In my last post I considered Physicist John Barrow’s view of what science is:
So we find that Barrow’s view of science is that it is the process of how we use reason to find patterns in reality and then to algorithmically compress them into finite steps and formula that allow us to represent reality via processes that are computable.
I am going to suggest this as our starting theory of reality, but there is much that can be challenged about this view and therefore refined.
But first, I want to consider the idea of comprehending something. What does it mean to “comprehend” something? The problem with a word like this is that it’s a single word that maps to multiple possible meanings. Harkening back to my first post, if I ask you if you comprehend PI, what would that mean? Is it even possible to “comprehend PI” at all? It’s an infinitely large number, after all. It is therefore beyond comprehension isn’t it?
The Nature of Understanding and Explanation
David Deutsch’s excellent book, The Fabric of Reality, is an exploration on what it means to understand or comprehend something.
He starts his book with the story of how, when he was a small child, he had a dream of wanting to know everything.
It was not that I wanted to memorize all the facts that were listed in the world’s encyclopaedias: on the contrary, I hated memorizing facts. That is not that sense in which I expected it to be possible to know everything that was known. … By “known,” I meant understood.” (The Fabric of Reality, p. 1)
He goes on to give an example of the difference between trying to memorize all the known observational data in astronomy and understanding the motions of the stars. Obviously no one could possible memorize all the observational data, but many people already understand all that is known about the motions of the stars and could therefore calculate out all the observational data, at least in principle. Deutsch goes on to say:
This is possible because understanding does not depend on knowing a lot of facts as such, but on having the right concepts, explanations and theories. (The Fabric of Reality, p. 1-2)
Here we should pause and consider how this sounds oh so familiar to us. It would seem that to understand something is something akin to algorithmic compression. You can’t memorize all observational facts, but you don’t have to. You merely need to understand it and all the observational facts, in principle anyhow, are sort of already available to you.
Therefore, to comprehend PI is to understand that it is the ratio of the circumference to the diameter of a circle.
Assuming you also understand what a circle is and what the rules of Euclidean geometry are, then this definition of PI is alone enough to come up with a procedure that encapsulates PI in its entirely, as shown in my first post. Therefore, to comprehend something is to have the right (most right?) explanation of it. This is, in and of itself, a sort of algorithmic compression whereby we can take a impossibly large concept and encapsulate it into a simple set of explanations. (In this case the definition of PI, an understanding of what a circle is, and the rules of Euclidean geometry.)
So I want to propose a slight change to our current hypothesis about reality:
Science is the process of how we use reason to find patterns in reality and then to compress them into explanations that allow us to represent reality via processes that are computable.
However, algorithmic compression and explanation don’t seem to be exactly the same thing, though they are somehow profoundly intertwined. For example, if we actually have a computer program to calculate PI, would we really say the program ‘comprehended’ PI? Probably not. Therefore having an algorithmic compression alone is not to comprehend something. But the reverse does seem to be true. To comprehend something seems to imply you can always algorithmically compress it.
- Can you think of examples of things you comprehend but can’t put into an algorithm?
- What about ‘justice’? What about ‘beauty’?
- Can you comprehend yourself?
- Can you put yourself into an algorithm?
- To comprehend God would that mean we have to be able to put God into an algorithm?
- Are there non-algorithmic sciences?
- What about psychology?
- Is ‘art’ algorithmic?
Also, don’t miss out on my recent re-print on Millennial Star where I ask “What is Mormon Doctrine?” and try to explain (algorithmically compress?) the incompressible.
Just a little bit of nitpicking- pi is the radius of the circumference to the diameter, not the radius. Probably just a typo. Also, I would argue that the computer in the example DOES comprehend pi, but only in the purest sense of comprehension. Since it lacks the means or the desire to express it’s comprehension and the ability to comprehend it’s comprehension, it’s really the basest level of comprehension in-so-far as it sums up something large in terms of something smaller.