The colloquial definition is “Useless but impressive and flatters my vanity”.
The probabilistic definition is “Observable thing X signals quality A means P(A|X) > P(A)”.
The economic definition is “Alice signals P to Bob by X if the net cost of X to Alice is outweighed by the benefits of Bob ‘believing’ A, and X causes Bob to ‘believe’ A even when Bob takes in to account that Alice wants him to ‘believe’ A.” (note ‘believe’ A means ‘act as if A were true’.)
The definition of limit: “lim x → a f(x) = c ” means for all epsilon > 0, there exists delta > 0 such that for all x, if 0 < |x-a|<delta then |f(x) - c| < epsilon.
The definition of derivative: f’(x) = lim h → 0 (f(x+h) - f(x))/h
That is, for all epsilon > 0, there exists delta > 0 such that for all h, if 0 < |h| < delta then |(f(x+h) - f(x))/h—f’(x)| < epsilon.
At no point do we divide by 0. h never takes on the value 0.
I will attend. Is it OK if I bring my boyfriend (User:MixedNuts) along via my iPad?
I’m open to coworking generally.
My ideal coworker is someone who is funny and interested in maths, physics and computer science. My plan would be to read books like Mathematics Form and Function or The Feynman Lectures on Physics and try to summarize / explain the content. For co working where I shut up, I am working on re-implementing MC-AIXI for my honours thesis.
Please contact me if interested, my email is patrick.robotham2@gmail.com my skype nick is grey_fox26
You’re accusing me of group selectionism? We might disagree on a point of terminology, but come on, I’m not a completely nutter. Anyway, my point in quoting the wikipedia article is that too much dishonest signalling makes signalling completely pointless (‘weakens the integrity of the signalling system’), so for signalling to work you need some way of keeping out the cheats. I’m not proposing anything as daft as “groups without cheats will prosper”. Indeed, that’s why I was making such a big deal about criterion 4 and cost asymmetry, because the analysis of signalling has to work on an individual basis, including the individuals that might be tempted to cheat.
In my limited imagination, the only way I could think of for keeping out the cheats was having an asymmetric cost structure for honest signalling compared to dishonest signalling. Thus cheating wouldn’t be worth it. I now realize this is not the only way. ialdaboth called my attention to Batesian Mimicry, where cheaters are “kept out” simply by the fact that mimics are comparatively rare. Doubtless other ways could be invented.
I think I prefer MagnetoHydroDynamics definition of signalling, and would reserve my criteria for describing costly signalling.
No. I think that because lying is common in human society, a credible signal must be costly to liars.
Well I’m happy to use “costly signalling”. I was under the impression that costly signalling was signalling. If it isn’t costly, at least for potential fakes, then I’m not sure how it can serve as an explanation for behavior. Why should I signal when the fakes can signal just as easily? What is there to gain? I think at the very least, there has to be some mechanism for keeping out cheats, even if it’s rarity. From the wikipedia article on signalling theory:
″ If many animals in a group send too many dishonest signals, then their entire signalling system will collapse, leading to much poorer fitness of the group as a whole. Every dishonest signal weakens the integrity of the signalling system, and thus weakens the fitness of the group.”
But what am I? Some kind of prescriptivist? Evidently my understanding of the term is a minority, and people far cleverer than I don’t use it my way. I’ll stick to “costly signal” in future.
“No! I must resolve the muddle” he shouted
The radio said “No, Patrick. You are the muddled one”
And then Patrick was a zombie.
A rube is a sucker, someone easily deceived.The slogan means that potential signalling explanations shouldn’t assume that the receiver of the signals is stupid.
Why not? Can’t we regard evolutionary signalling as completely analogous to cognitive signalling, just as played by genes over a much longer time scale?
That I’m a poor writer! Fixed.
I meant the peacock example evolutionarily. I got it from The Selfish Gene.
Don’t I feel like an idiot. Sorry Katja!
I agree. I think you can use signalling to explain this decision, but I wouldn’t say that it’s otherwise inexplicable. I guess I was being too cheeky.
I do think that cost asymmetry is a defining feature of signalling. To me, signalling is a way of getting around the problem of cheap talk. To me, a “cheap signal” is like an “unenforceable pre-commitment”. It defeats the point. (Of course, many people talk about pre-commitments without actually discussing the mechanics of enforcement. I view this as a grievous omission.)
I probably was too absolutist in my criteria, they should probably be read with an invisible “ceteris paribus” attached to them. I’m happy to talk of weak and strong signals.
I want to keep 4. because I make the assumption that the audience does not be deceived. Employers do not wish to hire lazy workers, and it’s in every worker’s interest to say that they aren’t lazy.
Regarding your birthday card example, I’d classify that as a white lie. Your coworker probably doesn’t care too much if he’s genuinely liked or not. Same thing with Republicanism. We could also call it a “cover story”.
Re: Good managerness, what you’re talking about is not signalling, but Gresham’s law. Decisiveness is meant as a proxy for good-managerness. Of course good manager-ness isn’t observable, that’s why we would tempted to invoke signalling in the first place! “How can I show that I’m a good manager? I know, I’ll act decisively!”.
I do agree I was being too absolutist, I do not agree that I should modify the theory. It seems to me that once we do that, we’re no longer talking about signalling as it was originally conceived. I don’t know how to argue for that other than to gesture at the economics literature, which talks about deceitful employees and employers without the werewithal to sort the wheat from the chaff.
Annendum: Katja Grace discusses signalling here and uses “costly signal” and “signal” as synonymous with my version of “signal”. (The previous version of this comment falsely attributed it to Robin Hanson, mental note: Always check the byline)
Now that you mention it, I think this does occur, although I think most of the judgement is directed at the ‘signaller’ (or in my language ‘panderer’) for being vain or duplicitous, although I don’t like saying I’m offended by it (“Offense is a sign of a weak and bourgeois mind” says my inner Dali.)
I think that ‘pandering’ does carry the connotations of how ‘signalling’ is used, but I’m happy to accept alternatives. One I can think of right away is “appealing to”, and I’d be happy to switch from ‘pandering’ to ‘appealing’ if you like.
I just mean the latter. I think explanations involving pandering can work. The trouble I have with models that postulate stupidity, is that they need people to be stupid in a convenient direction. Stupidity is a much larger target than intelligence after all. I think explanation involving pandering work if you can explain (like you did with the affect hueristic) why these tricks will work on people.
Out of curiosity, what are the connotations of the word “rube” that make you suspicious?
Fair enough. We could have “number expressions” which denote the same number, like “ssss0“, “4”, “2+2”, “2*2”. Then the question of well-definedness is whether our method of computing addition gives the same result for each of these different number expressions.
“Why does 2+2 come out the same way each time?”
Thoughts that seem relevant:
Addition is well defined, that is if x=x’ and y=y’ then x+y = x’+y’. Not every computable transformation has this property. Consider the non-well-defined function <+> on fractions given by a/b <+> c/d = (a+c)/(b+d) We know that 3⁄9 = 1⁄3 and 2⁄5 = 4⁄10 but 7⁄19 != 3⁄8.
We have the Church-Rosser Theorem http://en.wikipedia.org/wiki/Church%E2%80%93Rosser_theorem as a sort of guarantee (in the lambda calculus) that if I compute one way and you compute another, then we can eventually reach common ground.
If we consider “a logic” to be a set of rules for manipulaing strings, then we can come up with some axioms for classical logic that characterize it uniquely. That is to say, we can logically pinpoint classical logic (say, with the axioms of boolean algebra) just like we can we can logically pinpoint the natural numbers (with the peano axioms).
The belief that one can find out something about real things by speculation alone is one of the most long-lived delusions in human thought. It is the spirit of antiscience which is always trying to lead men away from the study of reality to the spinning of fanciful theories out of their own minds. It is the spirit which every one of us (whether he is engaged in scientific investigation or in deciding how to use his vote in an election) must cast out of his own mind. Mastery of the art of thought is only the beginning of the task of understanding reality. Without the correct facts it can only lead us into error.
-- Robert H. Thouless, Straight and Crooked Thinking
You’re straw-manning here. Not conceding isn’t the same thing as denying. To not concede something, one just has to omit the concession from one’s writing. But this is just quibbling. The real issue is the attitude, or the arrogance, that LW may have with respect to academia. Nobody wants to waste time justifying themselves to a bunch of arrogant amateurs after all.
Anyway, some web channels where academics hang out:
MathOverflow
LambdaTheUltimate
The arXiv
StackExchange
The N-Category Cafe http://golem.ph.utexas.edu/category/
ScienceBlogs
(Cracked.com probably does a better job of being a smart, general interest forum than Less Wrong, it’s a great deal more popular at least. But being the highest quality popular forum is a bit like being the smartest termite in the world. Specialized forums are where the elite action is.)