The net shift (as you describe it) is zero *on average*. Where you end up
after the 2 million coin flips will vary, however. Try your experiment of
2 million coin flips a million different times. How many times will you
end up with a net shift of zero? It is very unlikely that on any one
trial of 2 million flips that you'll end up with zero net heads or tails.
Try it yourself with 100 coin flips and see how often you end up at zero.

The distribution of excess heads and tails that you get can be described.
The shape of the distribution curve (the equation describing the
distribution) is known. When you increase the number of coin flips you
get a distribution that looks the same (i.e, is the same shape) but
increases in size. The more coin flips in the experiment the farther from
the zero point you're likely to end up in any particular experiment. With
2 million coin flips it's going to be common to have experiments end up
with an excess of 100 heads or tails. Limit the experiements to 1000 coin
flips and it's going to be very unusual. Limit it to fewer than 100 flips
and it can't happen at all.

Now pick a number of excess steps in one direction or the other that will
end the trial. For example, how many times will you exceed 1000 net heads
at some time during the trial of 2 million coin flips? This is analogous
to the situation in the Sun. Sure, some photons may be absorbed and
re-emitted millions of times and still be in the center but much more
often they will be somewhere outside the center. Once a photon descendant
happens to reach a distance from the center where it breaks free (e.g.,
the photosphere) it escapes. Given the number of photons pouring out of
the Sun's nuclear furnace and the almost infinite number of steps (coin
flips) that can occur it's not surprising that random processes result in
a lot of photons escaping.

The random model may not be appropriate for modeling the Sun's internal
dynamics but even if that's all there was to it we would still see light
escaping.

Mike Simmons

P.S. A frog is at the bottom of a 30-foot well. Every day he moves up 3
feet and during the night he slips back 2 feet for a net rise of 1 foot
per day. How many days does it take for him to get out of the well? If
you think the answer is 30 days then you haven't been paying attention.
:-)

On 06 Sep 2004 23:51:53 GMT, HAVRILIAK wrote:

TO: Guy Macon
Thank you very much for your comments. I've tried your suggestion to
prove the
point. Instead of flipping a coin I did the following calculation. If
you
flip an unbiased coin 2 million times it will come up heads 1 million
times and
tails 1 million times. Thus there will be 1 million moves in the
positive
direction and 1 million moves in the negative direction. Since the
moves are
commutative, i.e. a+b=b+a, the net result is no shift. Now if we bias
the coin,
there will be a drift in one direction or another depending on the bias.
There was a recent comment made that the bias is sort of site
dependent (my
words not his)
In the case of polymer chain statistics, the bias comes from unequall
energy states or you cant go where you came from.