Locklin on science

Great thinkers: Eudoxus of Cnidos

Posted in history by Scott Locklin on November 13, 2011

Εύδοξος ο Κνίδιος

It’s a modern conceit that we are the most sophisticated people who ever lived.

Much of what we know comes from a bunch of pederasts in ancient Magna Graecia, and most of that has been forgotten. The agglomeration of knowledge over billions of people and thousands of years has given us greater ease and power over nature than the Greeks had. But the Greeks in many ways remain our superiors as people, and they were in every measurable way our intellectual superiors. There was no other civilization we know of who remotely compared to what the Greeks accomplished. Not the Persians, the Chinese or the Japanese or even the Edwardian English (who probably came closest to the influence of the Greeks, if not their genius). I don’t know why Von Dainken talked about Aliens influencing the ancient Egyptians in his silly Chariots of the gods books. No pile of rocks can compare to even a minor work of Phidias.

A Greek whose ideas haunt me: Eudoxus of Cnidos. He was born around 408 BCE, son of Aischimes. Eudoxus was born poor. He walked miles every day to listen to Plato’s lectures. Eventually that cheesed him off (actually, I believe it was Plato’s lack of mathematical sophistication), and Eudoxus went his own way; ending up in Heliopolis where he learned Astronomy. Later in life he returned to Athens to rival Plato, and eventually he retired to Cnidos and was considered the greatest mathematician of his time.

Eudoxus is best known for his contribution to the theory of ratios to Book V of Euclid’s Elements in which he developed the idea of real numbers, which underlies much of mathematics today; in particular that which requires the floating point part of your computer. He also invented an early form of calculus, called the “method of exhaustion” -really, Leibniz and Newton didn’t do much beyond this which wasn’t notation. In fact, much of Euclid’s elements is just an exposition of Eudoxus work. Other achievements: he discovered the leap-year, invented a sundial and a lot of what we know about him was due to an epic poem. When was the last time any scientist or mathematician rated an epic poem? That’s how badass Eudoxus was.

Eudoxus was the first astrophysicist; his contributions in this regard are more or less how I first ran into him, via an idea called the Gutzwiller trace formula, which is an interesting mathematical object worth a blog entry or two on its own. Eudoxus developed a theory of orbital mechanics which is essentially how we do it today; it is perturbative in nature. In other words, his theory takes a rough answer, then adds terms to it to make it better. His theory is numerically very good. Variations on it were happily used for thousands of years; up to the time of Kepler. Eudoxus’ idea was really the first modern physical theory.

Eudoxus invented real numbers, orbital mechanics and a form of calculus, 2000 years before Newton. He also discovered the leap year, invented a sundial, described constellations, wrote epicurean philosophy, discovered many theorems in solid geometry, he is alleged to have been a pretty good interior designer; he wrote books of geography and sociology, meteorology, Egyptian theology and was revered as a wise lawgiver in his home town. His productive years were between 26 and 53, when he died. Compare him to the imagined smartest man who ever lived, Einstein, who started research when he was 21, and died at 76. Eudoxus accomplished much more in a shorter period of time. He did it before Alexander the Great; before the invention of the steam engine; before Rome became an empire; before the Great Wall of China was built. Eudoxus lived so long ago, he is at the bare edge of recorded history. He lived in a time which had more in common with myth and legend than with modern history, but his discoveries invented what we are.

“Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance.” -Eudoxus

Ancient Greek civilization produced at least many dozens and perhaps hundreds of men like this. How can we moderns hope to compare to the Greeks?

13 Responses

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  1. wburzyns said, on November 14, 2011 at 12:12 pm

    “How can we moderns hope to compare to the Greeks?”

    Just compare to the modern ones.

  2. rork azak said, on November 14, 2011 at 9:17 pm

    Immanuel Kant and Isaac Newton are both considered to comprise the smartest people to have ever lived. Based on some recent IQ conjectures, both of the above supposedly had IQ’s beyond the 250 mark. (With profound appologies to Marilyn vos Savant who considers herself as the smartest person alive today.)

  3. wr123 said, on November 14, 2011 at 9:25 pm

    Hey Scott, you got a great blog here. I was just wondering about your thoughts on the Indians…the ‘vedas’ and the ‘puranas’? Robert Oppenheimer considered access to the vedas the “greatest privilege this century may claim over all previous centuries.”

  4. wr123 said, on November 15, 2011 at 3:09 pm

    Hey Scott..you have a great blog here. I was wondering what you thoughts were about ancient India (vedas & puranas). Robert Oppenheimer considered access to the Vedas “the greatest privilege this century may claim over all previous centuries”.

    • Scott Locklin said, on November 16, 2011 at 4:11 am

      Kenneth Clark also said nice things. I haven’t read them yet myself.

  5. David said, on November 16, 2011 at 4:53 am

    How do you address the concern that discovery is “harder” today? That is, our ancestors solved all the easily-described problems (i.e. “What’s between 0 and 1?”), leaving all the nasty ones for us. It now takes us decades of education just to learn what humanity has already done, before even beginning to solve new problems – could this be a simple answer to why the ancients were so much more productive?

    • Scott Locklin said, on November 16, 2011 at 5:02 am

      The only reason they were “easily described” is because … them old guys actually did the describing. It’s easy to dismiss the “easy” stuff from a modern vantage, just as our present problems will seem “easy” in 100 or 1000 years. Genius is what makes hard problems easy via the conceptual leap. I mean, when studying special relativity in my upper level E&M class; it seemed easy to the point of obviousness, but it obviously wasn’t easy at the time.

      I also do not believe that one needs decades of education to get started on important problems, or much of anything else. That’s just make-work for pedants. Look at what was on a high school curriculum 100 years ago and despair.

  6. Kartik Agaram said, on November 17, 2011 at 4:49 am

    You seem to be on the same side as Mencius Moldbug on one question: “Should we judge a society by its best people, or all its people?”


    • Scott Locklin said, on November 17, 2011 at 6:04 am

      I just spent a weekend hanging around with guys like Paul Gottfried, so, like, I’m with Moldbug (who is more or less the breezy Cliffs notes internet version of Paul’s work). FWIIW, I may have actually introduced Moldbug to Carlyle (of the great man school of history) back when he was a long-winded liberal, rather than a long-winded neo-paleoconservative.

  7. Roger Bigod said, on November 25, 2011 at 2:56 am

    Thanks for this post. I’d never realized what a standout Eudoxus was.

  8. nikon said, on August 31, 2012 at 6:47 pm

    Euclid probably never existed, he supposedly lived during 300BC, but he was first mentioned only in 4th century A.D.

  9. Krigl said, on August 27, 2013 at 8:56 pm

    Shouldn’t there be something like “Megalé Hellada”? Magna Graecia is from the language of Johnny-come-latelys, from the Greek viewpoint.

  10. David said, on March 16, 2022 at 4:02 pm

    “When was the last time any scientist or mathematician rated an epic poem?”

    Well, there *was* a parody of Goethe’s Faust, put on as an evening’s entertainment in the 1932 physics conference in Blegdamsvej, which recounted the history of the preceding 30 years in physics in the form of poetic allegory; it was of course written in German, but George Gamow’s wife was kind enough to translate it into English, and I was thoroughly entertaining reading it even now, ninety years later.

    A sample from the prologue, comparing first Goethe’s original and then the version put on Blegdamsvej:

    The sun-orb sings, in emulation,
    Mid brother-spheres, his ancient round
    His path predestined through creation,
    He ends with step of thunder-sound.

    The angels, from his visage splendid,
    Draw power, whose measure none can say.
    The lofty works, uncomprehended,
    Are bright as on the earliest day.


    And swift, and swift beyond conceiving
    The splendor of the world goes round,
    Day’s Eden-brightness still relieving
    The awful Night’s intense profound.

    The ocean-tides in foam are breaking
    Against the rocks’ deep bases hurled,
    And both, the spheric race partaking,
    Celestial, swift, are onward whirled!


    And rival storms abroad are surging
    From sea to land, from land to sea,
    A chain of deepest action, forging
    Round all, in wrathful energy.

    There flames a desolation, blazing,
    Before the thunder’s crashing way…
    Yet Lord, Thy messengers are praising
    The *gentle* movement of Thy day.


    Though still by them uncomprehended,
    From these the angels draw their power,
    And all Thy works, sublime and splendid,
    Are bright as in Creation’s hour.


    As well we know, the Sun is fated
    In polytropic spheres to shine;
    Its journey, long predestinated,
    Confirms *my* theories down the line.

    Hail to Lemaitre’s promulgation
    (Which none of us can understand)!
    As on the morning of Creation
    The brilliant Works are strange and grand.


    And ever speeding and rotating,
    The double stars shine forth in flight.
    The Giants’ brightness alternating
    With the eclipse’s total night

    Ideal fluids, hot and spuming,
    By fission turn to pear-shaped forms.
    *Mine* are the theories that are winning!
    The atom cannot change the norms.


    The storms break loose in competition
    (The Monthly Notices as well!)
    And bum with violent ambition
    Important tidings to foretell.

    At heat of 10 to 7th power
    The gas degenerates in flame.
    Permitting us our shining hour
    Of freest flight in Fermi’s name.


    This vision fills us with elation
    (Though none of us can understand).
    As on the Day of Publication
    The brilliant Works are strange and grand.

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