Musings on Openness Theology, Part 5: The Quantum and Algorithmic Compression

The conclusion I reached in my last post is that I don't feel conformable, personally speaking, building theological structures upon free will. Again, this is not to say that free will doesn't exist. It's just that people dispute free will and if you want your theology to have broad intellectual appeal you can't have a whopper sitting right there in the middle of it. Christians are notorious for their cavalier deployment of free will and it hurts our intellectual credibility. So regular readers know that in this blog I routinely problematize free will, trying to resist cavalier deployment.

Okay, so I put free will on the sideline as not good working material. Could I find a way to go forward with an openness theology model? What follows are a few of my "theological experiments" on this topic.

The first notion I played with had to do with algorithmic compression. This idea comes from informational approaches to entropy. Specifically, entropy is the amount of randomness and disorder in a system. Scientists have long searched for ways to try to describe and quantify entropy. How can you tell how much entropy (disorder) there is in a system?

In computational physics the idea of algorithmic compression was hit upon as a measure of entropy. Imagine that the universe and its laws are just one big computer program. What we take to be "events" are just "computations", taking in input and producing output moving the "program" into the next configuration. And so on and so on. If we see the universe as a large computation, churning away through time, then perhaps the findings regarding informational entropy and algorithmic compression might apply.

Specifically, in purely informational terms, how much entropy/disorder/randomness exists in a data string? How could this be measured?

The breakthrough idea in this area was the notion of algorithmic compression. The basic idea is this: The degree to which a program or data string can be compressed is a measure of its entropy. Let me give you some examples.

Data String #1: 100 X's

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Clearly, this data string isn't very random. It doesn't have a lot of disorder or entropy. As as a result, it can be compressed. That is, you could write up a little program that produces that data string. It might look like this:

PRINT "X"
LOOP N = 100
END

You have here a little program that is the informational equivalent of Data String #1. But notice the difference in compression. Data String #1 has 100 characters and the program compresses to 20 characters. Note the idea: Low Entropy/Randomness = High Compression.

Now imagine a more random data string:

Data String #2: 100 Seemingly Random Letters

PHMVUFTCGXRSEWDZXASZEXRCTVGFBGHBYHNJKMIOKLJPHUERXC
HFYDREVSEXYFHAWQCXVHIUKHOMPNKHUGYVBGCTDVXIGOJPGID

The question is: Can you compress this?

The answer is, probably so. Although I tried to be random in my pecking at the keys I doubt if I achieved that. So it is probable that this string could get compressed. But not by much. Note the idea: High Entropy/Randomness = Low Compression.

Okay, now the take home point: What if a string of data were perfectly random?

If a string were perfectly random then it could not be compressed. Which is to say that the shortest way to describe a random program is to actually run the program and see what it will produce. For example, we don't need to run our program for Data String #1. Recall:

PRINT "X"
LOOP N = 100
END

We don't need to run this program to see what it will produce. The program is compressed, but it captures all the relevant information. But a random data string can't be compressed. To describe the program (i.e., to look at what it will produce) we have to run/execute the program. To describe and know is to compute.

Where am I taking all this? Well, here was my thinking. Maybe we can approach openness theology through the lens of algorithmic compression. That is, consider the universe to be like a computer program. Maybe God is passable (i.e., emotional) as the future unfolds because of low algorithmic compression. That is, if the universe can't be compressed very much then the only way to describe how the universe will unfold is to actually let it unfold. As we learned, to describe and know is to compute.

This is a very subtle point. What this argument is saying is that God's creation of Creation and knowledge of Creation are the same thing. This idea conflates describing, knowing, and computing/excuting/running the Creation "program." God knows/creates as the program unfolds. Phrased another way, God is creating right now. Creation isn't a point in the past. Creation is the unfolding, it is ongoing. God's knowledge and creating are synchronized. If so, God can be suprised by his Creation. God cannot know the outcome of the Creation "beforehand." Why? Because to describe/know the program is to actually run the program. Running Creation and knowing Creation are the same thing. God creates to know. He knows by creating. And, according to openness theology, God reacts/adjusts to the unfolding accordingly. Thus, God's interventions are not post-hoc "fixes" (as Hume famously complained about). God's interventions in the world are acts OF creation.

But here's the problem. This model only works if the universe is not compressible. But it clearly is. Look at Newton's Law of Gravity. It's a beautiful compression. All the laws of planetary motion compressed in a neat little formula. The movement of the spheres is not disorderly, random, and entropic. The movements of the spheres can be compressed. We call the compressions the Laws of Nature.

But then I wondered. Newton's Laws don't really hold, do they? Quantum Mechanics tells us that the universe, at its most elementary level, is random. And not pseudo-random, really, truly random. If this is so, maybe the universe resists compression. Maybe the Plank Constant sets a limit on how compressed the universe can be. Perhaps the universe can be compressed to a point, allowing short-term prediction, but ultimately resisting long term prediction via the mechanisms of chaos theory. (See my prior post for this discussion.)

And this is as far as I have gotten. Basically, I put aside free will and wondered if I could build an openness position by appealing to algorithmic compression, the quantum, and chaos theory.

This is the kind of stuff I think about in the shower...