Grothendieck has revolutionized the notion of mathematical space, as Einstein did in physics. He invented a new geometry, in which « the arithmetic world and the world of continuous quantities are now one ».
To combine the discontinuous and the continuous, the numbers and the quantities, to make them unite intimately, Grothendieck conceived the metaphor of their « marriages ». This marriage of paper had to be followed by proper consumption, in order to ensure the generation of new mathematical beings.
« For the expected ‘brides’,’of numbers and greatness’, it was like a decidedly narrow bed, where only one of the future spouses (i.e., the bride) could at least find a place to nestle as best as they could, but never both at the same time! The « new principle » that remained to be found, to consume the marriage promised by favourable fairies, was also that this spacious « bed » that the future spouses were missing, without anyone having only noticed it until then. This « double bed » appeared (as if by a magic wand…) with the idea of topos. » i
Grothendieck, the greatest mathematical thinker of the 20th century, explained a revolutionary breakthrough using a matrimonial metaphor, and all that follows.
Indeed, the metaphor of « marriage » has always been used to translate difficult ideas into philosophical contexts.
Two thousand years ago, the Jewish philosopher Philo of Alexandria used this same metaphor to present the « mystery of the divine generation ». To translate the idea of « divine generation » into Greek, Philo uses the word τελετή (‘telete’).
This mystery is composed of three elements. There are the two initial « causes » of the generation and their final product.
The two causes are God and Wisdom (who is « the bride of God », – remaining « virgin »)ii.
Wisdom is Virginity itself. Philo relies on the authority of the prophet Isaiah, who affirms that God unites himself with Virginity in itself.iii
Philo specifies elsewhere: « God and Wisdom are the father and mother of the world ».iv
In the Christian tradition, there are similar metaphors, derived from Jewish ideas, but transposed into the « union » of Christ and the Church.
A 16th century Christian cabalist, Guillaume Postel, uses the metaphor of the love of the male and female to describe this union:
« For as there is love of the male to the female, by which she is bound, so there is love and bond of the female to the male by which she is bound. This is the mystery of the most wonderful secret of the Church’s authority over God and Heaven, as well as over God and Heaven on Church by which Jesus meant it: Whatever you bind on earth will be bound to Heaven. »v
Teresa of Avila, a contemporary of Guillaume Postel, speaks through experience of « perfect union with God, called spiritual marriage »:
« God and the soul are one, like crystal and the ray of sunlight that penetrates it, like coal and fire, like the light of the stars and the light of the sun (…) To give an idea of what it receives from God in this divine cellar of union, the soul is content to say these words (and I do not see that it could better say to express something of them):
From my Beloved I drank.
For as the wine that we drink spreads and penetrates into all the limbs and veins of the body, so this communication of God spreads to the whole soul (…) The Bride speaks of it in these terms in the book of Songs: ‘My soul has become liquefied as soon as the Bridegroom has spoken’. »vi
Therese of Avila speaks of the Bride « burning with the desire to finally reach the kiss of union with the Bridegroom », quoting the Song of Songs: « There you shall teach me ».
The Song of Songs has incestuous resonances:
« Oh, what a brother to me, breastfed in my mother’s womb! Meeting you outside, I could kiss you, without people despising me. I’ll drive you, I’ll introduce you to my mother’s house, you’ll teach me! I’ll make you drink a fragrant wine, my pomegranate liqueur. »vii
This spicy passage was strangely interpreted by S. François de Sales:
« And these are the tastes that will come, these are the ecstasies, these are the summits of the powers; so that the sacred wife asks for pillows to sleep. »viii
Metaphors! Metaphors! Where do you lead us to?
iRécoltes et Semailles, §2.13 Les topos — ou le lit à deux places
iiPhilo of Alexandria. De Cherubim
iii Is. 66, 6-9
iv De Ebrietate, 30
v Guillaume Postel (1510-1581). Interprétation du Candélabre de Moïse (Venise 1548).« Car comme il y a amour du masle à la femelle, par laquelle elle est liée, aussi y a-t-il amour et lien de la femelle au masle par lequel il est lyé. Cecy est le mistère du très merveilleux secret de l’authorité de l’Eglise sur Dieu et sur le Ciel, comme de Dieu et du Ciel sur icelle par lequel Jésus l’a voulu dire : Ce que vous lierez sur la terre sera lyé au Ciel. »
viTeresa of Avila (1515-1582). The Interior Castle
viiiFrançois de Sales. Œuvres complètes. p. 706
When do you need a ‘veil’ ?
There are strong reasons to wear a veil, under certain circumstances. For example, it reads:
« And Moses hid his face, for he was afraid to look upon God. »i
Or: « When Moses had finished speaking to them, he put a veil over his face. »ii
In both cases, the veil seems to be justified, for very different reasons.
But there are times when, clearly, you have to remove the veil. For example:
« When Moses entered before the Lord to speak with him, he took off the veil until he came out. »iii
How can we explain that Moses sometimes veils himself, and sometimes reveals himself, when he is in the presence of God?
Moses, it seems to me, makes an essential difference between watching and speaking.
To make a long story short, this difference is as follows: the gaze kills, the word gives life.
It is certain that there is mortal danger in « seeing » the face of God. « Man cannot see me and live. »iv
To overcome this risk, Moses only looks at God’s « back » or the « cloud » in which He hides.
On the contrary, the word is the very instrument of prophecy. It does not kill, it gives life.
With a capital letter, the Word is Wisdom, Verb, Logos. It is even placed at the right hand of God, like Adonaiv. It names the Name. It sets out the Law.
In the extreme, the Word is a « scream ». More precisely, three screams.
It reads: « The Lord passed before him and screamed: ‘YHVH, YHVH, God, merciful and gracious!’ » vi
Why does God shout His name to Moses three times?
Why does He shout His name ‘YHVH’ twice in a row, and His name ‘EL’ a third time?
These three screams are not addressed to Moses alone, maybe.
They must be heard, long after, by all those who were not there, – all of humanity yet to come.
In order for these ‘names’ to be heard long after Moses days, they had to be screamed, to be shouted, very loud, to reach the extremities of Mankind. But above all, they had to be written.
« Put these words in writing »vii.
Words, screams, writings. How do you put a scream in writing ? With capital letters? There are none in Hebrew.
If Moses had put on a veil, he would not have « seen », and above all he would have heard badly enough, one can speculate – except for the screams. But, for sure, with a veil he could not have written.
And he could not have spoken (audibly). Moses did not have an easy wordviii. With a veil over his face, he would have been even more embarrassed to speak distinctly.
The veil would have been a barrier to exchange. It was therefore not really necessary, it was even strongly discouraged.
Especially since the interview environment was very noisy. « Moses was speaking and God was answering him in thunder. »ix
Moses had previously put a veil over his face for fear of dying in front of the Face, or when he had wanted to hide his own « shining » face from the Israelites.
The veil was then necessary, it seems, as a defence (against death) or as a modesty (against the jealousy of the people).
But when it came to speaking, hearing, writing, then Moses removed the veil.
The lesson is still valid today.
i Ex. 3,6
ii Ex. 34,33
iii Ex. 34, 34
iv Ex. 33,20
v Ps. 110 (109) -1
vi Ex. 34,6
vii Ex. 34,27
viii Ex. 6,30