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Comment by kumarvvr | Hacker News Reader

Is the question

"Is math behind everything or is that anything can be explained with math?"

a valid question?

Even for "chaos" we have a chaos theory. Where we cannot apply function/formulae to physical phenomenon, math tends to use empirical calculation and theory to study systems.

Is is that the universe bends to math or math bends to the universe?

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I like how Bertrand Russell viewed that:

"Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover."

Math isn't behind everything, and not everything can be explained with math. But it happens that the things that are mathematical turn out to also be quite useful.

> not everything can be explained with math

Can you give me any examples? I'm curious.

infinity

Was that meant as a joke or am I completely missing the point here? Mathematics provides plenty of tools to work with infinities. In plural, because there are quite literally infinitely many different infinities, which we know thanks to maths.

there is no math for dreams

Couldnt it be modeled as electrical activity inside specific areas of the brain under certajn circumstances?

It's the same as: There are more real numbers than you can write down. (Everything you can write down using symbols can only be enumeratable many (you can enumerate all symbol combinations starting with single symbols), but there are uncountable many real numbers)

So now you say: Could you give me an example of such a real number that we can not write down?

Answer: No such example can be given because even e or pi or any other real number constructed by an equation is given by just inventing new (countable many) symbols (like π) or by writing down an algorithm which consists of countable many symbols.

So to answer your question: There could be problems that can not be explained by math but in the same way you might not even be able express/name/describe the problem.

If framed as a logical equation, wouldnt math explain or have an answer?

Sure, i may not write an answer, when thinking from an algebraic perspective, but i sure can answer it from a logical or sets perspective.

Perhaps the answer is an empty set?

I am not sure I understand what you are saying. If you are speaking of equations you are speaking of symbols right? (∧,∨,¬,...) Whose combinations are only countable many.

The answert to what is the empty set?

>Could you give me an example of such a real number that we can not write down?

Thst this is a question without any answer can be quantified as a logical equation. The question might not have an answer that is a number, but has a superseding answer thst it is not logically consistent.

Well the answer to: > Could you give me an example of such a real number that we can not write down?

Is clearly: No, I can not.

But the answer to the question "Are there real numbers that can not be written down in _any_ way" is clearly: yes. If the question is understood as "Is the set of reals bigger than the set of naturals?".

So there are cases in which the answer to "can you give me x?" != "is there an x?".

So back to you original question:

> > not everything can be explained with math > Can you give me any examples? I'm curious.

I guess nobody might be able to give you any examples but they could still exist.

The same is true for functions. There exist many more functions (eg ℕ→ℕ) than you can write down because the powerset of ℕ is bigger than ℕ. So it could be that there could be a physical law that the property X of an object is a function of property Y but that function is one which we could not even see as a function because we can not encode it in symbols and probably our brain would not even recognize it as function at all (?)

I’m not sure exactly what you mean by your challenge, but there are several standard examples of noncomputable numbers.

because even e or pi or any other real number constructed by an equation

Not true. Most real numbers cannot be constructed at all [1] [2]. There is some interest in replacing the mathematics of real numbers with computable numbers, but this adds additional complexity to analysis (requiring a computable modulus of convergence).

[1] https://en.wikipedia.org/wiki/Computable_number

[2] https://en.wikipedia.org/wiki/Specker_sequence

Yes that's what I was trying to say with the later part of my setence you quoted:

Only coutable many real numbers can be given by name (like pi) or by an algorithm. But there are still many more numbers left which you can not name/point to/give as example.

I think this is an example: Math works well for electronic circuits, but it doesn't work well for psychology. Maybe coincidentally, we can predict circuits but not people.

I'm surprised by the downvoting on this thread. Kumarvr asked for examples of things math doesn't explain. Simple examples of things math doesn't (at this time) explain (e.g. psychology; dreams) were downvoted.

Why? There's no way to know why. Just downvotes. Maybe someone thinks math explains physics, which explains [...], which explains dreams. Maybe that's not it at all. Who knows?

I can only speak for myself here, but silly downvotes are the primary reason I'm disengaged with this otherwise really great site.

> "Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover."

Math isn't behind everything, and not everything can be explained with math.

Without myself making any claim about whether maths is or isn't behind everything....

that we may only be able to discover mathematical properties does not itself justify saying that "Math isn't behind everything, and not everything can be explained with math."

There is a large amount of work (I don't know what would be a complete proof for this) behind the idea that anything we can explain, we can do so with math. If we can't explain something with math, we can't explain it, period.

It's just an incredibly flexible tool.

Perhaps that points to our cognition being a mathematical product.

Are there ways of understanding things in a non-mathematical - meaning non-cognitive - way? Is there something greater than Turing Completeness?

Such an idea is silly because we're using reason to fathom the answer.

When we encounter some sort of alien cognition out there which is beyond the bounds of math, it either will be understandable and expand our mathematical vocabulary as we seek to formalize it...

Or it will look just like gibberish and passed off as 'too chaotic, or too self-referential', or some other unfathomable quality.

They are two different questions and both kind of true in my opinion.

You can use math analyse anything and say try running regressions on interest rates but that the reality is different from the equations and made of people doing stuff.

In particle physics you get things matching the equations so accurately that one might suspect that the reality actually is math.

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