The foundations.

I thought it might be useful to touch on a subject I pikced up from several good reads and a very helpful mathematics professor. There are different levels of understanding involved when solving scientific problems. These are levels I generally consider when pondering a physical problem (simple or complex):

1. Philosophy
2. Mathematics
3. Physics
4. Theory and Imagination

Interestingly enough though, the levels seem to form a Cartesian circle.

1. Philosophy
Without some basic axioms and foundations, mathematics would not exist. We take for granted to the scale to which our assumptions mold our ways of thinking.

2. Mathematics
A good read for a description of what I'm about to quickly cover is a book by Roger Penrose called The Road to Reality. A must read for any physics buff!
There are really three seperate 'worlds' that mathematics lives in.
a. The 'real world' - the world we live in
b. The 'mathematical world' - the world where all mathematics resides
c. The 'abstract world' - the world where mathematics lives, but has no relation to the real world. This would be the universe of ideal mathematical models and complex systems which do not and will never exist
All three of these 'worlds' are connected. The mathematical world lives in us, in our brains. We can come up with real math solutions for the 'real world', and abstract and ideal solutions to things which do not exist in 'real world'.

3. Physics - well, you know, you gotsta use da maths.

4. Theory and Imagination
These are the powers which drive scientific progress, and are the powers that are essential in making up your own science (mine is going to be part of the 'abstract world' :) )

The mathematical formalism.

So during electrical engineering class today, we covered voltage and current dividers... for the 100th time. I fell asleep then went outside and sat on a bench. I decided the best place to start when playing god is to make some rules for the game. How do you read a set of rules for the universe? With math silly. Being a visual person, I decided I would set up my dimensions.

Space... really a necessity to have if we're going to attempt to visualize or comprehend an already completely contrived imaginary universe.

So, how do we define space? Are we going to go with some ol'standbys? Euclidian geometry? Hyperbolic geometry? Elliptical geometry? Einsteinian space-time?

And how many dimensions of space? 1, 2, 3, 4???
1: One axis. Infinitely thin wire. Great for modelling, but falls short on the square-footage in my neighborhood.

2: Two axes. Infinitely thin plane. Bounded area (or unbounded). Seems nice enough. Is it just me or does this shirt make me look shorter in here?

3: X,Y,Z. Too easy and too familiar. I don't want a universe that is easy enough to drive around in my Geo Metro!

4: Four axes. One minute I'm passing you on the highway in my Geo Metro (as if.) the next I've disappeared from your review mirror somewhere down Highway 4. Do you think the review mirror message "Objects are closer than they appear." would be underestimated at this point?

I like 4 dimensions of space. That sounds fun.

The tools.

The tools required in such a task will most likely include:
1) Knowledge of math, physics, probability, and complexity
2) A broad knowledge-base of reference material
3) Sufficient computing software/hardware
4) Influences regarding the hypothetical laws and concepts (abstract mathematical models, philosophy, mysticism, imagination)
... that's all I can think of.

The laws.

I sat down one evening in my backyard and, as usual, started reading through a chapter of some half-price bookstore theoretical physics book, hoping to get a glimpse of some new idea or some POV shattering message. I am a hard geek, and usually add a bit too much grandeur into my imaginations. But I wondered, "What if I could redo the entire set of laws of the universe?" Granted, we don't know them all, but what if I could make up my own set: a set of laws governing whatever I want them to govern. Would this give me a greater understanding or ability to understand how our universe works? So here it goes... I've gotta go sit around with a pack of marlboros and come up with, as-so-far, the very basic underlying principle of my universe.

The purpose.

The purpose of this blog is to provide a medium for myself to record random thoughts. Not really for anyone else to get anything from.