Archive for December, 2015

How Magic Changes Configuration Indices

Posted in Uncategorized on December 31, 2015 by Patrick

Have you all stopped reading my blog yet?  No?  Really?  On hiatus for a year or so, and then a long string of posts about theory?  Okay.  Well.  You’re in for it.

Have you read this book?  Advanced Magick for Beginners.

Well, why the hell not? Do it. I’ll wait.

Okay, so what Chapman points out is that magic can be reduced down to a fairly simple procedure.  To summarize, and not do it justice:

  1. Select a desire.
  2. Select an experience.
  3. Decide that experience means the same as the desire.
  4. Experience the experience.
  5. Profit!

This seems too simple, and I resisted it the first time I read this book.  I recently read it more closely, and more carefully, and conducted some experiments.

He’s right.

One hundred percent correct, at least about this.

And the thing that gets me is that the experience doesn’t matter.  I’ve been deliberately selecting absolutely nonsensical experiences.  Not sigils.  Not words of power.  No spirits.  Just things like squeezing my finger and carefully arranging cue-tips into geometrical shapes.  And it works.  In fact, it seems to work best if I pick a completely different arbitrary act each time, but I’m still gathering experience there.

There are so many theoretical issues about this, and that’s another long string of posts that’ll drive readers away, until I can finally kill this blog.  So look forward to that.

Notice there’s nothing here about mystical energy, or goetia, or the information model.  It’s just experience.  So why would that work?

Because the index of the actual world among the infinite configuration space of possible worlds is determined by our experiences of that configuration.  Moreover, I suspect that we do not all dwell in the same possible world, or inhabit a single point in configuration space, but exist in a cloud of loosely linked actual worlds.  Tying an experience to a possible world and experiencing that experience drags our index closer to that world.

Note that it’s absolutely impossible, not just theoretically or practically, but logically, for the scientific method to ever confirm magic.  The scientific method only investigates the actual world, the indexical possibility currently selected.  It’s going to see a narratively consistent smooth contour of cause-and-effect, because that’s the result of moving the index in configuration space.

It’s clear to me now that possible worlds exist.  They are arranged in a continuous configuration space as an abstract object.  We call the actual world a world selected by a deictic index (or maybe cluster of indices — we may each have our own).  We move that index through our own mundane efforts, but also through magic.  It is the selection of experience and the process of choice that impels the index.  All other trappings of magic are culture, useful for empowering experience and for aesthetic effect, but none of them are absolutely necessary, which is not to say they’re not valuable, as culture itself is valuable.

That’s my conclusion.  I’d be happy to hear your reasoned arguments or reactions.  If I’ve made an error in my logic, correct me.  If you want to help me come up with some implications and experiments suggested by this way of thinking, I’d love to hear that too.

Index and Deixis

Posted in Uncategorized on December 28, 2015 by Patrick

Let’s go back for a moment to the actual world, and leave aside possible worlds.  When I say (1) below, it is false.

(1) I am president of the United States of America.

But when Barack Obama says it, right now, it’s true.  In a short time, though, when he says (1), it won’t be true.  It’ll be true when someone else says it.  In order to evaluate the truth value of (1) we have to know two things.  We have to know, first, who is saying (1); and we have to know when they’re saying it.

If I say it at any time, it isn’t true.  If Obama says it right now, it is.  If Reagan says it in 1983, it’s true.

We say that the word “I” is a deictic.  It’s a word whose semantic value points (deixis in Greek means “pointing”) to something in the actual (or a possible) world.  Without knowing what it points to, you can’t evaluate its meaning.  Other deictics include “here,” “there,” “now,” “then,” “tomorrow,” “he, she, it”, and so on.

Let’s look at another statement:

(2) I have a new car.

(2) is true just in case the speaker, the person pointed to by “I”, has a new car.  Let’s imagine that I is me, and I don’t have a new car.  It’s false, then.  But let’s recall configuration space from my last post.  How far away are those points in the possible worlds in which I have a new car?  Not very far away, really.  All I have to do is move the indexical world, the “actual” world, to one of those worlds in which (2) is true.  I’m not even changing the world: I’m just moving the index.

How will this look from the outside?  Well, the index in configuration space doesn’t move in jumps and starts, so a new car won’t appear in my driveway.  I’ll probably get a perfectly plausible windfall.  I’ll find a good sale.  I’ll get a high trade-in value.  All quite possible, even coincidental-seeming, things, and I’ll end up in a  possible world in which I have a car.

This is, of course, exactly how we know magic to work: by seeming coincidence.  In fact, if we trace back the chain of cause and effect, we often find the causes preceding our act of doing magic, as if the universe is weaving together a consistent story.  Some have tried to explain this weirdness of magic by calling it “retroactive enchantment.”  But if we think of magic as just moving the index across the configuration space of possible worlds, it makes absolute sense that such a thing would be.  We could not imagine magic working any other way than that, if that’s what it is.

We also know that magic in order to make me president is unlikely to work.  Sometimes people evoke probability, but there’s a problem with that: in classical probability, statistical certainty is merely the measurement of our ignorance.  To say there’s a 10% chance of something is only to say that in the past we have observed that one out of ten times have come to this outcome.  It says nothing about the situation itself, and if we knew more about it, we could get a more accurate number.  It’s a very deterministic view of the world.  If instead of invoking probability, we think in terms of distance in configuration space, we can see that some “improbable” things are actually fairly close to us in configuration space.  For example, there’s about a nearly zero chance that I’ll ever get married to a woman, but it’s only changing a few numbers describing my position in configuration space.  I know that if I did magic to do that, I’d probably succeed (gods forbid).

We can also see how the focus of magic changes when we think of it this way.  Winning the lottery is a magical goal that some people have.  But if you think in terms of configuration space, winning the lottery isn’t really a number that defines an index.  The amount of money you have is.  So doing magic to increase the amount of money you have will move you to a closer point in configuration space than doing magic to win the lottery.

So that raises the question — how do we move our index?  In other words, if magic is the selection of a possible world in configuration space, a world that already exists in the abstract sense, how do we get there?

Configuration Space

Posted in Uncategorized on December 25, 2015 by Patrick

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.

Modal Realism

Posted in Uncategorized on December 23, 2015 by Patrick

(1) If David Lewis were alive, he would not like that I am invoking his name here.

David Lewis was a philosopher who investigated modal logic, and concluded that all this talk of possible worlds — which goes all the way back to Leibniz — is a very handy way to get around a lot of the philosophical problems raised by modal if-then statements.  In fact, it’s as handy as a lot of mathematical concepts that we routinely use to solve problems, and regard as “existing” as abstract entities.  If, he suggested (and this is a brief abbreviation of his argument), we can get use out of abstract mathematical entities and regard them as existing, in some sense, then it makes sense to treat modal possible worlds as existing.

This idea is called modal realism, and it argues this:

We make sense of (1) by imagining a world in which David Lewis were still alive.  He’s not alive in this “actual” world, but he is alive — really, truly alive — in some other world about which we can make statements like (1).  We could just say that (1) is meaningless (which isn’t satisfying).  Or we could say that (1) requires us to construct some imaginary possible world.  But that’s not quite what we’re doing.  We’re not constructing such a world, he says: we’re making statements about such a world that already exists.

We exist in an actual world, but that “actual” is indexical.  It’s positioning ourselves within a framework of possible worlds.

For Lewis, and other adherents to this position, the possible worlds are causally separate.  You can’t travel between them, or communicate through them.  There’s a me who is president somewhere in the infinitude of possible worlds, but we’ll never talk or meet or anything.  Nothing I do affects him, and nothing he does affects me.  (And he is, of course, me.  And that raises whole other issues, many of them sticky.)

Don’t confuse this with the multiple universe hypothesis of quantum physics.  Completely unrelated.

Why does this matter for magic?  Because I think the causal separation of modal worlds is not entirely accurate, and I’ll explain why in my next post, when we look at configuration space and the flexibility of deictics.

Possible Worlds

Posted in Uncategorized on December 21, 2015 by Patrick

One solution to the modal logic problem presented in my last post is that such statements as this are meaningless:

(1) If I were president, I’d appoint Noam Chomsky to my cabinet.

You can just say, “Nope, the logic breaks down, so there’s no semantic content there.”  That’s an answer you can give.  I’m not president, and so anything following that arrow is nonsense.  Ip -> Cn is exactly equivalent to

(2) If I were president, I’d turpulate the gorganza bang.

This solution fails to save the appearances, though.  I’d really like to think that (1) means something, because when I say (1) people might say “Oh, no you wouldn’t,” or “he’d never accept the position” or “yeah, me too!”  If I say (2) I hope they’d rush me to the emergency room so they could see what just happened to my Wernicke’s area.

There’s another solution, and that’s that we can assess the P part of P -> Q according to possible worlds, and that the modal buried in if-statement signals us to search possible worlds for a world in which P is true (and it also implicates that P is not in fact true, in this world, which we’ll call the “actual” world, and later, for reasons that might make sense, the “indexical world.”).

So (1) means that we look through our imagination for possible worlds, and find one in which I’m president, and then see if I appoint Noam to my cabinet in that world, or if I tap Bernie Sanders instead.

Some worlds are not possible.  I don’t mean highly improbable — me being president is already pretty unlikely.  Possible worlds include anything I can say before an if-statement containing a modal that makes logical sense.  Logical sense isn’t used in its colloquial and loose meaning here, but means isn’t self-contradictory.  So:

(2) If I were a woman, I would wear a bra.

(3) If I didn’t eat meat, I’d go mad.

(4) If I were King of France, I’d wear a toupee.

And so on.  All of those imply possible worlds, in which I’m a woman, a vegetarian, and the King of France (which in our world doesn’t even exist, but we can imagine a logically consistent world in which the King of France does exist).

An impossible world would be something like this:

(5) If I were a man and not a man I’d be a dancer.

I can’t be both a man and not a man.  You can’t have A & ~A.  Just can’t.  One or the other.  So such a world isn’t possible.  I had to sit and think for a long time to come up with an example, by the way, because there are countless, countless possible worlds.

Now, here’s where things get weird — when I say “there are countless possible worlds,” I’m not speaking metaphorically.  There are countless possible worlds.  They exist.  In fact, they’re real.

And I ain’t just saying that ’cause I’m a crazy wizard.  This is an actual position of some logicians, because it solves a lot of problems with modal logic all in one fell swoop.

Modal Possibility

Posted in Uncategorized on December 18, 2015 by Patrick

Here’s a proposition:

(1) If Lincoln had not been assassinated, reconstruction after the Civil War would have gone a lot more smoothly.

In my last post, I talked about the problems with analyzing this statement according to traditional propositional logic.  But let’s reduce it to a few symbols anyway, using a somewhat more sophisticated form of logic that allows us to apply qualities to events:

~La -> Rs

In this L stands for the Lincoln, and the letter after it stands for his particular condition.  Here, it’s an a, for assassinated.  But the tilde means “not.”  So ~La means “Lincoln is not (was not, will not be) assassinated.”  The arrow is “entails,” which means that if the thing on the left is true, I am asserting that the P on the right is also true.  The P on the right is Rs, for “reconstruction” and “would have gone smoothly.”  Isn’t that nifty?  I think so.  There’s a lot more to it than that, but this lets us handle these statements in symbolic form.  If you don’t like it, well, piss off, it’s my blog and I hate the damned thing anyway, so I’ll do what I like.

Ahem.

So P(1) can be symbolized as ~La -> Rs, which is just the same as the form in traditional logic ~P -> Q, viz., The negation of the given proposition entails a second proposition.  If ~P is true (which is to say, P is false), then Q is also true.  So according to traditional logic, we’d look at this and say “Well, Lincoln was assassinated, so P is true, thus ~P is false, so therefore reconstruction would not have gone . . . more . . . smoothly?”

We have a very real sense that when I say (1) I am saying something that we could argue is true or false, but we live in a world in which Lincoln was assassinated (although other issues, such as the spelling of the Bernstein Bears, is up in the air).  We’re all quite certain that he died of a bullet during “Our American Cousin.”  We’re also mostly in agreement that reconstruction was a bit of a mess from which America is still recovering.

But we can say, if he hadn’t died, it wouldn’t have gone that way.  We can marshall evidence for how it would have gone, and make that argument, and others can argue with our argument.  They can say, “no, it made no difference,” or something.  We have a sense, in other words, that (1) can be true or false, but according to traditional logic, it’s just false.

This problem crops up only when we say “would” or “should” or “could” or some other modal verb, so this is called “modal logic,” and it leads to a startling conclusion about the nature of reality.

 

Possible Words

Posted in Uncategorized on December 17, 2015 by Patrick

Consider the proposition P

(1) I am a man.

P(1) happens to be true.  I am in point of fact a man, cisgendered and all.  Consider, now, Q:

(2) I wear a bra.

Q(2) is not true.  I don’t happen to wear a bra.  Some men do, I’m sure, and I have no problem with that at all (in fact, good on them!) but I am not one of them.  Now, consider this statement:

~P -> Q

(3) If I were not a man, I would wear a bra.

I’m aware that man and woman are not the only two options, probably more aware of that fact than most, but let’s for the sake of argument assume that ~P is equivalent to R:

(4) I am a woman.

So (3) is equivalent to:

(5) If I were a woman, I would wear a bra.

Is (5) true?

In traditional logic, R -> Q is true just in case Q is true when R is true.  But there’s a problem: What I wrote above isn’t quite accurate.  ~P -> Q isn’t (3) If I were not a man, I would wear a bra.  ~P -> Q is this:

(6) If I am not a man, then I wear a bra.

The difference between (5) and (6) is a different of modality.  (6) is making binary yes/no, true/false distinctions about the world.  (5) is making hypothetical statements about the world.  We have no problem saying that (6) is true or not true according to traditional logic, but (5) throws a wrench in traditional logic.

For a statement like (5) you need modal logic: a logic that takes into account the hypothetical.

But there are problems with that, problems that impinge on the nature of magic in ways that logicians might not like, or even be aware of.