Vampires in Chess

Ah, nice stroll in the big chess park. And well introduced.

Can you let us know where we might find shared thoughts about water molecules. We don't usually refer to amounts of water with the number of molecules in it. I thought it was stars in the ambient space of the material universe.. (Shannon). Amount of stars not usually known in volume (is it). So I was aesthetically pleased by this turn of phrase. Refreshing of sorts.

core rules: chess is turn game, white is color-side to move first, obligation to move.
also core rules, but for enumeration statements:
pawn moves are irreversible (well part of rule, property of rule)
> non pawn pieces have reversible mobilities.
spatial diagram symmetries and QK asymmetry: just by Q and K placements (not needed, just saying)
> only vertical flips of the diagram are mirrors

I think the basis of this non-legal counting or enumeration method, is propagating the 3 core rules I excerpted, it can explain (in intuitive logic, I guess, there is such a thing, not magics). I edited more rambling. I am summarizing my winks above.

bottom line: well done.. good level of reasoning made explicit. minimal SAN arguments. Good attention engaging choice of word. and self-contained concern clearly visible. math. is not just a bunch of scibbles on some blackboard.

We use it even without knowing, from just having had to learn to walk. Then there is counting. 1, 2, ... 2 many for me. small finite, medium finite, big finite, and .... both infinite and infinitesimal, are not need math. words for us to use. Which leads me to the question of small brain looking at above medium finite.

I think that being able to classify from parity is nice. But how far from initial positoin can we keep that up? Would it be not easier to just play also from the non-legal position. would the chess from there not be chess also? just thought of this angle. I know the blog is not about playing but about the science of chess (kudos for that). But even then I think we could generalize your presentation if we allowed discussing both i.e. not know if it came from legal positoin or not, as long as we stay legal from it, but then always consider the flip. A chess seed being a diagram and its immediate neighbors by symetry of the kind you considered, including color-side to move.

I am thinking of endgame study. Where this problem of whether the position proposed is legal or not is solved by considering systematically that color-side to move flip.. and no chess phenomelogy gets lost.`

I wonder if EGTB, has made sure all its calculate "seed" positions were legal descendants from initial.

yet. I think it makes for a more pedagogical presentation to have started from the initila positoin. In endgame the legal non legal flip, becomes outcome classes crossings. and so more imagination required.. I think this is still lots of rambling. but more organized. Thank you for this gem in the blog wall.

Honestly, just a great post. Had a good time reading this, thank you for introducing me to this concept!

Also, nice participation of the blog author in the discussion.

I think this is the game of Halloween

Thanks for your feedback @dboing !

> Can you let us know where we might find shared thoughts about water molecules.

I wanted to compare this order of magnitude with something and after some research I came up with water molecules. Do you have other suggestions? It's not easy to find an analogy to hit a specific order of magnitude. In this case I was targeting 10^44, given this: chess.stackexchange.com/questions/5592/what-is-the-number-of-legal-positions-in-a-chess-game

> I think that being able to classify from parity is nice. But how far from initial position can we keep that up?

Surprisingly far (according to me) as we will see in the next posts.

> I wonder if EGTB, has made sure all its calculate "seed" positions were legal descendants from initial.

I do not think such checks were performed, for example:
lichess.org/analysis/b3k3/1K6/8/8/8/8/6N1/8_w

lichess.org/study/6t2GtgMn/63kiLr8B ?

No I think water molecules are better that stars like Shannon. So that is your own thoughts. Great I had the same, wondering why Shannon did not use what was already in front of many of us and was hard to compute, so much that we refer to it in volumes. Like sand.. We might say loads of sand. but not that beach has so many grains of sand. Even hourglass, it measure time. in the past. Could have been to stiff with the counting thing.. but then high enough and far enough from cities.. It looks pretty much like sand in the sky... since I see a hemisphere of source lights, we don't get the distances in radius.. all we get is the intensity variation, and atmospheric noise. I found it difficult the few times to even count them in some limit angle arc.

No water molecules are perfect actually. We can start measuring rather than counting beyond our small brain abilities.

thanks for the intriguing answer. My question of our far was not just in depth. but it seems that you mean at least in depth, per instance. I should put careful reading of the blog examples on my list of interesting things to pursue.

One thing though. I think the kind of reasoning involved might be made equivalent to the way more theoretical endgame books actually always discuss both side to move, given a diagram. And that the criticality that your exercise on legality per some symetry operation, that might be sharpened, using chess science to raise imagination and chess understanding acuity for those trying it, that would transfer to more awareness of even play experience (accelerator of digestion of it, and possibly some higher level thinking while playing, even asking questions to the board while playing.. the hope, and my own way of playing/studying, I ask such questions, and have fun asking them, even if losing a game, if it had some such food in it, I would keep doing it, and I do). but now I have to look at yours examples and do them myself because of your previous answer. I am slow with example and reading about them.. The precise reasoning of others, is hard for me to read, if I can't fore-guess it myself. So I beat around the bush to see what are the essential arguments possible here.. And for legality, it seems to be "white moves first".

I find it a bit cheating that it means knowing the plys. would it not be more interesting to not know the depth? well. wrong forumulatino. both are interesting. but one can't be answered by counting. which raises the questoin back to 960. being more chessy that chess when we stop counting.. oh. I derailed..

@Folichon said in #17:
> lichess.org/study/6t2GtgMn/63kiLr8B ?

Bravo!

I looked at that study. So, I may be missing the point.. I guess I have to pay more attention.

in the last example above link. picture below. The leaf of the game segment.



What makes this a vampire (illegal by both vertically flipped and side to move flipped, my current understanding, this would be illegal, I might be missing the chess point)?

I might be slow on the uptake. Did we need to know the prefix sequence to know it would be. This could be a pedagogical repetition for others and has my question raised (often I need to be asking the question, or see someone asking a question to get the content of the answer, unless statement made at some abstract level like I have been trying, but if the concepts actually need the instance sequence information, then it might be difficult to make that sort of thing, very Chessy then, abstract self sufficient level language being difficult to build).

it was the sequence itself? working on it. by iterations.. (and induction)...
edit: the reversible prefix sequence (segment) of knight moves is not itself vertical mirror, so not that.
need to check on tempo leaks with the knight moves, before the directional chess time arrow of the pawn moves. But the bottom critical things might be escaping me still. what is illegal by what operation set again?... I can be blind sometimes.. sorry for the space taken.. discussion learning is not a concise while expressive endeavor.. can get ugly, why math. never dares go there in its teaching methods. (it would benefit some, I had to do it in my head to survive, in math.). can you try this exercise with me?