Meta-Compatibilism

Salviati

A few days ago, I bought a $5 desk toy on Amazon. Now that it's here, I'm regretting the purchase. It's not nearly as good as I expected. Oh well, it's not that much money.

Simplicio

Do you ever wonder if you could have done things differently?

Salviati

What do you mean?

Simplicio

Well, take that toy, for example. Could you have decided not to buy it?

Salviati

Well, if I had known I wouldn't like it, of course I wouldn't have bought it.

Simplicio

That's not what I meant. Could you have chosen differently if you hadn't known?

Salviati

What are you talking about? I didn't know and I did buy it. What more is there to discuss?

Simplicio

Were you making a real choice, or just following the laws of physics?

Salviati

What is a "real" choice?

Simplicio

A choice which could have come out differently.

Salviati

If I had decided by flipping a coin, then it could have come out differently. But that doesn't really strike me as much of a choice.

Simplicio

No, the coin's motion is determined by chaotic air currents and subtle physical factors. There isn't any real randomness there.

Salviati

OK, what if I use a Geiger counter hooked up to a radioactive mineral? Unless you subscribe to a hidden variable theory (which I do not), the counter's clicking is truly random. No matter how much you know about the situation, you can never predict exactly when it will go off.

Simplicio

We're missing the point. I don't want to know whether a Geiger counter could have made a different choice. I want to know whether you could have made a different choice.

Salviati

Either some part of my brain acts like a miniature Geiger counter, or no such part exists. If it does exist, then yes, I could have "chosen" differently, but I don't think you'll want to count that either. If it doesn't, then obviously not.

Simplicio

So you admit it! You did not make a real choice, because real choices don't exist. We're all slaves to physics.

Salviati

Nonsense. I wanted it, and purchased it because I felt like it. My action directly resulted from my desire. No one forced me to buy it. Physics isn't a person, actively controlling my life. You still haven't given me a definition of "real choice."

Simplicio

A real choice is a choice you could have made differently, under the same circumstances, under your own conscious direction.

Salviati

But why would I want to? At the time, I thought it was a grand idea. In that state of mind, why wouldn't I buy it?

Simplicio

That's irrelevant. The question is whether you could have chosen differently, not whether you actually would have.

Salviati

What's the difference between "I could have chosen differently, but never would have," and "I could not have chosen differently?" Those sound like the same thing to me.

Simplicio

They're not. "Could" is physics. "Would" is choice.

Salviati

But you just said choice doesn't exist. Besides, how can choice be independent of physics? Unless you want to start talking about an immortal soul or something...

Simplicio

It doesn't matter. A choice-making soul would have the same logical problems as a choice-making brain. And this quibbling is pointless. Choice, as I've defined it, doesn't exist. We both agree on that much, I think.

Salviati

It doesn't exist because it is ill-defined.

Simplicio

No, it doesn't exist because it fails to refer.

Salviati

The desk toy was just an example. Setting it aside for now, all of your arguments have been a priori, that is, logical reasoning divorced from empirical evidence. If you demonstrate by logic that something can't exist, it must be logically inconsistent. You've argued that your own definition of choice is logically inconsistent. Your position is the same as mine.

The above writing format is a blatant ripoff of Galileo. I find it rather convenient, but it is admittedly unoriginal.

Watch Your Back, Git

Changeset evolution is a big deal.  But nobody seems to be talking about it.  Well, except for this guy:

But even he says it's a small set of incremental improvements.  This is not small.  But it is all a little abstract right now.  Let's write a use case.

The Pendulum and the Winch

I often find that explaining computer science to non-computer-scientists is difficult.  It's been said that computer science is like no other field of study.  Well, I think that's a rather strong claim to make.  What follows is a translation of a standard problem in computer science into physics.  It is an analogy, unrealistic but nevertheless interesting.

I have a pendulum, supported by some apparatus ultimately connected to a pillar or pole.  It is possible to move the apparatus up or down, but only by manually detaching and reattaching it by hand.  I have a winch affixed to this apparatus which may raise or lower the pendulum.  It is connected to a coil of rope or string (which, for the purposes of this problem, is infinitely long yet magically takes up a finite volume), and can be remotely controlled at the press of a button.  The winch is also geared discretely; it only turns in units, and then only one at a time.

I wish to carry out a series of experiments involving varying the length of my pendulum.  In particular, I often want to lengthen the pendulum.  Most of the time, this setup suits me quite well.  But sometimes, I find I need a pendulum longer than the apparatus is high off the ground.  In these situations, I need to climb the pillar and move the winch up.  In so doing, I may need to start an entire experiment over again because the pendulum lost energy while I was climbing.  How can I avoid or minimize those climbs in proportion to the maximum length of the pendulum?  We must assume I do not know the maximum length in advance, perhaps because my experiments are highly complex and difficult to predict, or perhaps because they are directed by someone else's instructions, and they did not think to tell me in advance how long a pendulum I would need.

The Great Picard Theorem

The great Picard theorem states that, if an analytic function contains an essential singularity, then within any punctured neighborhood of the singularity, the function takes on every value with at most a single exception.