Thursday, May 7, 2009

The "Verbal Glissando" of SLJ

Have you ever been reading a Jaki text, perhaps referring to Leonardo or Aquinas and run into the term "Stagirite"? Perhaps most of you know who that means, but maybe you need to be told that it means someone from Stagira in ancient Macedonia - almost always Aristotle. But even if you did know, perhaps your breath had been taken away by the amazing leap across the millennia - which is even more common in Jaki's texts than his use of Aristotle's nickname.

Any of you who have read Chesterton may know his curious and powerful use of words to underscore the point he is making. Some critics refer to them as Chesterton's "Verbal Fireworks" - he delighted to use curious analogies, stunning word alignments, alliterations and other such things. Verbal devices as alliteration and other figures of speech can also be found in many of Father Jaki's texts, despite their otherwise scholarly tone. One finds alliterative titles like Cosmos and Creator calling to mind GKC's Lunacy and Letters. Another device, perhaps arising from a more ancient tongue is the chiasm (a shape like the capital Greek chi, X) appearing in titles like The Origin of Science and the Science of its Origin. (Such things appear in remarkable places, such as the Watson-Crick palindromes of rRNA and tRNA secondary structures.) Another device Jaki uses is the sudden leap through millennia of history from one linked idea to its correlate This may not be an official "figure" according to the rules of rhetoric, but Jaki's purpose often demands it, and to honor the device with a name I shall refer to these as Jaki's "Verbal Glissando" - I use a musical tag recalling Jaki's musical abilities - Chesterton was a trained artist so a visual tag is fitting for him. Please understand: I do not use these terms as criticism: for both GKC and SLJ, the subject matter often demands such mannerisms, and, like fireworks or glissandos, have the advantage of drawing the reader's attention to the topic at hand.

I have brought up "Verbal Glissandos" because I am about to make one of my own, as I wish to go into Tuesday's matter of the bridge a little more deeply.

No doubt you have read (or at least heard of) On the Consolation of Philosophy by Boethius, written while he was in prison. He tells of how Philosophy comes to comfort him, appearing as a lovely woman, and describes her appearance in some detail: "On the border below was inwoven the Greek Pi, on that above was to be read a Greek Theta. And between the two letters there could be marked degrees, by which, as by the rungs of a ladder, ascent might be made from the lower principle to the higher." [tr. W. V. Cooper] A footnote explains that these letters signify the two branches of philosophy Theta for theoretical and Pi for practical.

Without trying to delve into the vast issues raised my reference to this great philosophical work, I wish you to consider just this very elegant and beautiful image - and then to follow me as I turn to another, more modern, and even more issue-raising.

When I was doing my research for my doctorate, by which I assisted molecular biologists in their work to study prokaryotic rRNA (that is, the working machinery of the cells of bacteria) I stumbled up - or down - that ladder. Here is what happened.

One of the first things one does with a collection of data - be it stellar coordinates, or an interesting text, or an electronic collection of biological sequences - is to perform various searches. One wants to know (as Bessel used the work of Piazzi) whether the stars really are fixed - or how often Fr. Jaki uses the word "encomium" - or whether a certain pattern appears within a collection of DNA sequences. As you are most likely reading this through the INTERNET, you most likely know there are a variety of tools which permit all kinds of searches, and if you are a molecular biologist or a computer scientist you might even give various names to the tools (the programs, which are engineering solutions) or to the algorithms (which are the theoretical "recipes" or scientific solutions) for doing these searches. Remember, the difference between thesre things - think of the robe of Philosophy - a recipe is needed if you want a cake, but you cannot eat the recipe! Nor can you "hear" the musical score - you need a pipe organ or an orchestra to perform it. Similarly you cannot cross a chasm with the blueprints for a bridge, even if the Roeblings themselves drew them! (The Roeblings are the designers and builders of the Brooklyn Bridge in New York.) Nor can an algorithm, no matter how efficient, do the work of a search. There must be the ladder which links Theta and Pi - which Boethius said Philosophy herself had placed on her robe.

One of the curious things about the sequences I had to deal with was that, unlike simple texts of common human languages, or even the usual data found in many business or engineering problems, the data contained what are called "wild cards" -

They are the symbols which represent a degree of ambiguity at a given place in the sequence.

Do not worry - as interesting as this is, I am not about to give a full lecture on this here. If you want a little more you can find it here.

But I wish to point out this curious fact which as I said, I stumbled into.

You may have already noted that some searches want you to indicate whether you want them to be "case-sensitive" - that is to distinguish between the capital "G" and the small "g". Or you may have had to deal with a word which has diacritical marks, such as "Hélène" (the name of Pierre Duhem's daughter). The idea of a "wild card" is similar, but instead of the ambiguity residing in the query word, it resides in the original text, and one requires that the symbols match though they may not be identical! (Some other time I shall try to describe this in more rigorous detail, but not here and now.)

It is all very well to speak about engineering solutions to such things, which is probably what a typical programmer would attempt, but one might rush headlong into a completely inappropriate solution as I did, only to discover that the elegant solution does not work.

It took some study to find out why. Every kind of computer search contains as its kernel a very simple step of work: the comparison function or relation, by which two symbols (letters or characters) are examined and their equivalence decided - or their non-equivalence. (This is so rudimentary an operation it requires no more than a handful of logic gates to implement in electronics.) However, the elegant solution requires that the nature of this comparison relation must be transitive - that is, it must have the property that if
A "relates to" B,
B "relates to" C,
then it must be true that
A "relates to" C.
Clearly this is true when "relates to" is replaced by "equals" - or even "is less than".

But it is NOT true when one considers these unusual "wild cards" where the "relates to" is called "matches" - even though it first appears that the "match" is very much like "equals"!

(To be very technical, the famous efficient Knuth-Morris Pratt search algorithm requires that the string comparison operation be an equivalence relation: that is, reflexive, antisymmetric and transitive.)

But the "matches" relation in a wild card alphabet (such as used in DNA sequence analysis) is NOT transitive: for A matches M and M matches C but A does NOT match C.

And so, it was only by exploring some of the deepest theoretical parts of this issue that the purely practical goal of finding a certain pattern could be accomplished - even abstractly.

My point in mentioning this is not to justify a minor step in my research. It is to hint at the need to see both the theoretical as well as the practical - that the "divide" must not be shrugged off just because one finds a very strange difficulty. Some computer scientists (those devotes to the abstract) might have shrugged off the issue without any concern for the practical need: "we're not interested in such unnatural things as 'wild card' alphabets!" Others (referred to as "merely programmers") might have opted for a different though less efficient solution, and ignored the strange failure of the classic method to handle the unusual case. Meanwhile the biologists, intent on matters of disease and curious to know more about the reality of the natural world, resort to working problems by hand, while the Theta-side battles with the Pi-side.

No; we must work through (or by means of) that ladder, the degrees of the staircase which links the Theta and the Pi - the philosophical bridge across the "impassable divide". We cannot get stuck in the quagmires of the self - be it our own ego, or a "departmental ego".

The paradox is that the ladder is simultaneously theoretical and practical - it must be.

Though it means lengthening an already lng posting, I shall append a very instructive fragment from Chesterton which may give some enlightenment, if only by his spectacular "verbal fireworks"...
There has arisen in our time a most singular fancy: the fancy that when things go very wrong we need a practical man. It would be far truer to say, that when things go very wrong we need an unpractical man. Certainly, at least, we need a theorist. A practical man means a man accustomed to mere daily practice, to the way things commonly work. When things will not work, you must have the thinker, the man who has some doctrine about why they work at all. It is wrong to fiddle while Rome is burning; but it is quite right to study the theory of hydraulics while Rome is burning.

It is then necessary to drop one's daily agnosticism and attempt rerum cognoscere causas. If your aeroplane has a slight indisposition, a handy man may mend it. But, if it is seriously ill, it is all the more likely that some absent-minded old professor with wild white hair will have to be dragged out of a college or laboratory to analyze the evil. The more complicated the smash, the whiter-haired and more absent-minded will be the theorist who is needed to deal with it; and in some extreme cases, no one but the man (probably insane) who invented your flying-ship could possibly say what was the matter with it.
[GKC What's Wrong With the World CW4:43-4]

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