Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!samsung!dali.cs.montana.edu!milton!phys2094@waikato.ac.nz From: phys2094@waikato.ac.nz Newsgroups: sci.virtual-worlds Subject: Re: "Space" Message-ID: <1120.26b55980@waikato.ac.nz> Date: 30 Jul 90 22:12:16 GMT References: <9007250107.AA01311@hitl.vrnet.washington.edu> Sender: hlab@milton.u.washington.edu Organization: University of Waikato, Hamilton, New Zealand Lines: 157 Approved: hitl@hardy.u.washington.edu In article <9007250107.AA01311@hitl.vrnet.washington.edu>, william@hitl.vrnet.washington.edu (William Bricken) writes: > In reference to the nature of SPACE: > > The mathematical theory of measurement provides a concise summary ofthe > generic types of spaces. _Mathematical theory_ is introduced here to impress readers with the validity of the following conjectures. Beware! > Here they are, with slight elaboration. > This list is a hierarchy, each following type is an elaboration of the > preceeding ones. Note that each can be conceptualized as one-dimensional, > additional dimensions (2D, 3D, etc) are merely orthogonal products of > more than one space. Note that the topology of each one-dimensional space is expected to be homeomorphic to the real number line to match our concept of spatial dimension. > For grounding, it is commonly assumed that our everyday living space is > composed of three REAL spaces at right angles. In fact, this idea was > made up in the middle of the sixteenth century by Descartes. Cyberspace I'm afraid that I don't know what this _Cyberspace_ concept is, but I am probably in a minority in this newsgroup. > illustrates the notion that space is quite arbitrary, it provides an > opportunity to retrain ourselves to perceive all the other types of space. Is this perception sensual? What do you mean by perceive? > TIME is just another space, one that we have forgotten how to travel freely > in. Did we ever know how to travel freely in space? As children? Did our ancestors know how? Are you aware of the literature on the arrow of time (Stephen Hawking is a good author to refer to)? What happens to causality arguments (grandfather paradox, etc) if we travel in time? >So is SCALE. Is this some vague, quasi-impressive reference to scale-invariance which is used to refer to the scale-invariance of fractals? If so, be careful how you use the term dimension and check the difference between Hausdorff and topological dimension. >The technical challenge of cyberspace is how we will be > able to *mix* types of space in the same perceptual environment. Certainly is a challenge! > ***THE VARIETIES OF SPACE*** > > INDICATIVE: the elementary domain of perception. Where our mind is. > This one is not taught in school. See Spencer-Brown, Laws of Form. _________________________________ I can see why! How is this dimension homeomorphic to the real number line? > NOMINAL: a set, unordered collections of things. EG: the space of > cyberspace novels, of fish in a pond, of items on a menu. Have you ever studied set theory? You have just introduced a set which is bare of any operations? How this can be misconstrued as a _variety of space_ is beyond me! > ORDINAL: ordered, ranked things. EG: your list of most to least > favorite novels, pecking orders of fish, steps in an instruction. Congratulations, you have discovered ordering! > INTERVAL: order in which the distance between items is equal. Integers. > EG: pages in a novel, age in days of fish, cells on graph paper. Gosh, now you are beginning to _perceive_ what a metric is! > RATIONAL: intervals which support ratios. Numerical fractions. EG: > percentages of each letter in a novel, portions of a meal each fish eats, > comparison of monetary wealth. > > REAL: continuous space. Real numbers. EG: our model of the space > underlying words on a page, the weight and length of fish, physical > space. Finally a space that I can associate with my common-sense feel for dimension! > IMAGINARY: contradictory spaces. Sqrt[-1]. Both True and False. EG: > our construction of mental images from words, wave propagation, inside a > black hole. What drivel! Real and imaginary spaces are equivalent. They fuse together to form a plane with the complex product operation defined on it. Whereas multiplication in the real numbers allows contraction and expansion, multipli- cation in complex spaces allows contraction, expansion and rotations. That's it! Where do you get this idea of _contradictory spaces_? What is contradic- tory about _wave propagation_? What is so strange about the construction of mental images for which words are just labels? And the apparent contradic- tions about black holes are merely a consequence of the presence of a singu- larity in the equations which indicates a limit of the theory of general relativity. > Note how going down this hierarchy successively adds more mathematics and You mean self-delusion and confusion > less physical reality. Note how cognitive spaces bound both the top and the > bottom. Does anyone take this guy seriously? Is he just trying to justify some science-fiction genre, or is he trying to sell an attitude? > William Bricken > HITL, UW What is HITL and how do I avoid it? > william@hitl.vrnet.washington.edu Do me a favour. Enjoy your science fiction, but don't insert deluded crap into a science newsgroup. BTW, this criticism is not meant to be personal. Have a nice day. :)