Vampires in Chess

@ambrona said in #29:
> . You show your thinking process with or without an order.

Well, some of that could be that I might be writing many irons in some post as they pop up and would not fit with currently typed sentence, and each of them might end up rephrasing some of each other (because I do have some average points I want to share, in spite of apparent divergence), and then I get the genius idea of editing above and or below those different paragraphs. Which is kind of an argument for my journaling-no-looking-back, so only my internal chaos shows, not the added convoluted contritions. (this last 2 lines are me doing that, the editing).

But yes my thinking as expressed here in ASCII, a poor approximation of things from my visual thinking, grinding that in order, is an unreachable muse. I opted for iterations, and redundancy within, hoping some converging spiral would emerge.. but I also butcher upon second guessing that I might not have been readable.. So a mess. so kudos for not flinching. Or being resilient about that (other postedit, sometimes it does not derail).

Generally allergic to deep sequential procedures.. I wish we could write in parallel.. like we can think visually.

Also looking forward your other presentations.

Вкус глаз тяжело понять? Согласна вы все или нет?

@Fabulous111 said in #32:
> Вкус глаз тяжело понять? Согласна вы все или нет?
Приятного аппетита! :D

Fascinating post! If you don't mind a request for a basic explanation (and apologies for being a dimwit).

1. The argument that the starting position is a vampire turns on the statement that "it is impossible (illegal) to grant black the turn" in the mirror of the starting position—but black having the turn is constitutive of this mirror position.

If I am following, the notion that it is impossible to grant black the turn depends on a notion of "parity." I am hard pressed to understand, though, how a violation of parity enters into things. Consider these moves:

1) "original" game (white moves first): e4
mirror game (black moves first): e5

2) "original": Nc3
mirror: Nc6

Both the original and the mirror move are legal. In neither case is a privilege such as castling or en passant capture missing in the mirror but present in the original, or vice versa. Can you help me understand what I am missing? (I think I have correctly assigned original and mirror moves assuming the horizontal rotation of the board—forgive me if I am confused on this basic point.)

2. The further claim is made that "knights only make even cycles." This claim appears in the original as a strong restatement of the claim that parity is lacking between the original and the mirror image of the standard position—but then in the diagram below this statement, it seems that all knight moves and certain pawn moves are identified as the only moves that would preserve parity in this situation.

Can you restate this point in other terms? What, for example is a cycle? If by "cycle" is meant a circuit of pieces in which each piece attacks one other piece, and only one other piece, is an "even cycle" one in which the number of pieces involved is even? And if so, how would the moves described above (or any other set of moves from the mirror starting position) create an odd cycle?

Thanks for any light you can shed!

@Fabulous111 said in #32:
> Is the taste of the eyes hard to understand? Do you all agree or disagree?

Just in case, by ASCII, I meant main keyboard layout and any written language that goes from one side of text box, to the other then carriage return, and again.. one long string of characters or words, that are crawling toward approximating something that could be understood instantly if we had direct visual cortex to visual cortex communication. It could be handwriting if one did not dare to make drawings.

I hope google did not support my argument of inadequacy of languages to carry the full thinking experience attempts at being shared across individuals.

lichess.org/analysis/b3k3/1K6/8/8/8/8/6N1/8_w
Finally took the time to look at it. Just to be explicit.
It is not legal because of the retrograde question of how did the bishop get at that placement resulting in a check, in the first place.

It would appear to be a mate position. But it can't be obtained from the initial standard, and while at it not even from a 960. Or any other position legal or not, from which doing legal mobility continuations. Such a position would be a new initial position for a "from position" variant (where minimal mobility rules would be used, relaxing initial conditions of diagram and color-to move). Lichess board logic might be that. It does accept the "from position" variant, where we can input depth 0 at will. But that is not on topic.. I have deleted more derailing. (putting it elsewhere for the curious).

This is not about mirrors (3 bullet points definition) or vampire. Pretty sure here is a clash between occupancy (only one material unit on a board point), Bishop mobility, and King mobility.

I also have the same difficulty about the initial position being a vampire.
I do not see why the knight mobility is used as argument. But editing now to say, in this post I end up seeing something. At first sight it seems to be saying that the initial condition of standard chess being also "white moves first", means that it is illegal for black to move first, by the direct application of the rule.

Or there might be a subtlety about vampire and mirror.. It is not just that the position itself mirrored is illegal, but that there are no legal continuations of the standard initial one, that would end up on such position. The case above being the trivial case already illegal without any dynamic argument, just the core initial condition itself.

Somehow, I think there is a statement of depth. but not what I thought.

> Understanding the knight moves point of blog (maybe):
The other possibility at depth not zero, would be cycling moves (not positions cycles), and there I would understand that no white knight move can come back to its initial position without being there on a different color-side to move.

which maybe the parity argument. it takes even number of turns, and that should also be mirrorred by black. given there is not chess time leaks.. both side have to keep coming back to the same global position exactly on same parity as 0.

Ok: see again, I do have to ask the question, before I can understand an answer that I could read, but it was offered without me raising my what else could there be? instinctive thought pattern, to be then constrained back to seeing what you proposed at once. Did I make the correct argument at last?

@EudaemonicPhonix said in #34:
> Fascinating post! If you don't mind a request for a basic explanation (and apologies for being a dimwit).

Don't apologize. I have had similar questions.. And I see that you are struggling a bit through the text molasse too. All of this is best explained on a board. But we are using words beating around the bush to describe mathematically things that if not on board, in some other 2D medium as a sheet of paper, could represent positions as points and moves as links between those points. or other 2D representations of various chess concepts. Cycles of positions, cycles of moves, tempi counting..

Did you see @ambrona post where the same blog paragraph was laid without the obligatory natural language sentence syntax, in bullet form. Spacing things somehow transcending the left-right-linefeed-left right..

lichess.org/forum/community-blog-discussions/ublog-3MOYWXZY?page=3#27
> Coming back to vampires. They are *legal* positions that become illegal when you mirror them.
> The mirror operation does three things:
> - Reflect the board horizontally with respect to the center.
> - Invert the color of all pieces.
> - Invert the turn (and castling/en-passant rights).

I went too fast fast-reading myself on the blog corresponding paragraph in my first pass, assuming that the mirror was a pure board perimeter square symmetry operation, as you seem to be doing by rotation. and the turn would be discussable. But the turn is part of the definition (the color-side to move).

I think given that we might, many of us jump on that visual meaning assumption, making the bullets points has been helpful emphasis, and might reach other people heavy on the geometry assumptions or general experience (chess or not).

The mirror is an operation on more than the board. It is about the chess quirks about time and timing of movers on the board. The turn base game. But, then why not call white black and black white, was my first recent reaction rereading the standard initial position being a vampire paragraph... well because vampire is not just about flipping it is about all retrograde possibilities not getting back to initial standard.

But ambrona, is likely to help you better.

edit: board reflection with respect to its ambient plane center horizontal line. The board being 8x8, its perimeter square figure, its border, lies in the board ambient space R2, and so are the whole board symmetry centers, chess board being a graph embedded in that ambient domain. If it were 9x9, then it center file and center rank and even the center point (=small square) would also be symmetry centers and on the board itself (not meaning there is no need for an ambient domain as well, but that it would not need evocation as much).

Шахматы легко играть чем заниматься уроками! Кто его знает может и нет но а вы это знаете или нет

Или не правильно