Space Digest Mon, 9 Aug 93 Volume 17 : Issue 004 Today's Topics: Donkey Drivers of the Universe (3 msgs) Voyager: Where to get Info? Welcome to the Space Digest!! Please send your messages to "space@isu.isunet.edu", and (un)subscription requests of the form "Subscribe Space " to one of these addresses: listserv@uga (BITNET), rice::boyle (SPAN/NSInet), utadnx::utspan::rice::boyle (THENET), or space-REQUEST@isu.isunet.edu (Internet). ---------------------------------------------------------------------- Date: 9 Aug 1993 05:19:20 GMT From: Jeff Bytof - SIO Subject: Donkey Drivers of the Universe Newsgroups: sci.space [In response to S.H., a fellow Triton}: >Organization: San Diego SuperComputer Center @ UCSD > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >Hope this is not an insult. May I ask this: >"Are you a staff of SDSC or an *user* ? " Simply a user. >> -rabjab, AstroZionist Donkey Driver > Above is your signature. Who are the Donkey? Students? No, I identify with Milton Humason, who was once a donkey cart driver for supplies up to Lick Observatory. I believe he later became a night assistant at the observatory and went on to gather observational evidence for the Big Bang theory of the Universe. I am a lowly user and drive no human, even students. I hope that someday, before I am dead, I too will undeservedly participate in the exploration of the universe. On the side, I have great repect for the Amish and the American Indian. A dad of my friend's refused to believe in the Big Bang because a 'donkey driver' had something to do with it. There must be a great truth somewhere here. -rabjab, Galactically Stupid Doo-Doo from the Dog Star. ------------------------------ Date: 9 Aug 93 06:20:31 GMT From: "S.H." Subject: Donkey Drivers of the Universe Newsgroups: sci.space In article <244moo$e0i@pravda.sdsc.edu> u1452@sluggo.sdsc.edu (Jeff Bytof - SIO) writes: >[In response to S.H., a fellow Triton}: >>Organization: San Diego SuperComputer Center @ UCSD ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >>Hope this is not an insult. May I ask this: >>"Are you a staff of SDSC or an *user* ? " >Simply a user. Thanks A lot. This is All I want to know. Next time, if you are just the user, do not wear the Title of the Organisation which you are not belong to. Wearing somebody else's Title to send message is very ease to cause elusions. Sometime, it could be taken as done intensionly for political propaganda. Remember this: **You** do not represent San Diego SuperComputer Center @ UCSD! >>> -rabjab, AstroZionist Donkey Driver >> Above is your signature. Who are the Donkey? Students? >No, I identify with Milton Humason, who was once a donkey cart >driver for supplies up to Lick Observatory. I believe he later became a >night assistant at the observatory and went on to gather observational >evidence for the Big Bang theory of the Universe. I am a lowly >user and drive no human, even students. I hope that someday, >before I am dead, I too will undeservedly participate in the exploration >of the universe. When you start to talk about BigBang, it reminds me people I know at QMW - Queen Mary Westfield College Longond. Everybody there wanted a Big bang. The Whole college was a big bang of educations. Now, they think they treat `High Tech' as a Big Bang for them to gain Powers. >On the side, I have great repect for the Amish and the American Indian. How much do you know about Indias ? Why did you have to mention that ? >A dad of my friend's refused to believe in the Big Bang because a >'donkey driver' had something to do with it. There must be a great >truth somewhere here. Must be another fake story. May I ask here are you comming from. >-rabjab, Galactically Stupid Doo-Doo from the Dog Star. Anyway, following are some of the posts by A.H. Rodger of QMW. Enjoy, =================================================================== From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.math,sci.philosophy.tech Subject: Re: Math & science vs. math is science (was Re: Soliciting views on the scientific method) Message-ID: Date: 5 Aug 93 14:38:20 GMT References: <23nul6$au6@optima.cs.arizona.edu> <18135@blue.cis.pitt.edu> Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 24 Xref: sdcc12 sci.math:47739 sci.philosophy.tech:12115 In <18135@blue.cis.pitt.edu> tmkst6+@pitt.edu (Theodore M Kostek) writes: >This really boggles me. I just don't know how you can really say that math >is about the real world. Can you really show me a straight line in the >real world? A perfect circle? Can you show me a thought in the real world? A feeling? A twinge of toothache? An ache of disgust? A perfect love? A pernicious ideology? A vein of humour? A disastrous life? A hackneyed plot? An evil intention? A beautiful idea? Getting like Hollystone now ... (I hope.) ;) -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk ====================================================================== Article: 47744 of sci.math From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.math Subject: Re: 1 > 0 ? Message-ID: Date: 5 Aug 93 14:46:16 GMT References: Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 13 In mark_a@cix.compulink.co.uk (Mark Atkinson) writes: >BTW, I don't normally subscribe to this group, and I must say you guys have >one of the highest signal-to-noise ratios I've seen outside of alt.*. ^^^^^^^ So you don't subscribe to sci.electronics either? This is your first gratuitously nasty and ill-informed sci.math sneer! Enjoy. (Enjoy it even more if *I've* got it the wrong way round.) :) :) -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk ======================================================================== Article: 47745 of sci.math From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.math Subject: Re: Definition of exponents Message-ID: Date: 5 Aug 93 14:58:52 GMT References: <744321684snx@bslewi.atr.bso.nl> Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 24 In Benjamin.J.Tilly@dartmouth.edu (Benjamin J. Tilly) writes: >He probably was thinking of a "certain continuity", namely uniform >continuity. So he did not make a mistake. But I agree that he could >have been more clear. But the function y |--> a^y, for a in R, isn't uniformly continuous on Q, so that doesn't help us in the present case. As for Dedekind, I guess he might have had in mind monotonicity in each argument (as exploited in David Radcliffe's elegant 4-line answer), but neglected to mention it. [I'm a bit punch-drunk, still, after yesterday -- no, not the kind of punch you drink, unfortunately -- so pardon me if this is a boob on my part. ... But how I wish for a Net where one wouldn't have to say that kind of thing all the time! People could learn to keep the noise level down by receiving, or watching others receive, a few gentle corrections; and the few real (ego)maniacs could be killfiled; and the rest of us could get on with our conversations. Dream on.] -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk =========================================================================== Article: 47749 of sci.math From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.physics,sci.math Subject: Re: Getting mathematical results Message-ID: Date: 5 Aug 93 15:07:36 GMT Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 34 Xref: sdcc12 sci.physics:56559 sci.math:47749 In <1993Aug5.093753.3438@sun0.urz.uni-heidelberg.de> gsmith@lauren.iwr.uni-heidelberg.de (Gene W. Smith) writes: >Presenting the general concept should involve *why* you are presenting >the general concept to the extent possible. When I was in high >school, a kindly math professor donated me some books. One was on >general topology. I found it very interesting, and really liked T_0, >T_1, ultrafilters, uniform topologies and all the rest. >*But*, I thought it was all neat stuff people had cooked up for the >fun of it, to see how general they could make the idea of space and >geometry be. Not really the best point of view on the subject, but >the book gave little hint that there was another one. Almost exactly my experience, too. This was my point (which seemed to get lost) about the teaching of group theory without giving any motivation for some of its more elaborate constructions, which have visible roots in Galois theory. I would also love to quote from chapter 0 of Godement's _Algebra_, which I unfortunately bought for myself and began to read in my first year at university. It contains what I think is must be the single worst piece of advice ever given to students of mathematics (at university level, that is). (I'll fetch it in some time, and give the quote. I'd be interested to see what comments people have.) [In shock from having just agreed wholeheartedly with something Hollystone said ...] :) -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk ========================================================================== ***** Below is a basket of noise from a moving crab in the basket ****** Article: 47752 of sci.math From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.math,sci.logic,sci.philosophy.tech Subject: Re: Axioms for the reals (was: 1 > 0?) Message-ID: Date: 5 Aug 93 15:24:56 GMT References: Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 146 Xref: sdcc12 sci.math:47752 sci.logic:4899 sci.philosophy.tech:12119 [I've crossposted this, from sci.math to sci.logic and sci.philosophy.tech.] In Benjamin.J.Tilly@dartmouth.edu (Benjamin J. Tilly) writes: >I HATE making dumb errors on the net. "To err is human; to really foul up, you need a computer." It's like swimming in cold water: one gets used to it after a while. (Of course, one meets the occasional hungry shark, dreaming of being a big fish in a little pool; and then one can get mistaken for dead meat. But such pests are easily seen off, without any real blood being shed.) :) >Another example of an axiom system for the reals that is short but >would be a real pain to work with is to define it as a commutative >topological group it an element 1 different from the additive identity >0 such that the group is connected but if you take away 0 then it has 2 >disjoint connected components. Then multiplication by x can be defined >as the unique continuous group homomorphism that sends 1 to x. This >gives the reals but showing it is a *real* pain. I do not think that >anyone would actually want to *work* with this axiom system. I am not urging the adoption of any one "correct" axiom system for the real numbers: neither mine or anyone else's. I am advocating my axiom system because I like it; and I like it because it has certain virtues, and not because I think it is "the best" in any absolute sense. Whereas you, I imagine, are advocating the use of the axioms for a complete ordered field, on the grounds that, since you always need to have the operation of multiplication ready to hand when you are working with real numbers, you therefore need to have a description of the reals which tells you essentially everything that's true about that operation -- rather than having to construct it, in some painstaking way, and then still be left wondering what its properties are. There is no contradiction, nor is there even a conflict of interest, here. I believe that mathematicians ought to have free access to a whole hierarchy of axiom systems: all of them strictly categorical, each of them definable in terms each of the others, and none of them taken to be "better" than all the rest, just because of something about its position in the hierarchy. (A sort of "egoless axiomatics", if you like. Or perhaps even a "politically correct logic"; or "postmodern mathematics"; or ...) :) Indeed, it is obvious, on reflection, that this ideal situation is the one which already obtains (in reality, that is, if not yet in the minds of all mathematicians); and that what remains, therefore, is merely the job of acknowledging and ratifying this fortunate _de facto_ state of affairs. As a pertinent example of what I mean, there would be, in the hierarchy of axiom systems for real numbers, amongst many other arrangements, a sort of progression, consisting of these three axiom systems: complete ordered field; complete, dense, linearly ordered, Abelian group, with arbitrary positive "unit"; betweenness relation, congruence relation, and arbitrary distinct "origin" and "unit". The third of these systems (in comparison with which, the system I have been presenting can be seen as a compromise with the more usual system) is the one mentioned by A. Tarski in his 1935 paper: "Some methodological investigations on the definability of concepts", reprinted in _Logic, Semantics, Metamathematics_, Oxford (1956), and reviewed by P. Suppes in "Philosophical implications of Tarski's work", _J. Symbolic Logic_, vol. 53, no. 1 (March 1988), pp. 80-91. There's something curious about all this, but I haven't figured out quite what it is yet. No doubt Hollystone has a theory. (Sigh.) I'm pretty sure it is related to a painful folk memory of the need to wean mathematics off its dependence on geometrical intuition in the last century; however, that doesn't explain the neglect of the concept of strict categoricity, which seems to me to be central to the problem of understanding what a "number system" is. There are lots of ways of characterising R up to isomorphism as an object in some concrete category or category of sets with structure. See Arbib & Manes, _Arrows, Structures and Functors_, Academic Press (1975), or Manes, _Algebraic Theories_, Springer (1976), for definitions general enough for our purposes. (And note that this is another neglected area of research, as Manes observes in the latter book.) For instance (as I only hazily recall) there are characterisations of R as an ordered set, and as a topological space; but in both cases there will be lots of non-identity automorphisms, so that the elements "move around", and you can't pick them out individually. In order to pin down the elements, you need a category in which the object of interest has no such automorphisms. This is where Tarski's work is useful. If the structure of the set of real numbers in a certain concrete category is *rigid*, then we have, I think, a definition of *real numbers*, such as pi and e, as well as [an isomorph of] the "set of all real numbers". (I think we get numbers as "semantic operations", in Lawvere's sense. But I still haven't finally made up my mind as to the right way of going about this. And there are set-theoretical problems with the idea, which I don't know how to resolve. I hesitate, therefore, to announce this as a feasible programme -- even in sci.math! -- and it remains a speculation.) Finally: you objected that my axiom system would be hard to work with. And it would be, if we had always to ascend to the level of a set theory which is permitted to mention such things as models and isomorphisms. But in practice, we can work with Eudoxus's definition of equal ratios, developing the properties of this quaternary relation in a structure satisfying my axioms (not mentioning the "unit of measure", 1, yet); and then, when we are ready, plug in the unit, and derive the properties of the ternary relation of multiplication, arriving at the conclusion that R is a complete ordered field. And perhaps there are other feasible ways of doing the work; I haven't yet carried the programme through in detail. But it's easy, no? There is still metamathematical work to be done, which is not easy; but that's for another post. -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk **** [ good try. Singing other people's song ] ==================================================================== Article: 47757 of sci.math From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.math Subject: Re: Silly, aesthetic question... Message-ID: Date: 5 Aug 93 15:45:50 GMT References: <23cf8k$bds@agate.berkeley.edu> <23qkl8$l6i@holodeck.iss.nus.sg> <1993Aug5.150432.22542@black.ox.ac.uk> Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 12 In <1993Aug5.150432.22542@black.ox.ac.uk> mbeattie@black.ox.ac.uk (Malcolm Beattie) writes: >A fun sentence/theorem from the days when geometry/mechanics >talked more about osculation and less about instantons: >The polhode rolls on the herpolhode in the invariant plane. Unwin's Theormole! Deep joy. -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk =================================================================== Article: 47856 of sci.math From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers) Newsgroups: sci.math,sci.logic,sci.philosophy.tech,sci.philosophy Subject: Re: realism and mathematics Message-ID: Date: 6 Aug 93 15:28:53 GMT References: <1993Aug5.150210.10249@schaefer.math.wisc.edu> Sender: usenet@dcs.qmw.ac.uk (Usenet News System) Organization: Computer Science Dept, QMW, University of London Lines: 98 Xref: sdcc12 sci.math:47856 sci.logic:4924 sci.philosophy.tech:12163 [The initial article in this thread was posted to sci.math, and, separately, to all the other newsgroups in the above list. I've tried to reintroduce sci.math to the thread.] In <1993Aug5.150210.10249@schaefer.math.wisc.edu> ettinger@schaefer.math.wisc.edu (Mark Ettinger) writes: >Why restrict the world to what might be more accurately called the physical >world? From a phenomenological point of view the physical world is just >one piece of the whole world which is disclosed through various types of >experiences. Another equally "real" portion of the world is the mathematical >world where mathematical objects are encountered as independent objects. >[...] >Please note that no mysterious, mystical bent should be read into what has >been said here as has often been done in the past in criticisms of the >phenomenological point of view. Views which would condemn mathematical objects as unreal, just because they are invisible, intangible, and otherwise physically undetectable, would rule *our* existence out on the same grounds. Not the existence of our bodies, of course, but our observing minds -- including, ironically, those very empiricist minds which claim so much authority to pronounce on what does and does not exist. Extreme empiricism is a form of latent suicidal depression -- and is so widespread as to constitute a mental plague. And it *is* somewhat depressing, for a would-be mathematician, to be unable to locate the objects of his consuming interest in a universe which can be securely felt as "real", and seriously spoken of as such. If this is a philosophical howler, I would love to have it explained to me exactly why that is so; because it has seemed awfully convincing to me for an awfully long time; and I would dearly like to be dis- abused of it. Another of my obsessions, this. I'm sorry. But I promise not to start a whole new thread about it (written in predicate calculus notation) -- unless someone really annoys me, that is. 8-} On what grounds are we justified in asserting the existence of *the* domain of set theory $S$ as a well-determined reality in which, say, CH is true or false? The principal grounds are that $S$ is prehended and, on the foundation of this prehension, one can find many paths promising more complete prehensions of $S$ possibly decisive for CH. [...] [I]n the absence of [various experiences of disorientation], and in the presence of promising, increasingly complete apprehension of $S$, it is difficult to deny the existence of $S$ -- one's actual intellectual experience preserves one's sense of what is prehended, viz., $S$, as a well- determined reality having a life of its own independent of one's will and desire. This is essentially Godel's point [...] [There are other interesting passages on pages 23 and 29; but the interested reader can discover these for him/herself. I've already exceeded my bandwidth quota in sci.math more times than I care to think about.] It's all a bit misty and waffly for me (pot calling kettle black, no doubt); but it *is* worth saying -- and returning to the idea again and again, when lost -- that what is "real" is what can be *explored*. Or, one might even say: whatever is *unknown* is real; and to deny reality to something is often a way of pretending to know more about it than one does. Sour grapes scepticism? These things are the more worth saying loudly because they are not usually said at all. (Also it's fun to picture Quine et al. spinning in their graves, as one reads this sort of stuff.) ;) But this is psychology as much as philosophy, and it doesn't get us very far along the path of mathematics. I wonder if phenomenology ever does; but that could be just my sour grapes. I think a case could be made that the historical evolution of the number system -- as sketched in, for example, J.N. Crossley, _The Emergence of Number_, World Scientific (1987) -- presents us with a visible picture of a process of ever-deepening "apprehension" [p.30] of the phenomenon [?] of number, on a "phylogenetic" rather than an "ontogenetic" level. A historical study might help to tether down phenomenological ideas to something which can be observed. -- Just a thought (on re-reading p.29 of Tragesser's book). -- Gus Rodgers, Dept. of Computer Science, Queen Mary & Westfield College, Mile End Road, London, England +44 71 975 5241 arodgers@dcs.qmw.ac.uk ===================================================================== ` Song of a crab ' ------------------------------ Date: 9 Aug 93 08:48:14 GMT From: "S.H." Subject: Donkey Drivers of the Universe Newsgroups: sci.space just a correction: [ About Organizatio Title: SuperComputer Center @ UCSD Stuff ] >In article <244moo$e0i@pravda.sdsc.edu> u1452@sluggo.sdsc.edu (Jeff Bytof - SIO) writes: > >>A dad of my friend's refused to believe in the Big Bang because a >>'donkey driver' had something to do with it. There must be a great >>truth somewhere here. > > Must be another fake story. May I ask here are you comming from. ^ w H.S. UCSD ------------------------------ Date: Mon, 9 Aug 1993 08:54:06 GMT From: Frederick Roeber Subject: Voyager: Where to get Info? Newsgroups: sci.space In article <244g7i$lh@tribune.usask.ca>, lowey@jester.usask.ca (Dead Head) writes: >[...] > I'm especially interested in what exactly is on the "gold record" > which was attached to the spacecraft, as well as any pictures and > descriptions of the construction of the spacecraft. At about the time of the final voyager planetary encounter, the AIAA had its big meeting there in Pasadena. The big evening speach was given by Carl Sagan, and he talked about the Voyager craft, and the gold record. He briefly described the contents: "Hello" in scores of languages, whale song, a greeting from President Carter, and "Samples of some of the greatest music from history: Mozart, Beethoven, Bach, Chuck Berry ...." At this point the audience tittered a bit, so he paused and elaborated: "Johnny Be Good." Just after the encounter, there was a party at JPL to celebrate the entire Voyager project. The music was provided by CB himself, starting with JBG. -- Frederick. ------------------------------ End of Space Digest Volume 17 : Issue 004 ------------------------------