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The Final Frontier

An account of existing forms of three-dimensional chess would hardly be complete without a mention of the form of that game associated with the popular television series Star Trek.

The famous Star Trek television and movie franchise needs no introduction. While a critical review of the book The Making of Star Trek by Stephen E. Whitfield and Gene Roddenberry published in a science-fiction magazine did correctly note that "real" science-fictiion, of even higher quality than appeared in the original Star Trek, had already appeared on television in such shows as The Outer Limits, this seriously understates the significance of Star Trek for one very important reason.

The Outer Limits was indeed justly critically acclaimed, and so was Playhouse 90. (And, for that matter, The Twilight Zone, which is perhaps the only exception to the point I'm about to note.)

The Outer Limits was an anthology series; that is, each episode came with a completely new cast of characters. You tuned in to that show to watch a play, or the dramatization of a short story. This was percieved as a "highbrow" form of dramatic television, as opposed to the ordinary type of dramatic TV show that reached a mass market - shows with continuing characters.

This is why Star Trek, as the first major U. S. television show with continuing characters to present real science-fiction, instead of being meant for children, was so significant. "With continuing characters" wasn't just a trifling qualifier thrown in to exclude The Outer Limits from consideration; it represented a very real and impoirtant distinction.

The original television series Star Trek was produced by Desilu Studios. The name, of course, refers to the famous married couple who were able to found that studio due to their own enormously successful television series, I Love Lucy.

And after the first Star Trek pilot, The Menangerie, was rejected as "too cerebral", it was Lucille Ball, with the support of her husband Desi Arnaz, who, over the objections of the rest of the board of directors of Desilu, took the unprecedented step of authorizing funding for the show's second pilot, Where No Man Has Gone Before, without which Star Trek could never have made it to the air.

There is also an anecdote about a visit by Lucille Ball to the set of Star Trek, where she said something like "I don't understand what you guys are doing, but I know it's important". Maybe she was just referring to what the characters were doing in the scene being filmed, complete with technobabble... but when I read that, I interpreted it in quite another sense, as though she meant she didn't fully participate in Gene Roddenberry's politics, but had faith in his goals of transforming America. Perhaps I was unduly influenced by the political unpleasantness I will briefly allude to below.

The first episode of Star Trek was shown on NBC on September 8, 1966, and the first episode of Mission:Impossible, another television show from Desilu Studios, appeared on CBS on September 17, 1966.

Both of these shows were, in one important way, bold for their times. Each one featured a character who was intended to combat stereotypes, and who would create difficulty for the show in some U.S. television markets; Nichelle Nichols as Lieutenant Uhura, and Greg Morris as Barney Collier.

However, it was in the fall of 1965, a year previously, that another series, with Robert Culp as one of its stars, which was more genuinely a trailblazer in this area debuted; however, that series, as well, came from Desilu. (Yes, I support #MeToo. How did you guess?)

I had not been particularly aware, during her lifetime, that Lucille Ball was a crusader for social justice, even though I had no reason to doubt that her values were positive and constructive. However, shortly after her death, there was a story about her in the National Enquirer which claimed... that Red Channels was half right about her.

Yes, the story claimed that Lucille Ball was a Communist... for the FBI. (Just like Matt Cvetic, if you're too young to remember the allusion. Or, for that matter, Herbert A. Philbrick, who was the author of a similar memoir, "I Led 3 Lives".)

I could think of few claims about her more likely to endear her to mainstream America and to alienate the Hollywood community from her, but it should be noted that the National Enquirer is not universally considered to be an authoritative news source.

It would seem to be obvious that what her husband, Desi Arnaz, said about the matter would have settled it: "I was kicked out of Cuba because of Communism... We both hate Communism and everything it stands for", but there was, I have learned, one piece of documentary evidence that gave some substance to the original controversy: Lucile Ball had registered to vote in 1936 as a Communist Party supporter.

She said of it that she did so to please a relative who was of socialist beliefs; in any case, many people, during the Depression years, naturally questioned an economic system that seemed to place the unbridled operation of the stock market above human needs. The Soviet Union had concealed the crimes of Stalin, and managed to present itself as an alternative to many given the difficulties of those days.

No one came after the wealthy industrialists who heaped praise on Mussolini and even Hitler before the war started; the witch hunt against people who, decades before, were briefly taken in by Communist lies that is known as "McCarthyism" was not about defending America from the very real threat of Communist tyranny, but it was about serving moneyed interests by making life difficult for labor unions, hampering the fight for racial equality, and so on and so forth.

Leaving unpleasantness aside, and getting back on topic...

We have seen that Star Trek was a very significant television show in its day, and it is also still a very successful televisiion and movie franchise for Paramount.

That, in itself, however, does not guarantee that the form of three-dimensional chess played onscreen during its episodes is of any real significance in the history of three-dimensional chess.

And, indeed, initially the facts would have argued that it was not; the boards seen during the series were cobbled together from three-dimensional tic-tac-toe and checkers sets the prop department could find at ordinary department or toy stores, and a conventional chess set was used for pieces. No rules for the game were devised to ensure that any gameplay seen onscreen was consistent with one set of rules.

The Star Trek episode Requiem for Methuselah featured a character who turned out to have been known as Johannes Brahms; while I can't think of any other connection between Star Trek and another composer, Liszt, it happened to be the case that an enthusiastic fan of Star Trek by the name of Franz Joseph wrote - and, more importantly, drew, a book that would fill in the gaps of what was known about the fictional universe in which the episodes of Star Trek took place - The Star Trek Technical Manual.

One of the things included in this book was a set of rules for Star Trek's three-dimensional chess.

In 1978, Andrew Bartmess, with Franz Joseph's encouragement and permission, elaborated on the rules provided in The Star Trek Technical Manual with the aim of producing a fully consistent set of rules.

And when the Franklin Mint became officially licensed by Paramount to produce sets for Star Trek's version of three-dimensional chess in 1993, it was the rules as drafted by Bartmess that they included in the package. (Incidentally, an outfit by the name of The Noble Collection is licensed to make and sell a rather less expensive set for Star Trek's three-dimensional chess, so, yes, this is something you can own!)

Thus, as those rules appear on several other web sites, and this web site of mine discusses chess variants extensively, including variants of three-dimensional chess, and the version of three-dimensional chess as seen on Star Trek is almost certainly the one that the most people are likely to have even heard of... it seems only reasonable that I should give some account of them here.

I should note, though, without detracting from the great achievement of Joseph and Bartmess in creating a set of playable rules for a game of three-dimensional chess on a board... that was devised to look pretty on TV, without serious thought as to whether or not any reasonable game could even be played on it... that there are some things about the game and its rules that I don't particularly like.

There, I've said it.

To begin to understand the rules, first we must understand the board. The illustration below is intended to aid in obtaining that understanding.

The portion of the diagram on the left shows the three main boards, above a two-dimensional board on which the relative positions of the boards in a two-dimensional sense can be found.

The top board is made distinctive by coloring its black squares blue, the middle board is made distinctive by coloring its white squares yellow, and the bottom board is made distinctive by coloring its black squares green.

Each of those colorings indicates a four-by-four area within the two-dimensional board under the three main boards, to which the horizontal position of the main board bearing that coloring corresponds.

The board also comes with a set of four auxilliary boards which are two squares by two in size.

They may be mounted on the corners of the three main boards, so that their centers either stand above those corners, or are suspended below those corners, in either case by a vertical distance that is one-half of the vertical distance between the main boards.

One possible illustrative position of the four auxilliary boards is shown on the right side of the diagram.

The four auxilliary boards shown, and the central main board, are all distinguished by a special color given to their black squares, which may be found on the two-dimensional board below to give their positions.

The two-dimensional board below is complete, inclulding squares corresponding to all possible positions of the auxilliary boards.

The Rules

This is not a full account of the rules, but merely a brief sketch and overview of them.

Moving the attack boards: the small auxilliary boards may be moved, either if they are empty, or if they have only one pawn on them.

An attack board with a pawn on it may only be moved by the player whose pawn it is.

Attack boards may only be moved to the same corner of the main board immediately above or below the main board on which they are currently mounted, and they may also be changed from being supported by the corner on which they are mounted to being suspended below that corner, and in that latter case, they do not need to be moved to the same corner on a different board.

Moving the pieces: The two dimensional board as shown below the orthographic drawing of the three-dimensional board is fundamental to how the pieces are moved. A move from a proposed starting square on the three-dimensional board to a proposed ending square on three-dimensional board is possible if, and only if (excepting considerations such as moving into check), the same type of chess piece could make, on the two-dimensional board, a move from the squares which correspond respectively to the starting and ending square.

The move that will be made on the three-dimensional board will have the following characteristics:

It will follow a path including squares which correspond to the squares traversed in the move on the two-dimensional board.

It will not include any squares which are vertically higher or vertically lower than the vertically highest and vertically lowest squares respectively of the starting and ending squares of the move.

The actual move, consisting of a series of squares traversed from the starting square to the ending square, will be the unique move in which the squares of the move are as high as possible consistent with the move being possible.

This is a very brief and incomplete account of the rules, and in one respect I go by the original Star Trek Starfleet Technical Manual instead of later versions of the rules.

I have seen two versions of the initial array on web sites, both of which are depicted in the diagram to the right; the version that is further right is the one shown in the original Star Trek Starfleet Technical Manual.

The three main boards are placed one above the other, and the dotted lines indicate possible positions for the auxilliary boards in relation to the four corners of each main board. There are pairs of squares of dotted lines, with the top one corresponding to an auxilliary board standing on the corner to which they are closest, and the bottom one corresponding to an auxilliary board suspended down from that corner.

The initial array shown on the left is more closely derived from that of conventional Chess than the one on the right, which may have been refined for playability.

Note that for both White and Black, the auxilliary boards used are standing on the corners with which they are associated, and this is another asymmetry in this version of the game, in addition to the one created by the movement rules.

A more comprehensive version of the existing rules for Star Trek's 3D Chess, including some additional work at achieving even more consistency than Bartmess himself had managed, can be found here.

Incidentally, while a set of Tournament Rules for Star Trek 3D chess devised by Jens Meder appeared initially to be the Bartmess rules for the game, with additional rules added to cover the technical issues of tournament play, I now see that there is one substantive difference in the description of the rules for over-the-board play itself.

In Jens Meder's version, an attack board occupied by any one piece, not merely one pawn, may be moved.

How I View these Rules

I see these rules as having two very serious problems.

The first one is that they are not symmetrical. The Black player's pieces start at at the vertically higher end of the board, and the White player's pieces start at the vertically lower end of the board.

Thus, the requirement that moves go by the highest possible path is not symmetric with respect to the orientation of the initial board position.

The second one is that instead of movement being based on taking the moves of chess pieces, and making those moves in three-dimensional space, so as to foster three-dimensional thinking in Starfleet officers - as one might have presumed the game was intended to do even before The Wrath of Khan came out - the moves are built around a two-dimensional game, with the vertical third dimension tacked on.

I view the first problem as nearly fatal, and the second one as very serious, thus a bit less severe.

The first problem is trivially remediable, though; simply have moves by Black take the highest possible path, and moves by White take the lowest possible path.

Addressing the second issue is more difficult. I suggest below a modified set of rules for a game of chess played on the Star Trek three dimensional board which partially addresses that issue. However, it may be felt that these modified rules are too complicated.

My Proposed Set of Rules

Moving the attack boards: If an attack board is occupied by a pawn, it may be moved by the player to whom the pawn belongs to the same corner of the main board above or below. It may not be changed from resting upon, or being suspended below, that corner to the other situation.

If an attack board is unoccupied, it may be moved by either player to any of the other five possible positions of standing upon, or being suspended below, the same corner of any of the three main boards, including the original main board to which it was connected, as the first part of a move, the second part of which will be that the same player will move one of his or her pieces or pawns to one of the squares on that board.

Moving the pieces (I): To move a piece from a square on one of the main boards to another square on the same or another main board, the moves of the pieces shall be as set forth for the game of Raumschach as described on the previous page, where the three main boards are considered to be staggered at an offset of one square per level, instead of two squares per level, in order that squares of opposite colors will be considered to be directly vertically above and below one another.

Moving the pieces (II): To make a move which starts, ends, or both, on any squares of one of the attack boards, the following principles will apply:

The main boards are considered to be staggered at an offset of two squares per level, and to correspond vertically to positions on a two-dimensional board as depicted above.

The path of a move will be along squares which correspond to the squares on the two dimensional board in the path of the corresponding move between the squares corresponding to the starting and ending squares of the move.

The move will consist of moves from one square to another on one board, whether main or auxilliary, following the paths of the steps on the two-dimensional board, and of vertical moves to the same square immediately above or below a given square. Note that vertical moves can be to or from an attack board, or between two main boards, even though those moves involve a different vertical distance.

All vertical steps within a move shall be in the same direction.

In a move by Black, all vertically upwards steps are to be taken as soon as possible within the move, and all vertically downwards steps are to be taken as late as possible within the move. In a move by White, the reverse is the case.

Note that these rules are somewhat different from those for the existing game; this is done to make them less ambiguous.

As well, the initial array for this version of the game, shown to the right, is very different from that of the existing version.

One Additional Wrinkle

As if the game as described above is not complicated enough, I have one extra little possibility to add:

If the center main board is not occupied by any pieces, the player whose turn it is to move may, as his or her move, rotate the center main board.

After the center main board is rotated, if as a result two or more attack boards are attached to the same corner of a different main board, the principle that each of the four possible corners is used only once is to be re-established by moving the minimum number of unoccupied attack boards, whether those boards are attached to the center main board or another main board. If this is not possible, the move is not legal.

After this move is made, a move of this type may not be the immediately next move of either player.

If, as the result of a move of this type, the dark and light chequered squares of the center board are in the opposite orientation to those on the top and bottom main boards, then, for as long as this is the case, the main boards shall be considered to be staggered by an offset of two squares for moves between squares within the main boards, and by an offset of one square for moves involving the attack boards, the reverse of the situation described above for this set of rules.

On further reflection, instead of exchanging the offsets between squares, I am thinking it would make for a better game to reduce the offset by one for both cases: that is, the main boards would be considered to be staggered by an offset of one square for moves involving the attack boards, but for moves between squares within the main boards, the main bords would be considered not to be offset at all.

This little wrinkle adds... an interesting possibility... to the game, even if the special move it describes is not likely to be used very often.

Implications of these Rules

Because of the way the moves of the pieces in the Bartmess rules are based on the two-dimensional chess game, pieces tend to be quite powerful, having many possible squares to which they can move.

This may have avoided one problem I noted with Raumschach on the previous page: in that game, I felt that it might be almost impossible to checkmate a King that can move in three dimensions.

On that page, I noted as a possible way to address this, Bare King and/or Perpetual Check could be added as victory conditions.

As these alternative rules for the Star Trek board make use of the Raumschach moves for the pieces, this problem, if avoided in the Bartmess rules, is re-introduced. And the possible solution, of course, is the same.

Another possible solution for this issue, used in some forms of 3-D chess, would be to restrict the King to two-dimensional moves only when it is in check. I don't think that is workable in this form of the game, due to the tiny size of the attack boards.

This also means, because of the changeover between two sets of rules, depending on whether the attack boards are involved, that a piece sitting on one of the attack boards is much more powerful than a piece sitting on one of the main boards, as it has many more possible moves. This makes the attack boards very important.

Oh, Dear

I have just learned that the Star Trek three-dimensional chess set appeared in Star Trek: The Next Generation with six attack boards, or, as I have called them, auxilliary boards.

Both my set of rules, and the ones developed by Bartmess, are designed so that each of the four corners of the main boards are used only once for an auxilliary board; that is, Black's Queen's corner is used only once on one of the three boards, and so on. Thus, going to six attack boards is completely incompatible with the existing rule sets.

However, I am of the opinion that the game could be improved by making the board larger. However, I would do so by having four main boards instead of three, but still limiting the number of attack boards to four!

Of course, that would eliminate my cute move of rotating the middle main board. An alternative would be to make the three main boards 6 by 6 squares in size, but that would require changing the initial array.

Another option would be to have five main boards, and when the center board is rotated to make its colors alternate with those of the two adjacent boards... the top and bottom boards have their squares change color without moving.

I mean, they should have liquid crystals in the 24th century...

STAR TREK® is a registered trademark of Paramount Pictures Corporation.

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