Yeah, I'm sure the teacher wasn't making a philosophical argument. I can easily devil's-advocate for the teacher who may have thought, with some justification, that you first need to explain to children why "3 - 4" doesn't make sense and is "illegal", before you introduce negative numbers. A lot depends on the social context and the behavior of little Chris Hallquist, but it's not unusual that precocious little know-it-alls insist on displaying their advanced knowledge to the entire class, breaking up the teacher's explanations and confusing the rest of the kids. What Chris saw as a stupid authority figure may have been a teacher who knew what negaive numbers were and didn't want them in their classroom at that time.

Re: the existence of negative numbers - I was thinking more of the status of negative numbers compared to natural numbers. Negative numbers are an invention that isn't very old. A lot of very smart people throughout history had no notion of them and would have insisted they didn't exist if you tried to convince them. While natural numbers seem to arise from everyday experience, negative numbers are a clever invention of how to extend them without breaking intuitively important algebraic laws. Put it like this: if aliens come visit tomorrow and share their math, I'm certain it'll have natural numbers, and I think it likely it'll also have negative numbers, but with much less certainty.

Just as an aside, and not to criticize your frustration at your grade school math teacher, it may be worth spending some time thinking about whether negative numbers in fact exist and what exactly do you mean when you confidently assert that they do.

I'd venture a guess luck/chance in this context means winning against the odds, making decisions that should have negative or zero/little expected utility given the available information and becoming rich in spite of that.

Is luck really this difficult a concept?

I'm no theologian, but it seems to me that this view of the supernatural does not conform to the usual picture of God philosophers put forward, in terms of being the "prime mover" and so on. They are usually trying to solve the "first cause" problem, among other things, which doesn't really mesh with God as the super-scientist, since one is still left wondering about where the world external to the simulation comes from.

I agree that my definition of the supernatural is not very useful in practice, but I think it is necessary if one is talking about God at all :p. What other word should we use? I quite like your suggested "extra-natural" for things not of this world, which leaves supernatural for things that indeed transcend the constraints of logic.

Took the survey, and finally registered after lurking for 6 months.

I liked the defect/cooperate question. I defected because it was the rational way to try to 'win' the contest. However, if one had a different goal such as "make Less Wrong look cooperative" rather than "win this contest", then cooperating would be the rational choice. I suppose that if I win, I'll use the money to make my first donation to CFAR and/or MIRI.

Now that I have finished it, I wish I had taken more time on a couple of the questions. I answered the Newcomb's Box problem the opposite of my intent, because I mixed up what 2-box and 1-box mean in the problem (been years since I thought about that problem). I would 1-box, but I answered 2-box in the survey because I misremembered how the problem worked.

It defined "God" as supernatural didn't it? In what sense is someone running a simulation supernatural? Unless you think for some reason that the real external world is not constrained by natural laws?

Fun as always. Looking back at my answers, I think I'm profoundly irrational, but getting more aware of it. Oh well.

You can calculate wrong in a way that overestimates the probability, even if the probability you estimate is small. For some highly improbable events, if you calculate a probability of 10^-9 your best estimate of the probability might be smaller than that.

I've never been completely happy with the "I could make 1M similar statements and be wrong once" test. It seems, I dunno, kind of a frequentist way of thinking about the probability that I'm wrong. I can't imagine making a million statements and have no way of knowing what it's like to feel confidence about a statement to an accuracy of one part per million.

Other ways to think of tiny probabilities:

(1) If probability theory tells me there's a 1 in a billion chance of X happening, then P(X) is somewhere between 1 in a billion and P(I calculated wrong), the latter being much higher.

If I were running on hardware that was better at arithmetic, P(I calculated wrong) could be got down way below 1 in a billion. After all, even today's computers do billions of arithmetic operations per second. If they had anything like a one-in-a-billion failure rate per operation, we'd find them much less useful.

(2) Think of statements like P(7 is prime) = 1 as useful simplifications. If I am examining whether 7 is prime, I wouldn't start with a prior of 1. But if I'm testing a hypothesis about something else and it depends on (among other things) whether 7 is prime, I wouldn't assign P(7 is prime) some ridiculously specific just-under-1 probability; I'd call it 1 and simplify the causal network accordingly.

I fear I may be being rude by actually answering the question you put to me instead of engaging with your intended point, whatever it was. Sorry if so.

No, you're right. You did technically answer my question, it wasn't rude, I should have made my intended point clearer. But your answer is really a restatement of your refutation of Mitchell Porter's position, not an affirmative defense of your own.

First of all, have I fairly characterized your position in my own post (near the bottom, starting with "For patternists to be right, both the following would have to be true...")?

If I have not, please let me know which the conditions are not necessary and why.

If I have captured the minimum set of things that have to be true for you to be right, do you see how they (at least the first two) are also conjunctive and at least one of them is provably untrue?