Is there any rationalist equivalent of "good luck"? I've tried a few variants, such as "work well", "knock them dead", "we're with you" and certain situation-specific phrasings, but haven't found anything that worked generally - though a hearty "may all the gods of Olympus be with you!" can serve. Not a vitally important point, but it would be nice to have something similarly supportive and yet accurate to say.

Hello rationality friends!  I have a question that I bet some of you have thought about...

I hear lots of people saying that classical coin flips are not "quantum random events", because the outcome is very nearly determined by thumb movement when I flip the coin.  More precisely, one can stay that the state of my thumb and the state of the landed coin are strongly entangled, such that, say, 99% of the quantum measure of the coin flips outcomes my post-flip thumb observes all land heads.

First of all, I've never actually seen an order of magnitude estimate to support this claim, and would love it if someone here can provide or link to one!

Second, I'm not sure how strongly entangled my thumb movement is with my subjective experience, i.e., with the parts of my brain that consciously process the decision to flip and the outcome.  So even if the coin outcome is almost perfectly determined by my thumb, it might not be almost perfectly determined by my decision to flip the coin.

For example, while the thumb movement happens, a lot of calibration goes on between my thumb, my motor cortex, and my cerebellum (which certainly affects but does not seem to directly process conscious experience), precisely because my motor cortex is unable to send, on its own, a precise and accurate enough signal to my thumb that achieves the flicking motion that we eventually learn to do in order to flip coins.  Some of this inability is due to small differences in environmental factors during each flip that the motor cortex does not itself process directly, but is processed by the cerebellum instead.  Perhaps some of this inability also comes directly from quantum variation in neuron action potentials being reached, or perhaps some of the aforementioned environmental factors arise from quantum variation.

Anyway, I'm altogether not *that* convinced that the outcome of a coin flip is sufficiently dependent on my decision to flip as to be considered "not a quantum random event" by my conscious brain.  Can anyone provide me with some order of magnitude estimates to convince me either way about this?  I'd really appreciate it!

ETA: I am not asking if coin flips are "random enough" in some strange, undefined sense.  I am actually asking about quantum entanglement here. In particular, when your PFC decides for planning reasons to flip a coin, does the evolution of the wave function produce a world that is in a superposition of states (coin landed heads)⊗(you observed heads) + (coin landed tails)⊗(you observed tails)?  Or does a monomial state result, either (coin landed heads)⊗(you observed heads) or (coin landed tails)⊗(you observed tails) depending on the instance?

At present, despite having been told many times that coin flips are not "in superpositions" relative to "us", I'm not convinced that there is enough mutual information connecting my frontal lobe and the coin for the state of the coin to be entangled with me (i.e. not "in a superposed state") before I observe it. I realize this is somewhat testable, e.g., if the state amplitudes of the coin can be forced to have complex arguments differing in a predictable way so as to produce expected and measurable interference patterns. This is what we have failed to produce at a macroscopic level in attempts to produce visible superpositions.  But I don't know if we fail to produce messier, less-visibly-self-interfering superpositions, which is why I am still wondering about this...

Any help / links / fermi estimates on this will be greatly appreciated!

So, I were looking at this, and then suddenly this thing happened.

EDIT:

New version! I updated the link above to it as well. Added LOADS and LOADS of new content, although I'm not entirely sure if it's actually more fun (my guess is there's more total fun due to varity, but that it's more diluted).

I ended up working on this basically the entire day to day, and implemented practically all my ideas I have so far, except for some grammar issues that'd require disproportionately much work. So unless there are loads of suggestions or my brain comes up with lots of new ideas over the next few days, this may be the last version in a while and I may call it beta and ask for spell-check. Still alpha as of writing this thou.

Since there were some close calls already, I'll restate this explicitly: I'd be easier for everyone if there weren't any forks for at least a few more days, even ones just for spell-checking. After that/I move this to beta feel more than free to do whatever you want.

Thanks to everyone who commented! ^_^

old Source, old version, latest source

^{Credits: http://lesswrong.com/lw/d2w/cards_against_rationality/ , http://lesswrong.com/lw/9ki/shit_rationalists_say/ , various people commenting on this article with suggestions, random people on the bay12 forums that helped me with the engine this is a descendent from ages ago.}

I can't seem to get my head around a simple issue of judging probability. Perhaps someone here can point to an obvious flaw in my thinking.

Let's say we have a binary generator, a machine that outputs a required sequence of ones and zeros according to some internally encapsulated rule (deterministic or probabilistic). All binary generators look alike and you can only infer (a probability of) a rule by looking at its output.

You have two binary generators: A and B. One of these is a true random generator (fair coin tosser). The other one is a biased random generator: stateless (each digit is independently calculated from those given before), with probability of outputting zero p(0) somewhere between zero and one, but NOT 0.5 - let's say it's uniformly distributed in the range [0; .5) U (.5; 1]. At this point, chances that A is a true random generator are 50%.

Now you read the output of first ten digits generated by these machines. Machine A outputs 0000000000. Machine B outputs 0010111101. Knowing this, is the probability of machine A being a true random generator now less than 50%?

My intuition says yes.

But the probability that a true random generator will output 0000000000 should be the same as the probability that it will output 0010111101, because all sequences of equal length are equally likely. The biased random generator is also just as likely to output 0000000000 as it is 0010111101.

So there seems to be no reason to think that a machine outputting a sequence of zeros of any size is any more likely to be a biased stateless random generator than it is to be a true random generator.

I know that you can never know that the generator is truly random. But surely you can statistically discern between random and non-random generators?