This post is also found on my new substack page.  I think it's a view of free will that might be quite interesting to the LessWrong community, both for its clarity and originality, and for its coherence within the general rationalist framework, particularly a bayesian viewpoint.

The Time Traveller: A short narrative introduction

I know you don’t know me, but thank you: you saved my wife’s life.

You see, I was trapped.  After a while I gave up hope.  I started to feel my situation was inescapable.  I couldn’t change it.  It was set in stone and no matter what I did events would somehow conspire to arrange themselves as they had to be.  I was foiled.  Time and again, no matter how ridiculous, how preposterous the unfolding of events required; somehow time would always repeat as I remembered it.

Three years from now and five years ago I got a phone call.  I was working in my lab, on the time machine, when they called and told me my wife had died in a car accident.  Her heart stopped on the way to the hospital.

I’d tried a thousand different ways to prevent it, but time always had a way of ensuring that the future I came from was the future that transpired.

It was looking at you, that day in the coffee shop, that I had my epiphany.

I was sitting across from you feeling sorry for myself.  Trapped in my fate, I found myself wishing that I were in your shoes, for you this was the present, and the future lay unknown ahead of you, free to change at your slightest whim.  Whereas for me, this was the past, and what lay ahead was more of it, more bygone years all set in stone and unchangeable.

If only I could put on your shoes.

And so in my mind’s eye, I did.  I sat there looking at the carefree expression on your face, imagining myself not knowing what was to come; trying to change it.

I imagined myself sitting in your place, deciding about my future.  I imagined how you would go home tonight to your family, if you had one.  I imagined going home to mine.

But the thought died in my mind like a vine withering in the sun.  That was it.  I couldn’t. Because no matter what happened if I went to my wife now she would still be crushed by that car in three years. Even if I were you, even if the “past” became the future again, it still stood, solid and unbreakable.  You were in the same position as me.

But that meant that I was in the same position as you.

I watched you again, looking down at the menu and trying to decide whether to order the rice or the noodles.  I took a step back and thought to myself, “Well, I can make that choice, at least.  Should I have the rice or the noodles?”

At least in that way, we were the same.

So how were we different?

And I realized both you and I were in the same position I was in, before I came here.  You can change your future with the choices you make, because you’re not really changing it, but just determining it.

It’s true, there are some things that I know will happen, and as I’ve learned, they cannot be changed.  Lord knows, I’ve tried.  But there are other things.  Things that I don’t know any more than you do, like what I’ll order from that menu.  And with regard to those things, we are in exactly the same position.

My heart starting pounding in my chest as the next thought thundered through my mind: What do I know about my Rebecca’s death?

I got a phone call from the hospital.  They asked if I was Jacob Hoffman.  They told me Rebecca had been in a crash, that her heart had stopped.

Each time I’d tried to stop the crash, I’d gone back to that room and listened again to the phone call.  Each time it had still come.

But what if it happened for some other reason?

I stood up from my booth.  I ran, heart racing, feet pounding on the hard pavement.  I burst through the door to the little apartment I’d been renting in this time.  My time machine was there. My fingers trembled as I activated its circuits.  The strange warping of spacetime took me three years into the future.

I picked up the phone and made a call, “Is this Jacob Hoffman?” I asked, in my best impression of a hospital administrator.

That was yesterday.  So again, I know you don’t know me, but thank you, you saved my wife’s life.

Deconstructing Free Will: A New Compatiblist Perspective

Some say that free will doesn’t exist, that it is an illusion or an incoherent concept.  Before we can discuss this view, we need to understand what the idea of free will is meant to be pointing to.  A rock does not have free will, because it has no will which could be free.  But I am not a rock.  Do I have something that could be called free will?  Or am I like the rock, and if so is free will simply a meaningless idea?

Clearly there’s a difference between me and the rock.  I make choices in a way that the rock does not.  Those who object to free will may say, “No, you may have the illusion that you make choices, but you are just a much more complicated version of the rock, obedient to the deterministic evolution of the laws of physics: there is no choice being made but just the tumbling chain of a myriad of dominoes.”

This claim seems to be much stronger than the claim that free will is an illusion.  It is the claim that choice is a meaningless concept.  Before discussing free will, then, we must first make clear what is meant by choice, and whether or not this concept is both coherent and actually points at something in the real world.

Defining “Choice” in a Deterministic World

Am I, fundamentally, different from a rock in this way?  Before we move on, let’s assume a determinist view.  Given that determinism is generally seen as being opposed to the concept of free will, we can only strengthen the opposition to the view that choice exists by starting from this assumption, so in this way we face the strongest version of our opponent.  We carry no poisoned blade into battle.

This also helps because we need some framework from which to discuss the topic, and explicitly adopting a deterministic view will ensure that we maintain a consistent framework throughout.  The particular view likely won’t affect the outcome of the argument, but switching between frameworks within our thinking can potentially have this effect.

What is the difference between me and the rock?  Again, I claim that the difference here is that I make choices and the rock does not. But what is this difference?  A choice begins by taking information about the world, processing it in a goal-oriented way, and outputting a reaction.

The difference between a rock and me is that I undergo this process and the rock does not.  There is nothing here that contradicts determinism, yet we can clearly see that there is an important distinction between systems that are capable of making choices in this way and systems that are not.

You might note that I included in this description that the choice-making process is goal-oriented.  Am I smuggling something in with this aspect of the definition?

We might imagine two different systems.  One is goal-oriented in some way. For instance, it could be a robot programmed to solve mazes.  It enters a maze, and at each intersection applies a decision-making algorithm to decide which way to turn.  Eventually it finds its way to the center of the maze.  We can thus describe its decision-making process as being oriented towards the goal of getting to the center of the maze.

There may be another robot that simply chooses randomly at every step.  It takes one step forward, then makes a rotation in a random direction with a probability of 1/4 of continuing forward, 1/4 of turning left, 1/4 right, 1/4 of 180 degrees.  Now it takes another step in its new direction.

Unlike the rock, this robot will eventually get to the center of the maze.  It’ll take a while.  But we should view this random behavior not as goal-oriented.

There is a complication here.  It could be that such a random algorithm turns out to be the best one for solving a particular problem.  A system designed to solve the maze (or some other particular toy problem) might be optimized by such a random design.  For instance, if you have two programs playing rock/paper/scissors against each other, their best play will simply be to randomly choose rock/paper/scissors with equal frequency.  Deviation from this strategy can be exploited.  But this issue only arises with very small and simple systems.  An LLM that simply generated random words would never be useful because as the complexity of the choices being made grows, so too must the complexity of any system that can achieve its goals when faced with those choices.  Yes, in a fixed, small world like rock/paper/scissors, a random algorithm can be optimal, but that will never be the case in complex open world problems, so for the purpose of this discussion, randomness can be differentiated from goal-seeking behavior.

There is an analogy here to the fact that entropy can and sometimes does decrease in sufficiently small systems, but this (almost certainly) won’t happen when the system gets large enough.

Given this understanding of what making a choice entails, we can say that a chess-engine makes a choice when it decides which move to make next.  It takes in the information about the state of the board and, based on its goal of winning the game, decides which piece to move where.  In contrast, we might imagine a much simpler system that just makes a random move, which we would not consider a choice.

The ability to differentiate these two cases is important in understanding the world.  Yes, both can be seen as simply the outcome of the deterministic evolution of the state of the world according to the laws of physics.  But when playing a game of chess, modeling your opponent as an agent capable of making choices based on the choices that you make will improve your ability to win the game.  When the chess-engine plays a particular move, you ask the question “why did it make that move?”.  Perhaps it is developing an attack, defending a piece, or simply improving its position.  Understanding the nature of this move is useful in playing the game.  This isn’t the case if playing against the random-move-opponent: if you know it is moving randomly you can still examine the current state of the board, but attributing some motivation to its moves is no longer useful.

The usefulness of this exercise shows that there is something objectively different between these two cases.

One is an agent, capable of making choices, the other is a process whose outputs are unrelated to the goal of the game.

This relationship between action and goal is the defining feature of choice.  This can be true even when we decide to choose randomly.  For instance, you and your friend may want to go out for dinner.  You can’t decide between pizza and Chinese food.  Both seem equally good.  So you decide to flip a coin to determine where to go for dinner.  Doesn’t this show a choice that is unrelated to its goal?  No.  The goal here is to have an enjoyable dinner.  While both choices might be equally good, choosing neither is worse than either choice.  Any decision is better than no decision at all, and so flipping a coin in this case is a good, goal-directed, solution.

Freedom in Opacity: A Chess Analogy

Now we’ve got some way to discuss choice, one that applies even in a deterministic universe, and that can differentiate between me and the rock.  The rock makes no choices because its behavior is not related to any goal.  Whether a rock rolls downhill or stays resting on a mountainside is influenced by both external events and the state of the rock, but not by reactions of the rock to external events that are oriented toward achieving some particular goal.

This is actually subtle, because we can ask “what does it mean for the rock’s reactions to be oriented in that way?”.  The rock does react to its environment.  If I kick it, my foot will hurt.  If a bird sits on it, it will be supported by the rock.  Etc.  How can we distinguish goal-oriented reactions from non-goal-oriented reactions?

The former have this quality: Actions of the environment on the rock of the same basic form will receive different responses based on their relationship to the goal.  An example might be if kicking the rock would hurt when I kick it downhill but feel good when I kick it uphill.  This isn’t true of a rock, but we could imagine an animal with soft side and a hard side that could turn itself so that its soft side always faced downhill.  People kicking the “rock” would enjoy kicking it uphill, and help it to achieve its goal of getting to the top of the hill.

A similar example comes back to our chess engine.  We could imagine a simple program that always moves a pawn forward one square when its opponent does so and when doing so is legal.  Another is an advanced chess engine that only moves its pawns forward when it determines that this is the best move.  Both are reacting to their environment, but the latter is doing so in a way that is goal-oriented.

Given this framework, we can begin to discuss the nature of free will.  I’ll claim that an agent has a will if it is able to make choices, as defined above.

But in what sense is this will “free”?  The important feature of free will, the thing that we seek to capture when using this concept, is the ability to examine various options and choose one based on one’s own criteria, free from outside influence or constraint.

The rock, and the random actor, both fail this criterion because they lack the ability to choose.  But there is another failure mode here, which is the freedom from constraint.  An agent may have a will if it can choose, even if it is not free in this way, but it doesn’t have free will.

But doesn’t this criterion necessarily exclude all agents?  We already discussed how a choice takes information about the environment and determines a response based on its applicability to some goal.  This necessarily means that it is influenced by this information.  It could even be said to be determined by this information, if this information also includes knowledge about the world included in the agent itself.  This is the objection based on determinism restated: “how can an agent make free choices if its choices are predetermined?”  Our restatement makes clearer the objection: “Given that a choice is determined by the state of an agent with respect to its environment, how can it be free?”

Before addressing this objection, let’s first look at what I would consider to be uncontroversially non-free agents.

Take a game of tic-tac-toe.  You have two computers playing each other.  They each make choices about which move to make next based on the best move available given the state of the board with the goal of winning the game.  To do this they follow a simple algorithm.  The game of tic-tac-toe is solved.  These agents are constrained by the state of the board and the requirement to always play the best move.  Sometimes there are more than one move that are equally good, but a random choice (a “coin flip”) can decide between them.  There is no freedom in the random choice, and none elsewhere in the game.  While this is an agent, whose potential actions we must take account of when planning our own, it is not a free agent.

Now take a new scenario.  I’ve been kidnapped by a mad tic-tac-toe player.  He holds a gun to my head while playing against me.  He tells me that if I fail to play one of the set of best possible moves, he’ll shoot me.  He has taken away my freedom to follow some other strategy.  Assuming I’m motivated enough not to die that I consign myself to play according to this rule, I will, like the program, be playing without free will.  I may still have free will in other respects.  I am free in my thoughts.  I’m free to fidget or nod my head, to smile or frown.  But in the specific context of the game itself, I’m lacking free will.  I am an agent, capable of playing the game intelligently, but I am not a free agent.

However, my captor grows bored of the game of tic-tac-toe.  We draw game after game.  He says, “I’m done with this.  I’m going to kill you now.”

Fearful for my life, I desperately cry out, “Wait!”  Thinking fast, I make the first suggestion that comes to mind, “Tic-tac-toe is a solved game, but maybe you’d like to play something else?  Let’s play chess instead!” 

As we begin play, my captor makes the same threat: “Make any move but the best, and I’ll blow your brains out.”

Yet my captor seems unsure of himself.  Should he pull the trigger or not?  He’s uncertain about whether or not my move was the best possible.  Did I make a blunder, or a brilliant sacrifice?  And I also begin to sweat with each move, doing my best to find optimal play, I’m uncertain whether or not each move is the best one.  I find myself vacillating between different choices: should I attack his queen with my knight or my pawn?  Which is better?

I’m still making choices, just as I was in tic-tac-toe.  But the complexity of the game brings in a certain opacity to the choice.  It’s no longer entirely clear which is the best move.

I claim that this opacity, which comes from the complexity of the situation, is an important component of what we mean by freedom.  There are many different moves that I could make whose optimality my captor was uncertain enough about that he won’t shoot me; importantly I am also uncertain in the same way, and thus now I’m free to make any of those moves.

I am no longer constrained to make certain particular moves.  Yes, given determinism, it will turn out that I will make a particular move.  But no one can predict what that move is.  Whatever constraints there are on my choice, they are at a level of complexity that I can’t model.  This feature is what is being described by free will.  It is the simple fact that thinking in terms of constraints is no longer useful beyond a certain level of complexity.

This may seem like a mundane fact.  The fact that the choice is constrained, whether I’m able to model that constraint or not, seems like the important fact.  But language should be useful to the speaker.  Given that I am the one speaking, I should use concepts that best help me to understand the world.

Free Will and Bayesianism

Allow me to apply an analogy that I think helps to illustrate this point:

When flipping a fair coin, we generally think that it has a 1/2 chance of coming up heads and a 1/2 chance of coming up tails.  That’s what being a fair coin means.  And yet, in hindsight, each flip of the coin was either heads or tails.  From the post-flip perspective, you see the coin came up heads, and you know that the chance of heads is 1, not 1/2, the chance of tails is 0, again, not 1/2.

But if we assume determinism, this outcome was determined before the flip.  If you run back the tape from the exact same initial conditions, the coin will come up heads again every time.  Sure, in some other setup, with the coin balanced ever so slightly to the right, with the molecules in the air moving in that direction rather than this, you may get a different outcome.  But given these initial conditions, the outcome is predetermined.  There’s no chance to it.

This fact doesn’t help the gambler much, though.

Why not?  If the coin is predetermined to come up heads or tails with a probability of either 1 or 0, and no values in between, why can’t the gambler take advantage of this fact to win an arbitrarily long sequence of bets?

Because the probability 1/2 isn’t a fact about the coin, it’s a fact about the gambler.  Specifically, it’s a statement about the gambler’s knowledge of the space of possible outcomes of the coin flip (or, in some sense, about the initial conditions leading to those outcomes), and their distribution.

To reiterate this crucial point: probabilities are statements about you, not statements about the world.  They are certainly influenced by facts about the world, but this is because they are, at heart, statements about your knowledge of the world.

But, clearly some aspects of probability are facts about the world.  Didn’t I talk earlier about a “fair coin”?  This is a claim about the nature of the coin, not about me.  And given that a fair coin is one defined to come up heads 1/2 of the time and tails 1/2 of the time, this is a claim about the probabilities of the coin coming up heads that’s unrelated to any fact about me.

Yes.  But let’s look again at what being a fair coin means.  It’s really a statement about the relationship of the coin to the space of possible initial conditions.  I’m not being rigorous here, but it’s something like saying that the space of initial conditions of coin-flips with a fair coin is such that it is evenly distributed between those that lead to heads and those that lead to tails.  A biased coin, in contrast, is one such that the space of initial conditions that leads to heads outnumbers those that lead to tails (or vice-versa).

This is just a statement about the way that the coin relates to the possible conditions of the world.  But when it comes time to make a coin flip, if we want to say that the probability of heads is 1/2 we need to further stipulate that I don’t know which part of the distribution of possible initial conditions that coin is in this time.  If I did, or even if I had some information that could bias me slightly toward heads even if not with certainty, then the fact that the coin is a fair coin wouldn’t force me to think the probability was 1/2; instead I might use this extra knowledge of the initial conditions (not the coin) to determine a probability of 3/4 say.

We may imagine a master coin flipper.  Someone who has practiced flipping coins for many years who is capable of biasing the result of a coin flip toward heads or tails.  He can take a fair coin and bias the outcome in one direction or the other, of his choosing.  This may not be possible for humans, but machines that can do this have been made, so the idea is at least physically possible.  The probability isn’t 1/2 anymore, not because we don’t have a fair coin, but because we know that we’re not choosing randomly from that evenly distributed set of initial conditions, instead we’re choosing from some subset which has more outcomes that lead to heads (say) than tails.

But now, imagine that I know that the master coin flipper both has this skill and is using it to bias the coin flip.  But I don’t know in which direction he’s applying himself.  Does he want heads or tails?  I don’t know.  What probability should I assign to each possible outcome here?  Clearly, 1/2.  Why?  Because, again, probabilities are statements about me, not about the coin.  1/2 is a credence, in the bayesian sense, that I assign to the outcome of the flip.  And that credence can change even if the physical set-up of the flip doesn’t change in any way, if my state of knowledge changes (for instance, if the flipper tells me his intentions).

All of this should be relatively straightforward.  It makes thinking about probability much clearer than it is from some other perspectives.  Free will can be thought of in much the same terms.

Just as determinism naively seems to break the idea of probabilities (in hindsight all outcomes are either 1 or 0, and determinism means that this was already the case even before it happened), it also seems to break the idea of free will.  But, much like probability, free will is a statement about our state of knowledge, not about the configuration of the world.

From this perspective, while it may be true that your actions were predetermined in some sense, this has no bearing on the question of free will, because you are unaware of the directionality of this predetermination.

Why should we adopt this perspective?  There’s certainly a coherent view in which we just define free will in such a way as to be false in a deterministic universe.  If we say that free will is defined as the ability “to have done otherwise”, such that if you took an action you can say “could I have done differently?”.  We then rewind the universe to its condition before your choice.  In a deterministic universe, you would then make the same choice.  What room for free will here?

But this concept is meaningless to human life, and also useless to understanding the concept of choice.  When I say I have a choice, using ordinary language, I’m clearly not making a metaphysical claim about the nature of the universe.

To take the above definition and tweak it slightly: do we mean “could have done otherwise” given a state of the universe in concordance with my knowledge about it, or given the actual state?  There are many possible states that are all consistent with my knowledge, but only one actual state.  If we mean the latter, then we don’t have free will, but we are completely unable to access the latter, it is only the former that we can actually access and talk meaningfully about.

When I say, “I have the free will to make a choice between these two options, and I’m going to apply a deterministic process to making that choice”,  I seem to be saying something contradictory, but this contradiction can be understood to be illusory.  It may be true that the deterministic decision-making process will inevitably come to a particular conclusion.  But the process itself is not aware of this conclusion until it concludes.  Much as saying that a coin has a 1/2 chance of coming up heads, we can also say that an agent has some chance of making one choice or the other.  Both are statements about our knowledge, rather than about the world.  If an agent deciding between Eggs and Oatmeal for breakfast knew more about its constraints, it may find that it cannot choose Oatmeal, in which case it would think that with respect to this particular choice it doesn’t have free will.  This is, again, a statement of its knowledge.

A Useful, Meaningful, Statement about the World

You may object to this framing.  You may say, “it is better simply to note that each choice will have only one particular outcome, whether we know what the outcome will be or not.”  But this objection is exactly as forceful as the objection to defining probabilities for coin flips.  Yes, each coin flip will have some particular outcome, either heads or tails, and not both.  In this sense, each flip has a 100% chance of coming up what it will come up, and a 0% chance of coming up differently.  This is an objective statement about the world.  But there is also a meaningful subjective statement about the world, an objective statement about our knowledge of the world, that the coin has a 50% chance of heads and a 50% chance of tails.  The same is true of our choices, and understanding this state of knowledge, and its implications, is important.  This importance arises when we deal with agents (including ourselves) whose state of mind and choice of actions has this quality of opacity.  Agents with this opacity are qualitatively different, in their actions, in the optimal way we should interact with them, from agents without this quality.  We need some way to conceptualize this difference.  Historically the concept of free will has taken this space, and I see no reason to discard it.