## Monday, July 21, 2014

### Why three dimensions at least

Found myself looking over one of my blog posts where I extended the methodology for what I call tautological spaces, identities used with conditionals for mathematical analysis.

And the concept there is so easy as you just subtract some equation from an identity and analyze the residue, which tells you about the equation! So it's like, you're probing the residue. That sounds, weird.

But one of the best things about that idea is you can look at familiar equations differently. Pull them through a tautological space and probe the leftover conditional residue. It's fun! But maybe it does feel a bit weird. Like playing with the cast off skin.

And it occurred to me that I haven't talked about the implications from tautological spaces requiring at least 3 variables with the v, so they automatically have at least 3 dimensions.

For instance the classic is: x+y+vz = 0(mod x+y+vz)

Note that here 'v' is an absolutely independent variable as its completely independent. That let's you set it to whatever you want, which is why I introduced it. I wanted to be the one, in control. That shifts the residue around. Like stirring that conditional residue in ways you choose. You can poke and prod that residue an infinite number of ways, regardless of the variables x, y and z.

Turns out there's no value in going to something with fewer variables. It's not hard to figure out why. Curious people can play with it and see if you can do anything with x, y and v.

For me considering such things was done years ago and I debated talking about it, but have often decided to stray from areas that can spark controversy.

The problem here is there may be mathematical reasons related to identities which can explain why you need at least 3 dimensions for reality like ours. But then again, these same ideas may indicate that a lot more dimensions are possible, with characteristics radically different from our own.

Sounds wild. I like the wild thoughts at times. Who knows how weird reality might really be?

Fun speculation but for now without more interest from others to pursue these lines of inquiry, it's something I'll mention with reticence in this post. And just wander off from there now.

James Harris