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


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:

LOOP N = 100

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


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:

LOOP N = 100

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...

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13 thoughts on “Musings on Openness Theology, Part 5: The Quantum and Algorithmic Compression”

  1. Kudos to you for delving into something most people would be afraid to pursue (from both theological and intellectual fear!)

    When you're are going into issues like this, science really has a big part to play in the discussion.

    I think science (quantum physics) stands firmly on the side of an infinitude of parallel histories.

    Thus, I think that God's knowledge of the future NECESSARILY means knowledge of multiple futures.

    Does God know which future WE will choose? The question is meaningless: WE choose ALL of them.

    The difference is that we see just one line of history; God sees them all.

    So there is both Free Will and Determinism; the Multiverse is Deterministic at the highest levels, from a God's-Eye View; but that determinism simply outlines EVERYTHING that will happen.

    For example, Determinism doesn't specify that you will choose to steal something; it specifies that you will choose to steal, and to not steal, and to steal but change your mind, and to attempt to steal but fail, etc.

    And all of those things do happen. And God loves all of those "YOUs" equally.

  2. What do you mean when you say "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 physics entropy is a specific physical quantity that can be calculated and used in equations. There's no trouble calculating and quantifying it, as far as I know.

    It is a measure of the "unavailability of a system's energy to do work." This means that energy is evenly spread through the system, which means that there is no gradient, and you can't do useful work. For example, a room with a bunch of cold air in one corner has less entropy than one in which the temperature is uniform, because the energy there has a tendency to go one direction, and thus can be made to do useful work.

    You can easily see how this generalizes to "disorder." For useful work to be done, energy has to be unevenly distributed, or "ordered."

    As far as I can tell, the problem is actually putting the concept into English words. It's easy enough to quantify it and describe it mathematically.

  3. @spaceman spiff:
    "It's easy enough to quantify it and describe it mathematically."

    Everything is easy once somebody's done it. =)

    "I think science (quantum physics) stands firmly on the side of an infinitude of parallel histories."

    Yeah, this is what I was alluding to in the previous post. I'm not sure how "firm" this stance is, though ... I mean, I'm not sure that you can draw a straight line from the idea of multiple dimensions/universes to the mental model we conjure up when we say something like "an infinitude of parallel histories".

    And I'm definitely leery of using the word "foreknowledge" to describe an all-knowing being's perception of the state of the universe at a given time, and of using the word "we" to describe selves that are contiguous across multiple realities, and of using the word "choose" to describe what a person does in a particular reality.

    Basically, I think I agree with the direction you're heading, but I'm not sure that I would be as bold in drawing conclusions.


    I feel obligated to comment on your information theory stuff, but I'm not sure what I want to say yet. =P

  4. Micah and Matthew,
    I'm familiar with the multiple worlds formulation of QM. Today I've been thinking about its interface with the idea of informational compression and I think the argument still holds. However, I'm at the limit of my knowledge and cannot say for sure.

    Correct, entropy in High School physics is easy to define and measure. What I was speaking to is the entire history of thinking on entropy which is huge with lots of controversy, puzzles, paradoxes, and diverse definitions.

  5. Richard,

    I've been with you half way on this. I concur with booting metaphysical free will (i.e., that the ghost in the machine runs the machine, as in Kantian autonomy). But I still think there is room for a physically immanent free will, and I won't surprise you by noting that it's William James' definition that I think leaves that possibility open--free will conceived as the will being a "free variable" in the mix of determining factors working their influence in the world.

    I like James' definition for several reasons. (1) It banishes black and white thinking about free will. (2) It jibes with human experience (we seem to have some limited ability to exercise our wills on ourselves and the world). And (3) it seems to be compatible with a non-metaphysical version of free will. To this I now add (4) that if free will is a "free variable," then it can't be compressed--it will always be a potential source of surprise and novelty. (I'm not ignoring your arguments from the last post, just setting them aside as rhetorically effective against ghost-in-the-machine, metaphysical free will ONLY.)

    I can desire what is not present, even what has never been. Call that evaluative creativity. I can think that things should be different than they are, even than they have ever been different. Call that moral creativity. I can see similarities in things that are not connected, except in my thoughts. Call that metaphorical creativity. And I could probably come up with a few more of these "creativities," all of them potentially relevant to what my will might be up to at any moment.

    The point is that human desires and wishes and sensibilities are creative, even obviously creative: the US patent office alone has over 7,000,000 certified innovations on file. And for every one of them someone was creative in evaluating the possibilities, placing a value on one of the possibilities, and envisioning a way to achieve it. This is unarguable, it seems--the evidence is unavoidable. None of this requires metaphysical free will, and all of it--I think--comports with what James had in mind.

    I note these things for three reasons. First, because it makes of human beings individual points of creativity, i.e., sources of action that cannot be fully comprehended from any set point of time, EVEN IF ALL THAT FOLLOWS ANY GIVEN POINT IN TIME CAN BE DETERMINISTICALLY TRACED, EVEN DURING CREATIVE PERIODS. Second, because it adds a dimension to your considerations about compressions and predictability: human experiences and proclivities combine in novel ways, thus setting up points of creative uncertainty in human consiousness as real as the random uncertainty in the quantum world. And Third, because the biblical meaning of humanity being made in the image of God (stated in the Genesis creation story) pretty clearly requires humanity to have a sphere of meaningful "say" in what happens in creation (the "let them have have dominion" part of Gen. 1).

    So this is pretty fundamental stuff, and pretty fun stuff too.

    Thanks, Richard!

  6. Richard,

    These last few posts tell me something about your end of the semester mental state. Being a recovering academic, I can speak to this condition, this flight into the ghostly realms of theory. Christmas trees, carols, candles, cheer, and food with wife, children, family and friends are a good cure.

    A counterintuitive: No matter how you dress it up or what shade of lipstick or make-up you use, the either/or "free will or determinism" debate is a pig. Intellectually slicing and dicing that pig will be bacon, ham, chitterling, and chicherone-making. But it ultimately neither fries a chicken nor lays an egg--never mind which comes first. Its solution is like the Cubs and the world series--it ain't gonna happen. At best, it is a distraction. At its worst, it can be the gnostic temptation of the garden. The same temptation of philosophy and especially the enlightenment to marginalize and disembody God, to exclude God from our conversation or to reshape God and God's creation to our liking. What is hindered is our adoration and fear of God.

    The biblical God will not have it so intellectually neat and tidy. Rather, God comes to us as paradox--at once a song of joy and a lament. Like the birth of a Jewish baby boy and the death of many toddlers at the hands of a would-be king. Rejoice and weep.

    God bless you for all you do. And all those who respond.

    George C.

  7. Now George!

    I always delight in your musings, including this last. However, I must protest that I tried to make a silk purse out of the old sow's ear, and you called it a "chitterling" anyway. Since chitterlings aren't stitched, and purses are, I thought I'd point out a few of my "stitches" so that you don't mistake my offering for ham, bacon, chitterlings, or any other porcine victual.

    Though I didn't say it outright, I made it clear that there is a way (I think) to talk about the question of free will that does not put it in opposition to determinism. Next "stitch": This non-oppositional view of free will does not require a Cartesian dualistic metaphysics (though it need not deny it either). Last "stitch" (again unstated, but pretty clearly intended): This kind of free will need not stir up Richard's rhetorical enmity, since it sidesteps the arguments against free will that motivated his present musings, all the while melding with those musings with the gist of the complaints to create something new.

    Now I suppose my offering is still mostly pig, but if you chew on it a while, I think that you'll agree it's no victual, and might even be useful for carrying the old argument foreward--to wit, it might be a purse of sorts, if not a silk one. I, however, remain hopeful that silk worms might be induced to eat this pig's ears, thus accomplishing the full purpose.

    Consider this. We are told that evolution moves along in its typically slow pace as random mutations create creaturely variations, which in turn interact with nature's broader contingencies to determine whether the variation is a better "fit" or not. But once consciousness became sufficiently plastic to harbor the contingencies in memory, all that was needed was a mind that could create variations from which to choose survival strategies and plan their implementation, and presto: a fitness adaption generator is born. (Not very eloquent, but "Homo farber" is already taken.)

    That was the intended gist of the "creativities" talk above. And don't blame this outlook on me. C.S. Lewis (Mere Christianity) introduced the idea into popular Christianity by writing--to the effect--that with Christianity God gives humanity the chance to choose which branch of the "tree" it will take. And the real innovator in this line of thought (I think) is C.S. Peirce with his articles, "Evolutionary Love" and "The Concept of God."

    As to the "gnostic temptation in the garden," I've been told that biblical knowledge is usually experiential, not intellectual, in focus, i.e., the Gen. 3 knowldege of evil means "experience evil," not Greek gnosis. But you're the former seminarian--so I'd like your take on that.

    BTW: My wife and I recently entertained a delightful couple, the husband who happens to be a pastor and an ABD doctoral candidate from a good sem. To my dismay, in responding to my story of deciding not to go to sem because of all the questions that came up while taking classes that I thought would prepare the way, this truly delightful Christian intellectual said, "I was too smart to take those questions seriously." And he WAS serious! We both ignored the foot-in-mouth remark, but it did spoil the moment. And it did get me to reflect on to what extent Christian intellectuals can afford to be anti-intellectuals at once.

    My conclusion? The gist of the warning "not to eat of the fruit of...the knowledge...of evil" is "don't play with fire," not "burn the books."


    The pig metaphor is apt for someone who uses up so much space in your comment section. I know that you wanted to consider positions staked out on the far side of the free will debate, and I would apologize for introducing George's old pig into this context, if not for the fact that I really do think that a silk purse might be made of that old sow's ear.



  8. @Tracy:

    I don't know as much about James as Richard does, so I'm going to need some help here. You say:

    "it's William James' definition that I think leaves that possibility open--free will conceived as the will being a "free variable" in the mix of determining factors working their influence in the world."

    Could you explain this idea of agency a little more? I'm having a hard time visualizing what James thinks is going on when I pick chocolate over vanilla.

  9. Tracy,

    A lot of what I said was tongue in cheek. No, I am not a former seminarian. Yes, I am aware that the temptation in the garden was less Greek than Hebrew, less gnostic and more passionate and experiential. But as it has been mediated to the 21st century it is far more Graeco-Roman than Hebrew.

    As to humans being conditioned, restricted, and determined, I am all for it. As to our having choice(s) within our condition qualified but not eliminated, I am all for that as well. Sadly, framing things in the either/or mode is all too common (and sometimes necessary) but is likely to lead us to establish a system and substitute it for the living God. And for living too.

    A silk purse while elegant is far less useful than a purse made from pigskin. And in a pinch you can fry it and eat it.

    More later.


    George C.

  10. Richard:

    OK, now I know what I want to say about the info theory stuff. You've got the twin ideas of compressibility and entropy, but another useful idea is computational complexity.

    From the little work human beings have done so far, it looks like there is a set of problems called NP-complete problems. These are problems that are tricky enough that even the most powerful "single-universe" computational machines (turing machines) can't solve them in any less time than it takes to enumerate all the answers and check to see if they're right. Common NP-complete problems are optimizations: one example is room scheduling, where you have a set of classes of given sizes that need to be scheduled to fit in your available rooms.

    Now suppose - as some people already have - that the universe is a simulation running on a computer (or is roughly equivalent to one). Our computational complexity theory suggests that there probably aren't any shortcuts for evaluating the "future" ... the only way to tell whether I will choose chocolate or vanilla on thursday (or whether I will go to the store so i can choose, or be born so that i can go to the store) is to simulate the entire system from time t. Add to that the gotcha that the computational hardware for evaluating something like this would also have to be fairly complicated ... at least as complicated as, say, a universe.

  11. George,

    Thanks for the laughs/clarifications/corrections. As usual, you seem to be able to make a silk purse...


    James' idea of agency? In "The Experience of Activity" James affirms F. H. Bradley's definition of subjective activity, and then comments:

    "We always felt our 'the expansion of an idea with which our Self is identified, against an obstacle': and the following out of such a definition through a multitude of cases elaborates the obvious so as to be little more than an exercise in synonymic speech." (President's Address before the American Psychological Assn., 1904)

    Richard will have to tell you whether psychology has yet got beyond James' assessment from the same address: [Descriptions up to the present] never take us off the superficial plane."

    Sorry, but James never got beyond the bare experience of agency that we all have...

  12. Matt,

    "Gotchas" are for the golf course, not the ice cream parlor.

    Tracy, Matt, Richard, others,

    If you haven't seen the movie "No Country for Old Men," do so. It is the best movie set in Texas since "Lone Star." It deals in a remarkable way with "computational complexity" and non-Cartesian human action: openness, freedom of choice and fatedness.

    A piece from theatre (later made into a film--two actually), Robert Bolt's play, "A Man for All Seasons" confronts conscience (and us) resonnates with my clumsy thinking about free will and fate. Bolt has Thomas More say in the face of possible death as a traitor to Henry VIII: "God made the angels to show him splendor--as he made animals for innocence and plants for their simplicity. But Man He made to serve Him wittily, in the tangle of his mind! If He suffers us to fall to such a case that there is no escaping, then we may stand to our tackle as best we can, and yes, then we may clamor like champions . . . if we have the spittle for it. And no doubt it delights God to see splendor where He only looked for complexity. But it's God's part, not our own, to bring ourselves to that extremity!"

    Blessings all,

    George C.

  13. Didn't Einstein's theory of relativity include the idea that the universe is constantly expanding and didn't Planck pick on Einstein's theory in his ideas about quantum mechanics?

    Just wondering how this fits.


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