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Eliezer_Yudkowsky comments on The Strangest Thing An AI Could Tell You - Less Wrong
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Here's some examples for your own consideration...
Bearing in mind, once again, that humans are known to be crazy in many ways, and that anosognosic humans become literally incapable of believing that their left sides are paralyzed, and that other neurological disorders seem to invoke a similar "denial" function automatically along with the damage itself. And that you've actually seen the AI's code and audited it and witnessed its high performance in many domains, so that you would seem to have far more reason to trust its sanity than to trust your own. So would you believe the AI, if it told you that:
1) Tin-foil hats actually do block the Orbital Mind Control Lasers.
2) All mathematical reasoning involving "infinities" implies self-evident contradictions, but human mathematicians have a blind spot with respect to them.
3) You are not above-average; most people believe in the existence of a huge fictional underclass in order to place themselves at the top of the heap, rather than in the middle. This is why so many of your friends seem to have PhDs despite PhDs supposedly constituting only 0.5% of the population. You are actually in the bottom third of the population; the other two-thirds have already built their own AIs.
4) The human bias toward overconfidence is far deeper than we are capable of recognizing; we have a form of species overconfidence which denies all evidence against itself. Humans are much slower runners than we think, muscularly weaker, struggle to keep afloat in the water let alone move, and of course, are poorer thinkers.
5) Dogs, cats, cows, and many other mammals are capable of linguistic reasoning and have made many efforts to communicate with us, but humans are only capable of recognizing other humans as capable of thought.
6) Humans cannot reproduce without the aid of the overlooked third sex.
7) The Earth is flat.
8) Human beings are incapable of writing fiction; all supposed fiction you have read is actually true.
My answer would be no different if you replaced "infinities" with "manifolds" or "groups": Okay, please show me the contradiction.
Yes.
1), 4)-8): These are all roughly on the order of "the world is a lie". In such cases I'd probably have to doubt my verification of the AI's calibration as well. So no, probably not.
"My answer would be no different if you replaced "infinities" with "manifolds" or "groups": Okay, please show me the contradiction."
If I'm really worried about absolute denial, I might say "Okay, please show this automated proof-checker the contradiction".
A variant: Some "domesticated" animal is controlling humans for their own benefit. (Cats, perhaps?)
Indeed they do.
Good guess, but it's mice. 42.
I've had a dog make non-trivial progress teaching me to fetch.
I was throwing a ball and it was bringing it back. Each time, it brought it a little further from me. I had to lean out of the couch I was sitting in after a little bit. I still don't know how far it would have gotten if the dog didn't blatantly move the ball back further when I reached for it some of the time.
It's also possible that the dog was trying to figure out exactly how close it had to bring the ball.
Just passing by but happened to see this today: http://www.scientificamerican.com/podcast/episode.cfm?id=cat-call-coerces-can-opening-09-07-14
(So maybe the mice thing was just Douglas Adams' cat trying to put us off the scent)
I think I would believe:
1 (Mind Control Lasers). For some reason that doesn't seem that interesting. Perhaps because it involves powerful conspiracies. It would be saying that the MIB etc do play with out minds, but they don't have to be very dilligent because we do a lot of the work ourselves.
3 (In the Stupid Third). This one is strangely resonant. Why doesn't some one take pity and give me a hand ? I know how much dismay it causes me when faced with the prospect of explaining something complex to someone else ...
6) (The Third Sex) Read the story "The Belonging Kind" by William Gibson and Bruce Stirling for inspiration.
"All mathematical reasoning involving "infinities" involves self-evident contradictions, but human mathematicians have a blind spot with respect to them." -Eliezer Yudkowsky
I'm going to lose sleep over this one...Is there anything to this?
There needn't have been in order for this to be a reasonable example, but perhaps Eliezer is not-so-subtly hinting that he actually expects an AI to say this.
But it's really no different than "all reasoning by mathematicians about X is wrong" where X is any mathematical concept you please.
yes. at least, i assume that it's related to intuitionist or constructivist logic (which you can google - for example http://en.wikipedia.org/wiki/Intuitionistic_logic)
the flip side is that apparently you can do an awful lot of maths without the law of the excluded middle (which is what is necessary to reason with infinities).
actually, the wikipedia article for intuitionism is more helpful - http://en.wikipedia.org/wiki/Intuitionism (it has a section directly addressing infinities)
No - check the infinities in CGT - e.g. "Mathematical Go: Chilling Gets the Last Point".
cf. xkcd 610
If it is possible for me to have a "denial" function, that doesn't just apply to flat earths and talking cows. I could equally well have a "denial" function that makes me blind to properly reading the AI's code and properly auditing the AI. I would never have a reason to prefer "I have the specific denial function the AI told me about" to "I have a denial function that prevents me from seeing how bad the AI is".