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Re: How do we know math is universal? [Re: Cyber]
    #3049769 -

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"

That is assuming that the Universe is infinite in size. This is most likely not the case. Though I do enjoy seeing fellow Shroomery members who have read The Hitchiker's Guide... :wink:


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.

This is a common "problem" given to math students to try and find where the flaw is. It's quite easy to do: the mistake is in step 4. When you divide out (a - b) you are dividing by zero which is not possible. This makes the rest of the work completely pointless, and the result of 2=1 is completely false.


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.
...

To be honest, I'm not even sure what you are trying to do here....it certainly says nothing about the validity of the expression 2+2=4.


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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: Scarfmeister]
    #3049773 -

To my knowledge, I've never read a word written by him...though I have heard of him before on many occaisions :smirk:


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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: Cyber]
    #3049787 -

Quote:
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 



I would argue that the universe is not infinite, partly for this reason.

As for that proof that 2=1, that is not true.  I have seen it disproved elsewhere, I can't remember how, but still :smile: I know you don't believe its true...

Quote:
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.




Sorry, I don't understand what you mean by "it".  Could you clarify?

As for your last comment, again I don't believe that the universe can be infinite, thus there aren't infinite possibilities.  There are lots of possibilities, but logic and the laws of physics makes sure there aren't an infinite number.

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Re: How do we know math is universal? [Re: deafpanda]
    #3049797 -

Maybe the universe isn't infinite in scope but time as we know it is infinite.


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We're the lowest of the low, the scum of the fucking earth!

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049800 -

What reason do you have to believe that time is infinite?

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Re: How do we know math is universal? [Re: deafpanda]
    #3049807 -

The "population of the universe" deal (which I'm sure was taken from The Hitchiker's Guide) also makes a bit of a mistake in thinking that N would be anything OTHER than infinity in a universe of infinite size. If the universe is infinitely large, then there must be an infinite number of planets. Only a certain percentage of those planets would be inhabited, yes, but any percentage of infinity is still infinity.

In an infinitely large universe, the population would equal infinity. This entire concept is a joke written by Douglas Adams.


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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: Scarfmeister]
    #3049814 -

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

Any math geeks want to enlighten me?


Godel answered this a long time ago. As a math geek, I shall enlighten you as to what he said, and add some of my own musings to it as well. Human minds are a very complicated and self-referential system, also known as loops. Naturally, as math is a system developed by the human mind to accurately predict the future by mirroring the model of our universe that the mind has created, it is also a self-referential system.
Godel proved, in his essay, that axiomatic logic (logic based on axioms, or projections that we beleive to be inherently true without proof) will never be able to fully describe any feild of inquiry. Also, he proved that all self-referential axiomatic systems of any complexity will inherently be capable of producing two true and contradicting statements. In other words, math WILL produce contradiction statements, both of which are true. Even derivations that use only cardinal number theory (a branch of math that involves all non-negative integers [0,1,2,3...]) will produce contradicting statements.
Now, what this means you to and me is pure speculation on my behalf. However, it is no great logical leap to understand that a system capable of producing two true and mutually incompatible statements is inherently flawed and innaccurate. I therefore consider math to be far from universal. However, as a tool, it is still pragmatic and the aforementioned contradictions rarely rear their ugly heads.


If you want an example, this is a favorite of mine. I was musing with this one back in high school, which lead me on my journey of mathematical inquiry and studies into meta-mathematics.

The square root of -1 is considered to be i. now, what is i^2?
there are two ways of thinking of this.

i^2 = sqrt(-1)^2 = -1

or

i^2 = i*i = sqrt(-1) * sqrt(-1) = sqrt(-1 * -1) = sqrt(1) = 1

We can logically conclude that i^2 = +1 and -1. A contradiction. Oddly enough, one of these answers is considered false by mathematicians because accepting it as true would cause their model of mathematics to be rife with contradictions and shortcoming.


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Re: How do we know math is universal? [Re: deafpanda]
    #3049832 -

Well.........time has neither a beginning or end, Its continuous and always in motion. Maybe time isn't a good choice of words since time really isn't a function of the universe. Maybe existence fits the bill better.


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We're the lowest of the low, the scum of the fucking earth!

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Re: How do we know math is universal? [Re: jux]
    #3049838 -

Interesting...

But the square root of 4 is +/-2, and that's not seen to be a problem?

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049845 -

Existence may well be "infinite", but the part of it that may be infinite, I would argue, must be outside our spacetime. We have every reason to believe and no reason to disbelieve that the rules that exist here exist everywhere else in our spacetime. We cannot speculate about anything outside of that.

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Re: How do we know math is universal? [Re: deafpanda]
    #3049860 -

That is because it won't cause problems later on.


sqrt(4) = 2
(2)^2 = 4

sqrt(4) = -2
(-2)^2 = 4

sqrt(-1) = i
i^2 = 1
sqrt(1) = 1 OOOOopss... can't get back to i!!!!

sqrt(-1) = i
i^2 = -1
sqrt(-1) = i AAAAahhh... safely back to i


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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049876 -

word and why does 2+2=4 and 2x2=4 whats sup wid that lol


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every thing dolo says is just for fun and should not be takin 2 heart i don't do drugs cause im a winner listen 2 my music http://www.soundclick.com/bands/9/febmusic.htm
na mean

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Re: How do we know math is universal? [Re: dolo]
    #3049891 -

Multiplication is just fast addition :wink:


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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: deafpanda]
    #3049894 -

if you make a circle(0) in the ground,there is infinte potential for anything to be in side of it.even the idea of the all universe being inside of that cirlce you drew would be acceptable.thats how i see the universe as being infinte.

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Re: How do we know math is universal? [Re: jux]
    #3049895 -

Ah, I see.

But since "i" doesn't describe anything that exists in nature, doesn't that just mean that its us humans messing it up?

Would you agree that, even if maths can be shown to not be universal, the underlying concepts are?

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Re: How do we know math is universal? [Re: Scarfmeister]
    #3049927 -

could we all agree that there must be one language to create an entire universe?here must be someway to define how to make thigns works and how to create them and such.

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Re: How do we know math is universal? [Re: deafpanda]
    #3049929 -

i^2 is the most convenient example I could remember off the top of my head. Whether or not it has any relation to actuall occurances in nature is unimportant, as it is derived from the same axioms that describe all of math.

Which leads me to your next question. My answer is a resounding 'no'. Math is based on axioms, axioms are accepted to be true, regardless of lack of evidence, because they are deamed to be self-evident. However, a look into eliptical geometry will show you that systems that function equally as well as our accepted standards can be composed of axioms that are contradictory to those axioms people currently hold to be self-evident. It is, therefore, no great stretch of the imagination to think that any form of axiomatic logic (read: math as we know it) is inherently flawed and innaccurate.
I have already extolled the value of math as a tool, but it should, as with all science and logic, be taken with a grain of salt.


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Re: How do we know math is universal? [Re: jux]
    #3049978 -

I'll take your word for it that "any form of axiomatic logic is flawed and innacurate", but let me ask you this:

The laws of physics can be expressed in maths.

If the laws of physics are universal, then surely it would follow that some of the underlying concepts that maths describes are universal?

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Re: How do we know math is universal? [Re: deafpanda]
    #3049992 -

well, I'm glad that you trust me, but, please, never take my word for it. Think about it, read up on it, research it, do some shrooms and think more about it.

Who says that the laws of physics are universal? They used to say that about newton's clock work universe. And what about all the anomilies we see now-a-days. I mean, modern theory states that at the center of a black hole lies a singularity, basically an infinitely dense and infinitely small point in which all the laws of physics break down. Or how bout at the quantum foam level, that's a whole different set of physical laws.


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Re: How do we know math is universal? [Re: jux]
    #3049996 -

I'm not talking about our best theories on the laws of physics. I'm talking about the *true* laws, whatever they may be. Surely there are natural laws, yes? And these natural laws could be expressed in maths, yes?

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