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 would be asked?
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: http://www.geocities.com/CollegePark/Quad/2435/ You can read more about simulations for students, and download 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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