[![Peter Galison "Computer Simulations and the Trading Zone", page 147][1]][1]

In the above diagram, the author (Peter Galison) describes the capillary-tube diffusion process (in "Computer Simulations and the Trading Zone") as modeled by a partial differential equation (top), and then as imitated by a Monte Carlo simulation of a stochastic process of, for example, flipping a coin and moving to the right when a head falls and to the left when a tail falls (bottom).

I've been struggling to understand how Monte Carlo simulations are used in physics. The author describes Monte Carlo simulation as an alternative to solving the partial differential equation. In this example of a Monte Carlo simulation for the capillary-tube diffusion process it is not clear to me what is known and what is unknown/sought to be discovered by the simulation:

1. The goal of the simulation as I understand it is to approximate the pictured the bell-shaped distribution obtained by analytic solution. What is on the x-axis in the bell shaped curve?
2. The author says that the simulation could be done by "flipping a coin and moving to the right when a head falls and to the left when a tail falls". Are we talking about a fair coin so that P(Heads)=P(Tails). By how much will we move to the right or to the left in each instance?

Big picture, I don't understand how we would build a Monte Carlo simulation and use it to learn something about a process, such the one above. What is assumed to be known? What is unknown? Obviously if I took a fair coin and decided to move to the right by 1 unit if the coin turns up Heads and move to the left by 2 units if the coin turns up Tails, 1) we would not learn anything useful from this model and 2) this model would have nothing to do with the capillary-tube diffusion process. How then do we build such a model? [1]: https://i.sstatic.net/YKD1a.png

In the above diagram, the author (Peter Galison) describes the capillary-tube diffusion process (in "Computer Simulations and the Trading Zone") as modeled by a partial differential equation (top), and then as imitated by a Monte Carlo simulation of a stochastic process of, for example, flipping a coin and moving to the right when a head falls and to the left when a tail falls (bottom).

I've been struggling to understand how Monte Carlo simulations are used in physics. The author describes Monte Carlo simulation as an alternative to solving the partial differential equation. In this example of a Monte Carlo simulation for the capillary-tube diffusion process it is not clear to me what is known and what is unknown/sought to be discovered by the simulation:

1. The goal of the simulation as I understand it is to approximate the pictured the bell-shaped distribution obtained by analytic solution. What is on the x-axis in the bell shaped curve?
2. The author says that the simulation could be done by "flipping a coin and moving to the right when a head falls and to the left when a tail falls". Are we talking about a fair coin so that P(Heads)=P(Tails). By how much will we move to the right or to the left in each instance?

Big picture, I don't understand how we would build a Monte Carlo simulation and use it to learn something about a process, such the one above. What is assumed to be known? What is unknown? Obviously if I took a fair coin and decided to move to the right by 1 unit if the coin turns up Heads and move to the left by 2 units if the coin turns up Tails, 1) we would not learn anything useful from this model and 2) this model would have nothing to do with the capillary-tube diffusion process. How then do we build such a model?

In the above diagram, the author (Peter Galison) describes the capillary-tube diffusion process (in "Computer Simulations and the Trading Zone") as modeled by a partial differential equation (top), and then as imitated by a Monte Carlo simulation of a stochastic process of, for example, flipping a coin and moving to the right when a head falls and to the left when a tail falls (bottom).

I've been struggling to understand how Monte Carlo simulations are used in physics. The author describes Monte Carlo simulation as an alternative to solving the partial differential equation. In this example of a Monte Carlo simulation for the capillary-tube diffusion process it is not clear to me what is known and what is unknown/sought to be discovered by the simulation:

1. The goal of the simulation as I understand it is to approximate the pictured the bell-shaped distribution obtained by analytic solution. What is on the x-axis in the bell shaped curve?
2. The author says that the simulation could be done by "flipping a coin and moving to the right when a head falls and to the left when a tail falls". Are we talking about a fair coin so that P(Heads)=P(Tails). By how much will we move to the right or to the left in each instance?

Big picture, I don't understand how we would build a Monte Carlo simulation and use it to learn something about a process, such the one above. What is assumed to be known? What is unknown? Obviously if I took a fair coin and decided to move to the right by 1 unit if the coin turns up Heads and move to the left by 2 units if the coin turns up Tails, 1) we would not learn anything useful from this model and 2) this model would have nothing to do with the capillary-tube diffusion process. How then do we build this model? What assumptions do we make? What are we looking to learn from this Monte Carlo experiment?

[![Peter Galison "Computer Simulations and the Trading Zone", page 147][1]][1]

In the above diagram, the author (Peter Galison) describes the capillary-tube diffusion process (in "Computer Simulations and the Trading Zone") as modeled by a partial differential equation (top), and then as imitated by a Monte Carlo simulation of a stochastic process of, for example, flipping a coin and moving to the right when a head falls and to the left when a tail falls (bottom).

I've been struggling to understand how Monte Carlo simulations are used in physics. The author describes Monte Carlo simulation as an alternative to solving the partial differential equation. In this example of a Monte Carlo simulation for the capillary-tube diffusion process it is not clear to me what is known and what is unknown/sought to be discovered by the simulation:

1. The goal of the simulation as I understand it is to approximate the pictured the bell-shaped distribution obtained by analytic solution. What is on the x-axis in the bell shaped curve?
2. The author says that the simulation could be done by "flipping a coin and moving to the right when a head falls and to the left when a tail falls". Are we talking about a fair coin so that P(Heads)=P(Tails). By how much will we move to the right or to the left in each instance?

Big picture, I don't understand how we would build a Monte Carlo simulation and use it to learn something about a process, such the one above. What is assumed to be known? What is unknown? Obviously if I took a fair coin and decided to move to the right by 1 unit if the coin turns up Heads and move to the left by 2 units if the coin turns up Tails, 1) we would not learn anything useful from this model and 2) this model would have nothing to do with the capillary-tube diffusion process. How then do we build such a model? [1]: https://i.sstatic.net/YKD1a.png