Tag Archives: Math

Autocorrelation

Last week, I wrote about how mobs might be predictable. One of the first tools that I mentioned was autocorrelation. This is a basic tool that we will use with the others in the list, so it’s important to understand exactly what it does. That’s what I want to explore this week.

Geometry

Parallelogram

Parallelogram (Photo credit: Wikipedia)

Let’s go back to high school geometry. We can define several properties and operations in terms of the angles and sides of the parallelogram to the right, though we’ll need to dive into the cartesian coordinate system a bit to see how to move on to the next step towards the autocorrelation.

We want to look at what it means to do mathematical operations on these line segments. We know that we can add numbers together to get new numbers, but what does it mean to add line segments? If we take the segment from D to E, and add the segment from E to B, it’s obvious that we end up with the segment from D to B. But what’s not as obvious is that if we take D to E and add from E to C, we end up with D to C.

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Predictable Mobs

As a kid, I read Asimov’s Foundation series in which Hari Seldon develops a mathematical description of society called psychohistory. The science in the books is completely fictional, but it always sat at the back of my mind. What if there was a kernel of truth in the fiction? What if people could be predictable?

Psychohistory has two main axioms (taken from the Wikipedia entry):

  • that the population whose behaviour was modeled should be sufficiently large
  • that the population should remain in ignorance of the results of the application of psychohistorical analyses

The first axiom has an analogy in statistical physics: the number of particles should be sufficiently large. A single atom doesn’t really have a temperature because temperature is a measure of how quickly disorder is increasing in a system. A single atom can’t increase its disorder, but it can have an energy. It just happens that the rate of entropy increase is proportional to the average energy of a group of particles, so we equate temperature with energy and assume that a single atom can have a temperature. The entropy-based definition of temperature is more general than the energy-based definition: it allows negative temperatures.

The second axiom is similar to what you might expect for a psychology experiment: knowledge of the experiment by the participants can affect the outcome. For example, using purchasing data instead of asking someone outright if they are pregnant because sometimes the contextually acceptable answer will trump the truth.

The important thing is that people are predictable¬†in aggregate. This is what allows a political poll to predict an election outcome without having to ask everyone who will be voting, though polls aren’t perfectly predictable in part because someone will be more likely to tell a pollster what they think is socially acceptable, which might not show how they vote when they think no one is watching, thus reinforcing the need for the second axiom.

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Hacking Information

This image shows a technique that can be used ...

This image shows a technique that can be used to plot prime numbers in binary. (Photo credit: Wikipedia)

While eating breakfast this morning, I decided to finish watching “Will We Survive First Contact?,” an episode of Morgan Freeman’s Through the Wormhole, a nice series on Science that does a reasonable job of translating science into laymen’s terms without simplifying too much. This episode dealt with how we might know when we encountered alien communication. The topic of aliens was just a vehicle for talking about information theory. Topic modeling made its appearance, though no one called it that.

One of the segments talked about efforts to understand dolphins. The problem with all the languages we already know is that they all come from the human mind. Trying to understand a language developed by a non-human mind helps us know what problems might crop up when trying to understand a language not from Earth.

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