Saturday, June 16, 2018

Geopolitical Geometry


I’m well into my physical therapy routine, and all seems to be going well with the shoulder (puh puh puh). Almost four months down, two months to go.  I must admit that when I left for Mykonos from New York City (and abandoned the Hospital for Special Surgery’s state of the art rehab facility), I was more than a bit concerned about the sort of therapy I’d find on an island in the middle of the Aegean that doesn’t even have a hospital. 

I had nothing to worry about. I’m so impressed with the progress I’ve made through the efforts of my therapist, that I’m willing to recommend those in need of shoulder rehab to seriously consider coming to Mykonos for the last four months of your program. Preferably in the summer.

And if you’re a writer, my therapist comes with an unexpected bonus. He has wonderful tales to tell of Greece, the island, and its people.  No violations of therapist-patient confidentiality, mind you, just a treasure trove of ideas for characters and plot lines. And then there are all those ideas for blog posts, like this one.

What I’m about to write is not what I’d originally intended.  Today has seen a bit of cataclysmic political theater in the Greek government (something we in the US are all too familiar with on a daily basis).  All hell broke loose over a proposed deal agreed upon by Greece’s Prime Minister with his counterpart in neighboring F.Y.R.O.M. (Former Yugoslav Republic of Macedonia).  Among the hot-button issues raising the hackles on the backs of the necks of a majority of Greeks is that the deal allows FYROM to call itself “North Macedonia,” and all that flows from that.  Why that is so significant to the Greeks ties directly into the essence of how they see themselves.

The proposed deal led Greece’s primary opposition party to call for a no-confidence vote in Parliament, and that vote is scheduled for today, Saturday (likely to fail as of this posting). It also prompted representatives of the Neo-Nazi party Golden Dawn (the third largest party in Greece’s Parliament) to call for the military to stage a coup and arrest the Prime Minister, among others. That led to those representatives being expelled.  As I said, there’s a lot going on for me to wax on about Greek politics.

But I’m taking a pass on that. Frankly, I’m tapped-out reading about what’s going on in the US and the UK, and I’m guessing many of you are too. So, I’m going to follow up on a recommendation from my PT guru (as he pulled and pushed my arm into positions I never though possible) that I Google “Ancient Greek Geometry.”  

His suggestion came after pointing out how gifted ancient Greeks were at understanding the way our world worked.  Since there seems to be a dearth of such folks hanging around in governments today, that sounded like a pretty good topic. So, here goes.

The ancients believed that the omphalos, or “navel” of the earth lay in Delphi, and many revered places in Greece were described in relation to their relative proximity to Delphi, e.g., the Temple of Poseidon at Sounion, the holy island of Delos, and the Acropolis. He said that even his home village of Amfissa, close by Dephi, thought of itself in relation to such sacred places.  As measured on a straight line, Amfissa lay equidistant between Mount Olympus, the tallest mountain in Greece and sacred place of the gods, and storied Mount Taygetus (aka Prophet Ilias), the tallest mountain in the Peloponnese.

Omphalos of Delphi

But, how could the ancients have accomplished such measurements in the absence of satellites and mapping software?

Answer: Geometry. 

The Greeks did not invent geometry (though perhaps “discover” is a more appropriate word); credit for that accolade goes to the Egyptians and Babylonians (with Indians getting at least an honorable mention), but the Greeks most certainly took it from its rudimentary roots and turned it into a science. 

Most give credit to Thales (624-546 BCE) as being the founder of Greek geometry.  He’d picked up the bug for it traveling in Egypt. 


It was Pythagoras (582-500 BCE) who turned it into a true science, naming it mathematics (meaning “that which is learned”), and even saw the numerical relationships of the musical scale.


Perhaps the most recognized name in the development of geometry is Plato (427-347 BCE). Best known as a philosopher, he established his Academy in Athens and inscribed over its doors the school motto, “Let no one ignorant of geometry enter.” (Some dispute that story, but not the point being made.)  Interestingly, although Socrates (c. 470-399) was not a fan of mathematics, Plato believed in teaching the Socratic method at his Academy as a preliminary discipline to the study of mathematics.


Of all the mathematicians in Greece, the one with the most long lasting influence turned out to be Plato’s student, Aristotle (384-322 BCE).  Aristotle laid down principles that Europeans continued to hold as the basis of all knowledge long after other Greek learning had fallen out of favor.

Aristotle contemplating a bust of Plato--Rembrandt

Other notable Greek geometry whizzes included Euclid (c.325-270 BCE), also called the father of Geometry by some, though he came along 200 years after Thales; Archimedes (287-212 BCE)—who can forget his bathtub experiment, one I think of every time I cause a bowl to overflow; and of course, Eratosthenes, who more than two thousand years ago proved the world was round by putting a stick in the ground and measuring its shadow.  NASA proved it more recently with a satellite…coming up with virtually the identical measurement as Eratsothenes.

Archimedes--Domenico Fetti

Sadly, Greece’s contributions to the study of geometry and mathematics fell away around the time of the destruction of the Great Library at Alexandra.

Alas, history once again taught us that giving up on a science-based world has far ranging effects on the development of civilizations.  Hmm.  Perhaps that’s the message my PT guy was trying to get across to me.  If so, he didn’t have to twist my arm to do it. :)

Thank you, Niko Drivas.



  1. Nice post. Bringing up my study of geometry and trigonometry. The Pythagorean theorum comes to mind.

    Glad to see that the Golden Dawn representatives were thrown out of Parliament. It's long overdue.

    What's going on in Italy is perturbing, a new alliance government with The League, a far-right, anti-immigrant party.

    1. Thanks, Kathy. First of all, sorry about the delay in responding, but we're having some technical issues with the site that doesn't notify us when a comment posts. Ah yes, the Samos guy Pythagoras...even has a town named after him on his native island. Not sure how meaningful the Golden Dawn ejection will be as the betting money is they'll do much better in whenever the next election is held because of protest voters, thinking "what harm can it do." Welcome to our populist world.

      As for what's going on in Italy...see my above last sentence. Sad, difficult times.

  2. Thanks, Jeff. Glad to see you're a mathematician at heart! The Greeks did a great job on what is known today as Euclidean Geometry and also laid the foundation for rigorous proof. But it was the Arab world that gets the credit for algebra. And the Indians invented the zero. Frankly, after the Greeks, the western world took a back seat.

    1. I actually did quite well in school in math...until hitting differential equations--and let's not go there. Yes, The Arabs and the Indians do get I think I said at the beginning of the post. Perhaps we can organize the whole mess of them to find some way to fix this $#@% technical problem with our site!

  3. My brother, geometry has always been my favorite branch of math, the only one I was ever a whiz at once I got into the heady (over my head) precincts beyond algebra.

    I also hasten to add that Archemides was, like my paternal grandparents, a Siracusan. Viva La Grecia! Viva Sicilia!