Configuration Space

Imagine you’ve got a chess set and you want to record a game of chess.  You want to be efficient, and taking a picture of the board at every stage isn’t very efficient.  But you decide to give a number and a letter to each rank and row of the board, and refer to pieces by their positions.  This allows you to keep track of an entire game by describing the configuration of a single piece with just two symbols, a number and a letter.

Now, imagine that instead of chess, you’re trying to describe a more complex system.  You want to keep track of your cat’s position, so you lay out your house in a grid, and give each row and column a number.  So, as your cat crosses the living room floor in a  straight line, you write: 1,5 2,5 3,5 4,5 5,5.  Maybe your cat pounces across the next square, so it’s 5,5 7,5.  But you’re also trying to keep track of your cat’s weight, because you have a fat cat, so you include the number of ounces your cat weighs: So now your cat goes to get some food:

7,5, 200

7,4, 200

7,3, 200

6,2, 200

6,2, 203

There, you see?  At 6,2 your cat ate three ounces of food.  Now let’s let’s say you want to make a chart.  You couldn’t just do a two dimensional diagram; you’d need to make a three dimensional one because you have three numbers.  No problem, though.  That’s easy enough.

But what if you wanted to record your cat’s height?  And mood?  And position of the tail?  and whether the claws are retracted or not?  Each of those can be another number, and would be another dimension added to your diagram.  We can get to the point where we can describe your cat as a single point on a very large multidimensional diagram.

Now imagine that you don’t just want to describe a cat in numbers, but the whole world.  In fact, you want to create a very large multidimensional chart that will record the state of the world.  You assign a number to every single quality about the world.  This will be a very large number (call it n), but probably not infinite (I don’t have a proof for that, but I suspect it for some good reasons I won’t put here).

So now, you can position a point in this n-dimensional space to describe the current state of the world, every detail about it (by “world” here I mean the entire cosmos, actually).

Why does this matter?  Well, for a few reasons, many of them significant to magic.  For one thing, the movement of this point is smooth.  It usually doesn’t jump around, but moves along its n-dimensions more or less in order.  Your cat doesn’t go from 103 oz. to 7 oz. in an instant, for the most part.  For another, there are some parts of your chart that are dead areas, impossible places to get to from other points on the chart.  Your cat can’t get to the moon.  The world can’t turn into cream cheese.

But every single point on this n-dimensional chart describe a possible world.  Somewhere there is a dot, or rather an entire region of dots, that represents me having been born a woman.  Or me having become president.  I can’t get to those positions from here, even though the path to the second one is probably a bit more possible than the path to the first one.  But both represent possible worlds.

So when I say “if I were P, then I’d Q,” what I’m saying is “In the possible word in which the value of X dimension is Y, then the value of A dimension is B.”  Again, this complex space — called a “configuration space” — is a mathematical abstraction, but it’s not hard to imagine it existing, since we are moving through it.

There is, at any given time, one world-dot that we call “actual.”  And now here’s the crux for us magicians: magic is the art of moving the actual.  How?  Well, that’s my next post.

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One Response to “Configuration Space”

  1. I’ve been following your thinking so far and looking forward to the next post, where you will be connecting all this to reach a novel interpretation of magic.

    But I find rather interesting that assigning numbers to every quality of the world task, which you suspect ends at some point. Can you say a bit more about it? And also, these qualities of the world, do you think they’re out there, pre-made, ready to be discovered and identified objectively? Or that qualities are constructed by human intellect but you can still identify them all? But what if there are no inherent qualities of the world, not even the notion of “quality”?

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