Yes. It’s much harder to find clear cases for ignorance than to find clear cases for randomness. That makes it telling that the P/P problem is about a case where it’s at least arguable.
Usually bread and/or cereal.
Your point that it might make sleep less effective even if it reduces falling asleep time is well taken.
Well, the disclaimer here is that I wrote that without giving it conscious thought, so I have to examine why I believe it retroactively. I notice that I’m pretty confident.
I think the biggest reason is just that it feels that way. The second is that I sometimes intent to go to bed, notice that I’m hungry, then eat something and go back to bed, and I seem to sleep better than average on those cases.
I’ve only tried to use it deliberately once. It was recently; I failed to fall asleep for about an hour, at which point I usually give up and just stay awake longer. Instead I got up, deliberately ate too much and went back to bed. It actually worked.
The meditation one in particular sounds interesting. I’ll try it. flux is something I’ve already experimented with, and I do exercise regularly.
I’ve had the opposite experience with eating – if I eat a lot right before going to bed, it seems to help. But I guess it’s not too surprising if that one differs from person to person.
Thanks. That is very useful to know.
I’ve already been convinced by gwern that melatonin is worth taking, but it’s prescription-only where I live. Still, you’ve given me a better sounding reason why I need it. I’m definitely going to ask for it the next time I see a doctor.
Is there anything one can do for shortening the amount of time needed to fall asleep, and making it more robust? Currently I will be unable to fall asleep if I’ve overslept on the previous day or engaged with something too stimulating before going to bed. This is still true even though I’ve followed a strict schedule for a fairly long time. It’s pretty annoying.
Something I already do is sleep with white noise, partially to make it less likely that I’ll wake up from unexpected sounds.
It could be argued that it’s all ignorance. The die will roll the way that physics demands, based on the velocity, roll, pitch, yaw of the die, and the surface properties of the felt. There’s only one possible outcome, you just don’t know it yet. If you roll a die in an opaque cup, the uncertainty does not change in kind from the time you start shaking it to the time you slam it down—it’s all the same ignorance until you actually look.
You can, if you like, believe that there is unknowability at the quantum level, but even that doesn’t imply true randomness, just ignorance of which branch you’ll find your perceptive trail following.
I’m not going to argue for unknowability at the quantum level, but I will argue (in the next post) that you are not sufficiently smart to differentiate precisely enough between the different possible situations, and that’s why you have to group a bunch of different situations together, and that’s how you get what I call randomness. I’m not arguing for or against any kind of “true” randomness. I agree that you can argue it’s all ignorance, but (I claim) not doing so will solve a lot of problems
If learning complicated things isn’t hard, then what’s the bottleneck on learning a new field?
Has anyone written a summary of all organizations that work on AI alignment? If not, what is the best way to keep track of that?
Yeah, your goal is not always to deeply understand the material you’re looking at, and the post only applies when it is.
Yes, great correction. I’ve modified the post to state that it only applies for Deep Things You Truly Want To Understand.
I’m often confronted with the difference you’re describing but haven’t ever articulated it as you just have.
I honestly don’t think the tradeoff is real (but please tell me if you don’t find my reasons compelling). If I study category theory next and it does some cool stuff with the base map, I won’t reject that on the basis of it contradicting this book. Ditto if I actually use LA and want to do calculations. The philosophical understanding that matrix-vector multiplication isn’t ultimately a thing can peacefully coexist with me doing matrix-vector multiplication whenever I want to. Just like the understanding that the natural number 1 is a different object from the integer number 1 peacefully coexists with me treating them as equal in any other context.
I don’t agree that this view is theoretically limiting (if you were meaning to imply that), because it allows any calculation that was possible before. It’s even compatible with the base map.
I wouldn’t be heartbroken if it was defined like that, but I wouldn’t do it if I were writing a textbook myself. I think the LADR approach makes the most sense – vectors and matrices are fundamentally different – and if you want to bring a vector into the matfrix world, then why not demand that you do it explicitly?
If you actually use LA in practice, there is nothing stopping you from writing Av. You can be ‘sloppy’ in practice if you know what you’re doing while thinking that drawing this distinction is a good idea in a theoretical text book.
That looks like it also works. It’s a different philosophy I think, where LADR says “vectors and matrices are fundamentally different objects and vectors aren’t dependent on bases, ever” and your view says “each basis defines a bijective function that maps vectors from the no-basis world into the basis-world (or from the basis1 world into the basis2 world)” but it doesn’t insist on them being fundamentally different objects. Like if V=Rn then they’re the same kind of object, and you just need to know which world you’re in (i.e. relative to which basis, if any, you need to interpret your vector to).
II don’t think not having matrix-vector multiplication is an issue. The LADR model still allows you to do everything you can do in normal LA. If you want to multiply a matrix A with a vector v, you just make v into the n-by-1 matrix and then multiply two matrices. So you multiply A⋅M(B,v) rather than A⋅v. It forces you to be explicit about which basis you want the vector to be relative to, which seems like a good thing to me. If B is the standard basis, then M(B,v) will have the same entries as v, it’ll just be written as ⎡⎢
⎥⎦ rather than (v1,...,vn).
Afaik, in ML, the term bias is used to describe any move away from the uniform / mean case. But in common speech, such a move would only be called a bias if it’s inaccurate. So if the algorithm learns a true pattern in the data (X is more likely to be classified as 1 than Y is) that wouldn’t be called a bias. Unless I misunderstand your point.