RE: How Much Do You Really Know? (Full Version)

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FullCircle -> RE: How Much Do You Really Know? (4/25/2008 5:16:49 PM)

You can't prove that anything is infinite can you? How do you go about that exactly?




LondonArt -> RE: How Much Do You Really Know? (4/25/2008 5:24:52 PM)

quote:

ORIGINAL: FullCircle

You can't prove that anything is infinite can you? How do you go about that exactly?

It's pretty easy to prove that there are an infinite quantity of prime numbers, Euclid managed it quite a while ago. The proof runs thus:
Consider any finite set of prime numbers. Call the product of this set P. P +1 will not be divisible by any of the primes in the set, doing so would give a remainder of one. Therefore either P+1 is itself a new prime, or it can be decomposed into a prime that was not present in the original set. As a result we can always produce a new prime, and thus can always increase the size of our finite set, and create a new prime. Therefore there are more primes than any finite number can be used to count.

There are  few other proofs for the infinity of the primes, but that should do. Also see above for a discussion of Cantor's Diagonal Argument, which by extension proves the existence of an even larger infinity.




FullCircle -> RE: How Much Do You Really Know? (4/25/2008 5:38:50 PM)

Very interesting but when you give space the quality of being infinite you are really using that word only to describe something beyond your understanding, something beyond your ability to measure. It does not make something infinite just because you can't measure it.

An even larger infinity? Qualative +1? Pure maths eludes me; I’ve always been more into the applied kind. Prime numbers, why is it people find them so fascinating? The problem with pure maths is that all it really proves is theory.

Maybe I should have said "it may just be a large number for all we know."




Griswold -> RE: How Much Do You Really Know? (4/25/2008 5:45:24 PM)

I actually know everything.

(And, I also know why you asked that question).




LondonArt -> RE: How Much Do You Really Know? (4/25/2008 5:46:09 PM)

quote:

ORIGINAL: FullCircle

Very interesting but when you give space the quality of being infinite you are really using that word only to describe something beyond your understanding, something beyond your ability to measure. It does not make something infinite just because you can't measure it.

An even larger infinity? Qualative +1? Pure maths eludes me; I’ve always been more into the applied kind. Prime numbers, why is it people find them so fascinating? The problem with pure maths is that all it really proves is theory.

Maybe I should have said "it may just be a large number for all we know."


Indeed, reliably applying the term infinite outside of maths is a lot trickier. It might be better to describe the universe as functionally infinite. If you follow the Big Bang theory through to Chaotic Inflation, which is fairly popular at the moment, our universe is an expanding bubble inside an unstable vacuum. As the vacuum's collapse and expansion is both constant and not constrained by light speed, the boundaries of our bubble are continually moving away faster than we can expand towards them. For all practical purposes, any finite limits cannot be observed, and cannot interact with us.

Infinities have different cardinalities, known as their Aleph numbers. Infinities of Aleph One (all the real numbers say), are not simply Aleph Null sets (say, all primes) plus one extra number, they're functionally larger, you cannot map them onto a direct relationship with the integers.




Real_Trouble -> RE: How Much Do You Really Know? (4/25/2008 6:07:16 PM)

quote:

Earth is the center of the universe.  Prove me wrong.

1) I see the sun and moon circling us, every day and night, we must be in the center.
2) There are stars all around us, we must be in the center.
3) Assuming space is infinitely large, we can travel infinite miles in any direction.  Since we can go exactly the same amount right as we can left, we must be in the center.


I hate to do this, but...

1) Any rotational motion would necessarily provide this as possible.  For example, having the earth rotating and the sun stationary would provide the same effect; you cannot determine motion  from a single point.  This is why things like triangulation are so important.  All you have managed to prove here is that there is motion of some kind occurring, or the illusion thereof.

2) Given a dense enough three dimensional spread, any location within a group of stars would have stars all around it.  This is not proof of a center, it is merely proof that we are not at the precise edge of a galaxy of stars (or multiple galaxies of stars).

3) How do you actually know this?  We aren't even totally sure space is infinitely large.  To quote Einsten: "I know of only two things which are infinite, space and human stupidity, and I'm not sure about the former."

I reject your claim of being able to travel in equal distances either way until you actually provide me evidence of having done so.  I believe this is a baseless claim; we suspect but cannot prove space is infinite, and in that context, every single point would be the center by your criteria.

So to counter your points:

1) You see the sun and the moon, but have you considered Venus?  In a geocentric solar system model, as Venus rotates around the sun, we would only be able to see the various solar phases as crescents, not full illumination.  In theory, Venus should remain between the Sun and the Earth during the orbit around the earth (unless you are positing non-circular, non-elliptical orbits, which would raise further questions about your initial sun assertion).  Experimental evidence disconfirms this.  We can observe Venus in full illumination as it rotates around the sun, giving evidence to the fact that, actually, it's probably the sun in the center of our rotational system.

2) Technically speaking, you have provided no evidence that the universe is actually filled with stars!  What if we posit a vast open space, in which one corner is filled with stars, and we are situated merely somewhere within that corner?  Of course, we would see stars, and they would be all around us, but no point within the star-field would actually be the center of the universe.  There would be a vast void surrounding it, and somewhere in that void would be the "center".

3) You've also not defined what a center is; are we talking the gravitational center in terms of a balance point of mass spread in every single direction, or are you talking about a distance-based center, in terms of the actual physical location of the center-point of the universe.  We can take a swag at the latter, based on the motion of all of the objects in the universe outwards (which is also evidence of the big bang), and if you review the accumulated research and experiments on the subject, it's clearly not us.  In fact, the earth appears to be moving very quickly AWAY from many other objects, and not at a uniform pace from all objects that would leave us at anything resembling a center.

I'm not going to bother to re-discuss virtually every major astronomical study of the past 100 years in this text box, if that is what you were hoping for, but some pretty basic use of google should enable anyone to do enough research to falsify the claim that the Earth is in the center of the universe.  It might, depending on definition, even falsify the claim that the universe has a meaningful center.




Raechard -> RE: How Much Do You Really Know? (4/25/2008 6:29:57 PM)

Good point about the centre being either the centre of mass or distance but there is a third definition:

Does he mean the centre in terms of the origin location of the big bang: because we all know that explosions can happen in non uniform ways spreading debris further one side than the other? It’s interesting to ponder why the big bang would produce an asymmetrical scatter pattern if there were no external forces acting to constrain the initial explosion.  It would suggest an asymmetrical lump of mass?

I was always more fascinated about the cause rather than the aftermath. What would cause such an explosion? Is it the case that an asymmetrical universe stops expanding and will then be drawn together in the exact same formation as it started?

This would bring a whole new meaning to the term infinity: it was it always will be. Funny if an explosion happens time and time again the same way and all actions are the direct result of that initial explosion, then surely we will all come to exist the same way and die the same way time and time again. All our actions are carried out as a direct result of others actions and the way we see the world around us. These two things can be constants.




HeavansKeeper -> RE: How Much Do You Really Know? (4/25/2008 7:45:49 PM)

quote:

ORIGINAL: bipolarber

Hope it helps you with your Astronomy final. (Which you are obviously fishing for
answers for.)


Now that hurts.  But in light of your accurate and understandable answer, you are formally invite to the next "Prove Me Wrong."  May I only suggest that when we try to prove that
1+1=/=3, you do not accuse me of needing help on my theoretical mathematics final.




HeavansKeeper -> RE: How Much Do You Really Know? (4/25/2008 7:54:49 PM)

I am defeated. 

I hope some of you learned a little.  I learned about a few things, mostly concerning infinity. I suggest we do another "fact."  anyone else want to start?




FullCircle -> RE: How Much Do You Really Know? (4/26/2008 4:20:28 AM)

I've said this before but you can prove 1+2=2 in remote areas of the world where the mathematical language of the culture only allows for two things and anything more than two things is still regarded as two things.




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