Quantum Computing Since Democritus Quotes

“Even there, something inside me (and, I suspect, inside many other computer scientists!) is suspicious of those parts of mathematics that bear the obvious imprint of physics, such as partial differential equations, differential geometry, Lie groups, or anything else that's “too continuous.”
― Scott Aaronson, Quantum Computing since Democritus

“What's the point of talking about philosophical questions? Because we're going to be doing a fair bit of it here – I mean, of philosophical bullshitting. Well, there's a standard answer, and it's that philosophy is an intellectual clean-up job – the janitors who come in after the scientists have made a mess, to try and pick up the pieces. So in this view, philosophers sit in their armchairs waiting for something surprising to happen in science – like quantum mechanics, like the Bell inequality, like Gödel's Theorem – and then (to switch metaphors) swoop in like vultures and say, ah, this is what it really meant. Well, on its face, that seems sort of boring. But as you get more accustomed to this sort of work, I think what you'll find is...it's still boring!”
― Scott Aaronson, Quantum Computing since Democritus

“More often than not, the only reason we need experiments is that we're not smart enough.”
― Scott Aaronson, Quantum Computing since Democritus

“By any objective standard, the theory of computational complexity ranks as one of the greatest intellectual achievements of humankind -- along with fire, the wheel, and computability theory.”
― Scott Aaronson, Quantum Computing Since Democritus

“One immediate consequence of the Completeness Theorem is the Löwenheim–Skolem Theorem: every consistent set of axioms has a model of at most countable cardinality.”
― Scott Aaronson, Quantum Computing since Democritus

“You haven't seen the proof of that either? Alright, alright. Let's say you have an infinite set A. We'll show how to produce another infinite set, B, which is even bigger than A. This B will simply be the set of all subsets of A, which is guaranteed to exist by the power set axiom. How do we know B is bigger than A? Well, suppose we could pair off every element a A with an element f(a) B, in such a way that no elements of B were left over. Then, we could define a new subset S A, consisting of every a that's not contained in f(a). Then S is also an element of B. But notice that S can't have been paired off with any a A – since otherwise, a would be contained in f(a) if and only if it wasn't contained in f(a), contradiction. Therefore, B is larger than A, and we've ended up with a bigger infinity than the one we started with.”
― Scott Aaronson, Quantum Computing since Democritus

“On the other hand, if someone gave me a practical quantum computer tomorrow, then I confess that I can't think of anything that I, personally, would want to use it for: only things that other people could use it for!”
― Scott Aaronson, Quantum Computing since Democritus

“Model 1: But if quantum mechanics isn't physics in the usual sense – if it's not about matter, or energy, or waves – then what is it about? Model 2: Well, from my perspective, it's about information, probabilities, and observables, and how they relate to each other. Model 1: That's interesting! The commercial then flashed the tagline “A more intelligent model,” followed by a picture of a Ricoh printer.”
― Scott Aaronson, Quantum Computing since Democritus

“What should we impose if we want to avoid Grandfather Paradoxes? Right: that the output distribution should be the same as the input one. We should impose the requirement that Deutsch calls causal consistency: the computation within the CTC must map the input probability distribution to itself. In deterministic physics, we know that this sort of consistency can't always be achieved – that's just another way of stating the Grandfather Paradox. But as soon as we go to probabilistic theories, well, it's a basic fact that every Markov chain has at least one stationary distribution. In this case of the Grandfather Paradox, the unique solution is that you're born with probability ½, and if you're born, you go back in time and kill your grandfather. Thus, the probability that you go back in time and kill your grandfather is ½, and hence you're born with probability ½. Everything is consistent; there's no paradox.”
― Scott Aaronson, Quantum Computing Since Democritus

“As was mentioned before, this does feel like it's “just philosophy.” You can set things up, though, so that real decisions depend on it. Maybe you've heard of the surefire way of winning the lottery: buy a lottery ticket and if it doesn't win, then you kill yourself. Then, you clearly have to condition on being alive to ask the question of whether you are alive or not, and so because you're asking the question, you must be alive, and thus must have won the lottery. What can you say about this? You can say that in actual practice, most of us don't accept as a decision-theoretic axiom that you're allowed to condition on remaining alive. You could jump off a building and condition on there happening to be a trampoline or something that will rescue you. You have to take into account the possibility that your choices are going to kill you. On the other hand, tragically, some people do kill themselves. Was this in fact what they were doing? Were they eliminating the worlds where things didn't turn out how they wanted?”
― Scott Aaronson, Quantum Computing Since Democritus

“STUDENT: Can we even define free will?

SCOTT: Yeah, that's an excellent question. It's very hard to separate the question of whether free will exists from the question of what the definition of it is. What I was trying to do is, by saying what I think free will is not, give some idea of what the concept seems to refer to. It seems to me to refer to some transition in the state of the universe where there are several possible outcomes, and we can't even talk coherently about a probability distribution over them.

STUDENT: Given the history?

SCOTT: Given the history.

STUDENT: Not to beat this to death, but couldn't you at least infer a probability distribution by running your simulation many times and seeing what your free will entity chooses each time?

SCOTT: I guess where it becomes interesting is, what if (as in real life) we don't have the luxury of repeated trials?”
― Scott Aaronson, Quantum Computing Since Democritus

“So, I feel like these are the sorts of game-theoretic forces that Dawkins and Hitchens and the other antireligion crusaders are up against, and that they maybe don't sufficiently acknowledge in their writing. What makes it easier for them, of course, is that their opponents can't just come out and say, “yes, of course it's all a load of hooey, but here are the important social functions it serves!” Instead, religious apologists often resort to arguments that are easily demolished (at least since the days of Hume and Darwin) – since their real case, though considerably stronger, is one that's hard for them to make openly!

In summary, maybe it's true that humans (if we survive long enough) will eventually outgrow religion, now that we have something better to fill religion's explanatory role. But before that will happen, I think that at the least we'll need to better understand the social functions that religion played for most of history and still plays in most of the world, and maybe come up with alternative social mechanisms to solve the same sorts of problem.”
― Scott Aaronson, Quantum Computing Since Democritus

“We are given a biased coin that comes up heads with probability p. Using this coin, construct an unbiased coin.”
― Scott Aaronson, Quantum Computing since Democritus