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Comment by zeitgeistcowboy | Hacker News Reader

The first section on randomness seems to imply that all you need to know is information. That if you knew all the data about the weather that you could predict the weather. I think it's more complicated than that. Even if you knew the position, type, and velocity of every molecule of the atmosphere at a given moment you would still need a model that explains how they interact over time in order to predict the future. So, I'm not sure that actually is a knowable unknown because that assumes there is a model that can be made in addition to the information. Maybe the weather is chaotic.

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But is that chaos predictable? Current weather predictions are based on statistical models. Storm trackers, for example, typically have bands that expand as time gets further out. Without knowing every molecule that affects a hurricane, for example, they can predict within some confidence interval where the storm will head. The data meteorologists have is relatively coarse, and yet they can make predictions within some level of probability. That level of probability allows municipalities to issue evacuation orders early as opposed to throwing hands up and saying there is no certainty in anything, so let's just see what happens.

Their discussion of die rolling doesn't say they can predict the outcome, rather that they can predict the probability of the outcome. In trading, life, and gaming that probability is one component of many that go into decision making. Knowing how much that randomness effects the outcome at what probability can be a successful strategy (but of course not guaranteed) in all of those domains.

> Even if you knew the position, type, and velocity of every molecule of the atmosphere at a given moment you would still need a model that explains how they interact over time in order to predict the future. So, I'm not sure that actually is a knowable unknown because that assumes there is a model that can be made in addition to the information. Maybe the weather is chaotic.

It is, but that doesn't mean you couldn't predict it with perfect information. A chaotic system is roughly speaking one that is

- sensitive to initial conditions, in the sense that the distance between nearby trajectories in phase space grows as e^{l*t} for time t and some positive number l

- mixing, meaning that given any two open sets in phase space X and Y there's at least one trajectory from a point in X to a point in Y.

and so if you have any error bounds at all on your measurement of the initial state (which of course you always do) then you can't predict where it ends up in the long term. But there are plenty of chaotic systems for which exact numerical computations are quite simple. The logistic map x_{n+1} = rx_{n}*(1-x_{n}) for instance, is chaotic for many values of r.

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