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Topic: Simple random number generator?
Replies: 24   Last Post: Jan 7, 2013 10:52 AM

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Michael Stemper

Posts: 671
Registered: 6/26/08
Re: Simple random number generator?
Posted: Jan 7, 2013 10:52 AM
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In article <3ivvc8lkeplmdhatavc11ilg6ehaatgbvt@4ax.com>, Wally W. <ww84wa@aim.com> writes:
>On Mon, 17 Dec 2012 18:43:41 +0000, Dr J R Stockton wrote:
>>In sci.math message <rubrum-0653B8.15431416122012@news.albasani.net>, Sun, 16 Dec 2012 15:43:20, Michael Press <rubrum@pacbell.net> posted:

>>>> The main assumption in this is that the probability that an
>>>> atom which has not decayed by time T will still have a probability
>>>> of decay between T and U which is independent of anything which has
>>>> happened before time T, and only depends on U-T.

>>
>>>I am asking for the basis of the unpredictability
>>>in physical theory. Assuming it is random is to
>>>beg the question.
>>>
>>>I hold that the wave theory of matter does not
>>>predict random occurrences.

>>
>>Little can be done about ignorance of such profundity. You reject the
>>mainstream physics of the last 85 years or thereabouts.

>
>It seems like a reasonable question to me.
>
>The completeness with which we understand small-scale physics doesn't
>affect whether something deterministic is happening under the hood.
>
>If radioactive decay is random, why should an isotope have a knowable
>half-life? Why wouldn't the half-life also be random, or more variable
>than it seems to be?


Let's try a few analogies.

First, a real simple case. Take a handful of coins. Shake them around a
little, and toss them onto a flat surface. Do you agree that the face
each one will show is a roughly random event, and that it's not correlated
with the face that any other coin will show? Do you also agree that
roughly half of the coins will show one face and half the other?

What about the motions and positions of air molecules? Even though each
molecule's position is (from a macro point of view) random an uncorrelated
with others' positions, do you still believe that roughly half the air
molecules in a room are going to be one each side of the room's center?

Assuming that you made it through those, let's get a little more
complicated. Get several thousand six-sided dice. Throw them all up in
the air. Do you agree that the face each die shows is more or less
random, and not correlated with the face that any other die shows? Do
you also agree that roughly one-sixth of them will show a 3?

Now, throw out all of the dice that show a 3. You've got an hour to do
that. An hour after the first throw, throw the remaining dice, and again
remove the ones showing a 3. Now, you should have about 70% as many dice
left as you started with.

An hour later, do it a third time. After cleanup, you should have about
58% as many dice as you started with. And after your fourth throw and
cleanup, the number of dice left should be down to about 48% of the
original number.

If you do this another four times, you'll be down to about 23% of the
original count.

So, every four hours, the number of remaining dice gets cut by roughly
one-half. That means this process has a half-life of about four hours.
This is true even though "half-life" is a macro-level property of a
collection of uncorrelated events.

As you can see from the examples given, this principle doesn't really
need any twentieth-century physics -- it's strictly classical. For more
information, a good starting point would be:
<http://en.wikipedia.org/wiki/Statistical_mechanics>

Followed by the first two chapters of:
<http://www.spms.ntu.edu.sg/PAP/courseware/statmech.pdf>

If you prefer lecture to text:
<http://www.youtube.com/watch?v=H1Zbp6__uNw>

--
Michael F. Stemper
#include <Standard_Disclaimer>
The name of the story is "A Sound of Thunder".
It was written by Ray Bradbury. You're welcome.



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