Euler's Equation: A sign from god?

[inquire4more]

I guess computers always existed too ! It just took someone to put the necessary pieces together...after all, there is a non-zero probability that a Thinkpad could have been created in a dust storm.

A computer is an entity, not an idea or truth. The truth of the statement 1+1=2 holds, ireespective. One object added to another object give us two such objects. We may have given names to the number, but we did not invent number, or truth.

 

[eNathan]

What a coincidence, I was just reading up on Euler's equation, and I check out physicsforums (considering starting a new thread), and there it is already.

Math is both an invention and a discovery. We invented our mathematical system based on the consistency logic which we observe in the universe. This consistency and logic existed before humans did, but we invented our systems of math to define it, if you will. But that's just my theory =)

By the way, Jin, I think what people here have tried to express is that the reason why the constants i and pi work soo beautifully in that equation is because they are already related. They are not just totally random, un-related constants. But I was thinking the same thing too when I saw the equation. That is like saying "why does e=mc^2, the equation is too perfect" -- I already asked this question, and as it turns out, it's merely because the units of joules were designed to work perfectly like this.

 

[Tide]

A computer is an entity, not an idea or truth. The truth of the statement 1+1=2 holds, ireespective. One object added to another object give us two such objects. We may have given names to the number, but we did not invent number, or truth.

You're saying that something physical is less real than an idea or truth both of which you further imply exist without mind. Did the corner that you just boxed yourself into always exist or did we just now discover it?

 

[inquire4more]

You're saying that something physical is less real than an idea or truth both of which you further imply exist without mind. Did the corner that you just boxed yourself into always exist or did we just now discover it?

If that corner I'm in is an idea, then it was always there...
In all seriousness, I do not imply in any way that physical entities are any less real. I only state that some things, though not all, require a construction for their existence as such. A computer requires a construction of its form from the material parts to exist, but the concept of number, or perhaps another such thing, reuires no such construction. Three computers is exactly three computers, whether we define a "three" or not. Take that, intuitionist!

 

[matt grime]

But an assmeblage of parts into a functioning computer is a computer irrespective of whether we define that or not.

You are commiting the cardinal sin of assuming that our western ideas of mathematics are absolutely correct, the ideal state of affairs, and just waiting for us to discover them. Many peoples have managed prefectly adequately without inventing the classfication of sets according to cardinality.

There is no right or wrong interpretation on that one, however mathematics is more than just saying '3 oranges' it is disassociating the 'threeness' from the 'orangeness' of the objects that is important, the idea that somethings can be discretized and that this is useful and independent of the objects is the achievement of mathematics.
I like the Blackadder thing:

Blackadder: If I have two beans, and I add two more beans, what do I have?

Baldrick: A very small casserole.And then there is the fact that mathematics is of course far more complicated than simply the natural numbers (though they are complicated enough - you might want to ponder what the natural numbers really are, and learn about the Peano Axioms; there are statements that are true about the natural numbers that do not follow from the axiomatic description of them, I think google and wolfram can help you there).

 

[Tide]

Inquire,

Take that, intuitionist!

LoL! I've been called worse. :)

So, did intuition always exist also? Like numbers, intuition requires mind.

 

[master_coda]

I think the idea that ideas have an existence independent of the human mind is an idea that doesn't have an existence independent of the human mind.

 

[fargoth]

if math is the way the universe works we didnt invent it, but i think that's not the situation.
math is a language in which we find it easier to look at the universe, it can't give all the answers (unsolvable problems).
and the basic assumptions we made inorder for our math to describe the world aren't given from the heavens, if we would have lived in a different universe where two parallel lines cross each other we'd have to invent different math...

 

[tmc]

A computer is an entity, not an idea or truth. The truth of the statement 1+1=2 holds, ireespective. One object added to another object give us two such objects. We may have given names to the number, but we did not invent number, or truth.

1+1=2 holds only because we defined it as such.

Of course, we defined it as such because it seemed like the most logical way to do it. But we still defined it.

 

[Zurtex]

To me it seems that Euler's Equation is more that we have a well set up notation. If we can express complex ideas in short meaningful notation then surely this is good?

 

[matt grime]

The truth of the statement 1+1=2 holds, ireespective. One object added to another object give us two such objects.

One drop of water added to another drop of water often gives us just one drop of water. One pile of stones added to another pile of stones is often just another pile of stones. Need I go on?

 

[saltydog]

The book, "Where Math Comes From" explores the Euler relation. Now . . . can I get off the subject too:

Over time I've grown increasingly convinced mathematics is created within the human mind. The illusion of it's discovery is but a reflection of a common origin of mind and number. From this perspective, I believe it important to judge mathematics within the context of Darwinian evolution of the human brain. I look outside my window and see a world massively non-linear at all scales. A non-linear brain evolved as a successful survival strategy for coping in such a world. And from that brain, the (non-linear) metaphors of mathematics emerge as one more survival strategy. I don't believe there is any math out there, rather only dynamics exists in the Universe, and because of the Darwinian synergy between nature and mind the metaphors we create to describe that dynamics become so successful that we erroneously conclude they're discovered.

 

[inquire4more]

One drop of water added to another drop of water often gives us just one drop of water. One pile of stones added to another pile of stones is often just another pile of stones. Need I go on?

I see your point, but I contest it. Two piles of stones dumped all together does indeed make just a larger, singular, pile of stones. But these piles are not irreducible. And, in any course, we may say that we have created a pile with twice as many stones as either of the two earlier piles. If I am following the argument of you lot correctly, were there no consciousness, then one stone and one stone would then not make two stones? Someone once told me that I didn't give mankind enough credit when I begrudged him his invention of mathematics. It seems to me you guys give us too much credit. The universe continues to operate, even without humanity. And one stone added to one stone gives two stones, whether I say it is so or not.

 

[Orefa]

But a bunch of stones is not mathematics. Stones may (or may not) be part of reality, but math is little more than the language and methods used to discuss it. Furthermore math, like natural languages, can be used to discuss concepts that do not even exist in nature just by changing a few initial postulates. I don't see how it can be said that math exists all by itself.

 

[matt grime]

I see your point, but I contest it. Two piles of stones dumped all together does indeed make just a larger, singular, pile of stones. But these piles are not irreducible. And, in any course, we may say that we have created a pile with twice as many stones as either of the two earlier piles. If I am following the argument of you lot correctly, were there no consciousness, then one stone and one stone would then not make two stones? Someone once told me that I didn't give mankind enough credit when I begrudged him his invention of mathematics. It seems to me you guys give us too much credit. The universe continues to operate, even without humanity. And one stone added to one stone gives two stones, whether I say it is so or not.

Philosophy has no absolutely right or wrong answers, but in this case you might want to ponder what a collection of stones is? when do two single stones stop being one stone and another stone and become two stones?

The mathematics of it is the counting and the divorcing the counting process from the objects involved, ie we can compare a collection of two stones and two apples and note that they have a common property, twoness, but what is that twoness really? is it something they have? what do i mean by have? I don't know, to be honest, but the day i stub my toe on something that *is* the number 2 i'll become a platonist. this is probably grossly misrepresenting the position of platonists. however as a good scientist occam's razor tells me to discard any unnecessary hypotheses, and that things have an existence in a platonic realm is unnecessary to do maths.

 

[roger]

Philosophy has no absolutely right or wrong answers, but in this case you might want to ponder what a collection of stones is? when do two single stones stop being one stone and another stone and become two stones?
The mathematics of it is the counting and the divorcing the counting process from the objects involved, ie we can compare a collection of two stones and two apples and note that they have a common property, twoness, but what is that twoness really? is it something they have? what do i mean by have? I don't know, to be honest, but the day i stub my toe on something that *is* the number 2 i'll become a platonist. this is probably grossly misrepresenting the position of platonists. however as a good scientist occam's razor tells me to discard any unnecessary hypotheses, and that things have an existence in a platonic realm is unnecessary to do maths.

It doesn't matter what it *is* all that matters is how it behaves.

 

[inquire4more]

Philosophy has no absolutely right or wrong answers, but in this case you might want to ponder what a collection of stones is? when do two single stones stop being one stone and another stone and become two stones?

Now, there you have given me some food for thought which I will mull over for some while and if I come to some conclusion I will get back to you. Don't hold your breath.

that things have an existence in a platonic realm is unnecessary to do maths.

You are quite correct here. I simply enjoy the existence arguments and this thread seemed appropriate.

 

[Mindscrape]

Icebreaker, math existed before we discovered it, and it will exist long after we're gone.

How so? The math as a way of thinking and describing things might have been discovered, but our axioms and such were definitely invented. We could have math other than base ten math, as I think either the Mayans or Babylonians did (base 8?).

 

[mathwonk]

when does one post appended to another pile of posts become simply a pile of----?

 

[masudr]

when does one post appended to another pile of posts become simply a pile of----?

After this post!

 

[gravenewworld]

Phi is actually also thought to be of "divine" influence. Curiously, if you take the sine of 666, you get exactly 1/2 the negative value of Phi, or what some people call the "anti" phi.

 

[ksinclair13]

Dan Brown talks about the divine qualities of phi in one of his books (either Angels and Demons or Da Vinci Code). It's actually very interesting.

I, like many, believe that math was invented and not discovered. However, I just got to thinking about irrational numbers. For instance, the digits of pi exist, but we have not yet discovered all of them. This isn't a good argument though, so I continue to believe that math was invented.

 

[masudr]

We imposed our invented structures onto the world. Hence it may appear that the results come from nature, but actually we said what a circle is in the first place, and of course the ratio between circumference and diameter should be the same -- we defined all circles to be similar shapes.

 

[HallsofIvy]

Phi is actually also thought to be of "divine" influence. Curiously, if you take the sine of 666, you get exactly 1/2 the negative value of Phi, or what some people call the "anti" phi.

Please don't say "Phi is actually also thought to be of "divine" influence" without saying BY WHOM that is thought! I seriously doubt that there are very many people today who think that.

 

[Doodle Bob]

For instance, the digits of pi exist, but we have not yet discovered all of them.

Actually, we have: they are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

 

[eljose]

this someway makes me laugh...although i,m a bit agnostic rather than 2believer" this would not prove nothing but a beatiful number relationship..similar to the thousands and thousands that there is in math..

-The argument of the equation reminds me the "controversial" of the prove of good make by Mapertuis and supported by others in the sense that for all good physical theories there is a variational principle in which the action S is minimized in the sense \delta{S}=0 then we have recalling Euler,s equation another identity:

e^{2i\pi}-1=0 would it prove the existence of evil?..

i didn,t want to offend anybody...of course i would like that god or something similar forgiving and almighty entity existed and gave us the "Garden of Eden"...

 

[ksinclair13]

Thank you Doodle Bob for clearing that up for me.

 

[-Job-]

If every coincidence is a sign from God, then not only does God give out random and possibly contradictory signs, but since we can define structures and produce events that will purposedly lead to coincidences, then we are able to tell God what signs to give us.

 

[Jimmy Page]

If one dinosaur met another dinosaur there were 2 dinosaurs, surely?

 

[Hurkyl]

Well, this thread has run its course (the mathematical content anyways), so I'm going to lock it, so there's no more necromancy. If anyone wants to continue the philosophical discussion, feel free to start a thread in the philosophy of math forum.