Mathematics dates our wound from the time of the ancient Sumerians1 and their sexagesimal number system. This is the wound we suffered when, after 300,000 years of human existence, quantity became more important than quality.
Mathematics cuts deeply into what we know. And we bleed a new strangeness that shames us into facing what we are not. Bless that.
No mathematician cuts deeper than Alexander Grothendieck2, one of the founders of algebraic geometry3. Trance and transformation4 merge in his innovative methods. They touch us with a topology called vector spaces5, where touched means mad and mad means crazy and crazy6 means infinite-dimensional space7.
With Grothendieck, back in the 1950s, quantity began to transform into a mad quality, and the Sumerian wound started to heal. Such an ancient wound did not heal easily. Grothendieck’s contribution of topological vector spaces8 did the stitching. The scar that eventually formed mended a decades-old paradox now known as the Einstein, Podolsky, and Rosen paradox9.
EPR predicted entanglement10 in quantum physics – the cornerstone of the qubit11 and quantum computing. From this, we witness how mathematics bridges the known world and our symbolic inner ecology12. There, in between domains, the realistic and the abstract coalesce into a landscape where there is nothing to say.
I’ll say it anyway. Mathematics is the deep space we fall through. Reality is the underside of the dream where we land.13
1 3,000 BCE
2 (1928 – 2014) perhaps the greatest mathematician of the 20th century.
3 most simply, the study of curves and surfaces using algebra (polynomial equations).
4 a poetic reference to Grothendieck’s intuitive, trancelike ability to use what he called ‘yoga’ and ‘Ariadne’s thread’ to generate “meta-theories” that transform complex geometries into algebraic structures.
5 a collection (set) of mathematical objects (vectors) that can be added or multiplied by simple numbers (scalars).
6 touched, mad, crazy: synonyms for insanity, used here to echo the psychosis Grothendieck suffered later in his life. Above is a photo of Grothendieck in the peasant’s garb he favored during the schizotypy of his final years.
7 a space (a set of measurable points) with an uncountable number of vectors (quantities that can’t be expressed with a single number; e.g. magnitude plus direction).
8 a set of measurable points that allow for connections and continuity.
9 Einstein and his colleagues’ effort to show the absurdity of the Copenhagen Interpretation in which quantum states (subatomic particles like electrons) exist in superposition (multiple states) until measured.
10 particles that interact instantaneously even when separated by large distances.
11 a binary state of information: a bit can be 1 or 0; a qubit is both: 1/0.
12 the dynamic relationship among subjective mental states such as fantasies, memories, and dreams.
13 our biological interpretation of reality is the phenomenal universe science measures, our human dream.