Dimensions.

Post by **_Imwashingmypirate** » Sat Dec 08, 2007 12:02 am

Having been thinking about dimensions, I thought about the number of dimensions and for some reason thought about prime factorisation. I thought "what actually is the first Dimension?" Then I though, "what is the fourth" Then I thought "Is 'the fourth just a name given to something" Then i thought "what if the only dimensions that exist are that of the prime numbers. And so they continue to infinity. And we cannot comprehend them in the same way we do not have an equation or formula to solve prime factorisations, hence encription.

Pirate.

Post by **_asbestosman** » Sat Dec 08, 2007 12:19 am

The spatial dimensions are all equal and labeling them is arbitrary. The dimension of time is different, but is relative to an observer. Asking what is the first or second dimension is like staring at a plaid kilt and asking which square is the first square.

Not all things have an integer number of dimensions. Fractals are shapes that have a fractional number of dimensions--any fractional number you can think of.

While there is no formula for prime numbers, there are algorithms for both generating them and for determining them. The reason encryption relies on prime numbers is because factoring numbers into their primes is currently much more difficult than multiplying two numbers together after determining that those two numbers are themselves probably prime numbers. Prime numbers can be generated and tested fairly easily. It is factoring that is currently the problem. Actually, a second difficult problem encryption relies on is the discrete logarithm.

As to why we live in 3 spatial dimensions instead of 2 or 4, physicists have various ideas. In 2 dimensions we might have trouble with digestion. In 4 spatial dimensions there are some interesting ideas about knots or something like that.

Post by **_Gazelam** » Sat Dec 08, 2007 12:27 am

Post by **_Imwashingmypirate** » Sat Dec 08, 2007 12:31 am

asbestosman wrote:The spatial dimensions are all equal and labeling them is arbitrary. The dimension of time is different, but is relative to an observer. Asking what is the first or second dimension is like staring at a plaid kilt and asking which square is the first square.

Not all things have an integer number of dimensions. Fractals are shapes that have a fractional number of dimensions--any fractional number you can think of.

I agree with you, but try looking at this, Fractions do not exist for they are whole entities in themselves. I can explain this if anyone likes.

While there is no formula for prime numbers, there are algorithms for both generating them and for determining them. The reason encryption relies on prime numbers is because factoring numbers into their primes is currently much more difficult than multiplying two numbers together after determining that those two numbers are themselves probably prime numbers. Prime numbers can be generated and tested fairly easily. It is factoring that is currently the problem. Actually, a second difficult problem encryption relies on is the discrete logarithm.

I knew this, hence the reason I mentioned it.

As to why we live in 3 spatial dimensions instead of 2 or 4, physicists have various ideas. In 2 dimensions we might have trouble with digestion. In 4 spatial dimensions there are some interesting ideas about knots or something like that.

I think your understanding of dimensions might be different to that of mine. But anyway, There are multiple dimensions all around us. We live in them all. We just abide by the rules of the third in terms of Physics. I think our minds are of another dimension greater than the third and fourth. We as humans cannot comprehend greater dimensions and so we don't know of them but if we can evolve more in the future in that direction we might even be able to "translate" to a greater dimension. But I think in order to do that one must remove the "material" aspect of them selves, seperate of there mind (thoughts, conscous, etc) so that the third dimension cannot hold them back. I guess this could be why people meditate.

Post by **_asbestosman** » Sat Dec 08, 2007 1:24 am

Imwashingmypirate wrote:I agree with you, but try looking at this, Fractions do not exist for they are whole entities in themselves. I can explain this if anyone likes.

What do you mean? Fractions don't exist? Do whole numbers exist? Or did you mean fractals? Fractals may exist by being embedded in an integer dimensional space, but I do not see why this is necessarily so. Riemann showed how one can take an intrinsic view to various topologies without reference to a containing dimension. I'm not sure how one would do that for fractals, but then I'm not sure how fractal topology would work in the first place.

I knew this, hence the reason I mentioned it.

I suppose you are right, but I think that prime factorization is more coincidentally a difficult problem. However, there are other sets one can use for encryption such as elliptic curves cryptography. Another possibility is to use a Gallois field (sure, we usually prefer a prime number raised to a power there too, but it can be a non-prime power such as 2^6).

I think your understanding of dimensions might be different to that of mine. But anyway, There are multiple dimensions all around us. We live in them all. We just abide by the rules of the third in terms of Physics. I think our minds are of another dimension greater than the third and fourth. We as humans cannot comprehend greater dimensions and so we don't know of them but if we can evolve more in the future in that direction we might even be able to "translate" to a greater dimension. But I think in order to do that one must remove the "material" aspect of them selves, seperate of there mind (thoughts, conscous, etc) so that the third dimension cannot hold them back. I guess this could be why people meditate.

It's possible. My own personal thoughts are that dimension is merely a convenience for understanding the universe as a way to explain how one object relates to another spatially or whatever. In reality things could potentially relate in other ways--perhaps in such a way that dimension doesn't become useful.

By the way, a weird result from mathematics is that of space-filling curves. It is possible to find a mapping from the real line to any point on a two (or higher) dimensional plane such that each point in the two dimensional plane has a corresponding point (or a finite number of points) on the real number line.

Post by **_Imwashingmypirate** » Sat Dec 08, 2007 1:52 am

Ab I will get back to you on this. I have a few points I would like to make but it is two in the morning and it might take a while.

OW

Post by **_Imwashingmypirate** » Sat Dec 08, 2007 1:55 am

I keep crashing when trying this. I had put two pictures on here earlier and so I made an attempt to delete one. And it did not work so I tried the other then they both deleated. So I will just tell you and you can look it up.

Klein bottle and Mobius strip.

Post by **_asbestosman** » Sat Dec 08, 2007 7:55 am

Imwashingmypirate wrote:Klein bottle and Mobius strip.

I am familiar with both. A Klein bottle is a surface with only one side--no inside and outside as it is all the same side and it has no edges. A Mobius strip is similar to that except that it has edges which a Klein Bottle does not have. A Mobius strip can be formed by taking a skinny strip of paper, putting a half-twist in it, and then connecting it to the other side to form a twisted loop. I find both to be quite interesting.

Both are very important to topology, but I'm curious as to what your thoughts are on them or why you brought them up.

Post by **_Imwashingmypirate** » Sat Dec 08, 2007 10:50 am

I brought them up because some things that were said reminded me of them. I am not entirely awake because I have only slep about three hours and so will have a longer reply for a previous post. I like these sort of structures. I find it fascinating. Have you ever tried cutting along the middle of a mobius strip?

Are you a Mathmetician?

Post by **_Imwashingmypirate** » Sat Dec 08, 2007 3:50 pm

I was thinking as these have infinate aspects one coult say dimensions might go to infinity.