From: len@schur.math.nwu.edu (Len Evens)
Subject: Re: averting doom
Organization: Dept of Math, Northwestern Univ
Date: Wed, 30 Dec 1992 14:10:19 GMT

In article <JMC.92Dec29211051@SAIL.Stanford.EDU> jmc@cs.Stanford.EDU writes:
>from a U.P. story

[Some very interesting speculation about the possibility of moving the
planet to avoid the consequences over hundreds of millions of years
---the last estimate I saw in a news story was just under a billion---
of the gradual heating of the sun.]

>
>
>By the way, it seems to me that if the above idea is sound, it settles
>the question of the stability of the solar system - in the negative.

If you don't mind a quibble from a mathematician, the mathematical question
of stability refers to whether a dynamical system following Newton's
laws and which is an idealization of the solar system stays bounded
for all time (or some related question of this type).   McCarthy's
speculation proposes the use of nuclear explosions to deflect an
asteroid.   This takes us out of the realm of dynamics.   If we depart
from that realm, it is perfectly obvious that the solar system is
not a stable system.  For example, what is likely to happen if the
the sun goes nova?



>Very likely an asteroid could be tamed over a sufficiently long time
>with as small an expenditure of delta-v as might be desired.  Once
>tamed it could be used with infinitesimal external force to expel a
>planet from the system.  This tells us that the current trajectory of
>the solar system is arbitarily close to one in which a planet is
>expelled.  Of course, the probability that a planet actually would be

You would need a whole lot more mathematics than the rough estimates
made in McCarthy's exposition to establish this.  I suspect the
clever people studying celestial mechanics have looked into
all the obvious small perturbations of this kind long ago, but
perhaps not.   I will ask my local expert.
 
>expelled by this mechanism in some particular finite time is extremely
>low, because maintaining the required sequence of encounters requires
>an improbable precision in the initial conditions.  I suppose a lower
>bound on the probability could be computed and from it an expected
>upper bound on the gravitational lifetime of the solar system could be
>obtained.
>
>Criticism and comments are welcome.  For a certain reason, I even
>welcome comments, however uninformed, to the effect that the whole
>idea is preposterous.  I prefer such comments to be postings rather
>than email.
>

It seems to me that this type of speculation takes us a bit beyond
science but perhaps not inexcusably.   Those interested in the earth's
history, particularly future history, certainly can't propose experiments
or observations which will directly confirm such predictions over
what is often called deep time.   McCarthy's point is basically that
the existence of intelligence may have profound effects.  This point has
been made before.  For example, Dyson proposed that advanced civilizations
might move all the mass in a star system into a sphere surrounding
the star thus capturing all its radiation and living on the inside
of the sphere.   As Steven Jay Gould has pointed out, this may be
a limited perspective.  We tend to think of evolution as an upward
process leading to us where it more or less stops.  In fact, it is quite 
possible that intelligence is an evolutionary side show which will shortly 
disappear.  There may be no ancestors around to engage in planetary
engineering when the time comes.

>What would be most welcome is a collaborator on a paper that could
>be published in _Nature_.
>--
>John McCarthy, Computer Science Department, Stanford, CA 94305
>*
>He who refuses to do arithmetic is doomed to talk nonsense.
>

I think the analysis needs a lot more mathematics than arithmetic.
Unforutnately, I don't know enough of the right kind to help, but
I will pass this idea on to my colleagues who do.


Leonard Evens      len@math.nwu.edu      708-491-5537
Dept. of Mathematics, Northwestern Univ., Evanston, IL 60208
Newsgroups: sci.astro