gcj@qmc-ori.UUCP (05/31/86)
This posting is a tangential response to Pat Hayes' posting in AIList Vol 4 # 125. It is obvious to every child that two things cannot exist in the same place at once. But a child does not know what is the other side of the cradle. A child (and therefore the adult) can never fully expand its spatial reasoning beyond what the eye can see. Hence, we enter a new realm; fantasy. For example:- It is even possible to believe that if I walk into this room, I will leave reality and enter into a fantasy, eg a film, OR I wake up one morning and am afraid to open the door in case I do not recognise the landscape outside. We carry childhood stories and myths with us to the grave; we remember the lessons we learnt not only in books and from our schooling, but also the fairy stories, eg "Alice Through the Looking Glass" and "The Lion, the Witch and the Wardrobe". This is more about the distinction between fantasy and reality than to do with spatial intuition. In the Mind's I, there is a discussion on whether or not a simulation inside a computer of a hurricane is any different from the machine's perception of the real event. To me there would be a world of difference! In "The Teachings of Don Juan: A Yaqui Way of Knowledge" by Carlos Castaneda, the author describes, at some point in the book, his transformation into a bird. His forward begins with the sentence - "This book is both ethnography and allegory." But my reading is that he wants you to *believe* his story. "Choose your own paradigm of reality." -- The Joka. Gordon Joly ARPA: gcj%maths.qmc.ac.uk%cs.qmc.ac.uk@cs.ucl.ac.uk UUCP: ...!seismo!ukc!qmc-ori!gcj
Laws@SRI-AI.ARPA (Ken Laws) (06/02/86)
Some thoughts on Pat Hayes' question: My own intuition is that either 1) the Tardis is simply bigger inside, as you suggest, or 2) the doorway is a portal to another dimension or reality that could contain anything at all. One way to test the intuition is to ask "What would happen if I cut a hole through the wall?" The answer would not completely distinguish the two cases, since it is quite possible that the entire wall (inside and out) is a portal that maps between two realities; cutting a hole would create a new door with exactly the same properties as the original, which would tell us nothing. My own guess, though, is that cutting a hole from outside the Tardis would reveal some kind of "machinery" or peculiar spatial structure (such as a gel, crystal, or other "matrix"), while cutting a hole from the inside would let you out into Gallifrey, Dr. Who's natural environment. Such portals have been frequent in science fiction, and the exact properties that we infer for each depends on the author's presentation. Some conceptions do lead to greater difficulties than others. In Robots Have No Tails, Louis Padgett (pseudonym) wrote about a box that was larger inside [partly] because it mapped into the future and the universe was shrinking. This lead to difficulties at the interface: things put inside would shrink, but only after a few seconds, and it is not clear what would happen to a single object (such as your hand) that extended across the portal for that length of time. I find Pat's "shrinking" hypothesis untenable for this reason. Similar problems arise at the boundary if the doorway is a transporter. Another such box is the chest that appears in one episode of the Dungeons and Dragons cartoon on TV. Move it to a particular place, open it, and you are likely to find a stairway to an alternate reality. (This is rather like the holes in time used in the Time Bandits movie.) The D&D chest has the property that the spatial mapping between realities is fixed and that the portal itself moves between them. I assume that the box cannot be moved while open, which covers the main conceptual difficulty: why can realities only connect at certain points, and what happens if the box straddles two such points. As for something simply being bigger inside, this doesn't bother me. As we move, we somehow update our internal maps of our surroundings. As I turn my head, I somehow rotate my mapping of where everything is relative to my focal direction. It seems unlikely that I actually store and update a position vector for every book on my bookshelves; instead I must be storing relative positions of items in the room and the relative orientation of myself and the room. One could argue that our natural tendency to build walls, and perhaps even our tendency to build rectangular rooms, arises from the mental savings in building these maps in hierarchically partitioned modules with related coordinate frames. If we store spatial relations in such a manner, it is easy to see how the spatial relationships inside a box need not be strongly linked to those outside the box. Just as we can move the box and its contents as a whole, we can expand it as a whole (on the inside only!) without affecting our mapping of the rest of the world. As for two things not occupying the same space, that's not really true. It all depends on what you mean by "thing". A forest and a tree occupy overlapping space. Properties such as color and texture certainly coexist. Fish and streams seem to interoccupy, and groping around in streams and holes may be a task for which our spatial decoupling evolved. I wouldn't even be surprised if fish were perceptually bigger on the inside than on the outside, since they disgorge a lot of "stuff" when you open them up that is perceived at a different level of detail than is the smooth exterior of a fish. -- Ken Laws -------
majka@ubc.CSNET (Marc Majka) (06/04/86)
> ...Einstein's theory of general relativity, which models the cosmos > as a 4 dimensional pseudo-Riemannian spacetime. ... *pseudo*-Riemannian? I think you mean Semi-Reimannian, and that applies to the metric, not the spacetime. --- Marc Majka