Actual photons

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.

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.

In the Sun, there are complicating factors (for instance, in parts of the Sun
where the mean path of a photon is very short, convection can become the
dominant process for transporting energy). Still, the "bias" in the random walk
of a photon in the Sun has little to do with any physical processes (as in your
polymer example) and everything to do with the statistical nature of a random
walk. In three dimensions, there is a near unity chance of the photon reaching
_any_ point inside the Sun given enough steps. Of course, once it gets close to
the outside, it escapes. In the case of the Sun, the time to do that is a few
tens of thousands of years, depending on the variant theory describing it.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

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.

HAVRILIAK says...

TO: Guy Macon
Thank you very much for your comments. I've tried your suggestion
to prove the point.

No you didn't.

Instead of flipping a coin I did the following calculation.

Your calculation is wrong. Do the experiment and you will see with your
own eyes that the actual results do not come out as you have calculated.

If you flip an unbiased coin 2 million times it will come up heads
1 million times and tails 1 million times.

Once again, a simble experiment will tell you that the above is wrong.

If you believe that if you flip an unbiased coin 2 million times it
will come up heads 1 million times and tails 1 million times, then
you must also believe that if you flip an unbiased coin 20 times it
will come up heads 10 times and tails 10 times. So do the experiment:
flip a coin 20 times and report the result.

Here is my result: 8 heads, twelve tails.

Again I ask you to do the experiment rather than making calculations.
The fact that the results of the experiment won't match the predictions
from your calculations will tell you that you have made an error in your
calculations.

Here is that experiment again. This time do the experiment.

************************************************** ************

You can prove this for yourself. Make a number line like this:

....-9 -8 -7 6 5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9...
^
POINTER

Now start flipping a coin, moving the pointer one place to the
right if it comes up heads, left if tails.

You will find that the pointer gets farther and farther from the
starting point, and less and less likely to get back to zero.

If you suspect a coin bias, flip twice as often and move the
pointer one place to the right on heads-heads or tails-tails,
left on heads-tails or tails-heads. Or you can take my word
that the results will not change.

You can even do a computer simulation if you have a source of
random numbers such as /dev/random/ on a Linux box.
(The pseudorandom generator that comes with your computer
language is *not* random.)

Do the experiment, then report the results.

In message , HAVRILIAK
writes
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.

Your calculation is based on a wrong assumption. I suggest you *really*
go and try this yourself with a genuine coin (probably very slightly
biassed). There is no substitute for doing the experiment here.

You should only need to do it 20 times to see that it is rather unlikely
that you get a result of *exactly* 10 Heads and 10 tails every time. Try
it a second time and you will get a different result.

For the situation where p(heads) = p(tails) = 0.5 you can fairly easily
compute the probability of getting a run of 10 heads, right through to a
run of 10 tails. The same applies to the case of 2 million trials. It
would be very rare to see *exactly* 1 million of each outcome.

The majority of the outcomes will be symmetrically distributed round
1000000 +/- 1000 with extended tails stretching out to either side.

Excel users can simulate the task easily enough by summing a column
containing the expression

if(rand()0.5,-1,1)

f9 to recalc and you will see a series of different answers each time.

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.

If you were right the universe would be a very dull place.

Among the first people to record detailed experiments on real (near
perfect 6 sided dice) was a Swiss astronomer called Wolf in the late
1800's. He did find manufacturing bias in the die as well as verifying
modern statistics.

Regards,
--
Martin Brown

Mike Simmons wrote:

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.
:-)

Hzzz... gjragl rvtug qnlf?

In article ,
(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.


No shift?

Any two 'moves' are rarely ever identical. There's 3 dimensions for
displacement and in this case, each dimension has 360 degrees of freedom.
It's not merely positive and negative directions. What are you assuming?


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 chaotic systems no 'bias' is needed since very small differences
accumulate - and these accumulations compel the set up of attractors - at
higher and higher scales.


In the case of polymer chain statistics, the bias comes from unequall
energy states or you cant go where you came from.


Yes, there is a dampening effect, but not in the Sun's plasma.


Defender

HAVRILIAK wrote:

Here is my result: 8 heads, twelve tails.



You have a biased coin


Prove it!

--

Rick S.

http://users.rcn.com/rflrs

Here is my result: 8 heads, twelve tails.

You have a biased coin

In article , "Richard F.L.R. Snashall"
wrote:

HAVRILIAK wrote:

Here is my result: 8 heads, twelve tails.

You have a biased coin

Prove it!

Actually a good observation, there is a Harvard Prof of
Stats & Probability that can toss a normal quarter and
get heads every time. He uses that trick the first day
of class.

tom

--
We have discovered a therapy ( NOT a cure )
for the common cold. Play tuba for an hour.