Tuesday, June 22, 2010

I'm feeling paradoxical today

Dear Albert,

As you are, of course, intimately and immediately aware, there's a strange universe out there. I was recently reminded of your remark, "The most incomprehensible thing about the universe is that it should be comprehensible". I recently had occasion for some metaphysical musing, and was struck by a strange intelectual discord among modern antitheists and so forth.

My remark arose from considering various sorts of metaphysical mythologies --- anyways, I'm going to suggest that there are, broadly, three categories of attitude to the Metaphysical Problem, and suggest that it just might be worth-while to consider each of the options, and that we can reason about which is the best.

But before that, I suppose I ought to explain what I mean by the Metaphysical Problem.

The Metaphysical Problem

To start with what I hope is an informative contrast, the Physical Problem, which underlies all the natural sciences, is the question of "how does everything we see fit together". To be sure, this is a vague statement of the problem; unwrapping things a little, we set out from the object of your incomprehension: that the universe appears to be comprehensible. That is, we see broad patterns, widely similar behaviour among the various bits of the observable universe --- some famous examples, wood and iron canonballs obey the same ballistics (up to terms arising from air resistance); electrons and various shapes of atom all obey intimately related statistics, a close cousin of which also describes the colour of hot iron, and says why it should be the same as that of equally hot coals; and so on.

Physics, our concerted attack on physical problem, is about giving these relations mathematical precision, and has been hugely successful. In Thomistic/Aristotelian language, we have been able to understand the various natural substances we encounter in the large world as accidental arrangements in various patterns of other, finer substances, each having various rules-of-thumb on the accidental patterns they will allow. In fact, this has been accomplished two or three times already, although the number of substances and rules hasn't often simplified. We're still looking for yet another, hopefully a more poetic itteration of the process. That's what Strings and Ms (LOL) and, alternatively, generalized spin-foams are about; maybe some day we'll find out how they're getting on.

Now, you might have noticed that one thing remains in common between our world-picture from step to step in the physics process: we always have substances, and we always have rules describing the possible accidents the substances can exhibit. There may well be dreams of finding a "basic" substance with rules so elegant and indecomposable that it might as well be a Platonic Ideal. In some ways we already possess such a picture with sufficient expressiveness, but it's rather involved and elaborated, making lots of people queasy; and that's why foundational physics is still a live field of study. But there's no need to ever finally hit upon the right rock-bottom substance, or the right basic rules. Consider an analogy: a bit of poetry will be the same poem whether it is written down in ink on paper, in chalk on a blackboard, graven in copper, or cast in moulded plastic with "Made in Taiwan" stamped on the reverse. At some point the particulars of underlying substances don't matter as far as the real-world applications are concerned.

The Metaphysical Problem, as I mean the phrase, is what's left of inquiry into the nature of what is after you recognize that physics itself --- observation and organization --- won't ever get underneath the physical universe. So, once we've figured out that we can't read beyond $\omega$ turtles downwards, it is a mute point to argue whether there is an $\omega$th turtle, whether the turtle tower is a countable ordinal or uncountable, or it might not cover the entire ordinal hierarchy. Instead, I believe we should skip all that unfathomable nonsense and, if still interested, talk about what it means for any of the turtles, or indeed the whole stack, to be there at all. This, I feel safe in saying, is the same as asking "Why is there any stack of turtles? Why is the Universe here?"

Three Responses

The range of possible reactions to the metaphysical problem can be put into three categories, which I'll outline in my arbitrarily chosen order:

"Nihilist fortuity"

You might be a Fortuity Nihilist if when I ask "Why is there anything at all" you answer any of
• "Who cares?"

• "That question makes no sense,"

• "It just is; deal with it."

It has the advantange of dealing with a problem of no obvious immediate practical application simply and straight-forwardly. It is subject to Chesterton's objection to atheism that, to really adopt this position, you can't ever think about the question again (unless someone asks; and even then... ). It's like agreeing to play The Game. The nihilists don't say much, and I've rather little else to say about them.

Various Platonisms

We hear from Plato's commentators (I don't trust myself to recall enough of Plato himself) the proposition that ideals of things have a real existence to them; thus, there IS a perfect circle, a perfect line, a perfect friendship. From the Cave dialogue, we also inherit the notion that the things of sense experience might well be less real than the ideals they suggest to us --- but I don't think this is necessary, either. The idea that I'm calling Platonism is the strengthened proposition that the internal consistency of an ideal is itself sufficient to confer some kind of existence to its subject: the mathematical consistency of Euclidean Geometry is enough to satisfy us that there IS a mathematical Euclidean Geomtry with its own perfect lines and perfect circles. (Mathematically, there ought to be MANY distinct Euclidean Geometries, but that's another matter)

There's an interesting ambiguity in this notion of Platonism, in that it's difficult to decide how elaborate of an ideal gets to be real: If it's mathematical, does it have to be in a first-order language? Does it have to be finitely expressible?

There's a joke warning against computing digits of $\pi$, because it is conjectured (conjecture still open) to be a normal real number, thus incorporating all possible digit strings, a vanishing fraction of which are still under copyright. Of course, one in between about $10^{30}$ and $10^{400}$ of these will come with appropriate copyright information attached, and a smaller fraction will have convincing documentation of licensing.

Adopt a sufficiently slippery Platonism (and I can't see good reasons to put the brakes on anywhere) and you will believe that there IS a constellation of red projective planes; a triune Godhead who creates a world into which He Himself enters and takes on Himself the form of a Man; another self-contained world that looks exactly like the created world just described, but without the God to create it; another self-contained universe containing only film footage of Regis Philbin leaving his house every morning.

The Expansive Platonist will --- must! --- believe in worlds he cannot ever see or touch, about which there are no general rules, and that in general will not follow any concise or poetic system of rules themselves. Some of them might look like they do for a space and a time, and then surprise you. And so, if we are expansive platonists, we cannot trust that the rules we have enjoyed in our own world for the last five hundred years or so (or throughout the history that we can see in our Telescopes) will persist long into the future; there IS a world in which the rules can fade away (I've just written about it, and are we Platonists or not?!), and there's litterally nothing to guarantee that we don't live there!

And it is that whereof I feel most paradoxical today.

Deo Volente

The third category of response supposes a Personal Deity --- the uncaused Cause, The Prime Mover, Who Is, Who Wills, Who Loves; and that whatever else is exists by His will.

The mathematician Laplace is said to have suffered an audience with the King of France, who remarked to him after a lecture on planetary motion "Tu n'as rien dit de Dieu en tout celà" (or words to that effect), to which Laplace replied "Je n'en ai pas eu besoin de cette hypothese". The rules are sufficient for describing whatever follows the rules; this is a truism. Modern thinkers with aversions either to God or to Science seem to imagine that this squeezes God out of the picture; and they respectively caricature this as a good or a bad thing about Science. Both such extremes miss the point: the Christian God is not only Who Is, but is also Truth. Science --- that is to say, experimental Knowledge --- certainly belongs to the Truth, and --- trusting that the Christian God indeed Is --- it is only by Divine gratuity that Science can hope in the ongoing success of the scientific endeavour.

The sufficiency of rules to describe what follows the rules moves our need to trust away from trusting ourselves, away from trusting the rules, and away from the trusting the universe to follow them, back to trusting in the Divine, who gave the rules in the first place, that He will uphold those rules for all time. Squeezing God out of any picture is a bad feature, not of Science, but of shoddy philosophy about science.

Is that everyone?

I think you'll discern from my shifting style which of these positions I personally hold to; I'm sure restrictive platonists could argue the consistency of their cases fairly well. I'm sure the nihilists won't much care except to be annoyed at my brining it up. But there is actually a fourth category of people, who ordinarily wouldn't much count, only there's rather a lot of them. These would be the people who don't get what I'm getting at --- who don't grasp the distinction I'm trying to articulate between prediction and explanation; between substance and matter.

Just last month I read a headline (always risky!) "Scientists Discover why universe exists". But that's not what they meant; the scientists in question had measured a trend in particle/antiparticle generation at an accelerator/collider to produce slightly more of the easily detectable "particles" of conventional experience than the easily detectable of their "anti-particles". They hadn't discovered this trend, because it has long been conjectured; nor is it why the universe exists; it's just an interesting and significant feature of the mechanisms --- the rules, as I've called them --- underlying the persistence of the kind of universe we see around us already.

I wrote privately to an atheist how I don't trust in physical theories themselves to keep the world running as it ought, and he thought my distinction between description and explanation to be "hogwash", asserting that it were just a matter of time before science finds "the explanations". It makes me sad.

It makes me sad that there are people who are prevented from forming trust in God because they don't understand what Science is.

I suppose, Albert, that it's a bit late for you yourself to do much about this confusion, publically at least; but, as I pray for your soul, don't be surprised if I hopefully ask for your prayers for the public understanding of Science and its place within all knowledge.

some mathematician on the street


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