Space & Astronomy/Space and Astronomy (October 1993).iso/mac/TEXT/SPACEDIG/V17/V17NO004.TXT

Text File | 1993-08-13 | 26KB | 589 lines

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?

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Date: 9 Aug 1993 05:19:20 GMT
From: Jeff Bytof - SIO <[e-mail]>
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." <[e-mail]>
Subject: Donkey Drivers of the Universe
Newsgroups: sci.space

In article <244moo$[e-mail]> [e-mail] (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: [e-mail] (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: <[e-mail]>
Date: 5 Aug 93 14:38:20 GMT
References: <23nul6$[e-mail]> <[e-mail]>
Sender: [e-mail] (Usenet News System)
Organization: Computer Science Dept, QMW, University of London
Lines: 24
Xref: sdcc12 sci.math:47739 sci.philosophy.tech:12115

In <[e-mail]> [e-mail] (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  [phone] [e-mail]

======================================================================
Article: 47744 of sci.math
From: [e-mail] (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: 1 > 0 ?
Message-ID: <[e-mail]>
Date: 5 Aug 93 14:46:16 GMT
References: <[e-mail]>
Sender: [e-mail] (Usenet News System)
Organization: Computer Science Dept, QMW, University of London
Lines: 13

In <[e-mail]>
[e-mail] (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  [phone] [e-mail]

========================================================================

Article: 47745 of sci.math
From: [e-mail] (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Definition of exponents
Message-ID: <[e-mail]>
Date: 5 Aug 93 14:58:52 GMT
References: <[e-mail]> <[e-mail]>   <[e-mail]>  <[e-mail]> <[e-mail]>
Sender: [e-mail] (Usenet News System)
Organization: Computer Science Dept, QMW, University of London
Lines: 24

In <[e-mail]>
[e-mail] (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  [phone] [e-mail]

===========================================================================
Article: 47749 of sci.math
From: [e-mail] (Angus H Rodgers)
Newsgroups: sci.physics,sci.math
Subject: Re: Getting mathematical results
Message-ID: <[e-mail]>
Date: 5 Aug 93 15:07:36 GMT
Sender: [e-mail] (Usenet News System)
Organization: Computer Science Dept, QMW, University of London
Lines: 34
Xref: sdcc12 sci.physics:56559 sci.math:47749

In <[e-mail]>
[e-mail] (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  [phone] [e-mail]


==========================================================================
***** Below is a basket of noise from a moving crab in the basket ******

Article: 47752 of sci.math
From: [e-mail] (Angus H Rodgers)
Newsgroups: sci.math,sci.logic,sci.philosophy.tech
Subject: Re: Axioms for the reals (was: 1 > 0?)
Message-ID: <[e-mail]>
Date: 5 Aug 93 15:24:56 GMT
References: <[e-mail]>
Sender: [e-mail] (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 <[e-mail]>
[e-mail] (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  [phone] [e-mail]


**** [ good try. Singing other people's song ]

====================================================================



Article: 47757 of sci.math
From: [e-mail] (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Silly, aesthetic question...
Message-ID: <[e-mail]>
Date: 5 Aug 93 15:45:50 GMT
References: <23cf8k$[e-mail]> <23qkl8$[e-mail]> <[e-mail]>
Sender: [e-mail] (Usenet News System)
Organization: Computer Science Dept, QMW, University of London
Lines: 12

In <[e-mail]>
[e-mail] (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  [phone] [e-mail]

===================================================================

Article: 47856 of sci.math
From: [e-mail] (Angus H Rodgers)
Newsgroups: sci.math,sci.logic,sci.philosophy.tech,sci.philosophy
Subject: Re: realism and mathematics
Message-ID: <[e-mail]>
Date: 6 Aug 93 15:28:53 GMT
References: <[e-mail]>
Sender: [e-mail] (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 <[e-mail]>
[e-mail] (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  [phone] [e-mail]

=====================================================================



` Song of a crab '

------------------------------

Date: 9 Aug 93 08:48:14 GMT
From: "S.H." <[e-mail]>
Subject: Donkey Drivers of the Universe
Newsgroups: sci.space

just a correction:

[ About Organizatio Title: SuperComputer Center @ UCSD Stuff ]

>In article <244moo$[e-mail]> [e-mail] (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 <[e-mail]>
Subject: Voyager: Where to get Info?
Newsgroups: sci.space

In article <244g7i$[e-mail]>, [e-mail] (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.

--
<a href="http://info.cern.ch/roeber/fgmr.html"><i>Frederick.</i></a>

------------------------------

End of Space Digest Volume 17 : Issue 004
------------------------------