Conference noted::sf

.0> It has a few really dull stretches ... but it more than
.0> compensates with some truly extraordinary conceits.

   Oh come now, Carl is really a modest fellow :-)

for those who don't get the pun, "conceit" has two definitions:
"too high an opinion of one's abilities or worth" and "an ingenious or
witty thought".  Also, "an elaborate or exaggerated metaphor", which
probably also applies in this context.

len.

"Contact" is now out in paperback.  Go out on your lunch break and 
buy it.  Sagan is not an sf fan, or even much of a novelist, but he 
knows what wonder is, and that's what drives us all.  Even the minor 
scenes, like the protagonist's midnight drives out in the desert, are 
suffused with it.  There are lots of good scenes of the real working 
life of scientists, and the most extraordinary way to prove the 
existence of God that I have ever read.  Sagan is an outsider to sf, 
but he has out-classed anything the field has produced for quite a while.

/jlr

    	To explain first, the reason there is nothing in 293.4 is that
    I unfortunately made some kind of error which the computer would
    not allow me to put my reply in NOTES.
    
    	So, to sum up my previous reply (actually a question)-
    
    	Does anyone notice just how much Ann Druyan, Sagan's third wife,
    had on CONTACT?
    
    	Why does Sagan frequently put down any kind of religious
    explanations for the Universe (ie, GOD created the Universe),
    yet his own reasons practically say that a Supreme Intelligence
    had something to do with the structures of the Cosmos?  I say this
    only in the sense of it's being such a contradiction in terms.
    
    	Larry
    

        Sagan seems to have created his own "science religion". 
        He's not the only one... it's amazingly common.  Maybe his
        aversion for the explanations of other religions is no different
        from the aversion of Christians for the American Indian or
        Chinese creation myths...
        
        Personally, in the absence of significant data, it seems
        useless to speculate (and such myths are, after all,
        speculation). 
        
        	/dave

re: .4

Who is Ann Druyan, besides being Sagan's third wife?

re: .6

Sagan suffers from teleologism, something that I have myself.  You look out at 
the beauty and wonder of the world and think there has to be someone 
behind it, but aren't happy with the petty God that goes around 
smiting the Philistines.  Sagan tries to imagine a bigger God, and I 
think succeeds with the Signature of the Artist chapter.

/jlr

    	Ann Druyan had a hand in writing Contact, as she did with several
    of Carl's other books; she is also writing on the screenplay for
    the movie version of Contact.
    
    	Dear readers, please say otherwise if you think so, but I found
    the ending of Contact rather anticlimatic.
    
    	Larry
    

    	Though this may not be read, here goes -
    
    	Carl Sagan has reprised his 1980 COSMOS series with the new
    COSMOS - A SPECIAL EDITION.  It will be three, two-hour shows on
    consecutive nights in syndication.  In the Boston area, it will
    begin on Channel 25, WXNE, on Monday, September 15 at 8 pm.
    
    	See Notes Astronomy 189 and Space 214 for more details.
    
    	Larry
    

    Billions and billions of Carl Sagans....
    
    What a thought!
    
    Steve Kallis, Jr.
    

Newsgroups: net.sf-lovers
Path: decwrl!amdcad!lll-crg!rutgers!caip!daemon
Subject: Sagan's Contact
Posted: 30 Sep 86 13:04:09 GMT
Organization: Rutgers Univ., New Brunswick, N.J.
 
From: [email protected]
 
 
	Contact, by Carl Sagan
 
Sorry, this book disappointed me, so this is a rather
negative review.  
 
**** Spoiler Warning ****
 
The title says it.  This book is about the first contact
of us peasants with Alien Intelligences.  Almost everything
in the book seems very, very familiar.
 
Dedicated scientists with radio telescopes are scanning
the skies.  They scan and scan.  Grumbles from colleagues
who want to use the equipment for something else.  Money
worries.  Will they shut us down?  Then, suddenly, POW -
the signals come in.  Prime numbers from Vega, yet.
 
Political worries.  Should we tell the Russians?  Should
we tell the UN?  Unfortunately, the earth turns on its
axis, so international cooperation is necessary if we are
to listen full time.  So the scientists simply tell all
their colleagues by electronic mail, and the politicians
realise pretty quickly this was the right thing to do (!)
 
Then more message is found.  Pages of binary code, meaning
something very important.  It turns out
 
*** SPOILER WARNING #2 ****
 
the message is instructions for building "a machine" of
some kind.  Not a female android, but a dodecahedron,
with five chairs inside.  Should we build the machine?
Is it a trap?  Is it a weapon?  Who gets to sit in it?
 
So the US and the USSR try to build the machine and sort
of foul up.  The real engineering work is done by private
industry under the control of a crazed billionaire who
isn't called Harriman.  It gets built.  Five people get
into it.  It travels through wormholes to Vega.  Five
explorers find themselves in constructed environment
talking to Super Intelligent Beings who look like old
friends.  They go back to earth.  Nobody believes them,
but one feels our place in the Galactic Community is
somehow secure.
 
Now, maybe Carl Sagan hasn't read The Andromeda Experiment,
The Man Who Sold the Moon, 2001 - a Space Odyssey, and the
other books from which plot, action and events seem to have
been blatantly ripped off.  Maybe he thought this up quite
independently.  But I still think the novel pretty bad.
There is no real conflict, for one thing.  I don't mean
fighting, I mean different valid viewpoints leading to
plot tension, excitement &c.  Most of the book reads like
a school history novelisation, where everything happens
in an orderly manner and everyone is sweet reason.
 
Then, the aliens are a cop-out.  They have no discernable
alienness.  Instead, we get the boring stuff about
fundamentalists, millenarians, atheistic godless
scientists, all upset or elated over the fact that
We Are Not Alone.  The only attempt to analyse what
such contact would do to us and our society is again
very familiar - in the face of the unknown our local
animosities die down and World Peace creeps slowly in.
 
The book ends with a "cosmic disclosure" that I shan't
reveal, but by that time it was all very boring.  The
story slipped down well enough in an evening, so maybe
for a free evening or a long aeroplane journey, it's
appropriate.  But at the end I felt nothing had really
happened.  Thank you for reading this far.
 
Robert Firth

    I read the book over the Thanksgiving weekend.  It's okay, I think,
    but not great.  His characterizations are better than those of Asimov
    or Clarke, but that isn't saying much.  He DOES punch home a sense
    of wonder a couple of times.  But the heroine's emotional development
    is basically uninteresting and the attempts to tie it to the main
    plot don't relly work very well.  This gets in the way at the climax.
    
    I understand that middle-of-the-road is not a very exciting position
    to write about, but I found it a little tedious that Western religion
    gets represented only by extreme fundamentalists or their close
    kin.  I mean, there are plenty of intelligent and educated Christians
    and Jews out there, and lots of them have no trouble believing in
    the standard scientific world-view -- with additions, of course
    -- but we hardly see anything of such people and barely  hear that
    they exist.  It's so much more entertaining (Sagan thinks) to stage
    face-offs between the agnostic astronomer and the TV evangelist.
    
    *** SPOILER WARNING***
    
    
                 
    
    
    
    
    
    
    
    
    
    
    
    The idea of hiding a message in pi is the best thing in the book.
    I don't know if Sagan has considered the matter, but the idea of
    any volitional entity being able to adjust the value of pi in any
    sense has breath-taking and mind-bending philosophical consequences.
    
    Re .5
    
    In some of the Socratic dialogues that compose a fair bit of the
    book, the heroine makes a big point about evidence.  She (and therefore
    perhaps Sagan) wouldn't mind believing in God if the evidence were
    better.  So Sagan makes up something that he would regard as plausible
    evidence.  At least, perhaps that is his motive for the message
    in pi.

    	I have always had the impression that Sagan wants to believe
    in a God, but not the one of Christian/Judean/Muslim teachings.
    
    	Larry
    

    	Has anyone ever done any research into what is "formed" by the
    value Pi?  Is there any "message", coincident or otherwise?
    
    	For those of you who do not know what I'm talking about, Sagan
    in his 1985 novel CONTACT had scientists find that computing enough
    digits of Pi created a circular "symbol" of what was beleived to
    be a message from a "Supremely Perfect Being" (a.k.a., God).
    
    	I just wondered if Sagan made this up totally, or did he or
    some scientist have an inkling about this concept?  Is there a
    "message" (for lack of a better word) in any mathematical systems?
    
    	Larry
    

  The idea was that, if you compute Pi to a certain precision, in the proper
  base, you'll find a string of digits that maps to an NxM array that shows
  a picture of a circle (whew -- hope I got that right).  I think the number
  of digits in the block was the product of two primes, M and N.

  I was thinking about this the other day.  Since Pi is an irrational number
  and the digits to the right of the decimal point go on without end, won't
  you be able to find any arbitrary string of digits in there somewhere?  Of
  course, the term "computationally infeasible" rears its ugly head at this
  point.  

  JP

    	I am obviously not a math expert - how can two letters, M and
    N, be prime numbers?
    
    	Larry
    

    I imagine M and N are being used as algebraic variables, as in the
    sentence, "Let M and N be two large prime numbers."
    
    No, there is no known "message" in pi or any other number.  It's
    a fascinating speculation, though, especially since it would seem
    that the value of pi is a matter of complete mathematical determinism,
    with no room for any choice or manipulation by ANYTHING, omnipotent
    or not.
    
    Pi can be an irrational with a never-repeating decimal expansion
    and still not have every possible sequence of digits in it.  (See
    next paragraph.)  Whether or not pi (or any other irrational) DOES
    have all possible sequences is another long-standing mathematical 
    speculation.
    
    Consider the number 0.010011000111000011110000011111...
    The pattern is one 0, one 1, two 0's, two 1's, three 0's, three
    1's, and so on.  The base is ordinary decimal.  This number will
    never repeat, and thus is irrational, but it does not contain all
    digit sequences, because it certainly doesn't contain any sequence
    including 2, 3, 4, 5, 6, 7, 8, or 9.
    
    Earl Wajenberg

  The product of two primes is a fairly old SF dodge.  The idea is that,
  if this string of X bits is received from outer space, and X is the
  product of two primes M and N, you display the bits (0 or 1) in an
  N-by-M array and enjoy the picture.  If it isn't the product of two
  primes, then you have to guess about the dimensions of the array.

  Clearly, I'm not much at math, either.  Earl, thank you for the analysis.
  It makes perfect sense in base 10 -- does it also hold if you can change
  the base?  In other words, might there be some base in which .010011000111...
  does turn up some other digits?

  JP

    	I understand how a number can be irrational and not infinite
    if it doesn't contain all the Arabic numbers, but what if it DOES
    contain them all and is infinite?  Then should it eventually do
    all the numeric combinations because it IS infinite?
    
    	Larry
    

    re .19:
    
    No.
    
    You could do a similar construction to Earl's with all 10 Arabic
    numerals that would be irrational that would not produce all possible
    strings as substrings.
    
    (I'm sure I've seen this in the MATH conference somewhere)
                                                   
                  /
                 (  ___
                  ) ///
                 /
    

    OK, some math answers:
    
    	A number that contains all the digits, but does not coantain
    	all finite sequences of digits:
    
    	.1234567890100100010000...
    
    	No big deal there.  So you say, a number that contains an infinite
    	number of all the digits, but does not contain all possible
    	finite sequences of digits?  Try this:
    
    	.1234567890<1-9>00<1-9>000<1-9>0000...
    
    	Here the "<1-9>" means the digits 1 to 9.  Clearly the sequence
    	"11" never occurs.
    
    	There are also known numbers that we can prove do have every
    	possible finite sequence of digits in them.  This would be 
    	pretty complicated for this conference however, so you'll have
    	to take my word for it (or ask in the MATH notes file).  It
    	is not known whether or not PI is one of those.
    
	
    --  Barry

re: the_last_few

Any consideration of numbers that might contain "messages from
the creator" should include _e_ (the base number for natural
logarithms) and _phi_ (the "divine proportion" number), as well
as _pi_.  Maybe the "message" might be just the revelation of
some heretofore unknown equation relating these mysterious
constants to one another.  I gather that we're basically looking
for the signature of the artist on Her work after all, right?

    re .22:
    
    If I believed in a creator (which I don't) I would take the following
    equation as proof of his/her work:
    
    		     -i*pi
    		1 = e                 
    
    where "e" is Euler's number
    	  "i" is the unit imaginary (colloquially, SQRT(-1))�
    	  "pi" is pi                                         
                                                   
                  /
                 (  ___
                  ) ///
                 /
    
    � "officially", 'i' is not defined as "the square root of -1".
       but as "that number, when squared, equals -1".
    	The subtle distinction is needed because rigorously, the operation
    	of taking a square root is not allowed on negative numbers. So
    	the square root of -1 is undefined.
    	(but who's being rigorous? I just felt like being pedantic this
    	morning)
    
    	 

It's been a long time since I saw a complex exponential, but 
shouldn't that -1 instead of 1?
     2*pi*i
1 = e

/jlr

    			 i*pi
    I remember it as:	e    = -1
    
    --- jerry

    .22>    		     -i*pi
    .22>		1 = e            => -1     
        
    .23>      		     i*2*pi
    .23>		1 = e            => correct
        
    .24>	    	     i*pi
    .24> 	       -1 = e            => correct
    
    
    I stand corrected. .24 was the one I was thinking of.
                                                   
                  /
                 (  ___
                  ) ///
                 /
        
    

    Re .21:
    
    > There are also known numbers that we can prove do have every
    > possible finite sequence of digits in them.  This would be 
    > pretty complicated for this conference however, so you'll have
    > to take my word for it (or ask in the MATH notes file).
    
    On the contrary, an example is extremely simple.  Ignore the spaces:
    
    	.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 . . .
    
    
    				-- edp 

    Re .27:
    
    Oops.  You are right Eric.  I had forgotten the easy one.
    
    --  Barry

Newsgroups: sci.physics,rec.arts.sf-lovers
Path: decwrl!decvax!ucbvax!ucbcad!ames!lll-lcc!seismo!rochester!pt.cs.cmu.edu!
Subject: Pi
Posted: 3 Mar 87 15:39:29 GMT
Organization: Carnegie-Mellon University, SEI, Pgh, Pa
Xref: decwrl sci.physics:799 rec.arts.sf-lovers:1844
 
    Well, while you've been busy debating whether the Heechee (or
whoever) changed the value of Pi, my computer program has been running
along decoding it. 
 
    Beginning at the 666666th place in base 60, there is a sequence of
digits that, when mapped onto the Roman alphabet, spells out the
sentence 
 
                	WHAT NOW LITTLE MAN
 
    Now for the REALLY bad news: the message is encoded in BCD. 
 
Robert ("on the 1.5th day, God created fractals") Firth


Newsgroups: rec.arts.sf-lovers
Path: decwrl!decvax!ucbvax!ucbcad!ames!cit-vax!tybalt.caltech.edu!myers
Subject: Re: Pi discussion
Posted: 3 Mar 87 19:56:43 GMT
Organization: California Institute of Technology
Summary:
Keywords:
 
    In article <[email protected]> [email protected] (Charlie Martin) writes:
>>
>>First you insisted that c/2r was *the* definition according to dic-
>>tionaries, at which point I pointed out that dictionaries go on to
>>define circles and diameters etc as certain mathematical notions that
>>live in *flat* planes.  Is that too strong for you?
>
>It's funny -- I've looked in a bunch of dictionaries, (I quoted a list of them
>which somehow didn't get into this copy over here) and I can't find one
>definition that says anything about the flat plane.  I admit I've not checked
>the OED (no easy access) but the NINTH WEBSTER'S I checked didn't say anything
>at all about it -- I seem to recall this as having been a source you cited.
 
    From the only dictionary I have handy at the moment: WEBSTER'S NEW
COLLEGIATE DICTIONARY. 
 
pi:     The symbol pi denoting the ratio of the circumference of a circle
	    to its diameter
	The ratio itself: a transcendental number having a value to eight
	    decimal places of 3.14159265
 
circle: A closed plane curve every point of which is equidistant from a
	    fixed point within the curve
	The plane surface bounded by such a curve
 
plane:  A surface of such a nature that a straight line joining any two
	    of its points lies wholly in the surface
	A flat or level surface
  
    Is this satisfactory? Pi is not the ratio c/2r for a circle analog
in any surface; it is the ratio c/2r for a circle, which is defined to
be in a flat surface. 
 
-------------------------------------------------------------------------------
 
Bob Myers                                         [email protected]
					...seismo!tybalt.caltech.edu!myers


Newsgroups: rec.arts.sf-lovers
Path: decwrl!decvax!ucbvax!ucbcad!ames!lll-lcc!seismo!rochester!pt.cs.cmu.edu!
Subject: Check me on this, please
Posted: 3 Mar 87 21:34:39 GMT
Organization: Carnegie-Mellon University
ReSent-Date: Tue,  3 Mar 87 16:35:39 est
ReSent-From: postman#@andrew.cmu.edu
ReSent-To: nntp-xmit#@andrew.cmu.edu
Return-path: <haste#@andrew.cmu.edu>
To: outnews#[email protected]
Newsgroup: rec.arts.sf-lovers
 
    The 'Pi' discussion has whizzed around so much that not even all
those who are interested have been able to keep track.  I know I
haven't.  Below, relatively shorn of opinion, is what I *think* is at
the core of what's being said.  Could someone please check me on both
my math and my history? 

1.  In Sagan's SF novel, CONTACT, strong evidence is found for the
existence of an intelligent creator of the Universe:  the decimal
(well, base 11) expansion of Pi turns out to contain ['relatively'
early in the expansion] a string of 0's and 1's which, when arranged
in a grid, gives a picture of a circle and its diameter.  Since the
probability of this happening by chance is barely worth talking about,
the alternative seems to be that some creator fine-tuned the Universe
so as to make it happen that way. 
 
2.  Note:  Some have suggested that since the expansion of Pi is
essentially random, any arbitrary sequence of digits, including this
one, will eventually turn up, so the miracle is no miracle at all.
Three problems with this.  a) As someone pointed out, the expansion of
Pi is known to be nonrepeating and nonterminating.  This does *not*
imply that it is random.  Classical counterexample:  .010010001...  b)
Even if the expansion is essentialy random, for the sequence in
question to show up early enough in the expansion to be found by
modern computers still constitutes either Divine Intervention or a
statistical miracle.  c)  The book implies that this picture is found
in the *first* greatly extended sequence of 0's and 1's. 
 
3.  The value of Pi, for the purposes of decimal expansion, has
nothing to do with physical geometry.  It is calculated as the sum of
any of a number of infinite sequences.  If one demands a geometric
interpretation, it arises from the axioms of the purely formal system
of Euclidean geometry (which happens to correspond to the geometry of
the plane in this Universe); Pi is the limit of the sequence of ratios
of circumferences of n-sided regular polygons to their radii, as n
goes to infinity.  Either way, it turns out that Pi will have its
current value in any universe in which our current *number* system
holds sway.  That means that to get any other value of Pi a creator
would have had to create a universe where numbers work differently,
whatever that means. 
 
4.  Actually, we do have something of a handle on what that means.
Number theory is derived from set theory and logic.  To change the
value of Pi we'd need different logic.  Not a little different, *very*
different. 
 
5.  On one side of the argument seem to be those who feel that only a
poverty of the imagination prevents us from imagining a viable (and
moderately interesting) universe with different laws of logic (and
hence mathematics). 
 
6.  On the other side are those who feel that only a lack of
mathematical intuition allows anyone to imagine such a universe.
Essentially, the underlying notion here is that the rules of logic
must apply even to a creator of universes, that "to be and not to be",
for example, is beyond even the scope of the omnipotent. 

==========
 
Have I got it right?
Have I missed some important points?

Dani Zweig
haste#@andrew.cmu.edu 
(arpa, bitnet, or via seismo)
 
   "God helpe the man so wrapt in Errours endless traine."  -- Edmund Spenser

    Mr. Zweig seems to have summarized nicely everything that *I* have
    thought about the "Contact" message (though I haven't been in the
    discussion he's in).  I think I agree with the position in #6, that 
    even omnipotence cannot fiddle with logic, hence set theory, hence 
    the value of pi.
    
    Earl Wajenberg

I haven't been following this discussion too closely, but the alleged
class of the irresistable force (the Omnipotent) and the immoveable
object (the value of pi) need never occur.
One only need postulate an extra dimension of space to demonstrate
the variability of pi;  consider a subset, and extend the argument
to three and four space.....

If we were two dimensional beings, we would not be able to observe
that the earth is a sphere.  We would be constrained to its surface.
If the sphere were big enough relative to us, we could not traverse
it in sufficiently short time to demonstrate that circumnavigation
is possible.  However, if we began to construct circles on this surface
by plotting sets of points equidistant from a given point, we would find 
that the ratio of the (given) radius to the (measured) circumference
would  change as the radius changed.  For small circles the value would be
near pi as we "know" it.  For the great circle, the value of pi would be 2!
In the limit,  the value of pi approaches 0 as the radius of the circle
approaches the size of the universe.

Fiddle no fiddles that the logic we know is fixed.  Russell's Principia
can't prove that 1+1=2 until after 236 pages of prerequisite axiom
and proof.  That leaves a lot of room for  side paths and options
in the fabric of spacetime.

- tom]

    Re .31:
    
    The ratio of the circumference of a generalized circle to its diameter
    that you describe is not pi.  Pi is the ratio of the circumference of a
    circle to its radius in Euclidean space.  That is a space we do not
    live in, yet we found pi. 
    
    Pi is a fixed entity -- an important mathematical constant.  It would
    be found by any imaginable beings, regardless of the nature of the
    space in which they lived.
    
    All that is needed to discover pi or closely related constants (like 2
    pi) is:
    
         Count. 
    
         Ask what happens when one counts to x and then counts to y.
         (Answer:  addition.) 
    
         Ask what happens when one adds x repeatedly, for a total of y
         times. (Answer:  multiplication.) 
         
         Ask what number x can be added to y to get 0.  (Answer:
         negative numbers, -y.)
         
         Ask what number can be multiplied by q to get p.  (Answer:
         p/q, rational numbers.)
         
         Ask about other operations, exponents, and so on.  The
         algebraic closure of the above numbers gives the real
         numbers.
         
         After years of history, you will be trying to define when a
         function is smooth and when it is choppy.  To this end, one
         will define the limit:  The limit of f(x) as x goes to a is L
         iff for every positive real number e there exists a real
         number d such that for every x between a-d and a+d except for
         a itself, f(x) is between L-e and L+e.
         
         From the limit, the rate by which a function is changing
         quickly follows:  The derivative of f(x) is the limit as d
         goes to zero of [f(x+d)-f(x)]/d.
         
         Next, what function f has a derivative whose derivative is
         -f?
         
         The period with which the answer to the above question
         repeats itself is 2 pi.
    
    The above takes no notice of the space in which we live.
    
    In your spaces, the beings would also find pi when they considered the
    limit of the ratio of circumference to diameter as the size of the circle
    went to zero.  That would single out pi as an important number.
    
    > Fiddle no fiddles that the logic we know is fixed.  Russell's Principia
    > can't prove that 1+1=2 until after 236 pages of prerequisite axiom and
    > proof.  That leaves a lot of room for  side paths and options in the
    > fabric of spacetime. 
    
    That proof is immutable.  It goes to the extreme of moving symbol by
    symbol.  When a being puts its "y" after its "x", it gets "xy".  Those
    236 pages are just such operations, forever unchangable.  What controls
    those operations is a set of selected, primitive strings (called
    axioms) that describe counting.  Those strings, which are the only
    things in the proof which could change to make the proof different, do
    not take up 236 pages.  Could they change to give us a different logic?
    Sure, if your beings of another space have no wish to count. 
    
    
    				-- edp 

    Remember that Kurt Goedel (I'm on a VT100 and don't feel like messing
    with diacritics) proved his incompleteness theorem which states
    (check me on this) that any axiomatic system must be either incomplete
    or inconsistent.  This is certainly not the exact wording, but I
    believe it is the gist of the theorem.  I'm sure someone will be
    able to clear up any misinterpretation I may have made.
    
    Russell was trying to eliminate inconsistencies from logic (like the
    ones that come up in set theory), but Goedel's theorem showed that
    this was impossible (true?).  This of course doesn't invalidate
    all of mathematics.  It just means that we have to live with some
    inconsistency.
    
    As for the discussion at hand, if we limit ourselves to inhabitants
    of our own universe for a moment, I see no reason why another race
    would not discover the basic mathematical constants that have been
    mentioned: Pi, e, 1, et al.  These numbers crop up all the time
    in analyzing physical phenomena and aside from choosing a base for
    your number system (2 is the simplest, no?) the worst problem would
    be deciphering the symbol system.
    
    Wook

    Re .33:
    
    > Russell was trying to eliminate inconsistencies from logic (like the
    > ones that come up in set theory), but Goedel's theorem showed that
    > this was impossible (true?).  This of course doesn't invalidate
    > all of mathematics.  It just means that we have to live with some
    > inconsistency.
    
    Since Godel's Incompleteness Theorem states any system must be either
    incomplete or inconsistent (a third alternative is a lack of expressive
    power), we need only live with incompleteness, not inconsistency.
                                      
    
    				-- edp 

    Re .33
    
    Also, it isn't logic that is incomplete or inconsistent, but arithmetic
    and systems that include arithmetic.  Logic is too simple to fall
    victim to Goedel's proof, rather the way flies are seldom felled
    by elephant guns.
    
    However, you need arithmetic to calculate the value of pi, so at
    first it would seem there is some room for "play" wherein a cosmic
    engineer could fine-tune the value of pi.  But at second I don't
    think you'll find one.  How could anything "adjust" the value of
    a number?  Try imagining adjustments being made on the value of
    5, or on the square root of 2.  It's meaningless to adjust the value
    of a number -- a number IS a value.
    
    Earl Wajenberg                     

    Re .35:
    
    Although it is true that Boolean Algebra is to simple to G�delize,
    the First Order Predicate Calculus IS G�delizable, and that is
    what most mathematicians and logicians mean when they refer to 
    "Logic".
    
    As an interesting aside, a subset of the First Order Predicate Calculus
    that allows only a single variable per predicate is not suceptible
    to G�dels Theorem.
    
    --  Barry

In my previous reply, I meant to demonstrate how pi could change
in a space the full dimensions of which its inhabitants could not
directly observe.
Let me conjecture that in a sufficiently multidimensional space
it would be possible to have a constant value of pi that is different
from the 3.14159... that we know (okay, perhaps only locally, whatever 
locally means).
In such a space, would the physics of simple harmonic motion
noted by edp (f'=-f) be different?  Must the frequency of such oscillation
in such a space be the same as in our space?

-tom]

    Re .37:
    
    The period of solutions to f''=-f will never be anything other than
    2*pi.  This equation is independent of space.  In space, any object for
    which the push (second derivative of position) back to a certain point
    is proportional to the distance from that point will display simple
    harmonic motion, provided space and distance are locally Euclidean.
    
    Beings living in non-Euclidean space may discover physical constants
    different from pi.  Those physical contants will not be different
    values for pi in their universe; they will be different numbers
    altogeter.  The beings will still discover pi as a mathematical entity. 
    
    After all, we live in a non-Euclidean space and we discovered pi.  We
    also use other numbers to describe the curvature of space
    (specifically, the Riemann tensor), but we do not call them pi.
    
    
    				-- edp

    As I recall, edp was not talking about a physical system at all,
    but an abstract mathematical one, which would be unaffected by the
    dimensionality of the space the mathematician happens to occupy.
    
    Earl Wajenberg

Path: muscat!decwrl!labrea!rutgers!seismo!mcvax!ukc!dcl-cs!nott-cs!pyr1!
From: [email protected]
Newsgroups: rec.arts.sf-lovers
Subject: Contact in CONTACT by Sagan.
Message-ID: <42000031@pyr1>
Date: 2 Sep 87 12:44:00 GMT
Lines: 56
Nf-ID: #N:pyr1:42000031:000:2764
Nf-From: Cs.Ucl.ac.uk!seasterb    Sep  2 12:44:00 1987
  
		   CONTACT, by Carl Sagan
 
    I've just finished reading Carl Sagan's book, CONTACT, and despite
the fact that I cant stand the man himself, the book is quite good. 
One thing that struck me as wrong-headed though was the bit about
deciphering the message, and I wonder if anyone has read it and
noticed the same. 
 
                   *SPOILER WARNING!*
 
    The aliens teach us their language by starting off with simple
arithmetic, so they give us phrases of the form (Can't remember the
exact ones used in the book): 

	2 A 2 B 4 Z
	2 A 3 B 5 Z
	3 A 4 B 7 Z

    From which we deduce that A stands for plus, B stands for equals,
and (by some comparisons with later incorrect arithmetic), Z stands
for true (the incorrect arithmetic ended in Y meaning false).  All
well and good, but when I sat and thought about this, I realized this
makes some vast assumptions about the way we do maths.  For instance,
in this example, A could equally well mean equals with B meaning
"subtracted from".  This may seem to be splitting hairs, but consider: 
We have a convention that our arithmetic is ordered in this way. 
Equally valid orderings exist, such as reverse polish notation, and in
computing we often put the function before the arguments giving
something like: 

	Z B A 2 2 4
    Meaning: 	true (equals (sum (2, 2), 4)
 
    So how come the aliens knew our conventions, and does anyone else
agree with my criticism?  The answer may lie in the fact that the book
doesn't actually say that we received messages exactly like these,
they are just given as an example to the President to try and explain
how the code was cracked.  However, I contest that the problem of
decoding messages from a totally alien culture is extremely hard, even
if they have tried to make it as easy as possible for us, and I don't
think Sagan covers this well. 
 
    One thing I did think sensible was the inclusion of a periodic
table of elements to teach us about various materials used in the
machine.  This seems like one thing that cuts across culture barriers
completely, and I remember seeing the same idea mentioned elsewhere (I
have a vague recollection of a story about archaeology on Mars of a
deceased civilization). 
 
    Now for some general comments about the book:  I found a lot of
interesting ideas in the book, but I always had the nagging suspicion
that the overall plot has been well-trodden by other SF authors.  For
some reason the general story reminded me of Arthur C. Clarke's 2001:
A SPACE ODYSSEY, especially towards the end.  The inclusion of lots of
religious activity reminded me of David Brin's SUNDIVER, which had a
similar inclusion of fanaticism, with his shirts and skins, (and which
I'd just read beforehand!).  Has anyone else noticed this?  Has anyone
else read the book?  Is anyone going to reply to this message?  Is
there anybody out there? 
 
				Steve E 

Path: muscat!decwrl!labrea!rutgers!seismo!mimsy!oddjob!gargoyle!ihnp4!occrsh!
From: [email protected] (Richard Michael Todd)
Newsgroups: rec.arts.sf-lovers
Subject: Re: Contact in CONTACT by Sagan
Message-ID: <[email protected]>
Date: 5 Sep 87 23:22:07 GMT
References: <42000031@pyr1>
Reply-To: [email protected] (Richard Michael Todd)
Organization: University of Oklahoma, Norman
Lines: 19
  
    In article <42000031@pyr1> [email protected] writes:

)One thing I did think sensible was the inclusion of a periodic table
)of elements to teach us about various materials used in the machine.
)This seems like one thing that cuts across culture barriers completely,
)and I remember seeing the same idea mentioned elsewhere (I have a vague
)recollection of a story about archeology on Mars of a deceased
)civilization).

    It was "Omnilingual", by H. Beam Piper.  The story involved an
archeological dig at what turned out to be a Martian university.  The
discovery of a Martian rendition of the Periodic Table hanging on the
wall (just like in every chemistry classroom on this planet :-)) was a
very important step in the decipherment of the Martian language. 

    For those of you who want to find a copy of this story, it's in
the collection FEDERATION. 
--------------------------------------------------------------------------
Richard Todd
USSnail:820 Annie Court,Norman OK 73069
UUCP: {allegra!cbosgd|ihnp4}!occrsh!uokmax!rmtodd

    My copy of the book stated that Contact was soon to be a major motion
    picture. Any word on this?
    

    
    		Not sure about the movie. My copy said so too.
    		
    		However-Sagan will be giving a series of lectures
    	on CONTACT at Cornell University where he is a professor. 
    	I, being a student at Cornell, plan on attending and if the
    	chance arises will ask him of these little concerns of ours.
    		After I get around to reading the $#%#$ book.
    
    					anyone want a ride to Ithaca??
    
    
    						sam(17)

	Very good, readable book.

	Didn't find it here in UK, still haven't seen it here either HB or PB.
	Got my copy in Spain !! (was looking for a book written in English at 
	the time as my spanish is non-existant).

I'm surprised that you couldn't get it in the UK. I bought my (hardback) copy
over 2 years ago, and since then I've seen inumerable paperback copies all
over the place!

Martin

	I think I should qualify that, I have never seen it in the
	Science Fiction & Fantasy shelves, and since this is where I mainly
	browse, could mean that it has been "classified" in another
	category.

	CJA

    The current issue (Sep '92) of Life's cover story "Is Anybody out
    There?" is almost right out of "Contact".  It seems that there
    is an actual SETI at Arecibo, a NASA mission funded quite well,
    looking for ET's via radio telescope!  Carl Sagan has been involved,
    of course.  There's also something about people making light of the
    whole effort and trying to cut the government funding.  Meanwhile,
    Sagan has managed to talk people like Steven Spielberg into contributing!
    Interesting.. makes the book (which I thought was very good) appear to
    be something of a plug for the project..

    agr

    There have been a number of SETI searches piggy-backed onto radio
    telescope operations over the years.  I'm glad to hear that
    Arceibo is trying - it should have the best range.  There was one
    in the Boston area a little while ago.  A professor at Harvard,
    Paul Horowitz, build a big digital signal processor that could
    analyze thousands of frequency channels at once.  He got time on 
    the Haystack Observatory, which is about 40 miles outside Boston.
    He didn't pick up anything, as you might have guessed.
    
    It's getting a bit disheartening, actually.  There should be
    pretty obvious evidence of macro-engineering in the universe, but
    we don't see it.  Of course, we may be mis-interpreting some
    artificial phenomenon such as quasars as being of natural origin,
    but surely intelligence would be a bit more distinctive.  At our
    present rate of increase, we'll be able to re-engineer the Solar
    System within a couple of centuries.  Even if our civilization
    doesn't make it that far, some other one would be bound to.  We
    should be seeing something already, but as it is, we're not even
    picking up radio signals.  Maybe we just haven't looked hard
    enough, but there should be something visible already.
    
    /jlr