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### Monte Carlo Method and Computer Simulation

```Date: 04/04/2002 at 21:26:34
From: Alina
Subject: Monte Carlo Method *Probability*

What is the Monte Carlo method? I know it's for estimating
probability, but what is the point of it? If it were on a test, what
```

```
Date: 04/06/2002 at 06:24:51
From: Doctor Mitteldorf
Subject: Re: Monte Carlo Method *Probability*

For many problems in physics, it is impossible to calculate what
actually happens. Sure, we know the laws governing the situation, but
if there are more than two or three objects obeying these laws, the
equations become so complicated that they're impossible to solve
exactly.

In the 1940's, when calculation machines were crude and the electronic
computer had not been invented, scientists were trying to calculate
the amount of uranium they would need to make an atomic bomb. They ran
into calculation problems where they understood the way atoms behave,
and could calculate probabilities for any one atom, but when many
atoms were placed together, the equations became too complicated to
solve. So they had an idea: get a whole lot of people in a room, and
let each one have the equations of one single atom. The person would
be instructed to act in a way that was partly predictable and partly
random, just the way real atoms do. In real atomic bombs, atoms
release neutrons when they split in two, and the neutrons have some
probability of hitting another atom, causing it to split in two as
well. Inside the room, people would decide when they were "split"
based on their equations, and if they did split, they would pass slips
of paper to their neighbors that indicated how many neutrons were
coming out of them, and that information was used to help calculate
the probabilities that the neighbor would "split" as well.

This was a very complicated and very expensive way to calculate
something, because it involved so many people with calculating
machines, working for many days. Only atomic scientists hired by the
government could afford it.

But once the computer was invented and became cheap, every scientist
could afford to do this kind of thing. The computer is really good at
doing many calculations quickly, keeping the information about what
happens in different places, and moving it around to other parts of
the calculation.

So now there are many thousands of scientists who do this kind of
calculation all the time. It is no longer called "Monte Carlo method,"
but is simply called "computer simulation" or sometimes "computer
modeling."

Computer simulation is a tool for calculating everything from weather
forecasts to traffic flow to stock market fluctuations. In my own
work, I use computer simulation to study biological evolution.

You can read more about the history of the Monte Carlo method at this
site by Sabri Pllana:

examples that you can try yourself from the Center for Connected
Learning and Computer-Based Modeling at Northwestern University:

http://www.ccl.sesp.northwestern.edu/

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Calculators, Computers
High School Physics/Chemistry
High School Probability

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