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
viiCt
8,1-2
viiiFrançois
de Sales. Œuvres
complètes. p. 706
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