Topic awaiting preservation: It's all done with mirrors

I was thinking (maybe a little too hard) but if you were to take two mirrors and set them up as though they were pages in a book rotating around a center point, set them both at 180 degrees of one another, and slowly turn the two mirrors toward one another and begin counting how many other mirrors appear in that mirror per degree turn until they both sit at the same angle, could one not calculate infinity?

Just a thought....



Maskkkk

- Face the Present

Not really, since infinity by definition is unquantifiable.

It is a common misconception that infinity is a number, or that it can be handled as anything other than a concept.

It's like the question of what would happen when an unstoppable force met an immovable object. The answer is that they could not both exist in the same universe, since the definition of one would contradict the other.

Yeah, the moment you counted up to infinity... it would no longer be infinity because by definition you can never count that high. Interesting way to think about the problem, how did you come up with the mirror example?

. . : slicePuzzle

I was in my bathroom tilting the pair of mirrors I have on my toothbrush cabnet when I noticed that the more you tilted the mirrors toward each other the number of mirrors in the mirror seemed to increase...*Shrugs* I mean I've seen it before but it just never occured to me the bit about the angles....



Maskkkk

- Face the Present

Any angle of any 2 mirrors that intercept creates an infinate number of reflected mirrors.

All things are immeasurable. Quantity is a fabrication devised to compensate the imperfections of the human mind.



::
~Existence is a mere pattern.~
::

aside from the problems already mentioned.......you couldn't possibly count all the mirrors in the reflections, as they don't end.

Now, infinity does get interesting, though... there's a book by Rudy Rucker called White Light, and it could best be described as "mathematical surrealism." He takes existing number theory and makes the examples come alive... anyway, one of the things I learned from that is that there are different levels of infinity. For instance, between 0 and 1 there are an infinity of partial numbers. But that's a smaller infinity than the infinity between 0 and 2, right? And yet, the very term is paradoxical. You can't have a "smaller" infinity, since infinity is infinite. But one infinity is definitely a subset of another.

So you've got "definable" infinities, ones that can be given a simple boundary. Then you've got the big crazy infinities, which get harder and harder to explain, until eventually the highest reaches of this "infinity theory" start to sound religious. Lest you say "well, it's a novel," most of the actual ideas come from respected mathematicians like David Hilbert. An intriguing read.

Yeah I think one of my teachers told me about that, I don't remeber how it goes, but it has something to do with Infinites stacked over top of one another, which makes them more inifate than infinite...

am I making any sense?



Maskkkk

- Face the Present

Perfect thunder: That's true, though the example you gave isn't the perfect example, since it could be shown that the degree of infinity between 0 and 1 is the same as that between 0 and 2, believe it or not.

Really? That's... strange. But then, virtually everything about infinity and its variations is strange. I don't pretend to really understand it.

Here's the proof for those who are interested:

Let's say I have two sets of numbers, A and B. If every element in A can be mapped to a unique element in B, and vice versa, then A and B have the same number of elements. For example:

A = {1,2,3,4,5}
B = {3,6,9,12,15}

If you take an element of A and multiply it by three, you get a unique element of B (for example, 2 * 3 = 6). If you take an element of B and divide it by three, you get a unique element of A (6 / 3 = 2). Therefore, we know that A and B have the same number of elements.

Of course, two sets can have the same number of elements and *not* have this property, but if they *do* have this property, then we can be sure that they have the same number of elements.

So here's the thing. If you take every number between zero and one [0,1] and multiply it by two, you get a unique number between zero and two [0,2]. And if you take something in [0,2] and divide by two, you get a unique number in [0,1].

So that's why there's the same "amount," if you will, of numbers in [0,1] as there are in [0,2].

But there is such a thing as degrees of infinity. For example, the infinity described by "the amount of rational numbers in [0,1]" is of lesser degree than the infinity described by "the amount of irrational numbers in [0,1]." The reason for that has to do with the fact that irrational numbers themselves have a sort of infinity built in. It's complicated =)

Okay, that hurts my head, but despite all common-sense logic, I have to admit that it's mathematically true. Bizarre!

Actually, there aren't an infinite number of mirrors...because, as anyone who has ever done the mirror thing knows, the reflections get smaller with each reflection...therefore, at some point, the reflection will be so small, that it will pass striaght through the material...or (if possible, with a really dense sort of material), it will eventually get smaller (well, not really, that would be the limit, actually) than the actual beam of light...so, it's not a 'real' infinity...it's finite.

All higher maths have the concept of infinity...I actually found the subject to be quite interesting, myself...but that's just me...



[This message has been edited by WebShaman (edited 12-08-2002).]

Actually WS, your sort of correct (and damn slime for getting here before me).

You see the only reason mirrors fade off the side is because we are looking at it from an angle. Take a see through mirror and but a camera behind it and then put it directly parelell from another mirrior of the exact same size, and you will see that it is all horizon! Strange concept.

No InSiDeR, you are again wrong *sigh* Why? Because of the distance of the mirrors to one another is responsible for the size difference in the reflections. And because one of the rules of physics state that two objects cannot exist simultaniously in the exact same spot, those two mirrors will always have distance from each other (irregardless of how small...). So the reflections become smaller, and smaller with each reflection...and thus, my statement is true...the light does not infinitely bounce back between the two...aside from being absorbed, at some point, the image is just too small...so, it's finite.

Hmm, I still disagree. If only we had an electron microsope....

*kick*

Suho where ya at man?

You are aware, that a particle of light is the smallest 'information carrier' that could hold a piece of the reflection, right? So...if you go to the quantum level (where we have quarks, etc) because these particles are actually smaller (well, some of them, anyway) than light, they would not 'reflect', in that sense. Thus, yes, the amount of 'reflections' would then, by nature, be finite. And yes, the reflections do get smaller with every reflection. If you do not believe me, then ask your physics teacher. Better yet, get two mirrors, and see for yourself...

And no, it is not all 'horizon', as you suggest. Rather, nothing is being reflected, in your example, other than the other mirror. Because that, in turn, is reflecting yet again a mirror, this is how the image appears.

[This message has been edited by WebShaman (edited 12-09-2002).]

Facinating WS, I never knew that quarks are smaller than light particles,
The only way we can see quarks are through electron microscopes or is it just through math?

But at what point does it no longer reflect?
When the light particles are so small that they can no longer reflect?

So since the number of mirrors is finite in theory it could be calculated then...
(Well in theory, it's not like I'm gonna do it)





Maskkkk

- Face the Present

Well, those are good questions. First, light is a strange thing. It is both a particle, and a wave, but that is rather unimportant, in light (pardon the pun) of your questions.

At some point, the particles are so small, that the light just passes them by...or is absorbed. And in case of the reflections, the energy of the light will eventually be totally absorbed/diffused by the matter of the mirrors (because no mirror is 100% reflective). Therefore, the light will not infinitely bounce back and forth between the mirrors. Now, quarks are well below the size level to be seen with an electron microscope...in fact, no-one has ever seen a quark. See here for more details...

And at some point, even if the light can bounce off of a quark (which I'm not sure of)...it will become even smaller (the reflection), that it is smaller than even a quark. And so to the next level...and since quarks also consist of something, would bounce off of that (if possible), until it eventually reaches a point of being the smallest thing...and would then pass through the object in question (no longer being reflected).

However, I find that scenario very unlikely...as the light would be absorbed/diffused well before that point, by the material of the mirror. That is also according to the laws of physics.

The whole reason they use electron microscopes is because the wavelength of visible light ranges from 400 to 700 nanometers. Therefore, you can only "see" objects bigger than this. So, in order to see objects much smaller than this, something had to be used, thus the electron microscope.

And electron has a radius of approximately 2.8179 x 10^-15 meters. So, by using a focused beam of electrons you can "see" an object smaller than the visible light wavelength. However, you're not really "seeing" it per se. What you are seeing is the computer representation of the object in 3 dimensions after calculating the information provided by the electron beam. This is why all electron microscope images you see are black and white. The visible spectrum doesn't apply.

Now, quarks, as Webs pointed out, are much smaller than even electrons.

As for the mirror thing, Webs is again right in that there is a finite boundary condition due to what you define as a reflection and the fact that you need light to even see a reflection.