I’d really like it if someone could explain to me what Aaronson is saying here:
I’ve often heard the argument which says that not only is there no free will, but the very concept of free will is incoherent. Why? Because either our actions are determined by something, or else they’re not determined by anything, in which case they’re random. In neither case can we ascribe them to “free will.”
For me, the glaring fallacy in the argument lies in the implication Not Determined ⇒ Random. If that was correct, then we couldn’t have complexity classes like NP—we could only have BPP. The word “random” means something specific: it means you have a probability distribution over the possible choices. In computer science, we’re able to talk perfectly coherently about things that are non-deterministic, but not random.
Look, in computer science we have many different sources of non-determinism. Arguably the most basic source is that we have some algorithm, and we don’t know in advance what input it’s going to get. If it were always determined in advance what input it was going to get, then we’d just hardwire the answer. Even talking about algorithms in the first place, we’ve sort of inherently assumed the idea that there’s some agent that can freely choose what input to give the algorithm.
Aaronson is just trying to make the point that it’s possible to make a formal distinction between nondeterminism and randomness. Mathematically, a nondeterministic function is a function that returns a set of values rather than a value, and a random function is a function that returns a probability distribution over values rather than a value. The fact that we can make such a formal distinction suggests that we ought to also be able to make an informal distinction.
I was confused by the way he was using the term “non-determinism”. Then I read this:
It’s important to understand that computer scientists use the term “nondeterministic” differently from how it’s typically used in other sciences. A nondeterministic TM is actually deterministic in the physics sense
Assuming that person was correct, then it seems like Aaronson is responding to an argument that uses the physics sense of “non-determined”, but replying with the CS sense—which I’m thinking makes a difference in this case. But that’s just what it seems like to me—I must be misunderstanding something (probably a lot of things).
This was my feeling as well, that Aaronson was inappropriately using the technical definition of “nondeterministic” from CS in a context where that wasn’t the intended meaning.
I’d really like it if someone could explain to me what Aaronson is saying here:
-PHYS 771 Lecture
Aaronson is just trying to make the point that it’s possible to make a formal distinction between nondeterminism and randomness. Mathematically, a nondeterministic function is a function that returns a set of values rather than a value, and a random function is a function that returns a probability distribution over values rather than a value. The fact that we can make such a formal distinction suggests that we ought to also be able to make an informal distinction.
Well, he’s saying that. I don’t know which part of this is the part you’re having trouble with.
I was confused by the way he was using the term “non-determinism”. Then I read this:
-Theoretical Computer Science Stack Exchange
Assuming that person was correct, then it seems like Aaronson is responding to an argument that uses the physics sense of “non-determined”, but replying with the CS sense—which I’m thinking makes a difference in this case. But that’s just what it seems like to me—I must be misunderstanding something (probably a lot of things).
This was my feeling as well, that Aaronson was inappropriately using the technical definition of “nondeterministic” from CS in a context where that wasn’t the intended meaning.