I heard a talk from a few decades ago where the 
wonderful English philosopher Alan Watts wondered 
aloud about the possible role of sentient civilizations 
in creation of astronomical bodies. 

Specifically, he wondered whether, if we keep on 
tinkering with nuclear fusion and the like, we might 
not one day accidentally set off a nuclear chain reaction 
that caused our planet to become a small Sun -- and 
whether in fact this might be how Suns sometimes 
come to life.

I've also heard that most of the solar systems in the 
universe are actually binary star systems -- often with
one star much older than the other. 

Now, I understand that our planet might not have
enough mass for a full solar sequence to happen, but 
I'd like a general opinion on all this from an astronomer ...
Is there well established knowledge that can dispel
the idea of this particular scenario being a possibility?

During the Manhatten project there was a concern that there might be a
runaway nuclear reaction in the nitrogen in the Earth's atmosphere.
Konopinski, Marvin & Teller (who went on to develop the H-bomb)
reported the odds as 1 in a million. It's now felt that a more honest,
but less quantified answer would have been "impossible (almost)". 
Their original paper is at
http://lib-www.lanl.gov/la-pubs/00329010.pdf , but it's now
inaccesible in the current security climate.

Most stars are part of multiple systems, but I don't believe one is
often *much* older than another. There's often a wide difference in
how evolved they are, because large stars burn much faster than small
ones.

Ian G.

Most star systems are multiple systems due to the way stars form from
nebulae.
In our own solar system a second sun would likely have formed if
Jupiter, Saturn, Uranus, and Neptune had not formed into individual
planets.

The Shoemaker-Levy 9 comet that collided with Jupiter is another
testimony that it is extremely unlikely for a single event to cause a
runaway nuclear reaction. Each peice of that comet hit with more
energy than all of Earth's nuclear weapons combined. And with an
atmosphere composed mostly of hydrogen and helium, Jupiter is much
more likely to support that type of reaction than a terrestrial planet
like Earth.

As far as a nuclear catastrophe causing the earth to burn as a star, I
would recommend reading Stephen Hawking's book "A Brief History Of
Time", it's a suprisingly easy read that deals with this issue and
many other interesting ones.  In it he makes the comment that if 100%
of the earth's water was changed into heavy water (for use in a
nuclear reaction), and all of the earth's nuclear weapons were
detonated, the reaction would be just barely enough to cause a small
black hole to form.  The mass of the earth would be caught in the
black hole and either emitted as radiation or would remain caught up
in the singularity and its fate unknown intil the black hole loses
enough mass as radiation to stop acting like a black hole.  A star
becomes a black hole when it loses energy, starts to cool, and is
massive enough (mass above the Chandrasekar limit) to be unable to
avoid gravitational collapse.  Stars below the limit cool to become
neutron stars.  This being said, if all of the earth's weapons could
barely create enough of a reaction to form a black hole, then there is
definitely not enough energy tied up in nuclear arms to cause a star
to ignite, since a star only becomes a black hole after losing the
majority of its energy.  Again, for a complete and accurate answer,
grab Hawking's "A Brief History Of Time" from your library, it's worth
the read.