Five Rocks

jesse hoey
5 min readOct 5, 2021

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Five Rocks?

Consider these five rocks. I’m only talking about the five medium sized rocks in the center of the picture, not all the other smaller and bigger rocks around.

They are all rocks, right? They are therefore all the same, in some way.

But wait! those five things are not all the same! One is sort of more round-ish and one is sort of more square-ish, for example. So those five things are different.

Are they different? Or are they the same? They are all “rocks” and so must be the same, but I can clearly see they are all different.

The rocks have some variation that I am ignoring!

Worse, perhaps the rocks are hiding information from me! Why do I think they are all the same?

It is simply because I have bounded computational resources. It would be very hard for me to operate in a world in which I had to model every single different object with a different model, as then I would also have to have a model of all the relationships between the different elements. Static rocks on a shore are not all that relevant to me, but consider if they were five hungry polar bears. I would suddenly gain a big advantage, as the hedgehog, in assuming they are all the same and my response should be flight. If I modeled each separately, as the fox, and tried to deliberatively analyze which one would be the one that was going to attack me, I would likely not survive. I refer here to Aesop’s fable of the fox and the hedgehog, who differ in their deliberativeness. The fox thinks of many options and chooses the right one, whereas the hedgehog only knows how to do one thing. The fox’s strategy works great most of the time, as it opens up far more opportunities for growth than the hedgehog. However, in the face of a Black Swan (more on this below), in this case a pack of hunting dogs, the hedgehog’s strategy is better. The fox spends so much time analyzing the options, he is killed by the dogs, while the hedgehog does what he always does and curls into a ball to save himself.

So, I allow my agent, nature, to hide information from me, the principal. The information that is hidden is the less important stuff. The fact that the polar bear who is attacking me has a burr stuck to its fur does not matter to me at this time. So this works great for polar bears.

What about for people? Now the story gets more complicated, exactly because the “polar bear” in this case is a person, and may realize that there is an informational asymmetry, that they can hide information from you. How can they do this? Well, this polar bear knows two things. First, it knows that it knows more than you about it. Second, it knows how you evaluate the information you give it. It knows you are seeking information only to decide if you should fight or flee. Therefore, it can choose which information to provide to you, and which to hide. A very small polar bear, for example, could roll in some mud, turning itself into a brown bear, which are harmless. You would let your guard down, maybe get set up to pose for a photo with the cute bear. Chomp.

Bears are clearly not going to do this, but people can. This is the principal agent problem of economics in a nutshell. As described by Mansfield and Yohe in one of the final chapters of the eleventh edition of their textbook on microeconomics, the principal agent problem invalidates many of the assumptions of modern economic theory. I don’t think I’ve ever read any other book that takes 16 chapters to describe a theory, and then says in chapter 17 that the theory is invalid.

Let’s return to our five rocks now. What information are these devious rocks hiding from me? Precisely the information that I have learned to ignore. That is, the rocks and I form an ecosystem aimed at survival. The rocks will try to fool me with all sorts of useless information that I don’t need, and I will try to ignore it, to focus on only those abstractions that are useful to me. Perhaps that is why we think of rocks as “dull” and “boring” (sometimes they are not, particularly if you are a rock climber). In the end, we will reach a happy somewhat stable state in which I am fine with this hidden information, and the rock is fine with the information it is providing to me. Notice that I am also doing the same thing in reverse to the rock, not that it cares. The state is only “somewhat” stable, however, as there may be some new rock that I have never met before that behaves very differently than any other rock. Perhaps it jumps around. This “Black Swan,” an unforeseen and unforeseeable rock, has challenged my abstract notion of a rock. It may be revealing new information to me about rocks that I did not know before (that they could jump). Reading Taleb’s “The Black Swan” (2007) may help you get a better grip on the dynamics of the unknowable, should you find it puzzling.

I can handle jumping rocks in three ways. First, I can change my definition of “rock” to not include jumping rocks. Now, I have to create a new category, “jumping rocks,” i’ll call them “jucks” for convenience. I start with very little information about “jucks,” although I can metaphorically carry over my (neutral) reactions to rocks with my (positive or negative) reaction to people or animals jumping around. What do I do when I meet a person jumping around? Suppose I am the sort of person who also starts jumping around if someone near me is jumping around (this happens often at punk rock concerts, and I have a Wicked Good friend named Monkey-Boy who consistently behaves in this way), then I can try the same thing with the first “juck” that I meet.

My second way of handling the jumping rocks is to change my definition of “rock” to include rocks that jump. This is somewhat difficult as one of the truly foundational properties of “rocks” is that they do not move.

Lastly, I can go and tie the rock to the ground so it stops moving. In essence, by believing that gravity is what keeps me and the rocks on the surface of our planet, I am implicitly tying the rock to the ground. I am united with the rock in our joint interpretation of gravity that requires the rock to stay still. The rock may even realize that jumping around is not rock-like, so if it wants to stay a rock (for me), it needs to stop jumping around. The fact that the interpretation goes both ways is what allows this to happen, and is also why rocks don’t jump around. They are simply hiding the fact they can jump around from you. Nasty, devious, rocks.

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jesse hoey

Professor of Computer Science and other things interest me too