Then the table base either wins or draws.
Of course. At no point did I suggest that it could lose. The 'horrible and very hard to hold in practice' was referring to the judgement of a hypothetical grandmaster, though I'm not sure if you were referring to that part.
"It’s relatively easy to define optimal chess by induction, by the min-max algorithm."
Once again, I agree. I failed to mention what I see as an obvious implication of my line of reasoning. Namely that optimal play (with random picking among drawing moves) would have a pretty unimpressive Elo [1](way lower than your estimates/upper bounds), one bounded by the Elo of the opponent/s.
So:
If we pit it against different engines in a tournament, I would expect the draw rate to be ~100% and the resulting Elo to be (in expectation) ever so slightly higher than the average rating of the engines it's playing against.
If we pit it against grandmasters I think similar reasoning applies (I'd expect the draw rate to be ~97-99%).
You can extend this further to club-players, casual players, patzers and I would expect the draw rate to drop off, yes, but still remain high. Which suggests that optimal play (with random picking among drawing moves) would underperform Stockfish 17 by miles, since Stockfish could probably achieve a win rate of >99% against basically any group of human opponents.
There are plenty of algorithms which are provably optimal (minimax-wise) some of which would play very unimpressively in practice (like our random-drawn-move 32-piece tablebase) and some which could get a very high Elo estimaiton in ~all contexts. For example:
If the position is won, use the 32-piece tablebase
Same if the position is lost
If the position is drawn, use Stockfish 17 at depth 25 to pick from the set of drawing moves.
This is optimal too, and would perform way better but that definition is quite inelegant. And the thing that I was trying to get at by asking about the specific definition, is that there is an astronomically large amount of optimal play algorithms, some of which could get a very low Elo in some contexts and some which could get a very high Elo irrespective of context. So when you write 'What's the Elo rating of optimal chess?', it seems reasonable to ask 'Which optimal algorithm exactly?'.
- ^
And very unimpressive level of play in drawn positions.
A problem with this entire line of reasoning, which I have given some thought to, is: how do you even define optimal play?
My first thought was a 32-piece tablebase[1] but I don't think this works. If we hand an objectively won position to the tablebase, it will play in a way that delivers mate in the fewest number of moves (assuming perfect play from the opponent). If you hand it a lost position it will play in a way that averts being mated for longest. But we have a problem when we hand it a drawn position. Assume for a second that the starting position is drawn[2] and our tablebase is White. So, the problem is that I don't see a way to give our tablebase a sensible algorithm for choosing between moves (all of which lead to a draw if the tablebase is playing against itself).[3] If our tablebase chooses at random between them, then, in the starting position, playing a3/h3 is just as likely as playing e4/d4. This fundamental problem generalizes to every resulting position; the tablebase can't distinguish between getting a position that a grandmaster would judge as 'notably better with good winning chances' and a position which would be judged as 'horrible and very hard to hold in practice' (so long as both of those positions would end in a draw with two 32-piece tablebases playing against each other).
From this it seems rather obvious that if our tablebase picks at random among drawing moves, it would be unable to win[4]against, say, Stockfish 17 at depth 20 from the starting position (with both colors).
The second idea is to give infinite computing power and memory to Stockfish 17 but this runs into the same problem as with the tablebase, since Stockfish would calculate to the end and we run into the problem of Stockfish being a ministomax algorithm the same as a tablebase's algorithm.
All of which is to say that either 'optimal play' wouldn't achieve impressive practical results or we redefine 'optimal play' as 'optimal play against [something]'.
- ^
This is impossible, of course, but I'm looking for a definition, not an implementation.
- ^
This is almost definitely true.
- ^
To be more precise, I don't see such a way that could be called 'optimal'. If we are satisfied with the algorithm being defined as optimal against [humans in general]/grandmasters/[chess engines in general]/[Stockfish 17], then there are plenty of ways to implement this
- ^
There are bound to be some everett branches where our tablebase wins but they would be an astronomically small fraction of all results.
Striking the ground on your heel and in front of the body is essentially creating a braking force, sending you backward. When you heel strike, you put excessive stress on your lower legs and knees, increasing the risk of injuries such as shin splints, stress fractures, and runner's knee.
I feel like this conflates overstriding with heel-striking[1]. Overstriding—one's feet land too much in front of one's center of mass. Even consulting your own image, the runner marked as 'mid-foot striking' could be heel-striking without changing anything in the overall posture.[2] Though, I agree that mid-foot striking is still definitely better than heel-striking on net.
1From Emily Oster's Expecting Better [Chapter 18]:
VBAC: The other common cause of a scheduled C-section is if you’ve had one before. Women who have given birth once by C-section are very often advised to have future babies the same way. Having a vaginal birth after a C-section is possible (it’s often called a VBAC, for vaginal birth after Cesarean) but not usually the default. Is this right? It’s actually a bit hard to know. There are no randomized studies.6 The best we can do is to compare women who had a C-section and planned a vaginal birth to women who had a C-section and planned a repeat C-section. This isn’t perfect—the kind of women who want a VBAC may be different from those who are happy to have another C-section—but done right it can be pretty convincing. And studies like this suggest that there are some
increased risks to a VBAC. In one case, researchers studying women in Australia found that women who planned a VBAC had more serious infant complications and a greater likelihood of maternal hemorrhage. Both of these outcomes happened for about 2.5 percent of the women in the VBAC group versus only about 0.8 percent of the planned C-section group.7 The women in the two groups looked very similar in many ways—age, race, etc.—so we can have some confidence that the choice of delivery mode was responsible for the differences. And this is pretty consistent with other, similar studies.8 Without randomized evidence it’s hard to be rock solid on this, and, unlike in the breech case, many doctors will be fine with this type of delivery. Because of the possibility of increased risks, though, you do probably want a doctor who has experience with this situation so that she’ll know what to do if things start to go awry. If you do decide to attempt a vaginal birth, be prepared: about half of attempted VBACs end in a C-section.
The references are:
6. J. M. Dodd et al., “Planned Elective Repeat Caesarean Section Versus
Planned Vaginal Birth for Women with a Previous Caesarean Birth,” Cochrane
Database of Systematic Reviews 4, article no. CD 004224 (2004).
7
. Caroline Crowther et al., “Planned Vaginal Birth or Elective Repeat
Caesarean: Patient Preference Restricted Cohort with Nested Randomised Trial,”
PLOS Medicine 9, no. 3 (2012): e1001192.
8
. E. Mozurkewich and E. Hutton, “Elective Repeat Caesarean Delivery Versus
Trial of Labor: A Meta-Analysis of the Literature from 1989 to 1999,”
American Journal of Obstetrics and Gynecology 183 (2000): 1187–97.
If the distinction between the Buddhist meaning and the typical meaning of 'suffering' was explained[1], I don't think I would have ended up confused enough to ask my question. The Buddhist conception of suffering was different enough to mislead me, at least.
- ^
In a footnote, for example.
[EDIT Actually, nevermind. After reading answers downstream of this comment, it's clear to me that when I asked about 'suffering' I meant something quite different from your conception of suffering. I'm no longer confused about why you would say that non-enlightenment is constant suffering, but I don't see why it would be worth getting rid of.]
The latter option would be a very tall order. What I meant was that among
Hypothesis 1: You suffered but somehow this information never arrived to verbal thoughts
Hypothesis 2: You didn't suffer, but after T=1 your perception changed and now the same things make you suffer.
Hypothesis 1. strikes me as very implausible a priori, for reasons I mentioned in my answer to Kaj. So, do you have an argument that it is not as unlikely as I think, that would be, indeed, "Understandable by someone who has not had the experience".
Thanks, I think this could be what is happening. But:
1. Your examples that illustrate confusion/mistakes about one's mental state are, how to put it, small-scale. I feel like there's a huge leap between "Sometimes a person doesn't realize how tired they are for a few hours (maybe days)" or "Some fraction of people who get depressed don't realize it for months (maybe years)" and "Basically everyone's default state is suffering they're unaware of, and they don't realize this during their whole lives". Maybe you could come up with examples where misconceptions about one's mental state are more severe, longer-lasting or more common than in my depression example, but I think there would probably be a huge gap between that and the "default state is suffering" hypothesis.
2. My understanding is that the typical reported experience of high school is mostly negative valence, but as people grow up they start to look back on that time in their lives ever more fondly. I don't have a great model of how this works psychologically, but, when it happens, I'm inclined to think that the changed perspective is wrong. That the high-school-version of a person was more correct about his mental state than the current-version. All of which is to say that when one thinks "My past-self was unaware (or mistaken) of important parts of their conscious experience", in most cases, this is correct, but in the high school and constant-suffering cases, it seems likely to me that one is wrong.
[Re-asking a question i phrased awkwardly]
You have previously described your pre-enlightenment state as being full of suffering you were unaware of. Do you have externally legible reasons to think that your current perspective is correct and the perspective of your past-self about his experience is not?
Or, how a different commenter phrased it:
You're like:
T=0: "I'm fine"
T=1: Meditation
T=2: "Oh, I actually wasn't fine, it was a torment!"Hypothesis 1: You suffered but somehow this information never arrived to verbal thoughts
Hypothesis 2: You didn't suffer, but after T=1 your perception changed and now the same things make you suffer.Why do you think it's the first one that is correct?
I think it's totally fine to have basically one deck for everything. I have such a deck, containing history facts alongside math alongside friends' birthdays, and this is not a problem.
I think this was fine with the old anki algorithm, but less so with FSRS.
It's sensible a priori to expect that your forgetting curves for birthdays and math are different. If you optimize parameters for a single deck, anki will treat every card in the set {birthdays, math, historical trivia} the same. But if you have separate decks (and deck groups) for each topic, FSRS will be able to extract more signal and pick better parameters.
Admittedly, using a single deck probably isn't a huge mistake, but it seems like an unforced error to me.
Reminds me of 2 hbomberguy videos:
ROBLOX_OOF.mp3,: Video game composer Tommy Tallarico reapetedly lies about easily verifiable matters (the content of his Guiness world records, having been featured on MTV Cribs (he wasn't) &c).[1]
Plagiarism and You(Tube): Multiple people making successful youtube careers out of plagiarism, while, often, putting ~no effort into rephrasing (i.e. anyone could find the source/s by googling the words they were saying).
Feel free to skip to the 'Tommy's lies' section or farther if you just want the brazen lies