Comments on p i x e l s c r i b b l e s: I feel dumb.

Also, from my understanding, "time" is a real phys...

2005-10-23T04:10:00.000-04:00

Also, from my understanding, "time" is a real physical fourth dimension, but we only experience it as time. Unlike the other three dimensions, we do not have free movement in the fourth, and are sort of dragged along it and thus experience "time." In current string theory models, the universe is understood to exist in four macrodimensions (and seven microdimensions).

There is a very good annotated edition of Flatland...

2005-10-23T04:08:00.000-04:00

There is a very good annotated edition of Flatland out. See if your local library has it (fat chance; I'm sure it's not on many reading lists).

Dude, that's like the second time I've heard of th...

2005-10-21T14:10:00.000-04:00

Dude, that's like the second time I've heard of that this week!

Must read.

I highly recommend Edwin Abbott's Flatland. It ex...

2005-10-21T14:05:00.000-04:00

I highly recommend Edwin Abbott's Flatland. It explains all this stuff in a way that a language-minded person like me could make sense of it. (That it was written in the late 1800s, which makes it all the more amazing.)

Yeah. They're totally imaginary.Math is like a cha...

2005-10-21T13:35:00.000-04:00

Yeah. They're totally imaginary.

Math is like a chain of islands with little bridges linking them in ways you'd never expect. Geometry and Algebra are linked together, so there are a bunch of algebraic results that for example tell us how many possible kinds of wallpaper symmetry there are. Any wallpaper pattern can be classified into one of 17 different symnetries.

So...these dimensions don't represent anything "re...

2005-10-21T13:22:00.000-04:00

So...these dimensions don't represent anything "real"? It's all intellectual? Like adding a layer of complexity to something that already exists? Or what?

Let me try, though I don't promise to be successfu...

2005-10-21T12:53:00.000-04:00

Let me try, though I don't promise to be successful :)

You've seen pictures of cubes or tetrahedrons or the other regular solids in books, on websites etc?

Well, if you think about it, those pictures are actually two dimensional, and are just a two dimnensional representation of a three dimensional object.

This sculpture is a three dimensional representation of a four dimensional object. It's been projects onto three dimensions, in the same way the cube is projected onto two dimensions.

As far as mathematicians go, we don't really see a whole lot of difference between 2 dimensions, 3 dimensions or 4 dimensions. We really think of N dimensions, where N could be some arbitrary number. The concept of width, depth, height and time are just constructs for dealing with a particular type of physics.

The software I write with is really an N-dimensional space where the dimensions are colors, but because computer displays are flat, we let the user work with one or two dimensional projections of that space. Kind of like plan views and side elevations.