CLASS NOTES (Sorry for the delay)
One-dimensional random walk: Imagine a telephone wire with birds on it that each time step can either hop right or left one unit. After several time steps the bird could be at its starting place. You don’t have an ability to predict where the bird will be before everything happens.
A description of a bunch of x’s vs. the description of a process. That process could be deterministic or random. In a deterministic process the initial condition s will determine the outcome. But are random processes truly random?
When we model random processes, or processes that we perceive as random, we use the computer’s ability to generate random numbers. Yet the computer does not have the ability to generate true random numbers, an algorithm written by a man predetermines the numbers that it outputs. Rather than being truly random they are numbers the user cannot predict. In a similar way some of the processes that models try to explain and are assumed to be random might not be truly random, but rather a be determined by factors we fail to understand.
This idea generates a falsifiable hypothesis: that randomness is a way to model deterministic processes. * At a local level you can’t predict random * if there is an underlined probability you can predict the long term outcome. * Can we den say that a 50:50 probability is more random than a 70:30 probability?
Model manipulation and discussion: Look at the model we used in class (Browninn motion):
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Resembles city growth (without pop growth), deforestation, spread of rumor, etc.
· no direction drift. · it gets bigger with each time step. Each time step the space is made discrete and there only four directions (the four diagonals)
