Half a croissant, on a plate, with a sign in front of it saying '50c'
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Infinite Hyperbolic Scrabble Board

Board which widens without limit away from the starting position
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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.

nineteenthly, Sep 18 2017

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]






       [+]
//People work in teams from various points on the board, towards each other, conquering each others' territory by linking words//
FlyingToaster, Sep 18 2017
  

       The team/'Go'/territory approach to Scrabble is really interesting but I don't see what the hyperbolic geometry adds to this idea
hippo, Sep 18 2017
  

       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.
nineteenthly, Sep 18 2017
  

       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?   

       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?
pertinax, Sep 20 2017
  

       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.
nineteenthly, Sep 21 2017
  

       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.
nineteenthly, Sep 21 2017
  

       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.
nineteenthly, Sep 21 2017
  

       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.
AusCan531, Sep 21 2017
  

       I think M.C.Escher draw some rather fine wireframe examples of such boards, and then coloured them in.
Zeuxis, Sep 22 2017
  

       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.
nineteenthly, Sep 22 2017
  

       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?   

       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".
pertinax, Sep 22 2017
  

       I shall leave the hypergolic Scrabble board as an exercise for the Borg.
pertinax, Sep 22 2017
  
      
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