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Again an idea based on [Voice]'s annotation to my
"Infinitely Long Name For Pi".
I feel that infinite boards have been done to death, notably
in 'Walking On Glass' by Iain Banks with his Open-Plan Go,
so whereas this is an infinite board, it's not the usual
infinite board.
A Scrabble board
consists of a grid of squares with a
pattern of special squares for double and triple letter and
word scores. This arrangement, which I'm informed is
copyrighted, is adequate for words up to fifteen letters
long. There are of course a number of words which are
well over that length even in English, which are however
not particularly typable on the HB. However, there are
also much longer strings of letters (which are arguably not
words) which are mainly the names of proteins, and these
could also, as [MaxwellBuchanan] has pointed out, be
expanded to full organic chemistry nomenclature, which
would make them a lot longer. It's probably these words, if
words they be, which would form the bulk of the
vocabulary required for extremely long sequences of
letters, possibly accompanied by the standard organic
nomenclature for genes in terms of base pairs and the like.
Hence there is no shortage of words for this game, many of
which have thousands of letters. On a smaller scale there
are such words as "pneumono" *ultramicroscopic"
"sillicovolcanoconiosis" (as one word) and the thunder
words in Finnegan's Wake, whither I shall link, so it doesn't
get all chemically for quite a while.
The board is infinite. Also, it's based on hyperbolic
geometry in that the further from the starting point one
goes, the further apart are the rows and columns, although
this is gradual. The individual "squares" are also not really
square-shaped, although they appear so on a small scale,
because parallel lines diverge, meaning that, say, two
words each of a hundred letters separated by fifty letters
at their fiftieth letter might be separated by something
like fifty-five or sixty letters at the start and end, assuming
they both start in the same column, and the same applies
to vertical words.
Moreover, it doesn't stop at triple scores. Zooming out
from the starting point of the board reveals unlimited
though increasingly rare higher score quadrilaterals,
meaning that something like a centuple word score on a
3000-letter long "word" is possible.
The scoring of the letters is not based on the frequency of
letters in English as a whole but on their frequency in the
largely biochemical words on which the game is likely to be
based. For instance, Y only scores one This gives
humanities people an advantage on the small scale and
science people an advantage on the larger one. It's also
possible to prefix amino acid residue names.
Each person starts off with 343 letters (7^3) to get the
game going. People work in teams from various points on
the board, towards each other, conquering each others'
territory by linking words, making it a bit like Go.
Alliances can also be made between teams. There is
scoring but an arbitrary end to the game, so it can go on
forever, and of course an infinite supply of letters is
available, but the limit is time or number of moves rather
than a specific state of play.
There is a problem "left as an exercise to the reader".
Firstly, each team starts in a location from which the words
are close together, becoming increasingly widely separated
further from home, but for another team a rival team's
starting point is more divergent than their own. I think
this can probably be exploited, or the landscape of the
board can be considered as starting at peaks on a plane for
each team.
Thunder Words in Finnegan's Wake
http://www.finnegan...tegory:Thunderwords A series of hundred-letter words [nineteenthly, Sep 18 2017]
Hyperbolic Chess
http://www.math.uri...erbolic%20Chess.pdf While there are hyperbolas in this chess variant, they're not stretched out into infinity, but instead are used to invite a third player to have their mind gently boggled. [Zeuxis, Sep 22 2017]
Circle Limit
https://www.d.umn.e...isis4/section5.html Here's some hyperbolic examples, the tilings are fixed, i.e. each tile is adjacent to the same number of tiles across the whole space. Except, perhaps the central one,though that I think can be fudged. [Zeuxis, Sep 22 2017]
[link]
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//People work in teams from various points on the board, towards each other, conquering each others' territory by linking words// |
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The team/'Go'/territory approach to Scrabble is
really interesting but I don't see what the
hyperbolic geometry adds to this idea |
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It's the opposite of a spherical board, [hippo]. Having an
infinite board or one which wraps round in one way or
another has been done, one of them on here just now. A
hyperbolic board, as far as I know, hasn't. It adds the
element of surprise. It means, for example, that the
intuition that a territory consisting of a square twice as
long on a side is four times bigger is incorrect. Spherical
Go would allow an opponent to sidle up from the opposite
side than expected to capture your territory. A
hyperbolic surface leads to higher stakes the larger the
number of words you can put down. You need more
letters but the potential score is higher, particularly if
you encounter a multiple letter or word score. That's like
a match point in tennis. |
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So ... does this divergence of parallel lines imply that there are
some spaces on the board which are adjacent to more than four
other spaces? Or fewer? |
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Supposing that there are such spaces, is there a criterion
determining whether three or more adjacent letters lie in a
straight line (for game purposes)? Or do we allow words to spiral
or zigzag arbitrarily? Or to be spelled sdrawkcab? |
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No, it means that the spaces on the board, from a Euclidean
perspective, do not consist of straight parallel lines. Each
space is slightly wonky. It's like it's on a series of frustra. I
will try, probably vainly, to draw a wireframe
representation. |
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No, it means that the spaces on the board, from a Euclidean
perspective, do not consist of straight parallel lines. Each
space is slightly wonky. It's like it's on a series of frustra. I
will try, probably vainly, to draw a wireframe
representation. |
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No, it means that the spaces on the board, from a Euclidean
perspective, do not consist of straight parallel lines. Each
space is slightly wonky. It's like it's on a series of
intersecting pseudospheres. I
will try, probably vainly, to draw a wireframe
representation. |
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No, it means that the spaces on the board, from a
Euclidean perspective, do not consist of straight parallel
lines. Each space is slightly wonky. It's like it's on a series of
intersecting pseudospheres. [nineteenthly] should try,
probably vainly, to draw a wireframe representation. |
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I think M.C.Escher draw some rather fine wireframe examples of such boards, and then coloured them in. |
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Yes, that works well, thanks, and you will have gathered
that I was struggling because I seem to have lost the ability
to make computers do wireframe graphics since the last
time I did it in the mid-1980s. |
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OK, so, using the linked hyperbolic chessboard as an example,
suppose you laid down the word "ambivalent", starting from the
white king's space. The "l" would then fall on that space with the
green bishop, but where would the ent go? I gf imagine you'd
have a choice of two directions. Is that the intention? |
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I mean, if you then wrote "frustrated", starting from the white
knight's position, you might be able to use the "t" of "ambivalent",
but that "t" would oriented at right angles to the rest of
"frustrated". |
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I shall leave the hypergolic Scrabble board as an exercise for the
Borg. |
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