Time
Travel
Institute of
Columbia
Time Traveler's Chess
Time traveler's chess is played exactly like standard chess except
that chessmen
can travel backwards in time. As an introductory remark we
might say that in science fiction there are various notions about what
time travel is or could be. One species of time travel, for instance,
involves the idea that there are many universes, a manifold of
universes, in fact, capable of containing branching time lines and
alternative histories. The conception of time travel in time
traveler's chess is different from the "many universe" conception and
different from a large number of other interesting conceptions.
The Concept
In time traveler's chess, there is only one world, and time travel is
always continuous. If a chessman begins
to move backwards in time at move 30 and travels all the way back to
move 20, then the time traveling chessman will be on the board,
moving backwards in time, at move 29, at move 28, at move 27, and so
forth. There will be at least two versions of the chessman on the
board from move 20 to move 29, since in the "personal history" of this
chessman, the chessman first moved forward in time to get to move 30
and then began to move backwards in time. So there will be a forward
moving version and a backwards moving version. To make matters even
more confusing, at move 20 in our example, when the time traveling
chessman begins to move forward again in time, a second forward
moving version of the chessman appears on the board. Then, so long
as this second forward moving version survives there will actually be
three versions of the chessman on the board through move 29!
A time traveler's chess set, then, has three varieties of chessmen.
In the starting position - the same starting position as
for standard chess - all chessmen are "untraveled" in time. For
each of these chessmen there should be on hand,
in case need arises, a corresponding "traveling" chessman. When
a traveling chessman appears on the board, that chessman
should be understood to be currently traveling backwards in time.
(If we could be such a chessman, stationed in a safe spot
on the
chessboard, we would see astounding sights. We would see pawns move
backwards. We would see chessmen occasionally spring into
existence on squares being vacated by other chessmen. Gazing
beyond the perimeters of the board, we could observe chess clocks
running backwards, pens leaping into players' hands, doughnuts
miraculously forming whole,
unbite by unbite, from the mouths of humans.) For each
traveling chessman
there must be be a "traveled" chessman. Traveled
chessmen are grizzled veterans; they have moved backwards in time
and are again moving forward in time.
The three versions - untraveled, traveling, traveled - are three
stages in a personal history. Each such personal history is folded
back through time in such a way that all three stages play out
simultaneously on the board.
A time traveler's chess set can easily be fabricated from three
standard sets and some modeler's paint. Untraveled chessmen might look pristine, traveling chessmen strange,
traveled chessmen experienced.
The Rules
Again, in time traveler's chess there are three versions of each chessman: the untraveled version, the traveling version,
and the traveled version.
In the initial setup - identical to the initial setup for standard chess - all chessmen are untraveled. Untraveled
chessmen move exactly like chessmen in standard chess, except in the case of "annihilation", explained below.
Traveling chessmen are the Cageian musicians of chess, sitting quietly for the entire duration of their incarnations.
They appear in "explosions" and disappear either in annihilations or by capture, the latter case ending the game in defeat
for their armies.
Each traveled chessman appears on the chessboard simultaneously with a traveling chessman of the same piece type,
in an explosion. In the very first move of a traveled chessman's appearance, the move that is part of an explosion,
the traveled chessman has a restriction upon his ability to capture, but for every move thereafter
the traveled chessman moves exactly like a chessman of standard chess.
There are three types of moves: the explosion, the normal move, and the annihilation. The player to move makes one move of
one of these types. A player's move only directly affects chessmen of the player's assigned color except when the move is a normal
move that captures an enemy piece or an explosion that captures an enemy piece.
The Explosion
An explosion requires an "explosion square".
An explosion square is an empty square reachable
in no more than three moves by a friendly untraveled chessman of the piece-type of interest.
Such an untraveled piece is called
an "explosion support", and there is an additional requirement that after each explosion a player causes, there must be at
least one way to pair past explosions with associated explosion supports such that no two explosions are paired with the same
explosion support. For instance, if the player to move
wishes to cause a "rook explosion" at a given square, the given square must be empty and the player must have at least
one untraveled rook (or pawn that could promote to rook) on the board which, in the hypothetical circumstance that
the player were allowed to make moves in succession, could reach the given square, as untraveled rook, in no more than
three total moves. (These hypothetical moves could include captures of enemy chessmen. Some of the moves also could be of
friendly chessmen other than the rook, in order to free lines for the rook.) Further,
at least one of these explosion supports must
not have been required to justify an earlier explosion.
There is one final requirement for a square to serve as an explosion square. This requirement
introduces the term "resonator". A resonator is any untraveled chessman which could
possibly annihilate with an existing traveling chessman. (See the discussion of annihilation below.) The requirement is that a traveled chessman of the piece-type
of interest can move from the explosion square without capturing an enemy traveling chessman or a resonator.
The player to move causes an explosion by placing traveling and traveled chessmen of the same
piece-type on a qualified explosion square and then making a legal move with the traveled chessman
without capturing a traveling chessman or a resonator.
When the explosion has been accomplished two new, friendly
chessmen are on the board. A traveling chessman has appeared on the
explosion square. A traveled chessman of the same piece-type has appeared one legal move from the explosion square. The
traveled chessman may or may not have captured an enemy chessman but certainly has not captured either a traveling
chessman or a
resonator. For the new traveling chessman there will be at least one friendly resonator of the same piece type no more than
three moves distant.
The Normal Move
Traveling chessmen may not move, but untraveled and traveled chessmen make normal moves exactly
like their counterparts in standard chess. Untraveled, traveling, and traveled chessmen may all be captured as in standard
chess. In normal moves, traveled chessmen are not restricted from capturing enemy traveling chessmen or resonators. That
restriction only applies during an explosion.
The Annihilation
In standard chess, chessmen are blocked by friendly chessmen; a chessman may replace an enemy
but not a friend. This rule largely obtains in time traveler's chess also, but there is a single, very major exception.
In time traveler's chess a traveling chessman does not block a friendly resonator of the same piece-type. A resonator
one move away from an
traveling chessman of the same piece-type may move onto the square occupied by the traveling chessman. When that happens,
both chessmen
vanish; both leave the board permanently. This event is an annihilation.
We can now round out our exposition of the rules of time traveler's chess by discussing grammatical correctness, checkmate,
winning, and odds and ends.
Grammatical Correctness
The grammatical rules reflect the fact that traveling chessmen are supposed to be
annihilated, that the player undertaking an explosion is obliged to make this happen. At any time the position of a
player's pieces is either grammatically correct or grammatically incorrect. If a player has caused no explosions,
his position automatically is grammatically correct. If a player has lost a traveling chessman to enemy capture,
his position automatically is grammatically incorrect. If a player has caused one or more explosions but has not lost
a traveling chessman, his position is grammatically correct if and only if there is a theoretical possibility that each of
his traveling chessmen on the board can be annihilated. It is illegal for a player to make a move that leaves
his position grammatically incorrect. Otherwise it is legal - and very desirable - for the player to force his opponent's
position into grammatical incorrectness.
Checkmate
A player with one or more traveling chessmen is said to have an "unresolved" position. A player to move
is in check if and only if he is under one-move threat of having no king (or else of having both an untraveled king and a
traveling King but no traveled king) at the same time that his opponent has a resolved position. If this one-move threat is
unanswerable, the player also is in checkmate.
Thus, a player might lose his king without ever being placed in check! And he can play on, kingless, so long as he can
prevent resolution by his opponent!
Winning
A player wins by checkmate or by forcing his opponent into grammatical incorrectness.
Odds and Ends
Castling is legal in time traveler's chess as in standard chess and under the same strictures, but
with check being defined as above. The rook and king must be untraveled, of course.
En passant capture is legal in time traveler's chess as in standard chess and under the same strictures. Since an
annihilation is always initiated by a move of an untraveled chessman,
an en passant capture can on occasion "undo" an annihilation.
An advanced untraveled pawn can be the explosion support of a traveling chessman of piece-type other than pawn by virtue
of promotion.
An untraveled pawn promotes to an untraveled piece. A traveled pawn promotes to a traveled piece.
As in standard chess, the game is drawn by stalemate if the player to move has a grammatically correct position
and is not in check but can make no move without placing himself in check (as defined above).
A traveling chessmen, despite its weirdness is a real piece. No piece of either color can move through it as if it were not there.
Notation
A simple extension of the algebraic notation of standard chess is sufficient to record time traveler's chess games. Double
slashes mean annihilation. Thus an annihilation involving squares d2 and d4 would be expressed as "d2//d4". A single
slash indicates an explosion. The format is piece-type followed by explosion square
followed by slash followed by other square. The move "Qd4/g7" is a queen explosion with explosion square d4.
A White, noncapturing pawn explosion on h3 goes "h3/h4".
Illustrative Games
Game 1
1.Nf6/e8 This move is legal. The explosion square f6 was empty as required, and f6 has an appropriate explosion support,
the knight on b1. The knight on b1 is an explosion support because it can reach f6 in three moves. It is also true that the
movement of the traveled knight from f6 to e8 met the requirement of not capturing a traveling piece or a resonator.
So, the move is legal. Legal but bad. 1...gf 0-1 White's position is now grammatically incorrect, so White
loses. Notice, by the way, that Black lost his king but was never in check. He was not in check because it would
have taken more than one move for White to achieve a resolved position.
Game 2
1.e4 d6 Pirc alert: the Pirc doesn't work. 2.Bb5/e8+ Check, because White has captured Black's King and now
threatens to resolve in one move. 2...d4/d3 There is no meaningful defense for Black. 3.Bxd3+ Again check. Now Black can delay mate for exactly one move more, by intervening on c4. Quiz: How many different chessmen can Black now place on c4? 3...Qe6/c4 Answer: Four: Q,QB,QN,QBP. 4.Bxc4++ 1-0 It's checkmate because Black is kingless and cannot prevent the resolving annihilation on White's next move. Remember, the resonator on c4 and the traveling chessman on b5 are immune to immediate capture by an exploding traveled piece. The game is over, but let's now contemplate what has happened from the noumenal point of view. To facilitate this contemplation, let's pretend that White has made that forbidden final, fifth move and has thus reified the royal murder. What has happened? Okay, the WKB sat on his original square until move three. On move three he sprang to the square d3, capturing a pawn. On move four he captured a queen on c4. On move five he leapt to b5 and immediately began to time travel. He time traveled (in place, of course, since traveling pieces do not move) back to move four, then to move three, then to move two. On move two he turned forward again in time and immediately rushed to e8, capturing the Black monarch.
Game 3
1.e4 e5 2.d4/e5 White, trying to use time travel to obtain a dominating center, counts on a quick annihilation to avoid grammatical problems. 2...c5! But this counterattack places White in grave danger. If now 3.d2//d4 then 3...Qa5/e1 leads to a quick checkmate. White is now forced to capture on c5 via time travel, but his grammatical difficulties naturally snowball. 3.b4/c5 Nc6 Attacking two traveling chessmen. If either is captured the game is over. 4.Bb5/c6 dxc Black now attacks two traveling chessmen with two different pieces. It's hopeless. 5.Qh5/f7 This desperate move does not help in the least. Black is not in check because White is not resolved. Qxd4 0-1 White has lost grammatical correctness.
Game 4
1.e4 e5 2.Nf3/e5 Nc6/e5 3.d4/e5 b8//c6 4.d2//d4 White has set a trap, into which Black now falls. 4...Bb4/e1 5.Qd6! cxd6 6.a3 dxe5 7.axb4 1-0
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