I used the metaphor of the size of the niche that two people or cultures create as being a slice of pie, with the difference between the people or cultures corresponding to the angle at the point of the slice of pie.
In mathematical terms, that's an "inner product", and the inner product of two things "a" and "b" is written as
The value of this product computes to be |a||b|cos(theta) or the size of a times the size of b times the cosine of the angle between the two, usually called by the greek letter theta.
Those who remember some math from school may recall learning that the cosine function is trapped between zero and one and looks like the surface of a pond with waves, like this:
But, that is only a tiny special case. The cosine is really a squashed down version of something called an exponential, and the exponential can have an "argument" (or angle) that grows without limit and has values mathematicians call "complex".
Skip exactly what complex means, and just get that the implication of this is that the actual "inner product" of any "a" and "b" can be as large as you want it to be.
In other words, we don't really have to be operating in the realm where the best you can get out of two people working together is less than you'd get if they worked alone - we could be operating where two people can do anything.
The "pie" is limited only by our sluggish imagination.
If you think of ever larger slices of a pie, with the angle at the point increasing, we don't actually have to stop at one pie. The world is actually a helix, as the picture at the top, and if we open the angle up far enough we can go around the whole helix twice, and still have room to keep on going.
Wade
The picture at the top of this page, as the other one, are from this site:
http://www.pacifict.com/ComplexFunctions.html
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