From Pattern Bushes, a portfolio by Ben Lerner and Thomas Demand in The Paris Overview difficulty no. 212 (Spring 2015).
When requested if there was “an in depth intimacy” between him and his sister, André Weil replied, “Very a lot so. My sister as a baby all the time adopted me, and my grandmother, who preferred to drop into German sometimes, used to say that she was a veritable Kopiermaschine.” Biographers have emphasised—overly so, in keeping with André Weil—the episode described by his sister in a Might 1942 letter to Father Perrin, generally known as her “Non secular Autobiography”: “At fourteen I fell into a type of suits of bottomless despair which include adolescence, and I severely considered dying due to the mediocrity of my pure schools. The distinctive items of my brother, who had a childhood and youth corresponding to these of Pascal, introduced my very own inferiority house to me.”
The biggest a part of the identified correspondence between Simone and André Weil dates from the interval when André was imprisoned for being absent with out depart from his navy duties; he was held first in Le Havre, then Rouen, from February to early Might 1940. These circumstances gave Simone Weil a possibility to discover scientific, and significantly mathematical, questions that have been vital to her. Specifically, one should notice the significance given to the disaster of incommensurables in her correspondence. The rationale this second within the historical past of thought performs a central position at this level in Simone Weil’s reflection on science is properly outlined by André Weil in a letter dated March 28, 1940: “A proportion is what is known as; the truth that there are relations that aren’t nameable (and nameable is a relation between entire numbers), that there have been λόγοι ἄλόγοι, the phrase itself is so deeply shifting that I can’t consider that in a interval so basically dramatic … such a rare occasion might have been seen as a mere scientific discovery … what you say about proportion means that, on the beginnings of Greek thought, there was such an intense feeling of the disproportion between thought and world (and, as you say, between man and God) that they needed to construct a bridge over this abyss in any respect prices. That they thought they discovered it … in arithmetic is nothing if not credible.”
The disaster of purpose that Simone Weil apprehended in up to date physics led her to revisit the beginning of the scientific spirit. The connection between this disaster of science as a disaster of purpose and her curiosity within the query of incommensurables is evident. Rationalizing irrationals was on the coronary heart of the mathematical drawback of incommensurables. In accordance with Simone Weil’s interpretation, the identical issue was encountered in her day with quantum principle (see her examine “Classical Science and After,” in addition to the article “Reflections on Quantum Idea”). How will we rationalize what seems—in keeping with her interpretation—to be an “irrational” of this principle, particularly its makes use of of discontinuity and chance, notions on which the brand new physics rested? May the disaster of purpose, which can be a disaster of the notion of reality in up to date physics, trigger the identical psychological aberrations because the one produced by incommensurability, an aberration that led the Sophists to be skeptical of Logos and reality? Simone Weil’s references to Plato and her fixed attraction to a brand new Eudoxus characterize a want to flee the skepticism of a brand new sophistry. She would write to her brother: “The popularization of this discovery casts discredit upon the notion of reality that has lasted to today; it … contributed to the looks of the concept one can equally properly display two contradictory theories; the Sophists unfold this viewpoint among the many plenty, together with data of an inferior high quality, completely aimed on the conquest of energy.” This marriage of a purely operative and combinatory science with the search for energy is what Simone Weil feared.
—Robert Chenavier and André A. Devaux
Saturday [February 1940]
Expensive André,
I see that for the second your morale is nice. I hope this may final. Your letter introduced us appreciable consolation. You ask us for a lot of particulars; it’s not very simple. I don’t actually know what to let you know about myself; my life is at present devoid of any memorable occasions. I wrote an article evaluating politics in historical Rome to the occasions of our period for Les nouveaux cahiers [The new notebooks]; I discovered singular analogies, however I feel I already advised you about it final winter. Solely the primary a part of the article may very well be printed; it’s such a disgrace. In the midst of the preparatory studying I did, I found somebody admirable: it’s Theodoric, the one who has his sepulcher in Ravenna. Procopius, who was within the camp against him, stated that in his whole reign he solely dedicated one injustice, and that he died of sorrow over it. His letters (Theodoric’s) are pleasant. Apart from that there’s an article by me on the Iliad awaiting publication by the N.R.F. I don’t know what is going to come of it. It incorporates bits of translation during which I used to be ready, for sure traces, to maintain the precise order of the phrases; in any case I used to be all the time in a position to translate line by line, I imply to have one line (of irregular size) of the French textual content correspond to every line of verse. If you realize bits of the Iliad by coronary heart, you possibly can attempt to translate them; while you use a way like this one, it typically takes a half hour or extra to complete a line. It’s additionally glorious for forming fashion. Translating Keats into French (in French verse, for instance) should even be a enjoyable train. I’ve by no means tried.
A very good occupation when one has an excessive amount of time would even be to think about a approach to let laypeople resembling myself glimpse what precisely the curiosity and significance of your work is. For even though that it’s completely not possible, as you keep, the actual fact of making an attempt certainly wouldn’t be with out profit to you. The profit can be, I feel, appreciable. And even in the event you don’t reach formulating one thing I can perceive, I feel I’d glimpse sufficient for it to be extraordinarily fascinating to me. Particularly since I’m much less desirous about arithmetic than in mathematicians, as with each different discipline.
To return again to me, lastly, to utilize these moments when my capability for work is weak (they’re frequent), I’ve began finding out Babylonian. I’ve a collection of Assyro-Babylonian texts, with the textual content transcribed in Latin characters, and the interpretation reverse, line by line; I’m taking part in round with making a juxtalinear translation and not using a grammar or a dictionary. On this manner, I made the acquaintance of a sure Gilgamesh, the hero of an epic translated from the Sumerian. Friendship is its driving spirit; Gilgamesh loses his pal and instantly begins fearing loss of life and working by the desert in search of everlasting life, however he doesn’t discover it. Later, he evokes his lifeless pal’s shadow, which supplies him not very comforting details about existence past the grave. I learn just a few phrases traces of it to Evelyne, who has already retained just a few phrases of Babylonian from it. As language and as poetry, it’s removed from being nearly as good as Homeric Greek. Egyptian can be extra fascinating, nevertheless it’s too laborious.
See you quickly, I hope. I hope we’ll be capable of deliver you books. Would you like Retz’s Memoirs and Pepys’s Diary? I deeply hope we’ll be capable of see one another tomorrow or the day after tomorrow, because it’s not possible for us to commerce locations, which might be my deepest want.
Simone
[February 1940]
Expensive André,
We nonetheless want to attend somewhat, it seems, earlier than we’ve the authorization to see you as a lot as we wish. Within the meantime, there’s nothing to do however write. However I hope that with some paper and books now, you aren’t bored, and that you simply train to maintain in good condition.
Who is aware of, possibly you’ll uncover some fascinating issues? However right here’s one other distraction, now that you’ve got leisure time. I don’t bear in mind if I advised you about this within the letter I wrote you from Le Havre, and that you could have acquired by now, however by no means thoughts. It could be to search for a approach to make commoners (me, for instance) recognize the worth of your present analysis. I’m positive this is able to be an excellent train for you. What do you threat? You don’t threat losing your time, since you’ve time to waste. It’s all superb and dandy so that you can make enjoyable of individuals like one in every of my former mates at rue d’Ulm who philosophize about arithmetic with out realizing something about it, however maybe it’s the mathematicians themselves who ought to strive to do that work. Not like your pal Claude, in fact. Not just like the hero of Balzac’s Unknown Masterpiece when he meditates on portray. However possibly there’s a manner for one to turn out to be conscious of what one is doing, and the worth in what one is doing. And if one turns into conscious of it, it should be doable to let nonspecialists at the very least get a glimpse of it. What wouldn’t it value you to strive? I’d be fascinated.
I feel you have been already now not in Paris after I managed to get a duplicate of the e-book on Babylonian and Egyptian arithmetic. I don’t know if I wrote you that I used to be in a position to get it. I wish to write to the creator a few query he leaves unresolved, that of the means by which the Egyptians have been ready, with a geometry he considers extraordinarily crude and empirical, to discover a remarkably correct approximation of π, that’s to say floor space of the circle = (8/9d)^2. This appears fairly simple to think about, if one assumes the strategies are very crude. If the circumscribed sq. is split into eighty-one little squares, one can take into account that the circle’s floor space might be discovered by subtracting three of those squares from every nook, plus the approximate sum of three half-squares.
There’s a very pleasant Babylonian drawback. One is given the scale of a canal to be dug, a employee’s every day output in quantity of earth displaced, and the sum of workdays and staff. One should discover the variety of workdays and that of staff. I’m wondering what college students’ dad and mom would say if an examination right this moment included an issue formulated in comparable phrases? It could be enjoyable to strive it. Unusual individuals, these Babylonians. Personally, I don’t very similar to this summary considering. The Sumerians will need to have been much more congenial. Initially, they’re those who invented all of the Mesopotamian myths, and myths are much more fascinating than algebra. However you, you should be straight descended from the Babylonians. As for me, I do suppose that God, because the Pythagoreans put it, is ever a geometer—however not an algebraist. Be that as it could, I used to be happy, after I learn the final letter I acquired from you, to see that you simply denied being a member of the summary faculty.
I keep in mind that at Chançay or Dieu-le match [sic] you stated that these research of Egypt and Babylon solid doubt on the position heretofore attributed to the Greeks as creators within the self-discipline of arithmetic. Quite the opposite, I feel that to this point (topic to later discoveries) they supply a affirmation of this position. The Babylonians seem to have targeted on summary workout routines regarding numbers, the Egyptians to have proceeded in a very empirical method—The applying of a rational technique to concrete issues and to the examine of nature appears to have been particular to the Greeks. (It’s true that one would wish to know Babylonian astronomy to have the ability to decide.) What’s singular is that the Greeks will need to have identified Babylonian algebra, and but one doesn’t discover a hint of it in them earlier than Diophantus (who lived, if I’m not mistaken, within the fourth century A.D.). The Pythagoreans’ algebraic geometry is one thing else completely. Spiritual conceptions should be behind this; apparently the Pythagoreans’ secret faith made use of geometry, and never algebra. If the Roman empire hadn’t destroyed all of the esoteric cults, possibly we’d perceive one thing about these enigmas.
I feel I advised you that I printed half a examine evaluating historical Rome to sure up to date phenomena in Les nouveaux cahiers. The second half was deeply appreciated by those that had the chance to learn it, however their numbers have been very restricted. The primary half bought me a letter that gave us a superb snigger and which I’ll copy for you right here:
Madam,
Lowered to immobility and never realizing “who” I might seek the advice of, I flip to you to tell me: Who’re you? An article within the January 1st difficulty of Les nouveaux cahiers is behind this query.
Sincerely,
The signature is unknown to me. Your mom thinks it’s somebody burning with a want to avenge the Romans, and that “decreased to immobility” means: If I wasn’t decreased to immobility, I’d present you. … On the off likelihood, I didn’t reply. I wished to answer: And also you, sir?—or else: sum qui sum—or to ship a photograph of myself—or a duplicate of my identification card. Nevertheless it nonetheless appeared preferable to me to save lots of twenty sous. He won’t ever know who I’m. The query is formulated in a very admirable method.
I’m solely telling you about issues of no curiosity, however I don’t discover “cast-iron prose” on the tip of my pen day-after-day.
Thanks for saying that the longer term wants me, however, as I see it, it doesn’t want me any greater than I want it. If solely I had a time-travel machine, I wouldn’t level it on the future, I’d level it on the previous. And I wouldn’t even cease on the Greeks, I’d go at the very least so far as the Aegeo-Cretan period. However the mere thought takes impact on me as a mirage would on a person misplaced within the desert. It makes me thirsty. It’s higher not to consider it, since we’re confined on this tiny planet and it’ll solely turn out to be huge, fertile, and various once more, because it as soon as was, lengthy after us—if it ever does once more.
Within the meantime, get pleasure from Aeschylus and the Sanskrit texts, which I hope you’ll quickly obtain.
Simone
[March 1940]
My pricey brother,
I’m sending again your dedication in a barely modified model. You’ll discover the explanations for the modifications your self, I feel. Most are prompted by issues with logic and magnificence, and particularly the priority with preserving the unity of tone. I’m inclined to completely reduce the metaphor about sowing, wheat, and so on., as a result of it’s actually not within the Louis XIII fashion of the entire thing, and the distinction is damaging. (Moreover, the time period plowing on this metaphor couldn’t be extra unsuitable, for apparent causes.) I barely modified the phrases of the temple metaphor, primarily for a similar purpose (to keep away from a break within the unity of tone), and in addition to attenuate it and make it somewhat vaguer; it could prob ably be unpleasant for É[lie] Cartan, and in each respect inappropriate, for it to be written in such a manner as to recommend an opposition between him, alone on one aspect, and everybody else on the opposite. Within the final line, I modified one phrase, as a result of your lawyer completely advises in opposition to leaving the one you used. General, I believed it smart to vary just a few nuances of element that might lead ill-intentioned individuals to doubt whether or not you’re severely expressing what you suppose.
Now simply use these options as you please, and ship Henri Cartan the definitive textual content you’ve settled on.
I feel it’s higher to surrender on the: “To Monsieur Monsieur …” One reader in 100 would possibly know this was the customized within the seventeenth century, and even he gained’t suppose it’s severe.
We’ve given the proofs to the writer. He’s asking for the dedication as quickly as doable, in fact.
I’m happy to see that studying my pal Retz has given you a style for that interval’s fashion. It’s infinitely superior, in my opinion, to that of the second half of the seventeenth century.
Fraternally,
Simone
[March 1940]
My pricey brother,
No matter you say about it, “some disquiet,” works very properly. However discussing particulars of favor in writing can be lengthy and tiresome. I feel your textual content has now reached the state of perfection, if as Valéry places it perfection is outlined by the exhaustion of the need to switch.
How might you’re taking my coadjutor for a Neapolitan! What blasphemy! Has anybody ever come out of there, by way of political geniuses, apart from low schemers? Doesn’t he exude Florence from each pore? And don’t you bear in mind the Gondi Palace, in Florence, on Piazza della Signoria, set again on the left when one seems on the palace della Signoria? It isn’t adorned with a lot, however is most lovely. I suppose the Neapolitan abbot you communicate of is Abbot Galiani; all I’ve learn by him are excerpts of letters, however I’m fairly positive he had little or no in frequent with Retz. In Mme d’Épinay’s entourage, there have been solely frivolous, skeptical individuals with low souls. Whereas my coadjutor was at first an trustworthy man and a fantastic soul, although that’s considerably hidden beneath the heap of adroitly intertwined intrigues. Right now he would possibly give the impression of a traitor, as a result of in that joyful interval there have been no political events, and loyalty to an summary thought, even a non secular one, would have appeared utter foolishness. One was loyal to residing human beings to whom one was sure by friendship, by commitments made, by the responsibility of safety or obedience, or by esteem. In that sense, the priority for loyalty and honor dominates all my coadjutor’s intrigues. The priority for public good additionally dominates them. The sense of every thing he did was a determined try and destroy Richelieu’s work; when he was defeated, one thing perished forever. The start of the seventeenth century was, in France, Spain, and England, one thing terribly luminous; an undefinable inspiration reached its peak right here and perished impulsively, by no means to reappear. Personally, excluding Racine, I don’t esteem something that got here after 1660 (to the current day) as a lot as what got here earlier than. I’m not together with Corneille, for whom I don’t have a lot esteem the least bit. However have I advised you about Théophile?
Les astres dont la bienveillance
Se despatched forcer de ta vaillance
Sont apprêtés pour t’accueillir;
Déjà leur splendeur t’environne;
Dieu comme fleurs les vient cueillir
Pour t’en donner une couronne
Qui ne pourra jamais vieillir.
(Ode à Guillaume d’Orange)[The stars whose benevolence
Feels strengthened by your valor
Are ready to welcome you;
Already their splendor surrounds you;
God picks them like flowers
To give you a crown of them
That will never age.]
And this, on the civil battle of 1620 (during which Richelieu was on the insurgent aspect, by the best way)
La campagne était allumée
L’air gros de bruit et de fumée,
Le ciel confus de nos débats,
Le jour triste de notre gloire,
Et le sang match rougir la Loire
De la honte de vos combats.[The countryside was burning
The air thick with noise and smoke,
The sky chaotic with our disputes,
The day sorrowful with our glory,
And blood made the Loire blush
With shame for our battles.]
And doesn’t this appear to be the most effective of Valéry?
Je sentis mon sang se geler
Et comme autour de moi voler
L’ombre de ma douleur future.[I felt my blood freeze
And as if around me there flew
The shadow of my future pain.]
He too had that sense of friendship and that generosity of soul that hasn’t been seen since that interval. He wrote to Balzac: “What acquires me mates and the envious is just the easiness of my morals, an incorruptible loyalty and the open career I make to like completely those that are with out fraud and cowardice.”
Naturally, he was made to undergo horribly and die prematurely. If he’d had somewhat baseness in his soul, he might have lived to a ripe outdated age, and would maybe be regarded right this moment as one of many two or three best French poets. Personally, I see Villon, Maurice Scève, him, and Racine as above all of the others, and by far.
I’m undecided that the invention of incommensurables is a ample rationalization for the Greeks’ obstinate refusal of algebra. They will need to have identified Babylonian algebra from the start. Custom holds that Pythagoras traveled to Babylon to check there. Naturally, they transposed this algebra into geometry, lengthy earlier than Apollonius. Transpositions of this type present in Apollonius in all probability concern quadratic equations; these of the second diploma might all be solved as soon as the properties of the triangle inscribed within the semicircle have been identified, a discovery attributed to Pythagoras.
(This fashion one finds two portions of which both the sum and product are identified, or the distinction and product.) However the singular factor is that this transposition of algebra into geometry appears to not be a aspect difficulty, however the very mainspring of geometric invention all through the historical past of Greek geometry.
The legend regarding Thales’s discovery of the similarity of triangles (when a person’s shadow is the same as the person, the pyramid’s shadow is the same as the pyramid) relates this discovery to the issue of a proportion whose time period is unknown.
We all know nothing of the next discovery, by Pythagoras, of the properties of the suitable triangle. However right here is my speculation, which is definitely in line with the spirit of Pythagorean analysis. It’s that this discovery comes from the issue of discovering the imply proportional of two identified portions. Two comparable triangles having two noncorresponding equal sides characterize a proportion with three phrases:
If the 2 extremes are constructed on a single straight line, the determine turns into a proper triangle (for the reason that angle between a and b turns into a straight angle, half of which is a proper angle). The fitting triangle’s important property is that it’s shaped by the juxtaposition of two triangles much like it and to one another. I feel that Pythagoras found this property first. The fitting triangle additionally gives the answer to the alternative drawback: if the imply proportional and the sum or distinction of the extremes are identified, discover the extremes.
As for conics and their properties, the inventor on this case is alleged to be Plato’s pupil Menaechmus, one of many two geometers who solved the issue of doubling the dice posed by Apollo. (The opposite is Archytas; he solved it with the torus.) Menaechmus solved this drawback with conics (two parabolas, or a parabola and a hyperbola). So, it doesn’t appear unlikely to me that he invented them for this objective. And the issue of doubling the dice comes right down to discovering two imply proportionals between two identified portions.
It’s simple to think about the method of the invention. For the cone consists of a circle of variable diameter, and the parabola gives the sequence of all of the imply proportionals between a hard and fast time period and a variable one.
So, there’s a steady sequence of issues: a proportion with 4 phrases of which one unknown— a geometrical development with three phrases of which the center time period is unknown—a development with 4 phrases of which the 2 center phrases are unknown.
Simply as the suitable triangle’s properties made it doable to resolve second-degree issues, these of the conics made it doable to resolve these of the third and fourth.
Observe that whereas we resolve the equations by supposing that the expressions √,∛, and so on., have that means, the Greeks gave them a that means earlier than tackling the equations of corresponding diploma.
Additionally notice that the assimilation of the unknown to a variable goes again at the very least so far as Menaechmus, if not additional. One can hardly suppose that the Babylonians, with their numerical equations, had this notion. The fifth-century Greeks had the notion of perform and of representing features by traces. The story of Menaechmus gives the look that for them curves have been a way of finding out features, moderately than an object of examine in their very own proper.
In all this, one sees progress whose continuity is rarely interrupted by the disaster of incommensurables. To make sure, there was a disaster of incommensurables, and its affect was immense. The popularization of this discovery solid discredit on the notion of reality that endures to today; it led to, or at the very least contributed to bringing about the concept one can equally display two contradictory theories; the Sophists unfold this viewpoint among the many plenty, together with data of an inferior high quality, completely aimed on the conquest of energy; beginning within the late fifth century, it resulted within the demagogy and imperialism from which it’s inseparable, with penalties that ruined Hellenic civilization; it’s by this course of (to which different elements such because the Greco-Persian Wars naturally contributed) that Roman weapons have been lastly in a position to kill Greece, with none doable resurrection. My conclusion is that the gods have been proper to have the Pythagorean responsible of divulging the invention of incommensurables perish in a shipwreck.
However I don’t suppose there was a disaster among the many geometers and philosophers. Pythagoreanism was ruined (insofar because it was) by one thing completely totally different, particularly the mass bloodbath of Pythagoreans in Magna Graecia. In actual fact the star pentagon, which represents a relation between incommensurables (the division of a line into excessive and imply ratio), was one of many Pythagoreans’ symbols. However Archytas (one of many survivors) was a fantastic geometer, and he was the instructor of Eudoxus, who’s accountable for the speculation of actual numbers, the notion of restrict, and the notion of integration as described in Euclid. There’s nothing to recommend that when the Pythagoreans spoke of numbers, they solely meant entire numbers. Quite the opposite, by saying that justice, and so on., and so on., are numbers, they made clear, it appears to me, that they have been utilizing this phrase to confer with any form of proportion. They have been definitely able to conceiving of actual numbers.
For my part, the important level of the invention of incommensurables lies outdoors of geometry. It consists of the truth that sure issues regarding numbers can typically have an answer and typically be insoluble; for instance, that of a imply proportional between two given numbers. That alone suffices to show that the quantity within the slim sense of the phrase just isn’t the important thing to each factor. Now, when was this realized? I don’t know if there’s any details about this. In any case, it was doable to understand it earlier than geometry; one merely wanted to make a particular examine of issues of proportion. And in that case the geometric course of to search out imply proportionals (top of the suitable triangle) would instantly have appeared, as quickly because it was found, as not being topic to any comparable limitation. A lot in order that one can surprise if the Greeks may need studied the triangle to search out proportions expressible different smart than in entire numbers, and if consequently they could have conceived of the road as a perform from the beginning, as they later did with the parabola. One can discover objections to this principle, however in my view they fall flat if one remembers the position secrecy performed amongst Greek thinkers and their customized of solely diffusing by distorting. The truth that Eudoxus is the creator of an ideal and accomplished principle of actual numbers on no account guidelines out that the geometers might have glimpsed this notion from the start and continually strived to know it.
One would possibly ask oneself why the Greeks have been so dedicated to the examine of proportion. It’s definitely a query of spiritual preoccupation, and consequently (since we’re speaking about Greece) {a partially} aesthetic one. The hyperlink between mathematical preoccupations on the one hand and philosophical-religious ones on the opposite, a hyperlink that’s traditionally identified to have existed in Pythagoras’s period, definitely goes again a lot additional than that. For Plato is a traditionalist to the acute and infrequently says, “the ancients who have been a lot nearer to the sunshine than we’re …” (clearly alluding to an Antiquity much more distant than that of Pythagoras); moreover, he posted “Nobody enters right here who just isn’t a geometer” on the door of the Academy and stated, “God is ever a geometer.” The 2 attitudes can be contradictory—which can’t be—if the preoccupations from which Greek geometry arose (if not the geometry itself) didn’t date again to early Antiquity; one can suppose that they arrive both from the pre-Hellenic inhabitants of Greece, or from Egypt, or each. Moreover, orphism (which has this twin origin) was such an inspiration to Pythagoreanism and Platonism (that are virtually equal) that one can surprise if Pythagoras and Plato did rather more than touch upon it. Thales was nearly definitely initiated into Greek and Egyptian mysteries, and was consequently steeped, from a philosophical and spiritual perspective, in an environment much like that of Pythagoreanism.
I due to this fact suppose that the notion of proportion had been since fairly a distant Antiquity the article of a meditation that constituted one of many processes for purifying the soul, maybe the principal course of. There might be little question that this notion was on the heart of the Greeks’ aesthetics, geometry, and philosophy.
The Greeks’ originality by way of arithmetic isn’t, as I see it, their refusal to simply accept approximation. There is no such thing as a approximation within the Babylonian issues, and for a quite simple purpose: it’s as a result of they’re constructed from the options. Thus there are dozens (or a whole lot, I don’t bear in mind) of fourth-degree issues with two unknowns that each one have the identical answer. This reveals that the Babylonians have been solely within the technique, and never in fixing issues really posed. Likewise, in the issue of the canal I discussed to you, the sum of staff and workdays is clearly by no means given. They loved supposing unknown what’s given, and identified what just isn’t. It’s a recreation, clearly, that does the best honor to their conception of “disinterested analysis” (did they’ve scholarships and medals to stimulate them?). Nevertheless it’s solely a recreation.
This recreation will need to have appeared profane to the Greeks, and even impious; different smart why wouldn’t they’ve translated the algebra treatises that will need to have existed in Babylonian on the identical time that they transposed them into geometry? Diophantus’s work might have been written many centuries earlier. However the Greeks didn’t see any worth in a way of reasoning for its personal sake, they valued it insofar because it allowed the efficient examine of concrete issues; not that they have been avid for technical purposes, however as a result of their sole object was to conceive increasingly clearly of an identification of construction between the human thoughts and the universe. Purity of soul was their solely concern; “imitating God” was its secret; the examine of arithmetic helped to mimic God insofar as one noticed the universe as topic to mathematical legal guidelines, which made the geometer an imitator of the supreme legislator. It’s clear that the Babylonians’ mathematical video games, the place the answer was given earlier than the info, have been ineffective to this finish. What was wanted was knowledge really supplied by the world or motion on the world; so what was wanted was to search out ratios that didn’t require the issues to be artificially ready to “come out proper,” as is the case with entire numbers.
It’s for the Greeks that arithmetic was actually an artwork. Its objective was the identical as the aim of their artwork, particularly to make perceptible a kinship between the human thoughts and the universe, to make the world seem as “the town of all rational beings.” And it was actually product of stable matter, matter that existed, like that of all the humanities with out exception, within the bodily sense of the phrase; this matter was area really given, imposed as a de facto situation to all of man’s actions. Their geometry was a science of nature; their physics (I’m considering of the Pythagoreans’ music, and particularly of Archimedes’ mechanics and his examine of floating our bodies) was a geometry during which the hypotheses have been introduced as postulates.
I worry that right this moment it’s moderately towards the Babylonian conception that we’re shifting, in different phrases taking part in video games moderately than making artwork. I’m wondering what number of mathematicians right this moment see arithmetic as a course of aimed toward purifying the soul and “imitating God”? What’s extra, it appears to me that the matter is missing. There’s a variety of axiomatics, which appears to be nearer to the Greeks, however aren’t the axioms largely chosen at will? You communicate of “stable matter,” however isn’t this matter basically shaped by the whole thing of mathematical work completed to today? In that case, present arithmetic can be a display between man and the universe (and consequently between man and God, as understood by the Greeks) as a substitute of placing them in touch. However maybe I’m disparaging it.
Talking of the Greeks, have you ever heard of a sure Autran, who has simply printed a e-book about Homer? He has put ahead a sensational principle, particularly that the Lycians and the Phoenicians of the second millennium B.C. have been Dravidians. His arguments, that are philological, don’t look like unworthy of curiosity, as a lot as one can decide with out realizing the Dravidian languages and the inscriptions he quotes. However the principle is most interesting— too interesting, even—in that it offers an very simple rationalization of the analogies between Greek and Indian thought. Local weather is perhaps ample rationalization for the variations. Be that as it could, how might one assist feeling nostalgic for an period during which the identical thought was discovered in every single place, amongst all of the peoples, in all of the nations, the place concepts circulated over a prodigious expanse, and during which one loved all of the riches of range? Right now, as beneath the Roman Empire, uniformity has descended upon each factor, erasing all of the traditions, and on the identical time concepts have virtually stopped circulating. Properly! Maybe in a thousand years it will likely be a bit higher.
Fraternally,
Simone
Translated from the French by Nicholas Elliot.
From A Life in Letters, edited by Robert Chenavier and André A. Devaux in collaboration with Marie-Noëlle Chenavier-Jullien, Annette Devaux, and Olivier Rey and translated by Nicholas Elliot, to be printed this month by the Bellknap Press of Harvard College Press.
Simone Weil (1909–1943) was a French thinker, mystic, and political activist, broadly thought-about one of the crucial unique thinkers of the 20 th century.
Robert Chenavier is president of the Affiliation for the Research of Simone Weil’s Thought and the creator of 4 books, most not too long ago Simone Weil, une Juive antisémite?
André A. Devaux (1921–2017) was a professor of philosophy on the Sorbonne.
Nicholas Elliott is a author and translator based mostly in New York Metropolis. He has labored extensively in theatre in New York and France, is a contributing editor for movie at BOMB journal, and was the American correspondent for the French movie journal Cahiers du cinéma from 2009 to 2020.
