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General Interest > Philosophy, Sociology & Psychology
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How do we know math is universal?
    #3049354 -

How can we really know human mathematics is right? And is it really universal?

Yes mathematics works and can be proved, but the fact is that it is something we have invented. What about an alien civilization that uses a totally different set symbols? They can have totally abstract symbols that in the grand scheme of things makes perfect sense. Maybe they have invented a different form of math that is allso characterized by perfect logic.
Sure one can argue that it doesn't matter what symbols you use because you will always utilize the same constant rules. But can we be sure?

What if their system is so complex that it wouldn't be possible to apply them to even the Pythagoras? What if there is another flawless system where everything come together in perfect harmony. What if the development of our number system prevents us from ever being able to discover it?


Any math geeks want to enlighten me?


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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049373 -

Maths works all around the universe. Just look through a telescope, 1 star + 1 star = 2 stars however far away you look. And replace those numbers with alien symbols if you will, the concept still holds.

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049382 -

i agree. maths is discovered, not invented. however different the symbols etc are, the point is the same. one whatever plus another whatever will always equal two


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Re: How do we know math is universal? [Re: deafpanda]
    #3049388 -

It makes perfect sense to us but what if some alien life form doesn't think in 1 and 2. What if the concept of a single unit of anything is unknown to them because in their universe they don't think linearly.


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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049399 -

i sort of see where you're coming from but that is too vague, at least for our understanding.


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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049406 -

Then you can say that maths is universal to linear thought but not necessarily other types.

Also, I remember a maths teacher at my old school doing a PHD in the philosophy of maths or something like that and he said that 2+2 doesn't always have to equal 4. There is some complex thinking behind it which I don't know and don't imagine i'll ever understand :P I'm not sure about this but I thought I'd throw it in.

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Re: How do we know math is universal? [Re: Zoso_UK]
    #3049418 -

thanks that put my mind at ease


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Edited by Shroomnoob (08/25/04 04:54 PM)

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Re: How do we know math is universal? [Re: Zoso_UK]
    #3049465 -

Then that guy takes a very contoversial position - there are few philosophers that don't believe that maths is universal.

Apparently there is a tribe somewhere that only uses the numbers "1", "2" and "many".

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049471 -

I was just freaking out thinking about if someone viewed the world in several dimensions where the sum of the parts doesn't equals the whole and where there where no start or end, yet was based on a constant rule set just as logical as 1+1=2


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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049484 -

math isn't complex.its simple.but all if it is sure beyond all of my understanding.

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049522 -

First what it "isn't." Math is not a "reality." It did not come down from the mountain on tablets written by God or anything. It isn't something you can point to and say, "Look, there goes a two. There goes another two! They are making a four!"

Math is simply a description of A reality. This reality as we perceive it.

Now to begin to prove that 2+2=4 you start with the axiom ax-1. Propositional calculus (axioms ax-1 3 through ax-3 5 and rule ax-mp 6) can be thought of as asserting formulas that are universally "true" when their variables are replaced by any combination of "true" and "false". The theorems of propositional calculus are also called "tautologies". Tautologies can be proven very simply using truth tables, based on the true/false interpretation of propositional calculus. This is called the "semantic" approach. Now all of this is based on Theorems. Using the basic science logic a theory can NOT be proven. It can only be dis-proven. At which time a new theory is devised that better fits the situation. So if 2+2=4 is based on interpretation and theories then there is a finite probability that 2+2!=4. This finite probability (governed by quantum phisics) shows that 2+2 may not always equal 4. Although it does at this time and this place does not make it always true.

Foot Note: There are 20,616 steps to proveing that 2+2=4 each of which is based on theorems.

The universe as we know it is both infinitely large in size as well as infinitely small. It encompasses 11, or more, dimensions and there is a possibility that there are an infinite number of universes. This excludes hyperspace, subspace, whichspace, etc. Science has shown that space, height, width, depth, gravity, and time itself are not constents in the universe. This simply leads one to conclude that with our limited observations, knowledge, and understanding of the whole, that any truth we may understand can easily be changed simply by placing our self some where else in the universe.

So human mathematics is just that, human mathematics. There are no grantees that any of this will work any place but here. Should we encounter a being that can see and comprehend 4 dimensions the math that he understands will be vastly different than our own. If only because it is a description of his reality.


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Re: How do we know math is universal? [Re: Cyber]
    #3049556 -

Thanks that makes total sense. I never really understood why "1 + 1 = 2" is a true statement about reality.


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Re: How do we know math is universal? [Re: Cyber]
    #3049562 -

*In this universe* maths is absolute.

You say that using "basic science logic" a theory cannot be proven. Maths is not science, maths is logic. Maths is made up of tautologies (2+2=4 is a tautology, for example, because 4 means 1+1+1+1, and 2 means 1+1)

Just as the statement "A vixen is a female fox" is necessarily true since vixen *means* female fox, 2+2=4 is ncessarily true because 4 means 2+2.

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049580 -

Math is the language of the Universe...it is not something we have "invented". We created symbols to describe the relationships and transformations in the language...but the concepts themselves are not something we can lay claim to.


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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

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Re: How do we know math is universal? [Re: trendal]
    #3049625 -

How do you know we are not merely sitting on the shoulders of giants? What if math is just the brainchild of the man who first though "1 + 1 = 2"? Maybe it isn't a universal system to describe reality. Maybe its just our way to bring order in to chaos.


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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049686 -

"Maybe" doesn't go a long way towards proving anything...

We know math is the language of nature because it (math) describes nature to a degree of precision not available anywhere else. The more we learn about math, the more we find that it describes nature.

Many times a new part of math will be discovered and then, down the road, we will learn that this "abstract" concept is actually a perfect description of a process/configuration in our Universe. The Fibonacci sequence, for example. The Golden Mean. The Euler Beta function. These were all well-known mathematical concepts (at least to mathematicians) long before they were found to describe, in some cases perfectly, various parts of nature.

In science, we don't believe in "coincidence". There is a reason for everything. So to have two seemingly separate areas intersect in such a profound manner...well it is very indicative of an underlying connection.


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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

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Re: How do we know math is universal? [Re: trendal]
    #3049742 -

I am somewhat familiar with Fibonacci's work and i cant deny that the correlation to nature is interesting. Personally i think its circumstantial at best.

If you ask me mathematic is a faith bases science.


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Re: How do we know math is universal? [Re: deafpanda]
    #3049748 -

deafpanda said:
*In this universe* maths is absolute.



Only when it works. Then it is just a discription of reality as we see it.

Example: There are a nominative number of inhabited worlds in the universe represented by N and the size of the universe is infinite represented by "OO"

thus the population of the universe is

N * OO = 0.0000

So far math says, you do not exist!

Quote:
You say that using "basic science logic" a theory cannot be proven. Maths is not science, maths is logic. Maths is made up of tautologies (2+2=4 is a tautology, for example, because 4 means 1+1+1+1, and 2 means 1+1)



So you are saying that there is no way for 2 = 1? hmm

a = b
a2 = ab
a2 - b2 = ab - b2
(a - b)(a + b)= b(a - b)
a + b = b
b + b = b
2b = b
2 = 1

Thus 2 = 1.

Quote:
Just as the statement "A vixen is a female fox" is necessarily true since vixen *means* female fox, 2+2=4 is ncessarily true because 4 means 2+2.


The problem is with the finite probility that 2+2!=4.

The base theories of quantum mechanics states It is part of the inner law of the concept that it should change in a given manner, that is, if left to itself in a given initial state, that it should continuously run through a given sequence of states, each one of which it reaches at a fully determined time.

Heisenberg uncertainty relation states.

Delta-x . Delta-p_x >= hbar.

If even at any given moment not all variables are determined by some of them, then of course neither are they all determined for a later moment by data obtainable either. This may be called a break with causality, it is nothing essentially new. If a classical state does not exist at any moment, it can hardly change causally. What do change are the statistics or probabilities, these moreover causally.

This only goes to show that 2+2 may not always equal 4.


You have to let go of the concept that truths and absolutes even exist. Our universe is a wonderfull and glorious thing, We as humans barley understand just how vast and complicated it is. To try to state that something that is true here is true everywhere does not do justace to the infinite possibilities that exist in the universe as a whole.


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Shop SMART, Shop S-MART!
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How to build a Martha
Self Healing Injection point lids
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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049749 -

If you ask me mathematic is a faith bases science.

Forgive me for saying it (as I mean no offense), but such a statement appears to be from a lack of understanding when it comes to math.


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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.

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Re: How do we know math is universal? [Re: trendal]
    #3049766 -

and you sound like an Immanuel Kant fan boy.

The prevailing schools of thought in the profession of mathematics have fulfilled their own philosophical prophesy: They can validate neither the foundation of their science nor the meaning of their methods.


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