How does it work?
Below is a graph which represents a number of paths from different starting points to different ending points. The arrows represent the direction you MAY go. You may NOT take a route against the direction indicated by the arrow. Welcome to the Internet.
Suppose you start at A1 with A6 as your destination. There is a short way to get there. But after two mouse clicks you find yourself at A4. How did that happen? The geeks are watching. They “help” you, guiding you from a pattern detected in your browsing history to a place they want you to go which may or may not be where you want to go.
Here is a second graph, your search was redirected, unbeknownst to you, along this slightly different path
It turns out that a graph may be represented by a matrix. Below are three matrices. The first is the matrix representing the Original Graph, the middle is the matrix representing the New Graph, the third is the difference between the two, the result of subtracting the Original Matrix from the New Matrix. Notice the “Difference” matrix results from just changing just one element in the top row, fourth column of the Original Matrix from a 0 to a 1.
It doesn’t take Russians to influence elections
Suppose we have two political candidates. Suppose further that it is known that 100% of the people supporting Candidate R also believe that Elvis is alive and living in a trailer in Van Nuys CA. Another survey proves that 100% of those supporting Candidate D believe that smoking banana peels is the only way to Ultimate Truth.
Back to the top. Remember you started at A1 with the intent to travel to A6 where you expected to find positive information on Candidate R. But I know you support Candidate R and I want to mess with that. I want you to see a message supporting Candidate D located at A4. I change one element in the matrix from a zero to a one and you find yourself where I want you to be rather than where you wanted to go.
The Problem
This, highly simplified example has many problems. Here are two:
Not much is 100% certain. Think of each 1 value in the matrix as 100% probability and each 0 value as zero probability. Imagine that the first row, fourth column of the matrix is a sign at a fork in the road that has an icon of Elvis pointing in one direction (value = 0) and an icon of a banana peel in the other direction (value = 1). Changing that single element from zero to 1 amounts to swapping those two signs. The Rube is now guaranteed to go down the path you want him to go. The first problem is that very few things - nearly nothing - are 100% certain. Many a Dufus at that fork will harbor at least some doubt, making it less than 100% - thus uncertain - that changing the signs will actually divert him.
It does not scale. It can be very time-consuming to change out two signs for each nitwit web surfer/voter. You need a way to repeat the process with large numbers of people.
Enter Probability
If things are neither 100% sure (probability = 1) or 100% not likely (probability = 0), reality must be somewhere in between. Let’s allow our probabilities to vary between 0 and 1. Our matrix becomes
Conditional Probability
Some people know what conditional probability is. Your reading this is conditioned upon your having a computer. It is also conditioned on my having a computer. So, for you to be reading this, we have two conditions and joint probability. The number of people who understand how these concepts relate is a very small fraction of humanity. Those who understand the mathematics behind these concepts constitute an even smaller fraction. Still smaller is the fraction that can work with the math to implement effects or solutions to society’s problems using these concepts.
Take a close look at the last matrix. What do you notice about it? Hard to see anything special? You have just been manipulated. Suppose I told you (because I did it) that last matrix is the Original Matrix where the 1’s have been replaced with probabilities less than 50% and the 0’s with probabilities more than 50%. To help you see this we add color (something humans require that computer don’t).
Earlier, we were working through various populations down to the small number of people who could deal with this situation. Next, ask how many of this already tiny percentage of humanity can make conditional probability calculations VERY FAST? We are now very close to zero people with those skills.
Are you one of them?
[next week: Solving all the world’s problems at light speed]