My understanding is that the "appeal to authority fallacy" is specifically about appealing to irrelevant authorities. Quoting a physicist on their opinion about a physics question within their area of expertise would make an excellent non-fallacious argument. On the other hand, appealing to the opinion of say, a politician or CEO about a physics question would be a classic example of the appeal to authority fallacy. Such people's opinions would represent expert evidence in their fields of expertise, but not outside them.

I don't think the poster's description makes this clear and it really does suggest that any appeal to authority at all is a logical fallacy.

Is it really off-topic to suggest that looking at the accuracy of the courts may amount to rearranging the deck chairs on the titanic in a context where we've basically all agreed that

1. the courts are not terrible at making accurate determinations of whether a defendant broke a law

2. The set of laws where penalties can land you in prison are massively inefficient socially and in most people's minds unjust (when we actually grapple with what the laws are, as opposed to how they are usually applied to people like us, for those of us who are white and not poor).

3. The system of who is tried versus who makes plea bargains versus who never gets tried is systematically discriminatory against those with little money or middle/upper class social connections, and provides few effective protections against known widespread racial bias on the part of police, prosecutors and judges.

How different is this in principle from TimS's suggestion about lower hanging fruit within evidentiary procedure, just at a meta level? Or did you consider that off-topic as well?

Eliezer has proposed that an AI in a box cannot be safe because of the persuasion powers of a superhuman intelligence. As demonstration of what merely a very strong human intelligence could do, he conducted a challenge in which he played the AI, and convinced at least two (possibly more) skeptics to let him out of the box when given two hours of text communication over an IRC channel. The details are here: http://yudkowsky.net/singularity/aibox

Confidence that the same premises can imply both ~T and T is confidence that at least one of your premises is logically inconsistent with he others -- that they cannot all be true. It's not just a question of whether they model something correctly -- there is nothing they could model completely correctly.

In puzzle one, I would simply conclude that either one of the proofs is incorrect, or one of the premises must be false. Which option I consider most likely will depend on my confidence in my own ability, Ms. Math's abilities, whether she has confirmed the logic of my proof or been able to show me a misstep, my confidence in Ms. Math's beliefs about the premises, and my priors for each premise.

The present value of my expected future income stream from normal labor, plus my current estimated net worth is what I use when I do these calculations for myself as a business owner considering highly risky investments.

For most people with decent social capital (almost anyone middle class in a rich country), the minimum base number in typical situations should be something >200kUS$ even for those near bankruptcy.

Obviously, this does not cover non-typical situations involving extremely important time-sensitive opportunities requiring more cash than you can raise on short notice (such as the classic life-saving medical treatment required).

I, too, find it hard to care about Sleeping Beauty, which is perhaps why this post is the first time in years of reading LW, that I've actually dusted off my math spectacles fully and tried to rigorously understand what some of this decision theory notation actually means.

So count me in for a rousing endorsement of interest in more practical decision theory.

I'm not sure it isn't clearer with 'x's, given that you have two different kinds of probabilities to confuse.

It may just be that there's a fair bit of inferential distance to clear, though in presenting this notation at all.

I have a strong (if rusty) math background, but I had to reason through exactly what you could possibly mean down a couple different trees (one of which had a whole comment partially written asking you to explain certain things about your notation and meaning) before it finally clicked for me on a second reading of your comment here after trying to explain my confusion in formal mathematical terms.

I think a footnote about what probability distribution functions look like and what the values actually represent (densities, rather than probabilities), and a bit of work with them would be helpful. Or perhaps there's enough inferential work there to be worth a whole post.

I think of this as "heresy", and agree that it is a very useful concept.

Bringing myself back to what I was thinking in 2007 -- I think we have some semantic confusion around two different sense of absurdity. One is the heuristic Eliezer discusses -- the determination of whether a claim/prediction has surface plausibility. If not we file it under "absurd". An absurdity heuristic would be some heuristic which considers surface plausibility or lack thereof as evidence for or against a claim.

On the other hand, we have the sense of "Absurd!" as a very strong negative claim about something's probability of truth. So "Absurd!" stands in for "less than .01/.001/whatever", instead of a term such as "unlikely" which might mean "less than .15"

I was talking only about the first sense. It seemed to me that Eliezer was making a very strong claim that the absurdity heuristic (in the first sense) does no better than maximum entropy. That's equivalent to saying that surface plausibility or lack thereof amounts to zero evidence. That allowing yourself to modify probabilities downward due to "absurdity" even a small amount would be an error.

I strongly doubt that this is the case.

I agree completely that a claim of "Absurd!" in the second sense about a long-dated future prediction cannot ever be justified merely by absurdity in the first sense.

You have to be careful with counterfactuals, as they have a tendency to be counter factual.

In a world in which soldiers were never (or even just very very rarely) deployed, what is the likelihood that they would be paid (between money and much of living expenses) anywhere near as well as current soldiers and yet asked to do very very little?

The reason the lives of soldiers who are not deployed are extremely low-stress and not particularly difficult is because of deployment. They are being healed from previous deployments and readied for future deployments. In the current environment where soldiers are being deployed for much longer periods with much shorter dwell times, it's very likely that the services are doing everything they can to make the dwell time as low-stress as possible. 3 hours at the gym and 3 hours doing a relatively low-stress job in your field sounds like what a lot of people I know who are "retired" do. It sounds like a schedule designed to make your life as easy as possible while still keeping you healthy and alert, rather than falling into depression.

In a counter factual world where the army was almost never deployed, they would surely be used for some other purpose on a regular basis, police/rescue/disaster relief/etc. or simply be much much smaller, with pay not needing to be as competitive. We've even experienced this to an extent -- during peaceful times, the active duty military shrinks dramatically, and most of our army is in a reserve or national guard capacity, where they have day jobs, and do not get full time pay from the army unless they are called up to active service. This is still to most accounts a pretty good gig (especially if you use it to get free college tuition) even though it can't replace full time work -- as long as you don't get called up.

In fact, I think that's what some of the people my age that I know in the service were expecting when they joined in peacetime. Very rare callups for crucial work they felt obligated to do well for the good of the country or world. Didn't work out that way though.