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Information, Entropy and Equality

September 18, 2020

I have been studying lately the concept of entropy in Information Theory. This concept tells us that entropy equals the surprise value in a given set of information. It can be explained quite simply as follows:

Say that I am tossing a coin that is perfectly balanced. In this way it will randomly come up with a series of results of heads and tails with no order and connection to each other, and with no patterns to be discovered in the data. In this case, the data offers maximum surprise, and hence maximum entropy. Likewise, say I am tossing a weighted coin that always comes up tails. In this case, the result is always the same, there is no surprise in the data and you have zero entropy.

The interesting case in reality is the in between case. As for most things we encounter in the world, they are neither fully random, like a perfectly balanced coin toss, nor fully predecided like a perfectly weighted coin that always gives the same result. In reality, we have something always in between these two extremes whenever we code data as information to be read by someone else.

Take this heads and tails results and convert it to binary code, where heads is 1 and tails is 0. The important fact then about this is that the data will have some patterns in it, that can be read by people who know the way in which the data has been coded. It won’t be perfectly random as a sequence of 0’s and 1’s, and neither will it just be 0’s or 1’s for the whole sequence. It will be come combination of 0’s and 1’s, in which a person can read off the pattern of as to what that represents.

The connection with equality here comes in. I have just been taking a quick look at a book called The Upside of Inequality, 2016, by Edward Conard. In this book he is arguing for how inequality is valuable to the economy. Unfortunately, also in the book he is conflating and equivocating on this idea with the idea that good intentions undermine the middle class. I will get on to my critique of his second point in a moment. But firstly, regarding his point on inequality. I think we can see how inequality gives value by comparing it to the notion of entropy.

The case of purest inequality would be when one person has all the wealth and everyone else has nothing. An absolute tyrant. This would be akin to a zero entropy state of no surprise, where the result is the same every time, tails, tails, tails,.. or 0000000 in binary code. It would perhaps be a bit like how some imagine also God. The annoyance we all may have when people invoke God in an argument as something akin to a deus ex machina. We are right to be annoyed because invoking God in this case is the predictable and zero surprise option. However we would be similarly be right to be annoyed if someone invoked the machine (i.e. determinism or materialism), as the machine in this case would also be a zero surprise entropy state.

On the other side, the purest case of equality would be when all have exactly the same amount of wealth. In this case, of pure egalitarianism, we would have an equally unappetising situation. Because this would be akin to a random sequence of 0’s and 1’s or heads and tails, from which no pattern or information of value can be extracted. The ironic thing about economic value, is that when one person has all wealth, all value terminates, and similarly when all have equal wealth, all value terminates, just like with information in a message. If the message has zero entropy, there is no interesting information to be extracted, as it is just a predictable endless sequence of 1,1,1,1,1,.. or 0,0,0,0,0,0… , while if it has maximum entropy then there is also no interesting information to be extracted, as it is just a random sequence of 0’s and 1’s with no pattern.

The pursuit of pure economic equality would thus be as redundant a pursuit as to aim to decide all of societies decisions by flipping a coin. Life and humanity, meaning and information, all thrive in the area between zero and maximum entropy, between zero surprise and infinite surprise, where we can find some patterns and meaning to the things around us. Thus, indeed, it is actually very easy to say that inequality has some upsides, because pure equality would definitely destroy all economic value, as surely as a purely random coin toss would present us with an infinite surprise and entropy that could never be reduced to any order, and would represent something like a state of chaos.

Of course, the author of that book is wrong to then confound with this the idea that having good intentions is a bad thing. Yes, if those good intentions aim at pure equality in an ideologically blind, driven way, then they will lead us to the chaos and infinite surprise mentioned above, where nothing has any value anymore. But those good intentions can be driven also by more realistic visions relative to our position in society, rather than absolute ones. Further, his idea that good intentions are what is undermining the middle class, is clearly just one side of the story.

Think about the middle class as representing some middle state between maximal entropy of a random sequence of 0’s and 1’s, and the zero entropy state of merely, 1,1,1,1,1,1,… with no element of surprise. To maintain that middle state we need to be aware both of the dangers of the 1,1,1,1,1,1 and of the random sequence of 0’s and 1’s, at the same time. One, in other terms, could compare this to living on the boundary between order and chaos. This is what life and living beings do. Thus, the problem is not good intentions, in allowing the middle class to persist. The problem is perverted good intentions in line with an absolutist abstract ideology of pure egalitarianism that would destroy all value. Just as, on the other side the problem is a wealth concentrated too much in too few people, to the extent that they could come to be an absolute tyrant, rendering our society a zero entropy state of no value, just repeating the same 1,1,1,1,1 to infinity. Like the yes men who comply to that tyrant.

The point is: what we always need is a balance between these two extremes, and so the issue is where to find a healthy balancing point of maximal or tolerable value for all, or at least for the maximum number of us in society. In other words, all the ideological talk in economics between the free market lovers and the socialists is shown to be driven by a misunderstanding of what equality and inequality fundamentally are. And just how inequality to some degree is inevitable in any society that has any value in it.

The extreme emotional rhetoric of the left and the extreme rationalist rhetoric of the right become like dependent delusions that feed off each other. The bottom line is that we cannot have pure equality in society without creating a state of maximal entropy, where there is no value in that society anymore, just as we cannot have pure inequality in society of an absolute ruler or tyrant without creating a state of zero entropy where the pure predictability of everything also renders everything valueless. We have to face that boundary between chaos and order, and survive and thrive on that boundary, anything else is ultimately a death wish.

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