Tuesday, March 20, 2007

The Peril of "Beauty"

Lately I've been reading The New Story of Science by Robert Augros and George Stanciu. It's an excellent book so far—the second chapter on "Mind" is enough for me to HIGHLY recommend the whole book—but the third chapter mightily aggravates a pet peeve of mine.

The idea of the chapter is that beauty has re-entered our picture of the universe through developments of modern science. While Augros and Stanciu are writing from the realist tradition of Aristotle and Aquinas, the situation of the discussion in the shifting sands of mathematical physics lures them into an over-abstracted account of beauty insufficiently grounded in objective reality. The error in which Augros and Stanciu find themselves mired is rather subtle, but for that reason especially important to recognize.

Before I get started, let me note the worthwhile truth at the core of Augros and Stanciu's praise of beauty: we moderns have a nasty tendency to deny the truth in beauty and to revel in the ugly as if it were the mark of truth. We get wrapped in our own wills and our power to create that we forget that goodness is largely something that we receive from a world much bigger than ourselves.

To return to the over-abstracted notion of beauty, the authors write, "In physics, beauty reigns supreme. Experiment often errs, beauty seldom" (41). It would better read "experiments often err": while individual experiments can err, experiment in the universal sense is the touchstone of modern science, including theory. In 1919, when his assistant asked Einstein about the possibility that experiment had not supported general relativity, Einstein reportedly said, "Then I would feel sorry for the good Lord. The theory is correct anyway." Einstein's statement was probably justified in regard to a single experiment or perhaps even a small number of experiments, but not for a large number of well-conducted experiments. Real science ultimately has to be grounded in objective reality. Forgetting this fact is the basic error of the chapter.

As we all know, beauty in general is no sure-fire window on truth and goodness. Although one can always pick out the protagonist of a movie by looks, real life is not so simple. Famous are the fables of the femme fatale. Even more apparent these days is the divergence between beauty and goodness evident in the lives of modern celebrities. Should I emulate Liz Taylor or Britney or Paris just because she is attractive? So much for the evidential power of beauty.

Even otherwise solid philosophers are not immune from the mania for beauty, albeit to a lesser extent. Many of them have an unreflective tendency to elevate beauty to stand among the "big three" transcendental perfections synonymous with Being: the True, the Good, and the One—sometimes displacing the last, Oneness or Unity.1 As Fr. Ashley points out, beauty is only "a particular goodness of truth": "truth as we desire its contemplation" (174, 328). And all too often its essential relation to the (imperfect) knower makes it but an apparent goodness. It is perilous to exalt "beauty" with insufficiently context.

Augros and Stanciu educe from the words of many prominent physicists that beauty comprises "simplicity, harmony, and brilliance" (42). Similarly Aquinas speaks of beauty as the splendor of truth or of form thusly in the Summa:

For beauty includes three conditions, "integrity" or "perfection," since those things which are impaired are by the very fact ugly; due "proportion" or "harmony"; and lastly, "brightness" or "clarity," whence things are called beautiful which have a bright color. (ST I, Q 39, a 8)

So according to Aquinas, harmony is synonymous with proportion, and brilliance (or brightness) with clarity. But equating simplicity with integrity or perfection is a bit harder to understand. Augros and Stanciu write, "The principle of simplicity implies two things—completeness and economy.... A theory beautiful by this standard must take into account all the facts and must include only what is necessary" (42-43)— in other words, it must possess a wholeness validly described as integrity or perfection. Harmony, the authors write, requires not only that a theory harmonize with previously established theories, but also implies symmetry. Augros and Stanciu are manifestly writing in the Thomistic tradition.

Unfortunately any discussion of mathematical physics necessarily tends toward mathematical abstraction, which is a human construct, a human creation.2 The slippery sand sneaks in through the mathematical notions of completeness and simplicity (along with symmetry). Abstracted from actually existing reality, "completeness" takes on arbitrary boundaries. Modern scientific theories necessarily omit parts of that reality. Newton's Laws of Motion, for example, leave out the fact that bodies are composed of parts which interact separately; you could never come up with the laws of thermodynamics purely from Newton's Laws. Mathematical abstraction methodologically ignores some facts: Newton's law of inertia ignores the fact that no body exists untouched by outside forces. Theoretical completeness in modern science contains a large dose of arbitrariness (for lack of a better word).

Taken with the arbitrariness of completeness, "simplicity" in the context of mathematical abstraction becomes a weird perfection: the more complicated a thing becomes or the more parameters it requires for its description, the less of the perfection of simplicity (economy) it apparently possesses. (Symmetry is similar in that it increases simplicity.) One atom is simple, but a molecule is comparatively complicated. Life, and in particular human life, is a messy affair, very unsimple. Apparently unbeautiful too. But there's little doubt that a human has more being and goodness than an atom. What could be simpler than a perfect, sterile sphere? The world itself is messy. While the laws of nature have a symmetrical generality, applying "always" and "everywhere" the same, there's no avoiding the asymmetry of the particular, the scandal of the concrete reality in front of you: why does this exist and not something else?3 The unfortunate side-effect of elevating simplicity in this context is a tendency to see all existence is a wart on the perfect symmetry of Nothing.

These days what we call good or beautiful follows the lead of physics in consisting simply in what is easy or useful, or conveniently meets our purposes, and in willfully shutting out the less pleasant bits. The world would be more beautiful (simple) if no children were born with birth defects, but not every way of achieving that end is good. The world would certainly be more democratic (symmetrical) and simpler if there were no moral absolutes, since everyone regardless of behavior would have an equal claim to goodness, but its apparent simplicity doesn't make such an idiotic idea true. Likewise, the history of mathematical physics is littered with the remains of theories that appealed to their authors as beautiful, but which turned out to have zero bearing on physical reality.4 Truth is a correspondence between the mind and (extra-mental) reality; in place of truth, the modern world settles for consistency, e.g., harmony with preceding theory.

Conversely truth and goodness are often ugly, or at least appear under the guise of the ugly. Sometimes the good that the truth requires is repellent, like sacrificing ourselves for family or country. Francis of Assisi is a saint because he was able to find the beauty in a leper. Teresa of Avila is a saint because she was able to find God in the emptiness of spiritual purgation. What could be more horrifying than a crucified man? What could be more asymmetrical than a people who lay unique, historical claim to the Absolute?

The problem with the modern world is not our lack of attraction to beauty, but our failure to recognize what is truly beautiful. Just as everyone desires the good, everyone finds beauty attractive. The controversy is the content to attribute to the perfection (beauty, goodness), and the challenge is how to know it.5

The world has forgotten true beauty, so there's great value in its exaltation, Augros and Stanciu are writing for that worthy end, and its difficult to blame them for missing the subtle error to which they fall prey in this single chapter of an otherwise excellent book. Examining the results of mathematical physics can broaden our minds to recognize the beauty of the world. Unfortunately, taking the example of mathematical physics as a guide for discovering beauty only more firmly shuts us up within our uneducated tastes. The way out of our morbid fascination with the ugly is not so much allowing whatever chances within our tortured definition of beauty to guide us, as in training our hearts to recognize what is truly good and beautiful. What our hearts perceive as beautiful, they inevitably follow.


1. Fr. Dubay's The Evidential Power of Beauty merely elevates beauty without displacing unity (p. 45-7), apparently based on the thought of Hans Urs von Balthasar. Dubay doesn't seem to clearly distinguish goodness and utility (a common modern confusion), at least on p. 46. Goodness, unlike unity and truth, has no entry in Dubay's index.

2. Cf. "The expressions ‘the order of nature’ and ‘the biological order’ must not be confused or regarded as identical; the ‘biological order’ does indeed mean the same as the order of nature but only insofar as this is accessible to the methods of empirical and descriptive natural science.... The ‘biological order’, as a product of the human intellect which abstracts its elements from a larger reality, has man for its immediate author." (Karol Wojtyla, Love and Responsibility, pp. 56–57)

3. The scandal of the particular is the source (philosophically speaking) of the need for probability in quantum mechanics, the so-called collapse of the wave-function in some versions of the Copenhagen interpretation, as well as the alternative "many worlds" interpretation.

4. Contrary to Augros and Stanciu's claim that "If occasionally a supremely elegant theory does not fit one group of facts, it inevitably finds application elsewhere" (41). But I suppose the wiggle room is in the word "supremely."

5. That naive acknowledgment of lovely appearance was easier in pagan times, before the centrality of the Cross laid bare the inner contrariety of our created existence. Maybe the Misfit was right: "Jesus thrown everything off balance." More likely Jesus exposed what had always been lying behind the "beautiful" face of the world, and what we ignored to our own destruction.

Robert M. Augros and George N. Stanciu, The New Story of Science (New York: Bantam Books, 1986).

Benedict Ashley, The Way Toward Wisdom: An Interdisciplinary and Intercultural Introduction to Metaphysics (Notre Dame, Indiana: Notre Dame Press, 2006).


CrimsonCatholic said...

I do think that the question of symmetry was a subject well presented in Stephen Barr's Modern Physics and Ancient Faith. That observation, along with your intriguing remark about probability in quantum mechanics originating in the "scandal of the particular," have certainly whetted my curiosity about your opinion on how exactly quantum mechanics connects with philosophy (it sounds like you disagree with Barr in some respects). While I concur with the sage observation of Vadim Kaplunovsky that "many have wandered down that dark path, never to return," I suspect you would be able to shed some light on the subject. I've been musing about the notion that quantum mechanics seems to demonstrate the reality of potency and formlessness in created matter, and it would be helpful to have some other people's thoughts on how Dirac meets Aristotle.

Lawrence Gage said...


Steve Barr and I have a long-running conversation over our disagreement on quantum mechanics. I was actually writing a post responding to his recent First Things piece on the subject, when I realized that I really don't understand how his interpretation of quantum mechanics coheres. I wrote Steve and got a reply, but still require further clarification. I do hope to post on the subject in the not-distant future.

In the meantime, you might find helpful this excellent article by David Schindler:

"Beyond Mechanism: Physics and Catholic Theology"


P.S. Are by any chance you associated with Harvard's Saint Jerome Society? LG

Lawrence Gage said...

P.P.S. I had some difficulties with Barr's account of order in his book, mostly around his univocally equating symmetry and order (notice that uniformity is a kind of symmetry as well as being a state of maximal entropy in some contexts). I was using a different email account at the time and will try to dig up the exchange. LG

CrimsonCatholic said...

That really is a good article. I wonder if this isn't an area where Eastern Catholic theology could be helpful. The use of the Aristotelian concepts of dynamis (in the sense of a characteristic power of a nature) and energeia (activity) doesn't bear the connotation of determination in the sense of force. That's how St. Maximus explains that the two wills in Christ remain distinct without the human will simply being dominated by the divine will (for that matter, his entire cosmology was devoted to reconciling the particular with the universal). I'd also argue that the deterministic idea was destructive of theology even before it was destructive of physical science; just look at John Calvin!

Are by any chance you associated with Harvard's Saint Jerome Society?

Sorry, no. I had just begun my trek back to the Church when I was there, so I wasn't involved in any Catholic organizations. Harvard was a large spiritual influence on me primarily by contrast; after seeing all the pomo, relavist goofiness, I was impelled to look for something better!

I'll look forward to whatever comments you can dig up. I liked the hierarchical idea of symmetry in Barr's work, but I take your point that there has to be some idea of symmetries being useful (and ordered to) some bigger picture. Symmetry for symmetry's sake is, like any other created end, ultimately inadequate. But I think it's a fair point that a number of people don't even understand that there IS an ordering of symmetries, let alone try to explain it, so I wasn't inclined to nitpick.

The Tetrast said...

Excellent article, and it's good to find folks trying intelligently to relate traditional ideas to modern physics.

The conflation of "simplicity" and economy with integritas sive perfectio is definitely a central error in their discussion. In Summae Theologiae, Prima Pars, Quaestio 39, Articulus 8
(not that I've read a great deal of Aquinas), Aquinas says:

Nam ad pulchritudinem tria requiruntur. Primo quidem, integritas sive perfectio, quae enim diminuta sunt, hoc ipso turpia sunt.

(Tr. mine) "For in fact for beauty three things are required. First certainly integrity or perfection, indeed things which have been dashed to pieces [or destructively violated], by this very fact are ugly [base, disgusting, 'gross']."

Some perhaps have confused diminuta with "diminished" which would have been deminuta. Aquinas seems to mean structural integrity, which is not the same thing at all as simplicity or economy -- in fact in a sense it is the opposite.

The associated requisite for beauty isn't really among Aquinas's three, but is closer to Aristotle's idea of due magnitude, for it is in the case of magnitudes with directions that simplicity, economy, directness, extremality, become guiding ideas.

One should think of forces acting on a system, forces striking or arresting it (compare versus Joyce's likewise mistaken concept of integritas sive perfectio as corresponding to arrest as the initial aesthetic stage) rather than (as with structure) thinking of forces balanced within a system (which, stabilized, is more entelechy than agent cause).

The equations or "balancements" which "govern" or "are enforced by" the play of forces are not the same thing as an actual structure constituted by balanced forces, any more than the ordering in a structure is the same thing as the direction associated with a magnitude like force, momentum, etc. The opposition is one between distance and nearness, space and place, chôra and topos, instability and stability.

It is to be compared against the opposition between harmony/rhythm and radiance --- an opposition between process and culmination, development and bloom, chronos and kairós, patience and "impatience" (act), etc.

I'm not sure of this, but it may be that the symmetry which is celebrated by physicists and which tends to be translational and algebraic, is more to be associated with claritas than with harmony and due proportion per se. This is in the same sense as order is associated with actual structure (which is idiosyncratic) and equations (balancings) are to be associated with unbalanced forces acting on a system.

The Tetrast said...

My final paragraph got cut out, sorry, and please don't worry that I'm going to persist with further editings. Here is the missing paragraph.

In the distance between the abstract and concrete, versions of some of the ideas become associated with the opposites of those ideas. It is good, as you say, to remember the distances between abstraction and the concrete experience of the beautiful -- in its arresting onset, fascinating development, enchanting culmination, and (pace Joyce), attachment-bringing establishment or "firming up."

The Tetrast said...

Okay, one more "edit" -- in order to withdraw my remark two days ago about symmetries (in the physical-theoretic senses of universality, invariance, conservation of quantity, etc.) as perhaps pertaining to claritas (radiance, brightness).

To keep it brief, I'll say that that such symmetry is a universality is more distributive than collective. Harmony and rhythm pertain to a more collective kind of universality. To put it another way, harmony and rhythm pertain more to gamut or totality (as of a total population or its parameters and systematically exhaustive alternatives and divisions) than universality as of a law, a kind of simplicity or economy, which pertains to due magnitude, or due directed magnitude, as its "enforcer."

Lawrence Gage said...

Tetrast, this last paragraph is rather dense (particularly the first sentence). Could you unpack it?


The Tetrast said...

I'll try to unpack and clarify in the form of a rewrite. I'm not always so good about putting in words like "yet," "irrespectively," etc., and I apologize for that.

I withdraw my remark of two days ago about symmetries (in the physical-theoretic senses of universality, invariance, conservation of quantity, etc.) as perhaps pertaining to claritas (radiance, brightness). It doesn't seem useful to explain why I would have thought so even temporarily.
Leaving claritas aside, the question remains that of whether symmetry in the physical-theoretic sense corresponds to harmony and due proportion in the Thomistic sense. "Taking the example of mathematical physics as a guide for discovering beauty" leads us to focus on the properties of mathematical abstractions -- where the invariance of proper time, for instance, is a "symmetry." Yet the basic idea of harmony, rhythm, and due proportion is not the idea of a distributive universality or rule with ever more cases to govern, a la the "miraculous jar" of positive integers, but rather the idea of a universe and its parameters and divisions -- a keeping, a key, a tonality, a temperament, etc., a set of parameters which are fulfilled collectively and in combination by different divisions of a total population or universe of discourse. In this connection one ultimately should think on matter, the gamut of elements and gamuts of their combinations, chemistry, stochastic processes, mutually cancellative fluctuations, etc. more than on physics, extremal principles, and fundamental forces. At this point I would refer up to remarks in my first comment, and I should rewrite them a bit for readability's sake:
Diminuta means "dashed to pieces" or "destructively violated," and should not be confused with deminuta which means "diminished." Aquinas opposes diminuta and turpia ("ugly," "base," "'gross'") to that which has integritas sive perfectio, by which he therefore seems to mean structural integrity, which is not the same thing at all as simplicity or economy -- in fact in a sense it is the opposite, in such sense as beauty's aspects may stand in oppositions to each other.

The requisite for beauty associated with economy and simplicity isn't really among Aquinas's three, but is closer to Aristotle's idea of due magnitude, for it is in the case of magnitudes, and of magnitudes with directions, that simplicity, economy, directness, extremality, shortest distances, cutting Gordian Knots, etc., become guiding ideas. Here one should think in particular of an external force imposed on a system, a force either unbalanced or at any rate making for instability. We can think of Joyce's initial aesthetic stage as involving the work's striking its audience, not into motion, but, as Joyce says, into stasis -- arresting its audience, and we can think of this as arising from the work's having due magnitude, due force, rather than Joyce's having it arise from the work's integritas sive perfectio, which is more entelechy than agent or agent cause.
Then I go on to point to an opposition between the due directed magnitude idea and the structural integrity idea, which lend themselves to conception as space ideas, and I say that their opposition is to be compared against an opposition between the harmony/rhythm/due proportion idea and the radiance/claritas idea which, in the comparison, come into relief as opposed time ideas. Please pardon the tildes, they are in order to maintain the spacing of the table form.
due magnitude ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~radiance, claritas
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ X ~ ~ ~ ~ ~ ~ ~ ~ ~
harmony, rhythm, due proportion ~ ~ ~ integritas sive perfectio
I make some further associations, but perhaps I've unpacked enough for the time being! The subject obviously fascinates me but pertains to only one or two aspects of your original post, and one way or another I don't want to presume upon your patience.

- Ben Udell