develop Math language by saying that our abilities to develop Math is not mathematical but a philosophical question?

Please be aware that not some of but most of the professional mathematicians have Matt's opinion on these questions, and the reason is very simple, beside learning Math in the universities they also learn from their teachers that the logical realm of "pure" Math has no connections with the real world.

And when we say: "the logical realm of "pure" Math has no connections with the real world", don't we use philosophy?

 

[matt grime]

But only you have said that the logical realm of pure mathematics has no connection with the real world, so I don't think we can say what we are using as we haven't said it.

Why don't you also quote the other part where I explain why (some, if not almost certainly most) mathematicians don't bother with the original question? Whether or not you are a platonist, formalist, logicist or other, it doesn't influence one jot how you do mathematics - when we solve a problem we all come up with the same answer, eventually.

You are confusing whether mathematics is part of reality or defines and exlpains parts of reality. We are talking about the ontological question of mathematics, what *is* it, not how well it models reality, and how much attention we need to pay to the physical.

The logical realm as you term it has plenty of connections with the real world - bundles over algebraic curves, projective varieties - very abstract and difficult stuff but appears to be useful in cryptography. The Riemann zeta function defined by a n analytic continuation of a construction very pure in nature, sorry, essence, may control (in fact does control) quantum chaotic states.

 

[Organic]

But only you have said that the logical realm of pure mathematics has no connection with the real world, so I don't think we can say what we are using as we haven't said it.

No dear Matt, my game is an open game because I clearly say right in the beginning of it that no theoretical system can fully use a part of reality as its input because the reality itself is always beyond the scope of any theoretical system.

Therefore any theory cannot be but a model of some part of the reality, and any model is no more than a trivial representation of the real thing.

And when I say that any theoretical system is nothing but a trivial representation of the reality itself, you have no choice but to understand that no theory can exists without reality influences on it.

We can develop our theories, but they will never be the reality itself, because if they are reality itself then you have no theoretical system anymore but only reality itself.

I am talking about what you call "Pure'" Mathematics, so please tell me what is the meaning of the word "Pure" and "Applied" when they are connected to the word "Math"?

I will never say that philosophy has nothing to do with Math because both of them are theoretical systems and both of them are influenced by reality.

So, please tell me how can you say:

Speaking up for (some of ) the mathematicians: we don't care. If we did we'd be doing philosophy.

 

[matt grime]

The distinction between pure and applied is hazy, as all these arbitrary distinctions have the the liability to become. Roughly, a reasonable slogan is that in Applied Maths, the answer is what counts, in Pure it is the method of arriving at the answer.

 

[Organic]

I will never say that philosophy has nothing to do with Math because both of them are theoretical systems and both of them are influenced by reality.

So, please tell me how can you say:

Speaking up for (some of ) the mathematicians: we don't care. If we did we'd be doing philosophy.

 

[matt grime]

I have, at least twice. here, for the final time, I will repeat myself.

Whatever your personal belief about the nature and ontological implications of the objects you work with in mathematics there is no practical difference between how you solve the problems that arise. Whether or not I believe that there is actually something that is n'ness for every n a natural number, and that addtion etc reflect the innate properties of this n'ness , or whether I treat them as abstract objects defined in whatever abstract way I chose (say the smallest rig generated by 1 element) doesn't alter how I define divisiblity and then prove there are an infinite number of indecomposable elements (primes). The advantage and necessity of the abstract approach is that without it you would be struggle to do almost any mathematics. If you don't believe me try and define the cotangent bundle of an arbitrary manifold.

So whatever philosophical position one takes about the nature of mathematics, and there are many, it doesn't affect one whit how you do maths, which is after all what mathematics is.

 

[Organic]

Also please tell me is it a wise thing to develop Math without any connections to questions and researches that try to understand, for example, our abilities to count?

 

[Organic]

So whatever philosophical position one takes about the nature of mathematics, and there are many, it doesn't affect one whit how you do maths, which is after all what mathematics is.

People of this forum, please look how the heart of science, which is the Math language, find its way step by step to become a closed and scholastic system that running after its own tail because it is used by, so called professional Mathematicians, that will not let anyone that not think exactly like them to touch or change anything in their new developed religion.

If we check the way of how religions were developed through the years we shell find that one of the stages is: "we don't care about anything that we don't do, because we have decided what we are doing and if you do not think exactly like us, you are not belong to we(=us).

Therefore go to philosophy, go to theory development and leave us alone."

 

[matt grime]

Is this going to help? When I say that as a mathematician I don't care about X as it is "not mathematical" that doesn't mean I don't care about X full stop. If I didn't care then how can I have a position as a formalist? Does Maths need a philosophy? Yes and No as the argument I read recently runs, and I can tend to agree with it. Where have I said that you cannot have a different opinion? I have said that the opinion you hold doesn't affect how you do mathematics only how you think about the nature of mathematics, they aren't the same thing. That is a different position from the one you are saying I espouse. I am trying to point out that whatever interesting philosophical arguments the question brings up, and there are many as I say, they don't alter what mathematics does, which in the Wittgensteinian view is what matters. What i *is* in a physical sense, if such a thing can be answered at all, does not alter the fact that all you need to know about it mathematically is that it squares to minus one.

 

[Organic]

I have said that the opinion you hold doesn't affect how you do mathematics only how you think about the nature of mathematics,

Show me the word "opinion" in my previous post.

I am not talking about opinions on Math.

If someone, which does not belong to the professional Mathematicians society,
tries to express ideas which are paradigm shifts in fundamental concepts like
Logic, Infinity, natural numbers, our ability to count, model and reality, real numbers,
the transfinite system, the connections between symmetry and information clarity-degrees, the relations between redundancy_AND_uncertainy as fundamental properties of natural numbers, and more..., immediately you will send him to philosophy or theory development forums.

Shortly speaking, professional Mathematicians society cares for itself much more than it cares for Math.

 

[matt grime]

Oh, right so you aren't debating from some objective position, you're working out some of the frustration you feel from having all your crank posts shifted somewhere else.

The you in that quote is the impersonal you, not you referring to, erm, you.

 

[Organic]

immediately you will send him to philosophy or theory development forums.

The important word here is "immediately", which means first you check if what someone says fits to your "holy books" and if not, immediately you will send him to philosophy or any other place.

Frustration, yes I feel it but not just because of my private case as a local point of view.

The global problem is that when I try to communicate with one of the members of the professional Mathematicians society, most of the times I find in front of me a religious and dogmatic person instead of an open minded scientist.

 

[matt grime]

perhaps if you tried to communicate with them using mathematics you might get further, just a thought.

 

[Organic]

There is not an objective unchaneged thing like Mathematics, unless Math Langauge is a dead system.

 

[matt grime]

You got to France and attempt to communicate by speaking Czech. You don't get very far. Whose fault is it?

 

[Lorentz]

You got to France and attempt to communicate by speaking Czech. You don't get very far. Whose fault is it?

What if the french language doesn't permit talking about anything else but France?

 

[Organic]

You got to France and attempt to communicate by speaking Czech. You don't get very far. Whose fault is it?

This is not a good example in my opinion.

My example is: we are both speaking English; we take some concept, infinity for example, and examine it together step by step by using English, after that we start to address our ideas by giving them notations but in any point we still connected to our understanding of the infinity concept, no matter if we are talking English or address it by special notations.

Shortly speaking, our understanding can be translated from informal(=non-special) to formal(=special) language and vise versa, without loosing our understanding.

Modern math says that there is a connection between the language you use and your ability to understand fundamental concepts like infinity.

I say that fundamental concepts are not depend on any language.

 

[matt grime]

You are confusing the philosophical and ontological debate about what maths *is* to each person and the reason why mathematicians label you a crank: it's not because you are thinking in a fundamentally different way but because you refuse to talk to them in their 'language' and adhere to the basics of formal mathematical discourse, and learn about the things you claim to know something of. You have not demonstrated that you have anything to say that is remotely interesting to them, and think it us up to them to meet you at your level, It isn't. But this is yet another debate on an entirely different topic, and isn't related to the underlying nature of what things in mathematics are, and whether they would be 'true' or 'exist' if we weren't here.

 

[ahrkron]

I think the initial subject has been addressed. Whether or not Organic's posts qualify as math is a different issue.

It has to be noted that (as even he has acknowledged several times) he uses math words to denote concepts that in no way correspond to their accepted definitions within math.