= 27d567bc2d48d9f40e9ccc20ea370b15)
Thanks to everyone. I was winging it with the biblical phrasing, only because I thought it added a little style to the piece overall.
Congratulations - now you are less wrong about that ;)
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.
As to the teacher, yeah that sounds plausible. If Chris wants to satisfy our curiosity he can expand a little on how that conversation went. In my experience, teachers can really be dicks about that kind of thing.
AFAIK, integers (including negative integers) occur in nature (e.g. electrical charge) as do complex numbers. Our everyday experience isn't an objective measure of how natural things are, because we know less than John Snow about nearly everything.
I'd bet any aliens who get here know more than us about the phenomena we currently describe using general relativity and quantum mechanics. If they do all that without negative or complex numbers I'll be hugely surprised. But then I'd be super surprised they got here at all :)
In response to
The Limits of Intelligence and Me: Domain Expertise
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 expect the math teacher wasn't making any kind of philosophical argument such as "do any numbers exist, and if so in what sense?" There is a different connotation, for my idiolect anyway, between "no such thing as X" and "X does not exist".
It's possible that the only numbers that exist are the complex numbers, and that more familiar subsets such as the hilariously named "real" and "natural" numbers are invented by humans. I appreciate that this story is usually told the other way round.
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.
Well, I can't find any use for the word supernatural myself, even in connection with God. It doesn't seem to mean anything. I can imagine discussing God as a hypothetical natural phenomenon that a universe containing sentient life might have, for example, without the s word making any useful contribution.
Maybe anything in mathematics that doesn't correspond to something in physics is supernatural? Octonions perhaps, or the Monster Group. (AFAIK, not being a physicist or mathematician)
In response to
2013 Less Wrong Census/Survey
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.
Heh. I also didn't care about the $60, and realised that taking the time to work out an optimal strategy would cost more of my time than the expected value of doing so.
So I fell back on a character-ethics heuristic and cooperated. Bounded rationality at work. Whoever wins can thank me later for my sloth.
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?
If everything in your universe is a simulation, then the external implementation of it is at least extra-natural from your point of view, not constrained by any of the simulated natural laws. So you might as well call it supernatural if you like.
If you include all layers of simulation all the way out to base reality as part of the one huge natural system, then everything is natural, even if most of it is unknowable.
In response to
2013 Less Wrong Census/Survey
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.
True. I suppose I was unconsciously thinking (now there's a phrase to fear!) about improbable dangerous events, where it is much more important not to underestimate P(X). If I get it wrong such that P(X) is truly only one in a trillion, then I am never going to know the difference and it's not a big deal, but if P(X) is truly on the order of P(I suck at maths) then I am in serious trouble ;)
Especially given the recent evidence you have just provided for that hypothesis.
= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d){kind=logo}
It made his life more interesting, and helped him socialize with classmates who believed in Santa.
I'm not going to criticise your decision, especially with regard to the social situation at school, which I can't speculate about. But I doubt it's more interesting to believe in the weird collection of junk memes that Santa Claus has become.
Maybe it's just me, but I think the truth is always more interesting, because there's aways more detail in it. Fake things are ultimately very boring; you poke at them a bit and there's nothing there. Flying reindeer are just pictures of approximately deer-like animals (usually more like red deer) positioned above the ground. Real reindeer are pretty amazing.