A very good point! If someone dies, I guess their expected recidivism rate should drop to zero so as not to affect the rate that the prison is targeting.
And I wonder what the incentives are for parole boards and officers? Who controls regulations, bonuses, and promotions for this group? This is definitely something worth researching.
This still incentivizes prisons to help along the death of prisoners that they predict are more likely then the prison-wide average to repeat-offend, in the same way average utilitarianism recommends killing everyone but the happiest person (so to speak).
I think that analysis is actually the easiest entry point to the kind of mathematical reasoning that I have in mind for people who have learned calculus. Most of the theorems are at least somewhat familiar, so one can focus on the logical rigor without having to simultaneously having to worry about understanding what the high level facts are.
I see. That could be right. I guess I'm thinking about this (this = what to teach/learn and in what order) from the perspective of assuming I get to dictate the whole curriculum. In which case analysis doesn't look that great, to me.
Oh, sure, in expressing agreement with Epictetus I was just saying that I don't think that you get the full benefits that I was describing from basic discrete math. I agree that some students will find discrete math a better introduction to mathematical proof.
Ok that makes sense. I'm still curious about any specific benefits that you think studying analysis has, relative to other similarly deep areas of math, or whether you meant hard math in general.
I agree with Epictetus' comment.
To my mind all of these things are better suited for learning the power of proof and the mathematical way of analyzing problems.
I think the main thrust of the article was less about the power of mathematics and more about the the habits of close reading and careful attention to detail required to do rigorous mathematics.
I'm not totally sure why, but I think a big part of it is that analysis has a pretty complicated technical foundation that already implicitly uses topology and/or logic (to define limits and stuff), even though you can sort of squint and usually kind of get away with using your intuitive notion of the continuum.
Seems like it's precisely because of the complicated technical foundation that real analysis was recommended. Theorems have to be read carefully, as even simple ones often have lots of hypotheses. Proofs have to be worked through carefully to make sure that no implicit assumptions are being introduced. Even great mathematicians ran into trouble playing fast and loose with the real numbers. It took them about two hundred years to finally lay rigorous foundations for calculus.
Seems like it's precisely because of the complicated technical foundation that real analysis was recommended.
What I'm saying is, that's not a good reason. Even the math with simple foundations has surprising results with complicated proofs that require precise understanding. It's hard enough as it is, and I am claiming that analysis is too much of a filter. It would be better to start with the most conceptually minimal mathematics.
Even great mathematicians ran into trouble playing fast and loose with the real numbers. It took them about two hundred years to finally lay rigorous foundations for calculus.
...implying that it is actually pretty confusing. There are good reasons for wanting to learn analysis because it is applied so widely. But from the specific perspective of trying to learn lessons about math and rigorous argument in general, it seems like you want a subject that is legitimate math but otherwise as simple as possible. To some extent, trying to do real analysis as a first real math class is like trying to teach physics class in a foreign language. On the one hand, you just want to learn the physics, but at the same time you always have to translate into your native tongue, worrying that you made a subtle mistake in translation. If you want to learn how to prove stuff in general, you don't also want the objects that you're proving stuff about to be overcomplicated to the point that it's a whole chore just to understand what you're talking about. That is an important but distinct skill from understanding and inventing proofs.
Could you say more about why you think real analysis specifically is good for this kind of general skill? I have pretty serious doubts that analysis is the right way to go, and I'd (wildly) guess that there would be significant benefits from teaching/learning discrete mathematics in place of calculus. Combinatorics, probability, algorithms; even logic, topology, and algebra.
To my mind all of these things are better suited for learning the power of proof and the mathematical way of analyzing problems. I'm not totally sure why, but I think a big part of it is that analysis has a pretty complicated technical foundation that already implicitly uses topology and/or logic (to define limits and stuff), even though you can sort of squint and usually kind of get away with using your intuitive notion of the continuum. With, say, combinatorics or algorithms, everything is very close to intuitive concepts like finite collections of physical objects; I think this makes it all the more educational when a surprising result is proven, because there is less room for a beginner to wonder whether the result is an artifact of the funny formalish stuff.
PSA: If you wear glasses, you might want to take a look behind the little nosepads. Some... stuff... can build up there. According to this unverified source it is oxidized copper from glasses frame + your sweat, and can be cleaned with an old toothbrush + toothpaste.
If the demons understand harm and are very clever in figuring out what will lead to it, what happens when we ask them minimize harm, or maximize utility, or do the opposite of what it would want to do otherwise, or {rigidly specified version of something like this}?
Can we force demons to tell us (for instance) how they'd rank various policy packages in government, what personal choices they'd prefer I make, &c., so we can back-engineer what not to do? They're not infinitely clever, but how clever are they?
There are ten thousand wrong solutions and four good solutions. You don't get much info from being told a particular bad solution. The opposite of a bad solution is a bad solution.
Probably yes, see: http://www.alexa.com/siteinfo/hpmor.com
Lol yeah ok. I was unsure because alexa says 9% of search traffic to LW is from "demetrius soupolos" and "traute soupolos" so maybe there was some big news story I didn't know about.
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(Upvoted, thanks.)
I think I disagree with the statement that "Getting direct work done." isn't a purpose LW can or should serve. The direct work would be "rationality research"---figuring out general effectiveness strategies. The sequences are the prime example in the realm of epistemic effectiveness, but there's lots of open questions in productivity, epistemology, motivation, etc.