Many Scientists, from Newton to Einstein to Sagan, have talked about a spirituality they find in science. But aside from some vague descriptions of “mathematical elegance”, they never really explain. I think there is a connection between spirituality and information theory which can be explained in simple terms, but in order to do that, I have to tell a story.
High school calculus, my classmate raises her hand. “I can apply the rules to get the correct answer, and I know it’s correct because I can un-apply them to get back to the question. But I don’t know why. I can do the math, but I don’t understand it.” The teacher, a petty, bitter man of limited imagination, dismissed her question as irrelevant nonsense. In retrospect, I suspect he didn’t understand what he was teaching either, because that was one of the most insightful and profound questions I’ve ever heard.
In the lobby of the Museum of Science in Cambridge MA, they used to have a machine built from Tinker Toys that had been designed to play tic-tac-toe (the featured image on this piece). A grid of levers represented Xs, Os, and unplayed squares; a crank on the side, when turned, would result a lever flipping to indicate the next move.
The design of the machine implements what is called a “model” of tic-tac-toe. There’s nothing special about Tinker Toys; the model could be implemented in many different mediums. For example, another medium which implements logic are the flows of systems of pressurized air or water; hoses connect to switches which turn on or off when pressure is supplied. Although these mediums appear very different, the model is always the same.
Computers are a natural choice for many models’ implementation, because they can support so many types of complexity. When I teach JavaScript, I use tic-tac-toe as an example model to implement. But models don’t have to be implemented directly; in more complex implementations they may arise by themselves.
Imagine if we modelled the Tinker Toy machine. Anyone who’s seen a modern first-person video game can picture this. First person video games use what’s called a ‘physics engine’, a program which models how reality behaves. First, we’d give the physics engine information about the Tinker Toy pieces, qualities like flexibility and weight. Then we’d specify how the pieces were connected: this rod connects to this hole in this hub. The physics engine would model that when pressure was applied to the rod, the hub would turn, and so forth. Now we’d be able to “play” the Tinker Toy tic-tac-toe inside of the computer.
Often when we talk about computers, we unconciously give them understanding. We say the computer is “thinking hard”, or that it doesn’t “want” to do some task. It’s obvious that the Tinker Toy machine doesn’t “understand” the game, that the understanding comes from the knowledge of the person who designed it. Does the computer “understand” that a model of tic-tac-toe is embedded within the model of the Tinker Toy machine? That’s harder to say. The physics engine could be “asked” to “predict” what the next move will be, and based on the physics alone, it could predict the answer correctly.
If the both the computable physics and our human “understanding” both give an accurate prediction, it’s hard to say that the human is “thinking” and the computer isn’t. So let’s just put aside the sticky question of whether the machine is “thinking” or “feeling”, and focus on results.
If two processes reliably generate the same results, then they have to be equivalent in some way. When a person executes the rules of tic-tac-toe and a machine executes them, they have something in common, something interchangable. This is the feeling my classmate complained about; she knew in her concious mind that the experience she was having while doing her homework was not that of a mathematician, but a calculator. She knew how to flip the levers and turn the crank, but not how to design and build the machine, embedding the model within it.
The human brain is often referred to as the most complex object in the universe. That’s true on at least two levels. One is the physical arrangement; microscopically, the neurons in the brain connect to and communicate with each other in fantastically complex ways. Another is the number of levels of models the brain can hold; to model the first-person version of the Tinker Toy machine, the programmer has to simulataneously hold models of physics, and the physics engine, and the implementation of the tic-tac-toe model, and also a model of how the computer itself works… in order to produce a fourth model, which would be the first-person program itself. Maybe another model, which is that of why the program is useful to the user and worth writing. The number of levels is not infinite, but it can go hella deep.
However, there’s another way in which that statement is not true at all. The cost to having such a complex brain causes human children to be dependant on their parents for an extraordinarily long time compared to other animals, who may be mostly self sufficient weeks down or even minutes after birth. During the years we are being raised, we unavoidably absorb language and culture and knowledge about the world from other humans around us. One human brain, with all its complexity, has never existed in isolation; it has to come from a network, a community of other brains.
There is therefore a result which can not be produced by one brain, but is only possible to get from many brains interacting. I’m still avoiding the question of whether many-brains experience a “feeling” in the same way there is a “feeling” of being one brain, or a machine; because it doesn’t matter. The result, the complexity is measurably greater.
We can’t model the complexity of many-brains within our one brain. But potentially we could someday model it within a computer. Current neuroscience is capable of modelling a mouse brain; that is, producing the same result inside the medium of the computer. It seems unlikely there is a limit which will prevent increases in computing power and technique from some day being able to simulate many-brains.
There is a limit to simulation though. Many-brains require bodies, which require breathable atmosphere, abundant fresh water, nutrients, gravity. You can simulate all of that, the entire planet, solar system, galaxy. But you can’t totally simulate the universe with a simulation inside it: if the simulation includes itself then the universe does too, which must then be simulated. It becomes a recursive problem, reflecting itself without end.
This result — a level of complexity we are prevented from ever directly interacting with — is indistinguishable from what is commonly called “a higher power”. They say the Lord moves in mysterious ways, and so do the inner workings of the cosmos.
I am humbled and staggered by the ultimate complexity of the universe, I fall on my knees and raise my arms to it. I beg for greater understanding, even while I accept my limitations. I look for the reflection of eternity in the eyes of my fellow humans.
My spirituality is scientific. I worship a force greater than myself by observing reality, which I am both inside and a part of. Which I can never truly understand, but has led me here for a reason.
All things are part of a greater whole. None of us are separate.
The reason is love.