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Did the survey.
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The dangers of zero and one
But can you be 99.99% confident that 1159 is a prime?
This doesn't affect the thrust of the post but 1159 is not prime. Prime factors are 19 and 61.
I agree that you can be 99.99% (or more) certain that 53 is prime but I don't think you can be that confident based only on the arguement you gave.
If a number is composite, it must have a prime factor no greater than its square root. Because 53 is less than 64, sqrt(53) is less than 8. So, to find out if 53 is prime or not, we only need to check if it can be divided by primes less than 8 (i.e. 2, 3, 5, and 7). 53's last digit is odd, so it's not divisible by 2. 53's last digit is neither 0 nor 5, so it's not divisible by 5. The nearest multiples of 3 are 51 (=17x3) and 54, so 53 is not divisible by 3. The nearest multiples of 7 are 49 (=7^2) and 56, so 53 is not divisible by 7. Therefore, 53 is prime.
There are just too many potential errors that could occur in this chain of reasoning. For example, how sure are you that you correctly listed the primes less than 8? Even a mere typo at this stage of the argument could result in an erroneous conclusion.
Anyway just to be clear I do think your high confidence that 53 is prime is justified, but that the argument you gave for it is insufficient in isolation.
Are the various people actually being presented with the same problem? It makes a difference if the predictor is described as a skilled human rather than as a near omniscient entity.
The method of making the prediction is important. It is unlikely that a mere human without computational assistance could simulate someone in sufficient detail to reliably make one boxing the best option. But since the human predictor knows that the people he is asking to choose also realize this he still might maintain high accuracy by always predicting two boxing.
edit: grammar
I don't think most people one-box. Maybe most LW readers one-box.
I have two real boxes, labelled with Newcomb's problem and using 1 and 4 quarters in place of the $10k and $1M. I have shown them to people at Less Wrong meetups, and also to various friends of mine, a total of about 20 people.
Almost everyone I've tried it on has one-boxed. Even though I left out the part in the description about being a really accurate predictor, and pre-seeded the boxes before I even knew who would be the one choosing. Maybe it would be different with $10k instead of $0.25. Maybe my friends are unusual and a different demographic would two-box. Maybe it's due to a quirk of how I present them. But unless someone presents contrary evidence, I have to conclude that most people are one-boxers.
This is interesting. I suspect this is a selection effect, but if it is true that there is a heavy bias in favor of one boxing among a more representative sample in the actual Newcomb's problem, then a predictor that always predicts one boxing could be suprisingly accurate.
I don't understand what the part about "fallible" and "infallible" agents is supposed to mean. If there is an "infallible" agent that makes the correct prediction 60% of the time and a "fallible" agent that makes the correct prediction 60% of the time, in what way should one anticipate them to behave differently?
It is intended to illustrate that for a given level of certainty one boxing has greater expected utility with an infallible agent than it does with a fallible agent.
As for different behaviors, I suppose one might suspect the fallible agent of using statistical methods and lumping you into a reference class to make its prediction. One could be much more certain that the infallible agent’s prediction is based on what you specifically would choose.
The problem here is that Newcomb’s problem doesn’t actually state whether you are dealing with a smart predictor or a dumb predictor. It doesn’t state whether Omega is sufficiently smart. It doesn’t state whether the initial conditions that are causally connected to your choice are also causally connected to the prediction Omega makes. So without smuggled in assumptions there is insufficient information to determine whether to one box or two box. You might as well flip a coin.
http://wiki.lesswrong.com/wiki/Omega
Omega is assumed to be a "smart predictor".
You may have misunderstood what is meant by "smart predictor".
The wiki entry does not say how Omega makes the prediction. Omega may be intelligent enough to be a smart predictor but Omega is also intelligent enough to be a dumb predictor. What matters is the method that Omega uses to generate the prediction. And whether the method of prediction causally connects Omega’s prediction back to the initial conditions that causally determine your choice.
Furthermore a significant part of the essay explains in detail why many of the assumptions associated with Omega are problematic.
Edited to add that on rereading I can see how the bit where I say, "It doesn’t state whether Omega is sufficiently smart." is a bit misleading. It should be read as a statement about the method of making the prediction not about Omega's intelligence.
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Open Thread, August 2010-- part 2
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Is this guy a crank? He seems to be claiming that he has found the E=mc^2 for intelligence, artificial or otherwise.
http://www.exponentialtimes.net/videos/equation-intelligence-alex-wissner-gross-tedxbeaconstreet
My alarm bells are going off but I am interested to hear peoples' thoughts.
Articles:
http://phys.org/news/2013-04-emergence-complex-behaviors-causal-entropic.html
http://www.newyorker.com/online/blogs/elements/2013/05/a-grand-unified-theory-of-everything.html
http://www.bbc.com/news/science-environment-22261742
Paper:
http://www.alexwg.org/publications/PhysRevLett_110-168702.pdf