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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

2019.0. "Problem based on Myst" by FLOYD::YODER (MFY) Tue Dec 12 1995 10:06

This puzzle is based on the Myst CD-ROM game (deservedly famous, in my opinion)
and on the book "Myst: the Book of Atrus."

Suppose a "descriptive book" creates a new "Age" or world which it links to;
that is, you can travel through it to the world it makes.  (It does not go with
you when you use it.)

Suppose further that a "linking book" allows you to travel to the place at which
the linking book was made.  This place must be within the world of a particular
descriptive book, which the linking book is attached to in some sense.  A
linking book is only attached to one such book.  (Actually, the assumption that
the locale must be within the world of the descriptive book is assumed and not
directly stated.  It is assumed because the statement that a linking book is
associated with a unique descriptive book makes no apparent sense otherwise.) 
As with descriptive books, linking books do not go with you when you use them;
but either sort of book can be carried through when using a *different* book.

From these assumptions, derive an interesting fact about the D'ni homeworld
which was the seat of the D'ni empire.  From here, the D'ni would travel back
and forth to their various created worlds, sometimes "harvesting" from them,
usually merely traveling.

T.R	Title	User	Personal Name	Date	Lines
2019.1	are any of these what you were looking for?	JOBURG::BUCHANAN		`Fri Dec 15 1995 00:04`	25
	(1) A world cannot hide books. ie: it cannot create worlds and hide books on them and shuffle the links around to prevent itself from getting at those hidden books again and bringing them back to the original world. (1') So from a world you can always visit any of its descendants. (2) A world's scope is itself and any of its direct and recursive descendants. If a world's scope contains a book leading to a world outside its scope, then in the future, it will always contain such a book. (call such a book an "alien artifact"). (3) From a world you can (if there is an alien artifact) escape outside the scope. You can carry on doing this until you enter a world which has no alien artifacts in scope. At this point you cannot escape the scope and can only move up if someone comes in with a book. (4) If a world has its own descriptive book in scope at any point in time, then prior to this and for ever afterwards it will have an alien artiact in scope. [These are just some interesting facts, in no particular order.] Cheers, Andrew.
2019.2	No, but they are interesting	FLOYD::YODER	MFY	`Fri Dec 15 1995 11:34`	39
	None of these are what I was looking for... I think it'll be obvious when you find it. Some further comments which may or may not help: First of all, assume that there aren't alternative means for traveling between worlds aside from books! If there are, you can't conclude much of anything without knowing something about those means. Despite the worlds being called "Ages," there is no clear use of time travel in the game or the novel, and none is meant to be implied here. Assume all worlds share a single uniform time, or, if you prefer, that the reference frame of a descriptive book is tied to the frame of the place it takes you to. Books of either sort can be destroyed: they can be burned, or simply torn apart, and then they cease to work. This doesn't affect the puzzle I'm posing. If torn apart, linking books can sometimes be repaired; it is reasonable to assume the same holds for descriptive books. There was a question posed in the novel about whether descriptive books really create their Ages, or merely connect to preexisting ones. For some varieties of the latter, the two cannot be distinguished experimentally; assume that this is so. In particular, if a descriptive book was made which produced a circularity, it would disprove the "books create their Ages" theory. Assume this doesn't happen. In the novel, it was stated that editing a descriptive book changed the Age it was associated with, so as to match the new description. This also doesn't affect the puzzle I'm posing. (It was mentioned that all associated linking books would automatically connect to new places in the edited world. This is the only strong evidence for my belief that the destination of linking books must be within the world the linking book is associated with.) It wasn't stated in the novel what happens to alien artifacts within a world W (in the terms of .1) when the descriptive book for W is destroyed. There ought to be two experimentally distinguishable cases, as follows: say you have a home base you can return to. Make descriptive books for worlds A and B, then make a linking book L to someplace within B and pull it out to home. Now carry the descriptive book for B into A, come home, and burn the book for A. If L still works, the book which creates B is still active in some sense. (Of course, L might now just annihilate all who use it...)
2019.3	minor comment on .1	FLOYD::YODER	MFY	`Fri Dec 15 1995 16:22`	8
	The conclusions (2) and (4) are only true if books are never destroyed. Since having the ability to destroy books doesn't affect the answer I'm looking for, you may find it preferable to allow such destruction. It was clear from the novel that destroying a linking book had no further repercussions. It was believed by the D'ni that destroying a descriptive book would destroy its associated world; as far as the puzzle is concerned you may assume that this is either true, or not experimentally disconfirmable.
2019.4	spoiler: solution given	FLOYD::YODER	MFY	`Fri Dec 22 1995 11:28`	8
	The funny consequence that I wanted was that the "home base" of the D'ni had to be a created world; they must have been exiled from their original world, which presumably had no descriptive book, and hence couldn't have a linking book made to it. Indeed, in the novel, the place described "felt" created, and this might be a clue that the authors realized this consequence. This implicitly assumes there isn't an infinite regression, of course. But I think most of us took that for granted...