by pku
3 min read20th Dec 20187 comments


I’ve always found the concept of Freedom confusing.

There’s a level on which it makes sense. When William Wallace is talking about being free from the yoke of Edward Longshanks, it’s obvious what he means – the English king and his goons regularly come to town, order people around, take their stuff and beat them up. Being free of English rule means they don’t do that anymore, and William Wallace and his friends can just go around farming and living their peaceful lives without having to worry about anything worse than the soul-crushing depression of living in Scotland.

On the other hand, what the heck does the word free mean in the context of “the land of the free and the home of the brave”? Is there even a reasonable definition? The original song is about being free from English rule, but it’s been two and a half  centuries since Edward Longshanks and his goons were ruling America, and not-being-ruled-by-the-King isn’t really a core property of most Americans’ identities these days.

I settle the first one by thinking of freedom as defined relative to a constraint. You can be free of something if you don’t have to worry about it when making decisions. This matches the common use of freedom – you’re free of having to worry about parking if you don’t have a car, free of a tyrant if you aren’t constrained by him telling you what to do, etc. This also explains why the second use seems so weird – it’s trying to use a fundamentally relative term without using it in relation to anything. So my response to the second use used to be to roll my eyes at people throw around empty deep-sounding terms.

But now I think we can resolve this. We start with the mathematical definition of degrees of freedom – your total freedom level at a given time is the number of options you have available to you at that time (if you want to sound all mathy, you can call this the local dimension of your options space or something)[1].

But there’s a fundamental problem here: At the end of the day you’ll only pick one of the options you had, because you can only pick one – once you eliminate the big constraints, you’ll just be subject to smaller and smaller constraints until you’re down to one option. Even if there’s no law forcing you to wear black socks, you’ll end up wearing black socks by the constraint that they were a dollar cheaper on Amazon and you were too lazy to scroll down. If you actually incorporate every single constraint you have, you end up having one action. Can we solve this using more math?

Yes. Let f(x) be the utility function on the space of possible positions you can be in. In this definition, the choice you make in a given position is simply to take a step in whichever direction increases f(x)the most. We generally think of constraints as cliffs in the utility function – if you disobey the tyrant he’ll probably kill you, so the “disobey tyrant” direction of decision space has a massive drop in f(x). Smaller constraints, like “white socks are a dollar more and involve scrolling down on Amazon”  are only minor dips in f(x).

In this case, we can think of absolute freedom as a measure of flatness of f – Some measure of how many directions you can go without falling down too big a cliff. There are a lot of ways to formally measure this, but the idea is that this should be a value that goes down more by wider or steeper cliffs (although steepness has diminishing returns – the difference between a specific option getting you badly injured or killing you is fairly minor if you can easily just not take that option). In a sense, this is just a measure of resilience – how many non-terrible routes do you have? Because your position and options are constantly changing, there’s a lot of value in having multiple non-terrible paths.

Finally, note that under this definition freedom definitely isn’t all we want – we also like having opportunities to massively increase our utility (instead of just saving ourselves from decreasing it too much). We can think of Welfare vs. Freedom as increasing our EV vs. reducing our variance.

[1] There’s an issue here with how to count/measure options – e.g. “go to the ball/don’t go to the ball” is clearly a freer choice than “go to the ball wearing white socks/go to the ball wearing black socks” – but like most measure issues you can mostly just ignore it and use your intuition.

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The thing that you are calling "freedom" seems to be the inability to act, to make a choice. Why would this be a desirable thing?

Here's something I've quoted a couple of times before on LessWrong. Time to bring it out again:

"You pride yourself on freedom of choice. Let me tell you that this very freedom is one of the factors that most confuse and undermine you. It gives you full play for your neuroses, your surface reactions and your aberrations. What you should aim for is freedom from choice! Faced with two possibilities, you spend time and effort to decide which to accept. You review the whole spectrum of political, emotional, social, physical, psychological and physiological conditioning before coming up with the answer which, more often than not, does not even satisfy you then. Do you know, can you comprehend, what freedom it gives you if you have no choice? Do you know what it means to be able to choose so swiftly and surely that to all intents and purposes you have no choice? The choice that you make, your decision, is based on such positive knowledge that the second alternative may as well not exist."

-- Rafael Lefort, "The Teachers of Gurdjieff", ch. XIV

Every choice you make removes that choice from you. If your first thought on making a decision is "Was that the right decision?" then you did not make a decision. When you have truly made a decision, the decision is no longer in front of you, it is behind, receding into the past. Every step in the dance moves on, cutting off from realisation all the steps that were not made in order to make this one.

No-one is granted a God's eye view of the whole garden of forking paths, from where you might experience all the different possibilities together without ever having to choose among them. You only get a single run-through of the game.

I'm very confused about this. Here's what I think you're saying:

Choices are bad, particularly with regards to regret. It is better to make a decision based on instinct and forget about it than to consider your options carefully and potentially regret the decision.

Is that about right or is there something that I'm missing?

The quote (in my undertanding of it) is not about "instinct", i.e. not knowing why you did something. Quite the opposite: it is seeing things clearly enough to make the right choice quickly and knowingly. Recognising what must be done and why, not dithering in "choice". And this is recommended as the way to live, or to strive to live. Achieving anything requires action, action requires choice, and choices must actually be made, cutting off paths as the sculptor cuts away marble, destroying all the sculptures that could be made except for the one that he has decided to make. The sculptor who sits beside a block of marble, merely contemplating the great works that he might make but never raising his chisel to the stone, is failing as a sculptor.

Thanks, got it! I hadn’t read the post as advocating a lack of decision but re-reading it now I can see how you read it.

Its not obvious to me why some things feel constraining and some do not. For example you could say that 'every country in the world has the death penalty for stepping in front of a moving bus'. Obviously transhumanists probably do feel constrained by a lack of technological solutions. But the bus death penalty just does not both me the way a human made law does.

If you actually incorporate every single constraint you have, you end up having one action.

You can't infer backwards to the idea that a decision was made deterministically (whether physical or rational determinism) from that fact that only one decision actually gets made.

In this case, we can think of absolute freedom as a measure of flatness of f

If f is absolutely flat, it isn't determining your decisions.