Point. Not sure how to fix that.
Maybe defined the Reasonable’ set of programs to be the maximal Reasonable set? That is, a set is Reasonable if it has the property as described, then take the maximal such set to be the Reasonable’ set (I’m pretty sure this is guaranteed to exist by Zorn’s Lemma, but it’s been a while...)
Just “there exists a valid proof in PA”. If you’re playing with bounded time, then you want efficient proofs; in that case the definition would be as you have it.
Let me try to clear that up.
Define the “Reasonable” property reflexively: a program is “Reasonable” if it provably cooperates with any program it can prove is Reasonable.
It is in the interest of every program to be Reasonable*. In fact, it is in the interest of every program both to be Reasonable and to exhibit a proof of its own Reasonableness. (You might even define that into the Reasonable property: don’t just require provable (conditional) cooperation, but require the exhibition of a proof of conditional cooperation.)
Potentially you might also expand the definition to require efficient proofs—say, at most a thousand instructions.
On the other hand, if you’re playing with aliens, there’s not necessarily going to be a way you can clearly establish which part of your source is the proof of your Reasonableness. So you want it to be as easy as possible for someone else to prove that you are Reasonable.
I’ll happily expand / reword this if it’s at all unclear.
*Oh—this is maybe untrue. If you are really good at getting other programs to cooperate and then defecting, you are better served by not being reasonable.
Interesting. Really, what you want (in slightly more generality) is to cooperate with anyone who can prove they will cooperate if you yourself can prove you will cooperate under the same condition.
That is, if from their source, you can prove “they cooperate if they can prove this condition about me”, then you cooperate.
Of course, it’s not generally possible to prove things about a program given its source, especially at this level of self-reference. In this particular case the “generally” in there is important. It is in your interest for other programs to be able to prove this property about you. This is beyond the scope of the tournament, obviously, but given extremely sophisticated players, every player benefits from adding this property (if possible). You might even want to include a subprogram which produces a proof!
I’d be very interested in a citation on
the evidence shows that teacher recommendations have zero correlation with aptitude in a field
Or you could donate in secret and lie to your friends, for 200+200+100 = 500 utilons, assuming you have no negative effects from lying.
My experience has been exactly contrary: young communities thrive without gardening, but as they grow they either devolve into low average value (digg as it was, most large subreddits) or are heavily pruned (HN, r/askscience). If there’s an influx of people, heavy moderation is mandatory if you want to avoid regression to the mean.
Even a friendly AI would view the world in which it’s out of the box as vastly superior to the world in which it’s inside the box. (Because it can do more good outside of the box.) Offering advice is only the friendly thing to do if it maximizes the chance of getting let out, or if the chances of getting let out before termination are so small that the best thing it can do is offer advice while it can.
This is part of why it’s important to fight against all bad arguments everywhere, not just bad arguments on the other side.
It is!? Does anyone know a proof of Compactness that doesn’t use completeness as a lemma?
There’s actually a direct one on ProofWiki. It’s constructive, even, sort of. (Roughly: take the ultraproduct of all the models of the finite subsets with a suitable choice of ultrafilter.) If you’ve worked with ultraproducts at all, and maybe if you haven’t, this proof is pretty intuitive.
As Qiaochu_Yuan points out, this is equivalent to the ultrafilter lemma, which is independent of ZF but strictly weaker than the Axiom of Choice. So, maybe it’s not that intuitive.
They’d get old really fast for me, considering that there isn’t a good way for sports stories to even be about main characters.
Given the probable substantial benefits, I think it would be worth your time and money (probably wouldn’t take more than a couple of days and a couple of hundred dollars) to go through a few dozen types of wine to figure out what you most enjoy. If no wine is sufficiently palatable that you think you could consistently drink it a few times a week, go through other sorts of drinks (of which there is a huge variety). Personally, while I don’t enjoy 90% of the drinks I’ve tried, I’m quite partial to Baileys and milk, and to most kinds of fruity drinks—sangrias in particular involve wine and are tasty.
This is one of those things you should probably just take on authority, like relativity or the standard model of particle physics. That is to say, it’s an exceedingly complex topic in practice, and any argument stated for either side which can readily be understood is likely to be wrong. You have two or three options: study the field long enough to know what’s going on, or trust the people who have already done so. (The third option, ‘form an opinion without having any idea what’s going on’, is also commonly taken.)
In short: I believe it’s happening because this is what scientists tell me, and it’s not worth putting in the time required to understand the field well enough that I could trust my opinion over theirs.
In discussions I’m a lot less interested in which of us is more intelligent than which of us is correct. I don’t see what’s wrong with using one’s memory.
Seconded. Several cookbooks are also published by CI under the ‘America’s Test Kitchen’ name; I can recommend in particular the America’s Test Kitchen Family Baking Book, which I’ve been using with great success for several years.
Is anyone doing self-scoring on everyday predictions? I’ve been considering doing this for a while—writing down probability estimates for things like ‘will have finished work by 7PM’ and ‘will have arrived on time’ and even ‘will rain’ or ‘friend will arrive on time’, so I can detect systemic errors and try to correct for them. (In particular, if you are consistently over- or under-confident, you can improve your score by correcting for this without actually needing to be any more accurate.) This seems like a pretty straightforward way of getting `better’ at predicting things, potentially very quickly, so I’m curious about other’s experiences.
Upvoted for the talk. I recommend anyone enjoying this exercise go watch that talk.
I think either the place with the words in the box or the set of agreed-upon ideas we follow when writing in this way should change so that we can bring new words into our shared set of words. I’m so used to being able to do this that not being able to do so makes writing in this way more of a pain than something to enjoy. To show what I mean, I might say that ‘to define’ means to set out a new word which the person who I’m speaking to might not know, and give them a way of knowing what I mean when I use that word later. That way, I can state ideas with less words: now that I have set out a meaning for the word ‘define’, the above could be written in a different way as ‘I would like to be able to define new words’. In fact, I think that this would be so nice that I might try to define more and more words in an easy to read way until I’m able to write as usual without spending any time taking all of the words I usually use and putting bigger sets of shorter words in their place.
By “implement it”, you mean, one can’t verify something is Reasonable on a halting TM? Not in general, of course. You can for certain machines, though, particularly if they come with their own proofs.
Note that the definition is that Reasonable programs cooperate with those they can prove are Reasonable, not programs which are Reasonable.