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        riddles >> general problem-solving / chatting / whatever >> Tesseract
        
(Message started by: Roy on Aug 14^th, 2006, 4:28am)

Title: Tesseract
Post by Roy on Aug 14^th, 2006, 4:28am

I found this (http://www.maa.org/editorial/knot/tesseract.html), interesting, but i always thought time was the 4th dimension

Title: Re: Tesseract
Post by towr on Aug 14^th, 2006, 5:01am

on 08/14/06 at 04:28:52, Roy wrote:

I found this (http://www.maa.org/editorial/knot/tesseract.html), interesting, but i always thought time was the 4th dimension

The numbering is rather arbitrary. Can you imagine something moving along a line? A line is 1-dimensional, time (change) would be the second.
How about starting with a point, and imagine it's color changing. The point is 0-dimensional, and time would be the first dimension.
So if you can have time in 0-dimensional space, it'd make sense to say length, width height are the 2nd,3rd and 4th, rather than 1st, 2nd and 3rd
It's still rather arbitrary though, why use length, width and height? You can use polar coordinates. You'd have one distance dimension, two angular dimensions, and a time dimension.

In the end, it just comes down to what and how you describe something. If you have a particle, you don't just want it's position in 3D space, but also it's velocity (or momentum), which adds another 3 dimensions (because you need it along each direction).
In maths you can have as many dimensions as you want (but to be fair, even physics goes over 4 these days. String theory uses 10 or 11 to describe reality). e.g. You can see a binary number with 32 bits as coordinates in a 32-dimensional space (or rather a 32-dimensional hypercube). Any bit of information narrows down the space you might be in by half.

Title: Re: Tesseract
Post by Icarus on Aug 14^th, 2006, 5:09pm

There is no actually ordering of dimensions. Classically, we describe the physical universe using 4 variables, or "dimensions": 3 of them are "spacial", which we usually call x, y, and z. The forth is time, or t. So time is the "4th dimension" in that it is the dimension other than the 3 spacial ones, rather than there being a "1st, 2nd, and 3rd dimension".

As towr has said, modern theories posit more spacial dimensions (I've never never heard of any adding more temporal dimensions, but offhand I don't know why you couldn't). In these theories, time is the "5th", "11th", "16th" or "26th" dimension, other than all those spacial dimensions. The new dimensions are all very small (like the surface of a hose has 2 dimensions, but one only travels a very short distance before it loops back on itself - on a large enough scale, it is hardly noticible).

Even in classical physics, we could have more dimensions, however. A single particle is described by a curve in 4D spacetime. But a pair of particles is described by a curve in 7D spacetime. There, time is the "7th dimension". Such "state spaces" could have any arbitrary number of dimensions.

Title: Re: Tesseract
Post by rmsgrey on Aug 15^th, 2006, 6:17am

The impression I've picked up is that String Theory involves only 3 space-like dimensions, 1 time-like, and the rest are too small to tell - if they were expanded, they could expand to space-like, time-like, or really weird dimensions...

Title: Re: Tesseract
Post by Astrix on Aug 15^th, 2006, 1:17pm

I think there are theories that have more than one time dimension. Anyone whose ever been to New York knows there exists Times Squared.
Well, maybe not scientific theories, but pseudoscientific sci-fi theories also suggest a second time dimension. Consider, if time is a measurement of change, then for time travel to be possible then time itself must be able to change, and that would require a time itself flows and changes.

Title: Re: Tesseract
Post by Icarus on Aug 15^th, 2006, 6:01pm

When I was dealing in String theories (back around 1990), everything I saw was with 1 temporal dimension. Maybe they've explored other possibilities since (or even then, but I didn't come across it), but at that time S.T.s had only 1 time.

For those who may wonder what is the difference: In 4D spacetime you measure distance (called "proper time") by the "pythagorean" formula:

ds² = dt² - dx² - dy² - dz²

(where x, y, z, t are measured in units for which the speed of light c = 1). For more dimensions, you add variables. Those with positive coefficients in the distance formula are "temporal", and behave like time. Those with negative coefficients are "spacial" and behave like ordinary distances. Note that the temporal distance has to always be >= to the spacial distance.

Title: Re: Tesseract
Post by rmsgrey on Aug 16^th, 2006, 8:15am

My "knowledge" comes mostly from popularisations, including a couple of years of New Scientist magazine in the late '90s. I know there was at least one article looking at why the universe unfurled into 3 space and 1 time dimension, and drawing the conclusion that the only universes where any sort of large-scale (say 10^-12m and up) structures would be possible are 3s1t and 1s3t - the implication is that it would be possible for the "rolled-up" dimensions of string theory to unfurl as space-like or time-like more or less arbitrarily, but only in 3s1t or 1s3t space-times would anything even remotely resembling observers (as we know them) develop.