A couple of big, abstract questions I hope a mathematician can answer for me. (As I'm a lousy mathematician)

0) Meta-question

Could there be a way to LookMathsUp?

1) System Fragmentation

Over all possible system dynamics. Do more systems have a tendency to find stability through fragmentation into smaller interacting specialist parts? Or more towards larger, more multi-functional groupings? Or are the tendencies balanced?

2) The Game Question

Over all possible games (in a GameTheory sense) are more ZeroSum, more encouraging co-operation (ie. co-operative behaviours can score better than competative). Or more inducing of competition? Or are these balanced?

: You need to develop a measure to ask those questions - that is you need to know how do you 'weight' each game (or rather a small sphere of games), because there is an infinite number of games. – ZbigniewLukasiak

: I know there's an infinite number of games, but I figured counting and reasoning about infinite sets is the kind of thing mathematicians can do in their sleep these days :-)

: What kind of "measure" are you thinking of? – PhilJones

: [Measure](http://planetmath.org/encyclopedia/Measure.html –ZbigniewLukasiak

I wonder if this is what NonZero is about?

Another thought, are these two questions related? (ie. optimum module size in systems depends on whether better for parts to compete or co-operate)?

I have to say, my hunch is that ZbigniewLukasiak is on the right track by bringing infinity into the picture. Then, with infinities you do indeed get different 'sizes' of infinity. However, I suspect that the different sub-sets of either dynamics of games that you are talking about above are both going to be equally infinite compared to other such generally defined sets of games / dynamics.

So, I guess this would make the answer to both your questions that they are both balanced, with each defined class having an equally infinite number of members.

Probably not much help to the argument you were hoping to make :(

OliSharpe

Counting elements is just not a good measure for infinite sets - for most practical cases it just inflates to two categories countable sets (like natural numbers) and Continuum (like real numbers). But there can be other measures. For example you can ask if there is more points in a 1x1 square or on a 2x2 square - the answer is that there is the same continuum amount of points, but you can use the plane area measure and say that the other square has 4 times more area than the first.

ZbigniewLukasiak