Which planet is closest to Earth, on average? I used to think it was Venus, followed by Mars. But this paper claims it is instead Mercury. At first this seemed to make no sense. Just picture the orbits of the planets: they're a bunch of concentric circles (approximately). Venus' orbit...
Judea Pearl's theory of causal models is a technical explanation of causality in terms of probability theory. Causality is a very fundamental part of our reasoning—if we want to understand something, the first question we ask is "why?". Then it is no surprise that this theory is very useful for...
This is a response to the post We Write Numbers Backward, in which lsusr argues that little-endian numerical notation is better than big-endian.[1] I believe this is wrong, and big-endian has a significant advantage not considered by lsusr. Lsusr describes reading the number "123" in little-endian, using the following algorithm:...
Which planet is closest to Earth, on average? I used to think it was Venus, followed by Mars. But this paper claims it is instead Mercury.
At first this seemed to make no sense. Just picture the orbits of the planets: they're a bunch of concentric circles (approximately). Venus' orbit completely encloses Mercury's. Every point of it is closer to the Earth's orbit than Mercury's orbit is. And indeed, that's how you get that Venus is the closest planet to Earth, followed by Mars, and then Mercury: take the difference between the radius of their orbits.
I think that's a good way of phrasing it, except that I would emphasize that these are two different states of knowledge, not necessarily two different states of the world.
I didn't think it would work out to the maximum entropy distribution even in your first case, so I worked out an example to check:
Suppose we have a three-sided die, that can land on 0, 1 or 2. Then suppose we are told the die was rolled several times, and the average value was 1.5. The maximum entropy distribution is (if my math is correct) probability 0.116 for 0, 0.268 for 1 and 0.616 for 2.
Now suppose we had a prior analogous to... (read more)
I could do better by imagining that I will have infinitely many independent rolls, and then updating on that average being exactly 2.0 (in the limit). IIUC that should replicate the max relative entropy result (and might be a better way to argue for the max relative entropy method), but I have not checked that myself.
I had thought about something like that, but I'm not sure it actually works. My reasoning (which I expect might be close to yours, since I learned about this theorem in a post of yours) was that by the entropy concentration theorem, most outcome sequences given a constraint have the frequencies of individual results match the maximum... (read more)
In the example in the post, what would you say is the "prior distribution over sequences of results"?
I don't actually know.
If it's a binary experiment, like a "biased coin" that outputs either Heads or Tails, an appropriate distribution is Laplace's Rule of Succession (like I mentioned). Laplace's Rule has a parameter that is the "objective probability" of Heads, in the sense that if we know our probabilities for each result giving Heads is independently. (I don't think it makes sense to think of as an actual probability, since it's not anybody's belief; I think a more correct interpretation of it is the fraction of the space of possible initial states that ends up in heads.)
Then the... (read more)
My guess that utopia happens and its inhabitants succeed in “bringing back” people preserved using cryonics is around 10%.
If you're saying this because the probability that utopia happens is low, that's unfair; if there's no utopia, none of the other interventions work either, so you should also be multiplying their micromort amounts by 10%.
If you instead think that "bringing back people is possible even in principle" has a probability of 10%, that makes more sense but I think that's way, way too low.
I'm confused about this. (I had already read Jaynes' book and had this confusion, but this post is about the same topic so I decided to ask here.)
In this example, Mr. A has learned the average numbers of red, yellow, and green orders for some past days and wants to update his predictions of today's orders on this information. So he decides that the expected values of his distributions should be equal to those averages, and that he should find the distribution that makes the least assumptions, given those constraints. I at least agree that entropy is a good measure of how little assumptions your distribution makes. The point I'm confused about... (read more)
Judea Pearl's theory of causal models is a technical explanation of causality in terms of probability theory. Causality is a very fundamental part of our reasoning—if we want to understand something, the first question we ask is "why?". Then it is no surprise that this theory is very useful for rationality, and is invoked at several points in the Sequences. This suggests a post explaining how causal models work and what they imply would be useful.
Well1, there is such a post: Causal Diagrams and Causal Models (henceforth CDCM), by Eliezer Yudkowsky, is meant as a standard introduction to the topic. But I don't think it is a very good explanation.
The bulk of... (read 7257 more words →)
When I was reading it I had the impression that the reactions of the people of Omelas to the child were meant to reference the readers' own rationalizations of suffering, in real life as well as fiction, especially in this paragraph:
... (read more)But as time goes on they begin to realize that even if the child could be released, it would not get much good of its freedom: a little vague pleasure of warmth and food, no doubt, but little more. It is too degraded and imbecile to know any real joy. It has been afraid too long ever to be free of fear. Its habits are too uncouth for it to respond to
In the FDT paper there is this footnote:
- In the authors’ preferred formalization of FDT, agents actually iterate over policies (mappings from observations to actions) rather than actions. This makes a difference in certain multi-agent dilemmas, but will not make a difference in this paper.
And it does seem that using FDT, but as a function that returns a policy rather than an action, solves this problem. So this is not an intrinsic problem with FDT that UDT doesn't have, it's a problem that arises in simpler versions of both theories and can be solved in both with the same modification.
This problem doesn't seem to be about trust at all, it seems to be about incomplete sharing of information. It seems weird to me to say Carla doesn't completely trust Bob's account if she is 100% sure he isn't lying.
The sensitivity of the test - that aliens actually abduct people, given someone is telling her aliens abducted him - is 2.5% since she doesn't really know his drug habits and hasn't ruled out there's a LARP she's missing the context for.
I would describe this not as Carla not trusting Bob, but as her not having all of Bob's information - Bob could just tell her that he doesn't use drugs, or that... (read more)
I had the same confusion when I first heard those names. It's called little-endian because "you start with the little end", and the term comes from an analogy to Gulliver
This is a response to the post We Write Numbers Backward, in which lsusr argues that little-endian numerical notation is better than big-endian.[1] I believe this is wrong, and big-endian has a significant advantage not considered by lsusr.
Lsusr describes reading the number "123" in little-endian, using the following algorithm:
Yeah, that is very neat, and I don't know how you would take it into account in the calculation. The paper does have a table comparing predictions from their formula, the old model (taking the difference of the radii) and a simulation they did, and eyeballing it, the Jupiter/Saturn distance doesn't seem to have a bigger error than other entries in the table. (Unfortunately the table only shows the planets of the Solar System, without Pluto.)