free_will

We'll start with the idea of "free."

There are two relevant notions of the word, and it's easy to fall into a habit of slipping between them. One is the notion of not being under someone else's control, while the other is the notion of an object which can change position or a variable which can change its value. The sensation that determinism brings to mind for many people is that of having lost freedom in the second sense, and of this feeling akin to a loss of freedom in the first sense. In other words "if my actions at time t+1 are fully constrained by the state of the universe at time t, this is no better than having my actions fully constrained by some outside force or entity."

What most people have failed to realize is that these two concepts are in fundamental conflict with each other. Control is the ability to determine an item or variable's state. If an item is "free" to change position or take on a different value due to the action of some outside force, it is by definition under the control of that force. Conversely, if my actions are under my own control and not someone else's, they are no longer free to be something other than what I constrain them to be. My actions are free in the first sense if and only if they are not free in the second sense.

Now, I'm guessing that for some of you this may feel like mere semantics. If that's the case, it probably doesn't help to just remind you that since you are physics, physics has to constrain your actions, and pronounce ourselves finished. That's why we need to take the next step and address your notion of self directly. Who are you? And more importantly, what are you? You're probably used to thinking of yourself as a chunk of meat that can think, a Homo sapien. And we'll work up to that. But we have to start with an intuition that your ancestral environment never prepared you for: framing your concept of self in terms of information causality. We're used to thinking about causality in terms of objects affecting objects, and I find that the following gedankenexperiment tends to be far more effective than just reminding someone that objects are themselves information too.

Imagine taking a video camera and hooking its output up to a screen of some kind so that it outputs what it sees live. Now imagine that you take that camera and point it directly at the screen. If you adjust the camera so that it shows only the output of the screen, and the equipment is of suitably high fidelity, you can obtain a stable feedback loop where some sort of signal is looping around and around. Do this for fun in real life sometime if you get the chance. It's hard to produce stable loops, but it is possible (color balance is the hardest part to nail down). Now, what's causing the picture on the screen to be what it is? It's true to say that the specific hardware used, combined with the precise sequence of setting it up caused that picture to be what it is. But it's also true to say that the picture is now causing itself. You'll get the best intuition for this if you're able to set up a pulsing or otherwise changing image in the loop.

This thought experiment is a reminder that information processes which can control their own states are active, dynamic entities, unlike the thumb drive in your pocket that the word "information" is more likely to bring to mind. Use that sledgehammer to bash your intuition into accepting that "you" is an active information process. The fact that that information process controls some meat is incidental, not fundamental, to your consciousness. Oh, and that meat? It's information too, because physics itself is an information process.

Physics is the ocean in which you are a current. Immerse yourself in that intuition for a while. Because once you've steeped in it for long enough, the notion that the laws of physics take away your control will seem ludicrous. A deterministic physics is your control. It is the mechanism by which you think. It is the mechanism by which you act. It is the mechanism by which you continue to be. Anything that is not controlled by physics is not controlled by you, and for that physics to be deterministic merely means that no entity outside our universe is reaching in and flipping bits based on some process we have no way to know about. Yup, you heard it here first: determinism is the very definition of free will.

Now, many of you won't be there yet. You're trying to think of yourself as an information process, but the idea even in theory that someone could "look ahead" and somehow know what you're going to do before you do it is driving you crazy. It does not sound free. It sounds like being controlled by someone else. Or even if not a "being" of some sort, being controlled by "the laws of physics" or "the state of the universe". So I've got an intuition pump just for you.

Let's talk about another screen, the screen on a far simpler device: a pocket calculator. Let's say I've pulled out my trusty calculator, punched in "2, +, 2, =" and some bits of my screen have ended up darker than others. If I was an alien asking why this is the case, you have at least two approaches you can take to explaining why. The first one I'll call The Physics Explanation, and it goes something like this:
Inside the device, a chemical reaction involving manganese dioxide, lithium perchlorate, and lithium metal creates a flow of electric current along a metallic conductive pathway. Pressing of the keys mechanically alters this conductive pathway so that as it flows by and through various materials such as conductors like copper or carbon, dielectrics like barium titanate, and semiconductors like silicon, a portion of the current is directed to an electrode where its field will alter the alignment of liquid crystal cholesteryl benzoate molecules. The alteration in alignment of these molecules causes a change in the amount of reflected light passing through the glass and various polarising films, darkening some areas of the display. So ultimately, it's because of the physical construction of the device that those areas are darker than others. If the physical construction was different, different areas would have darkened.

Compare that explanation with a second approach, which I call The Math Explanation:
The symbol "2" is a member of the ordered set of symbols "0,1,2,3,4,5,6,7,8,9" typically used to denote the correspondingly ordered elements of a free monoid on a singleton free generator of "1", with "0" corresponding to the empty sequence and elements past "9" being represented in a base-10 positional notation (a.k.a "the Natural Numbers"). The symbol "+" represents the associative and commutative binary operator that generates the monoid according to the rules "a + 0 = a" and "a + the successor of b = the successor of a + b" where a and b are elements of the monoid and "=" denotes equivalence between two expressions. Confusingly (due to historical reasons), the same symbol is used to tell the calculator it should execute the instructions keyed in so far and display the result on its screen. The electronics inside the calculator implement logic corresponding to the free monoid's behaviour below some arbitrary limit, and when the button with the "=" symbol on it is pressed, the implemented logic darkens the necessary areas of the display to show (in this case) the symbol "4". So ultimately, it's because 2 + 2 = 4 that those areas are darker than others. If instead it was true that 2 + 2 = 6, different areas would have darkened.

Don't worry if you don't understand anything except the "So ultimately"s in either of those two Explanations. The point is to realise that both The Physics Explanation and The Math Explanation are true, and in fact the entire purpose of the calculator is to make them coincide. When it fails to do so it malfunctions. So which one is the real explanation? They both are, obviously. But they differ in their applicability. The first explanation is the one you'd want if you were trying to invent electronics, while the second is the one you'd want if you were trying to invent math.

There are multiple competing explanations for the story you tell yourself to understand yourself, and The Physics Explanation can sound downright oppressive if The Math Explanation isn't getting included, because our experience of our own mental operations is Math-like instead of Physics-like. That is to say, on a mental level you're less concerned with the constituent parts that make up brain-matter, and more concerned with the active information process it runs (however implemented). It doesn't matter to your thoughts which physics implements them. It only matters that they are implemented (otherwise you are dead). Just like, when most people use a calculator, they don't care which circuits make it do Math. They only care that it does Math right.

Imagine that you were the equation "2 + 2 = 4" being evaluated out. Obviously you have many characteristics that a simple equation does not, but this is just an oversimplified metaphor. Imagine that the expression "2 + 2" represented your goals for yourself and that the number 4 represented a possible action in a situation that reflected those goals (whereas numbers like 5,6, or 7 did not). Then the expression of your will is the selection of "4" as an output (ideally). Importantly, you do not know that 4 is the fulfilment of your goal until you actually arrive at it. You is not the omniscient view of the situation. You is a process, and it takes at least some computational "work" (however trivial) to reduce the expression "2 + 2" to the single natural number "4". Your initial goals may include the requirement that your output will be a natural number, but you don't have the answer until you actually find it. This means that you're probably going to model the answer as a "free variable" (in the second sense of free from earlier) which can take on any one of those possible values until you actually select one. But it certainly doesn't mean that you're going to randomly select one of those outcomes. At least, not if you're actually achieving your goals.

Sometimes one of your goals may be to randomly/pseudorandomly select the value of a variable or an output, i.e. in a cryptographic algorithm so that your adversary won't be able to determine it. But not here. And either way, you still want to be the one in control of the output (freedom in the first sense). Apply this concept to the scenario of human power games and you get a pretty good motivation for the development of the idea of free will in the first place. But back to the metaphor...

Instead, you're going to use the resources available to you to constrain the output to a specific number which you eventually learn is "4". You want the little dark spots on the screen to be stuck in a really specific, particular shape. You don't want them freely taking on all different possible kinds of shape--because you're not the dark spot. You're the active information process that controls the dark spot. Hopefully this will make clear how fundamentally broken the idea of using quantum events (whether many-worlds style or, shudder Copenhagen-style "quantum randomness") to explain free will is. In worlds where your brain fails to constrain its future states to specific values, you wouldn't find an alternate you. You would find a dead you.

This is the key intuition: you aren't the stuff, you are the math. If you are alive, then the universe is implementing you, and its future states have to be constrained by what you think, just like a working calculator has to output the dark spots dictated by the meaning of "2 + 2".

This also explains, by the way, why we tend to identify with the whole bag of meat instead of just the activity in the gooey stuff up top. Our bodies are things whose macro-states are almost completely constrained by the active information processes inside them, as opposed to the active information processes inside of all the other bags of meat. So naturally we consider them part of "self" in the same way we consider the thoughts we control part of "self". If we could all control each other's muscles through some sort of central router, I assure you the human concept of "self" would not be at the bag-of-meat level.

So, let's finally get down to the someone-else-looking-ahead-and-knowing-what-you're-doing thing. In our example, the process evaluating "2 + 2" has only partial information about the output it's selecting until it gets there. But someone else could potentially already know where that process will end up, which is our whole theoretical problem. It makes the entire "free in the first sense will" thing seem like it's just an illusion, because this imaginary theoretical person is just sitting there at the finish line before we even run the race. In terms of our evolutionary experience, they are clearly holding all the power. But don't worry, little evolved ape. We are going to pull a fast one on them with a cunning little question.

How? How does this theoretical person know where the process is going to end up?

"Well," you might say, "they might already know that 2 + 2 = 4."

And how did they know that?

"Well, they might have discovered it through piling up rocks and counting them, or they might be good enough at math to mentally do what the calculator does."

Fair enough. Would you say that any given one of those methods qualifies as a way to evaluate the expression "2 + 2"?
"Sure."

Didn't we give a name to the evaluation of that expression before? I think we called it "you".

Yup, that's right. Our theoretical person who can predict what a universe implementing you will do does it by.....implementing you. If they made it to the finish line before you did, they did it by riding on the back of another you. Now, don't work this metaphor too hard, because you will quickly get tangled up in the problem of "what computation actually is" (or do, that's awesome). But for my purposes, we're just trying to get that inner ape to smile and embrace the deterministic universe like a long-lost friend. Any process that implements you is an alive you. In our universe, an alive "you" is a co-incident Physics Explanation and Math Explanation that both do the same thing in order to implement "you". You can use whichever explanation of yourself to yourself is most useful in a given situation, but as long as you actually exist, the two explanations are equivalent. And while they remain equivalent, the Universe is your bitch. Celebrate, little ape! Throw some poop!

To sum up in point form:
- Being "free of another's control" is different than "being free to change values or states".
- The fact that my will is free in the first sense (control over my own actions) constrains my actions NOT to be free in the second sense (they could be something else). Therefore determinism is the very definition of free will.
- I am more than "stuff". I am an active information process.
- When I am alive, a physics process is coinciding with this active information process, so that a Physics Explanation of me and a Math Explanation of me are both true and equivalent, if differently useful.
- Even though I don't always know where I'm going until I get there, any process which perfectly predicts my future actions is simply another copy of me, whether implemented in this universe or a (possibly theoretical) meta- one.
- If an implementation of me didn't constrain the universe to specific future states, I would be dead (i.e. it wouldn't be an implementation of me).
- My inner ape can relax, because as long as I remain alive, the Universe is forced to "make" me do what my own inner processes dictate (a perfect coincidence of the two explanations). It's NOT a bigger ape bossing me around.