Tuesday, December 1, 2009

Mathematics

Occasionally, I take it upon myself to launch into a post containing a whole lot of math – or at least, more math that can usually be found on a D&D blog. I’ve gotten both positive and negative responses to those posts; I’m sure I haven’t written the last of them. That’s because, honestly,


“Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.”
Robert A. Heinlein.

This being my honest and complete answer for anyone who tells me there’s too much math involved in doing something.

I'd like to dispute that money is the root of all evil.  I think rather - and I say this to the pleasure of all the student's who have pop quizzes first thing tomorrow, that the root of all evil is math.  Mathematics enabled the establishment of time, the division of property and the application of taxation. It also brought about the invention of interest.

How did it do these things? It brought an end to doing things ‘more or less,’ replacing that concept with exactitude.

Please to understand. Once upon a time, you would milk your cow and bring your share of milk to distribute among the various villagers, in accordance with village law. This was something that every cow owner did in a community that favored community property … and it was assumed that the amount of milk that you brought more or less compared with the amount of milk that other cow-owning members of the village brought.

If it was a little less, because you would casually suck a bit off heavy cream off the top for yourself, who would notice? And if your gourd was a bit larger than your neighbors, entitling you to a bit more milk when it came time to share things out, who would know? Granted, someone might notice if it was very much larger … but a little larger? No big deal.

The invention of mathematics brought in a very interesting concept, however – one that was applied to every aspect of human civilization. That concept was measuring ... which in turn defined, as it had never been defined before, just what your share was.  Exactly.

More importantly, it defined exactly who was contributing more than his or her fellow neighbor.  And those who consistently contributed more gained importance, and were rewarded in turn, while those who consistently contributed less could no longer rely on human perception to carry them along.  Everyone knew you contributed less.  Everyone knew your gourd was larger.  It was measured.

If it was your cow that produced the least milk in the village, guess who's cow got slaughtered when the time came?

Ah yes, time.  Once upon a time, there was no time.  No hours, no minutes, no measure for how much labor you performed except for how much labor you actually performed.  But mix time with labor, and you have invented the wage.  Add writing to the mix, and we have a measure for how many days you have spent at a labor, because everyone now remembers when you've worked and when you have not.  It is measured.  It is written down.

Once, I would have given you a cow and you would have said, "You may farm all of that field between that group of trees and that stream."  But now we know how far, exactly, it is between those two things.  And we know that I own more land than my neighbor does.  And that isn't making my neighbor happy.  So now we are squabbling and stabbing each other over sixty square yards of land, where once we lived in peace.

I could have written a pedantic, point-by-point discussion about the development of mathematics and its influence on social welfare, but I thought this would make the point more clearly.  Because, after all, this is very much what D&D lives and breathes ... an endless, furtive grubbing effort to divide treasure, to make sure that his +1 sword isn't improving his character better than my potion of levitation, that I'm not getting screwed somehow since my experience is 250 points less than the fighter's is.  After all, it was my shocking grasp that dealt the death blow to the ogre, not the fighter's three misses in a row.

Whatever you say or believe, D&D is all about measurement.  It is microcosm of human kind, from pissing contests about whose strength is higher to the number of times each character has rolled a critical hit.  And nothing gets measured against a player's valued to the party than the share of gold that is to be rewarded when the monster is finally dead.

It wasn't money that invented greed - money did not come into existence for more than two thousand years after the widespread application of mathematics.  Interest existed before money did, as did taxation, loans, debt and virtually everything else you can associate with wealth.  And the thing that made it possible to calculate all that in a bartering world was mathematics.  All I am trying to get across is that it wasn't counting that made the world move, it was MEASURING.

Hm.  I can't seem to make that point strongly enough.  That is, when I compare it to other points I've made in this post.

When it comes to creating a world - and this applies to every kind of world, even those in the far-flung future - the social structure of that world depends upon how wealth is distributed throughout the culture.  The wider the difference between the very wealthy and the very poor, the less accessible those people in power become.  A wide difference creates many, many poor, and only a few wealthy - so that the wealthy must defend their wealth.

In a culture, however, where wealth is truly distributed evenly, the people in power become very accessible.  There is no trouble sitting down and communicating with the chief of an egalitarian village; but it is nearly impossible to speak with the Emperor.

The narrower the distribution, the greater the number of measurements the society imposes - that's all laws really are.  Just a series of measurements.  You are entitled to this much money, this much space, this much return for your labor and so on.  Ask for more and it will be denied.  In a highly evolved society, your only choices for increasing your 'share' are to increase your labor (either quantitativally or qualitatively), or seize someone else's share criminally.

The wider the distribution, the less the number of measurements a society needs.  Everyone has the same.  Labor does not increase your share, though refusing to labor may reduce it.  Usually, in such a society, there is nothing to be gained by hoarding or being 'rich.'  You can only eat so much.  You only need a bed so large.  There is nothing you can steal that will increase your condition.

To create an extremely sophisticated society that enjoys at once a wide distribution of wealth and a lack of social imposition is easy, if fantasy is employed.  Our world only operates the way it does because there is dearth ... limited resources, limited space and so on.

But what about a world, set on an alternative plane of existence, that has no such limitation.  What if money isn't a limit?  What if everything that could be wished for or asked for literally grew on trees?  What if your fantasy world included a never ending abundance of trees which, upon being asked, freely produce everything your character could ever want or need?  What if, extending the fantasy, this happened in a universe with no boundaries, no limited space on a planet, just an endless environment that extended infinitely in every direction?  And finally, just to hammer the point home, what if you could travel to any point in this 'world' in the space of an hour, regardless of the actual distance?

There were still be measurements.  You may be able to pick flasks of oil from the trees like bunches of bananas, but you could still only hold so many at one time.  No matter how many +5 swords you could find, you can still only fight with them two at a time ... and the player with the highest dexterity would manage that feat better.  Remove wealth from the equation, and there's still room to covet those with better stats, with more experience, with a greater degree of imagination.

D&D makes it easier to compare those things than real life does, as it provides models by which all of those things are measured.  That is both the genius, and the evil burden, that is part of the game.

9 comments:

Ryan said...

This being my honest and complete answer for anyone who tells me there’s too much math involved in doing something.

When I say there is too much math involved in something related to roleplaying games, I mean to imply that there is too much math for something I consider to be a recreational pursuit. While I must use math in my daily life, I certainly don't consider it something I would do for fun. I recall that my last straw with GURPS came when I was using GURPS Robots, and part of the creation of a robot required me to calculate the surface area of said robot. I like my games with no more math than you find in D&D or AD&D. I simply have too little free time anymore to muck around with tedious calculations, and to wonder if my whole robot is out of whack because I made an error several steps back.

R said...

And finally, just to hammer the point home, what if you could travel to any point in this 'world' in the space of an hour, regardless of the actual distance?

I actually struggle with economic design in my campaign because it is set in Planescape. I have no idea how to simulate the economics when portals litter the dimensions and make travel across infinite space easy. Simply saying "the resources are still difficult to acquire and transport" seems like a cop-out, but that's my running answer currently (my PCs couldn't care less, of course). Treating the portals as roads almost works...except I don't have a model for temporary roads that crop up and then disappear at a moment's notice.

Any thoughts on that, Alexis?

Alexis said...

R,

Two thoughts.

Get rid of your economy. Economics are based on scarcity, and you're basically eliminating scarcity with supply. Limit your party's equipment to what they can carry, allowing no vehicle-driven 'portal-travel' ... ie., no trucks or mechanical devices. Living animals are fine, but there are ways to limit them as well, saying one animal per character, that sort of thing.

The second idea would be to go one step further. Take a page from the Terminator series and allow only naked travel between dimensions. Nothing EXCEPT living tissue. Then you can employ hundreds of economic frameworks, and insist that your players operate depots in each different plane where they travel.

Ryan said...

Alexis,

I have been meaning to ask you: where do you derive your economic data? Do you know of any good programs for a "gameable" economy? Sometimes I think I would like to have something in place, but something that runs in the background, as it were.

Kent said...

What you are calling mathematics would be better described arithmetic.

Sturat said...

It has to be said:

Math is not the root of all evil.

Math is the SQUARE ROOT of all evil.

My sincerest apologies!

Not really...

Alexis said...

Ryan,

The only simple solution I could suggest to solve your problem would be to steal. Many video games, Civ IV being the logical example, have "economic systems' that are abstract and thus applied to the game. You might try adapting such a system, using gold, food and hammers, for D&D.

Kent,

What an extraordinarily foolish thing to say. Surveying, geometry, astronomy and fluid mechanics are ALL fundamental to the art of measuring and to this post - and none can be classed as 'arithmatic.'

Sturat,

There can never be too many puns for my taste. Bring them on.

Kent said...

For me mathematics is algebra, analysis, topology, mechanics and related disciplines and it is concerned with *symbol* manipulation. Playing around with *numbers* is arithmetic. You are obsessed with the prices of ham and eggs and rope and such things. I haven't seen anything I would call mathematics in your posts.

Sorry for piercing your pretension, modesty is more endearing.

Ryan said...

Alexis-

I do have a copy of Civ IV, though I haven't gotten around to playing it yet. (Perhaps after the holidays) I have no compunctions with stealing good ideas. In the mean time, there are a few other strategy games I could pilfer as well.