This is probably a foolish venture (given my math ignorance) but here's some thoughts on an economic random walk. (Any pointers to elementary fuck-ups / blindingly obvious things I'm missing appreciated.) I've come across the graphs here in each of the simple models I've done of trade exchanges. This one isn't a real trade exchange - it's had price decisions removed entirely. So apart from the limit on the amount of money in the economy and the requirement that money is 'exchanged', they are random walks. It's like this. We start with:

• 100 people, 100 pounds each (so the amount of money in this 'economy' remains constant: the mean is always 100.)
• Run for 200,000 days
• On each day, each person randomly chooses someone, and gives them a pound if they have a pound to give. If they don't, on to the next person's random choice.

(See links below for graphs and code.)

So what? Well, it's a random walk with a peculiar constraint, that's illustrated by the fact that the standard deviation stabilises around the mean (but fluctuates in an awfully price-like way, which is always pleasing!) A normal random walk with a boundary spreads out forever (hence why Stephen Jay Gould claims random walks are responsible for much of the variation in evolved life.) In this model, the spread out from that initial 100 pounds is limited by the boundary of 'no-one can go into the red' - but indirectly, since it halts the spread of the richest by limiting the total amount of money available.

The histogram's stable state is the best bit: the vast majority of people in this little world have only zero to fifty pounds. Only one or two ever reach four to five hundred. (And it does seem to be four to five times the mean.) It's rather unusual, due to the two factors of a set 'fund' within the system and the zero boundary. I'm presuming there must be similar totally skewed distributions in other closed systems, but I've no idea where.

The gini coefficient starts at zero - total equality, one hundred pounds each - and (not surprisingly) closely follows the standard deviation. It seems to stick around the point exactly between total equality and total inequality. I love this: it reminds me of claims (still parroted without comparison to the real world) that Schelling found something important about segregation. Equally, this little random walk proves that wealth disparities are entirely to be expected. (I believe Sugarscape had a similar finding.)

That sounds flippant, but that's probably to hide my own worry: perhaps such models do say something important about the world. The power of randomness - and the stability it can produce - is an inarguable reality. The fact that our blood stays inside us, for example: pressure, on average, evens out to a perfectly stable state inside and out. Phew.

But then, people aren't random, and money exchange isn't random. But are real human interactions enough like (pseudo) randomness for their outcome to be predictably, stably similar to something in a model? Many famous books have been written on the matter - often looking for ways to find information in seeming randomness.

(Listening to the rain fall on the skylight last night added another thought. My brain was able to take that data to let me know very clearly that I was listening to rain (not wind, or background cars.) Earlier, through the slight gap in the window, the sound of cars in the distance was equally unambiguous. But putting that into data form, it would substitute well enough for randomness - indeed some might use it as a source of true randomness in place of the cyclic pseudo kind computers work with. But there's information in it. So if a model of (say) stock prices was sophisticated enough, could it find signals in that noise too? Could a brain of the right sort hear what was going on...?)

Anyway, I could probably witter on in a (not actually) stoned fashion about this, so I'll stop with a question: what criteria could be used to decide whether this 'model of the natural inequality level with a set money supply' or Schelling's segregation model was more useful? My answer would probably be none. Both might, if lucky, lead to new ideas. One of them has been used to justify the status quo.

Someone else, I guess, might say that at least Schelling's has some realistic representation of human behaviour. Oh, of course - people living on a bunch of adjacent squares and regularly moving, one square at a time. Humph. The only use I can see for the money model is to know what the simplest possible pattern is for a world where exchange occurs: it's a 'lowest common denominator'. If I'd made a much more complex model and seen the same pattern, I'd have spent a long time chasing my own tail trying to figure out what was going on. In fact, I think I did, if I remember...

Anyway: if any right-wing think tank would like to buy my model to increase the already long list of proofs for the necessity of inequality, I'll happily take your money - I can guarantee I'm nearer the boundary than any of them, so it'll reduce the world's gini coefficient just that little bit more...