It must be sought out

From Stravinsky’s Poetics of Music in the form of six lessons (1948), translated by Arthur Knodel and Ingolf Dahl:

For myself, I have always considered that in general it is more satisfactory to proceed by similarity rather than by contrast. Music thus gains strength in the measure that it does not succumb to the seductions of variety. What it loses in questionable riches it gains in true solidity.

Contrast produces an immediate effect. Similarity satisfies us only in the long run. Contrast is an element of variety, but it divides our attention. Similarity is born of a striving for unity. The need to seek variety is perfectly legitimate, but we should not forget that the One precedes the Many. Moreover, the coexistence of both is constantly necessary, and all the problems of art, like all possible problems for that matter, including the problem of knowledge and of Being, revolve ineluctably about this question, with Parmenides on one side denying the possibility of the Many, and Heraclitus on the other denying the existence of the One. Mere common sense, as well as supreme wisdom, invite us to affirm both the one and the other. All the same, the best attitude for a composer in this case will be the attitude of a man who is conscious of the hierarchy of values and who must make a choice. Variety is valid only as a means of attaining similarity. Variety surrounds me on every hand. So I need not fear that I shall be lacking in it, since I am constantly confronted by it. Contrast is everywhere. One has only to take note of it. Similarity is hidden; it must be sought out, and it is found only after the most exhaustive efforts. When variety tempts me, I am uneasy about the facile solutions it offers me. Similarity, on the other hand, poses more difficult problems but also offers results that are more solid and hence more valuable to me.

The confusion is not my invention

The rubric for a grade of C in Matt Bell’s brilliant “My Grading Scale for the Fall Semester, Composed Entirely of Samuel Beckett Quotes” at McSweeney’s:

We wait. We are bored. Confusion amounting to nothing. Despite precautions. The confusion is not my invention. You must not think of certain things, of those that are dear to you, or rather you must think of them, for if you don’t there is the danger of finding them, in your mind, little by little. A disturbance into words, a pillow of old words. All life long, the same questions, the same answers. The churn of stale words in the heart again. The sun shone, having no alternative, on the nothing new. This tired abstract anger; inarticulate passive opposition. I pushed and pulled in vain, the wheels would not turn. How hideous is the semicolon.

Recondite but fertile analogies

The opening of Bertrand Russell’s preface to a 1914 translation of Poincaré’s Science and Method:

Henri Poincaré was, by general agreement, the most eminent scientific man of his generation—more eminent, one is tempted to think, than any man of science now living. From the mere variety of subjects which he illuminated, there is certainly no one who can appreciate critically the whole of his work. Some conception of his amazing comprehensiveness may be derived from the obituary number of the Revue de Métaphysique et de Morale (September 1913), where, in the course of 130 pages, four eminent men—a philosopher, a mathematician, an astronomer, and a physicist—tell in outline the contributions which he made to several subjects. In all we find the same characteristics—swiftness, comprehensiveness, unexampled lucidity, and the perception of recondite but fertile analogies.

διπλοῦν ὁρῶσιν οἱ μαθόντες γράμματα

An inscription at the University of Edinburgh

My title, “Diploun horosin hoi mathontes grammata”—those who learn the letters [or alphabet] see double—appears in the Γνῶμαι Μονόστιχοι, Gnomai Monostichoi, of Menander, a collection of one-line sayings (not necessarily Menander’s own) with a long legacy in literary education. It is line 657, on page 359, in the version collected in Μeineke’s Fragmenta Comicorum Graecorum, Volume IV, Fragmenta Poetarum Comoediae Novae:

The only English translation is by John Maxwell Edmonds, The Fragments of Attic Comedy After Meineke, Bergk, and Kock, volume IIIb, where he renders the line “Who learns to read doubles his power of sight.” (Though it is not at all what Wittgenstein meant, I am reminded of 5.6 in the Tractatus, “Die Grenzen meiner Sprache bedeuten die Grenzen meiner Welt”—the limits of my language mean the limits of my world.)

The Gnomai represent the genre of the gnomologium, a sort of textbook anthology or chrestomathy of wisdom for rhetorical or moral instruction, especially popular throughout antiquity and the Middle Ages. Erasmus mentions the genre (and cites Menander) in his Adages:

There were those, especially among the Greeks, who willingly undertook the task of making gnomologies, collections of aphorisms, notably Johannes Stobaeus. I would rather praise their work than imitate it.

Compare the commonplace book.

Copies of both of them

Augustine to Jerome in 403 CE, some six years after his previous attempt to convey his perplexity at Jerome’s decision to translate the Old Testament into Latin directly from the Hebrew, rather than from the Greek of the Septuagint (collected in A Select Library of Nicene and Post-Nicene Fathers of the Christian Church, Translated into English with Prolegomena and Explanatory Notes under the Editorial Supervision of Henry Wace and Philip Schaff):

To my venerable lord Jerome, my esteemed and holy brother and fellow presbyter: Augustine sends greetings in the Lord.

Never since I began to write to you, and to long for your writing in return, have I met with a better opportunity for our exchanging communications than now, when my letter is to be carried to you by a most faithful servant and minister of God, who is also a very dear friend of mine, namely, our son Cyprian, deacon. Through him I expect to receive a letter from you with all the certainty which is in a matter of this kind possible. For the son whom I have named will not be found wanting in respect of zeal in asking, or persuasive influence in obtaining a reply from you; nor will he fail in diligently keeping, promptly bearing, and faithfully delivering the same. I only pray that if I be in any way worthy of this, the Lord may give His help and favour to your heart and to my desire, so that no higher will may hinder that which your brotherly goodwill inclines you to do.

As I have sent you two letters already to which I have received no reply, I have resolved to send you at this time copies of both of them, for I suppose that they never reached you. If they did reach you, and your replies have failed, as may be the case, to reach me, send me a second time the same as you sent before, if you have copies of them preserved: if you have not, dictate again what I may read, and do not refuse to send to these former letters the answer for which I have been waiting so long. My first letter to you, which I had prepared while I was a presbyter, was to be delivered to you by a brother of ours, Profuturus, who afterwards became my colleague in the episcopate, and has since then departed from this life; but he could not then bear it to you in person, because at the very time when he intended to begin his journey, he was prevented by his ordination to the weighty office of bishop, and shortly afterwards he died. This letter I have resolved also to send at this time, that you may know how long I have cherished a burning desire for conversation with you, and with what reluctance I submit to the remote separation which prevents my mind from having access to yours through our bodily senses, my brother, most amiable and honoured among the members of the Lord.

There is none to praise it

Footnote 33 in Chapter 8 of Ernst Robert Curtius’s European Literature and the Latin Middle Ages, commenting on lines from Smaragdus of Saint-Mihiel’s didactic poem on grammar, “Partibus inferior jacet interiectio cunctis / Ultima namque sedet et sine laude manet”:

“Sad is the lot of the interjection, for of all the parts of speech it has the lowest place. There is none to praise it.” On the way from Latin to French, the penultimate syllable of the proparoxytone succumbed. Mallarmé was so touched by this that he wrote a prose poem on the “Death of the Penultimate” (Le Démon de l’analogie in Divagations). It ends: Je m’enfuis, bizarre, personne condamnée à porter probablement le deuil de l’explicable Penultième. Grammar too has its tragedies.

Admirers so few and so languid

Samuel Taylor Coleridge, age 18, to his brother George, with a very green poem setting Euclidean reasoning to verse:

Dear Brother,

I have often been surprising that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the case; viz. that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert. To assist Reason by the stimulus of Imagination is the design of the following production. In the execution of it much may be objectionable. The verse (particularly in the introduction of the ode) may be accused of unwarrantable liberties, but they are liberties equally homogeneal with the exactness of Mathematical disquisition, and the boldness of Pindaric daring. I have three strong champions to defend me against the attacks of Criticism; the Novelty, the Difficulty, and the Utility of the work. I may justly plume myself, that I first have drawn the nymph Mathesis from the visionary caves of abstracted Idea, and caused her to unite with Harmony. The first-born of this Union I now present to you; with interested motived indeed—as I expect to receive in return the more valuable offspring of your Muse.

This is now—this was erst,
Proposition the first—and Problem the first.


On a given finite line
which must no way incline;
To describe an equi—
—lateral Tri—
—A, N, G, E, L, E.
Now let A. B.
Be the given line
Which must no way incline;
The great Mathematician
Makes the Requisition,
That we describe an Equi—
—lateral Tri—
—angle on it:
Aid us Reason—aid us Wit!


From the centre A. at the distance A. B.
Describe the circle B. C. D.
At the distance B. A. from B. the centre
The round A. C. E. to describe boldly venture.
(Third postulate see.)
And from the point C.
In which the circles make a pother
Cutting and slashing one another,
Bid the straight lines a journeying go.
C. A. C. B. those lines will show
To the points, which by A. B. are reckon’d,
And postulate the second
For authority ye know.
A. B. C.
Triumphant shall be
An Equilateral Triangle,
Not Peter Pindar carp, nor Zoilus can wrangle.


Because the point A. is the centre
Of the circular B. C. D.
And because the point B. is the centre
Of the circular A. C. E.
A. C. to A. B. and  B. C. to B. A.
Harmoniously equal must forever stay;
Then C. A. and B. C.
Both extend the kind hand
To the basis A. B,
Unambitiously join’d in Equality’s Band.
But to the same powers, when two powers are equal
My mind forebodes the sequel;
My mind does some celestial impulse teach,
And equalizes each to each.
Thus C. A. with B. C. strikes the same sure alliance.
That C. A. and B. C. had with A. B. before
And in mutual affiance
None attempting to soar
Above another,
The unanimous three
C. A. and B. C. and A. B.
All are equal, each to his brother,
Preserving the balance of power so true:
Ah! the like would the proud Autocratix do!
At taxes impending not Britain would tremble,
Nor Prussia struggle her fear to dissemble;
Nor the Mah’met-sprung wight
The great Mussulman
Would stain his Divan
With Urine the soft-flowing daughter of Fright.


But rein your stallion in, too daring Nine!
Should Empires bloat the scientific line?
Or with dishevell’d hair all madly do ye run
For transport that your task is done?
For done it is—the cause is tried!
And Proposition, gentle maid,
Who soothly ask’d stern Demonstration’s aid,
Has prov’d her right, and A. B. C.
Of angles three
Is shown to be of equal side;
And now our weary stead to rest in fine,
‘Tis raised upon A. B. the straight, the given line.

Double, triple, quadruple hypothesis

from the first chapter, “Parole, Parole, Parole,” of Tobias Jones’s The Dark Heart of Italy (2003):

As I began studying postwar Italian history, it became obvious that surrounding any crime or political event, there are always confusion, suspicion, and “the bacillus of secrecy.” So much so that dietrologia has become a sort of national pastime. It means literally “behindology,” or the attempt to trump even the most fanciful and contorted conspiracy theory. Dietrologia is the “critical analysis of events in an effort to detect, behind the apparent causes, true and hidden designs.” La Stampa has called it “the science of imagination, the culture of suspicion, the philosophy of mistrust, the technique of the double, triple, quadruple hypothesis.” It’s an indispensable sport for a society in which appearance very rarely begets reality. Stendhal wrote about it in The Character-house of Parma: “Italian hearts are much more tormented than ours by the suspicions and the wild ideas which a burning imagination presents to them.”

Consider, as counterpoint, Moravia’s short story “Non approfondire” (Don’t delve too deeply). Compare, of course, the “hermeneutics of suspicion.”

There is an interesting discussion of the word at the Language Log, and it’s the subject of a column in the Economist from 2011.

Stupid for the rest of the day

From the Wikipedia page on Paul Valéry:

Valéry’s most striking achievement is perhaps his monumental intellectual diary, called the Cahiers (Notebooks). Early every morning of his adult life, he contributed something to the Cahiers, prompting him to write: “Having dedicated those hours to the life of the mind, I thereby earn the right to be stupid for the rest of the day.”

The subjects of his Cahiers entries often were, surprisingly, reflections on science and mathematics. In fact, arcane topics in these domains appear to have commanded far more of his considered attention than his celebrated poetry. The Cahiers also contain the first drafts of many aphorisms he later included in his books. To date, the Cahiers have been published in their entirety only as photostatic reproductions, and only since 1980 have they begun to receive scholarly scrutiny. The Cahiers have been translated into English in five volumes published by Peter Lang with the title Cahiers/Notebooks.