What's Inside? The Outside.

"God is ever a geometer."  Pythagorean motto

Ever watch the TV series "Numb3ers"?  The plot went like this:  someone commits a crime, and a brilliant mathematician solves it with equations.  This was "CSI" for math fans. 

"Numb3ers" embodied a 3,000 year-old notion: Numbers Rule.  Ancient Greeks believed that numbers—more precisely, ratio and proportion—saturated the fabric of the universe, from micro to macro, dirt to divinity.  

Pythagoras, that 6th century BC religious guru of triangle fame, was the original "Numb3rs" guy. He (or his followers) believed that planets moved around the earth with the same mathematical ratios found in harmonic intervals (octaves, 2:1; fourths, 4:3;fifths, 3:2,etc.), thus creating "the music of the spheres."

Doryphoros of Polykleitos, 450-400 BC: ideal  proportions

To classical Greeks, this idea of ratio and proportion as universal organizing principles was brain candy. They believed, for example, that healthy people contained the right proportions of earth, air, fire and water.  They also found the harmonics of celestial spheres was reflected in the proportions of human anatomy. Thus, the body’s interior was a sort of celestial atlas (and easier to study!). To know one was to know the other.  Either way, ratio—“reason”— and proportion were keys to decrypting the secrets of the big and the small. To investigate  this was to understand “order,” or, as the Greeks put it, “cosmos.” 

Parthenon

Brain candy became eye candy.  Greek sculptors and architects portrayed the human form and religious sites with symmetry and precision.  They reasoned, as we do still, by analogy.  Mathematics, art, anatomy, architecture, astronomy, music, even religion:  all are cut from the same bolt of cloth. (No academic silos here!)  The Parthenon is a prime example, not only for its mathematical and esthetic qualities, but also because it was synched with the stars.  What’s down here is what’s up there; what’s inside is what’s outside.  Above all, this meant the universe was orderly and  intelligible.  And that which could be known could also—perhaps—be controlled.  How cool is that?

1480s? Scanned from Trattato di architettura di Francesco di Giorgio Martini by Francesco di Giorgio http://leonardodavinci.stanford.edu/submissions/clabaugh/history/architecture.html

The Romans grabbed this idea and sprinted. Vitruvius, a 1^st century BC engineer and architect, understood the conjunction of anatomy and architecture, between what’s inside and what’s outside, between the micro and the macro.  In designing public spaces such as temples and other buildings, he made concrete the “cosmos” of the Roman empire.  Such structures weren't just buildings; they embodied the order Rome would bring to the world.  Taking a cue from Greek painters, sculptors and architects, Vitruvius described man's  ideal anatomical proportions in his Ten Books on Architecture.  These proportions, in turn, became the blueprints for Rome’s “living buildings”—and Rome's imperial vision. Vitruvius's designs thus legitimated imperial rule and, not incidentally, the divinity of Augustus, Rome's first emperor. 

da Vinci's Vitruvian Man, c. 1490

Fast forward to the 15^th century, when Leonardo da Vinci  read Vitruvius's Ten Books.  Da Vinci (preceded by others) sketched the ideal human as his own Vitruvian Man—a perfectly proportioned human form, his navel is centered exactly in a circle (symbol of the perfection of the universe) and a square (the earth)…in sum, an artistic, mathematical, cosmological expression of the Divine Geometrician’s creation, and man’s place in it.   Micro and macro, inside and outside, what’s up there and what’s down here:  Vitruvian Man embodied this “cosmos.”  

Fast forward again to the present, where environmental and biodiversity programs offer interesting parallels to all of this.  Take, for example, the Human Microbiome Project. One of the Project’s goals is to investigate the proportions of microbes on our skin and in our guts. If the proportion of these various communities gets out of whack, bad things happen.  But not to worry:  re-establishing the “intestinal cosmos” is possible (cue the medical procedure:  fecal transplants!).  One just needs the right proportions.

Neuron--NY State Dept of Health

Take another example.  Scientists know that atoms in supernova are identical to those in our brains—the organs that make external phenomena intelligible.  Even more, the correct ratios of such cosmic bits in our mental space make the external world explicable—by discovering or inventing order, or both, therein.

Supernova Remnant --NASA Hubble

   
Either way, the notion that our "internal" architecture is inextricably linked to the "outside" world reflects the fuzziness of such boundaries, and how much we are a part of the universe. Whether this inside-outside notion survives the advent of quantum physics is an interesting question.  For now, though, it’s like being in a hall of mirrors where inside and outside interact in countless recursive loops, ones that have captivated humans for millennia. 

Some ideas just won’t go away.