The Eureka Moment


“Eureka! – I have found it!”



I have often wondered about Eureka moments, sometimes known as an epiphany, which incidentally comes to us from the ancient Greeks, signifying a manifestation or striking appearance.   In the past, it was considered an insight given by the divine, or the supernatural, whereas today, it has lost much of this nuance.  Even so, when someone has an epiphany it usually means there has been a scientific, religious or philosophical breakthrough of grand proportions.

Archimedes is a shining example of this form of the extraordinary.  Diotima and her idea of Platonic love and Hipparchia’s decision to embrace the Cynic’s lifestyle, in my opinion, fit into this category.  In fact, all of the ancient great thinkers seemed to have encountered a new and deeper understanding or perspective. While we gratefully acknowledge their contribution, there is within all of humanity a wistful desire to experience a Eureka insight.

So let us consider the idea that most of us have, indeed, felt that moment without recognizing its profound meaning. We may be expecting a thunderbolt, when the reality may come as a gentle whisper.  Eureka insights usually signal a dramatic shift in thinking.  Some people consider it an “ah ha” moment. The catalyst may be a simple conversation, a line of a poem, or a book that challenged.

The ancients gave substance to their thoughts and ideas by sharing, teaching, documenting and living in accordance with their fresh awareness. Malcolm Gladwell in Outliers: The Story of Success suggested that, “Practice isn’t the thing you do once you’re good.  It’s the thing you do that makes you good.”

“People think of these eureka moments and my feeling is that they tend to be little things, a little realisation and then a little realisation built on that.”

Roger Penrose, Mathematical Physicist, Recreational Mathematician and Philosopher


The Library That Was


The Land of Pharoahs

“To add a library to a house is to give that house a soul.” 
Marcus Tullius Cicero

The ancients knew that to receive a proper education, they must travel to Alexandria, the celebrated city newly founded by none other than Alexander the Great in 331 BCE.  Alexander’s military genius was felt in every part of his empire that stretched from Egypt to Asia. His untimely death at 32 curtailed the conquests, and led to the division of his territory.

Ptolemy Soter (367-283BC), a Macedonian general of Alexander the Great proclaimed himself pharaoh of Egypt. Ptolemy was Egypt’s first Greek ruler and the founder of the Ptolemaic Kingdom that produced many other Ptolemys as well as Cleopatras, including the illustrious Cleopatra VII.  Modesty was not Ptolemy’s forte; instead, he flaunted the wealth of Egypt by commissioning what was to become the famed, almost mythological, Ancient Library of Alexandria.

The Ancient Library of Alexandria inspired remarkable intellectual and educational exploits.  It was likely that Euclid was the leading mathematics teacher. Archimedes came as a young man, when the library was scarcely 20 years old, shortly after Euclid’s passing.   Even then, the library boasted at least 100,000 scrolls, including all of Aristotle’s priceless personal collection. Archimedes probably met Eratosthenes, the brilliant thinker who measured the circumference of the world to within 4 percent of modern figures, and made a remarkably accurate measurement of the year’s length, even by today’s standards.

The Ancient Library of Alexandria was the hub of mathematics, engineering, physiology, geography and medicine. The breadth and depth of knowledge was unparalleled. Its destruction was catastrophic, the efforts of the early scholars and scientists forever lost.  Indeed, it was one of the greatest libraries that graced our world.

“History is full of people who out of fear, or ignorance, or lust for power have destroyed knowledge of immeasurable value which truly belongs to us all. We must not let it happen again.”

Carl Sagan (referring to the loss of the Library at Alexandria). 1988, Cosmos

A Legacy


“Don’t disturb my circles!” 



Rome wanted control of Syracuse, Sicily for strategic purposes.  Archimedes was an old man; some suggest nearing 80, when Roman ships closed in on his city in 212 B.C.  Even as Syracuse was being besieged, Archimedes continued inventing all kinds of clever contraptions to keep the enemy at bay.  But even his remarkable skills could not overcome the military might of Rome.

Archimedes’s legendary feats had reached the ears of the Roman commander Marcellus, who was determined that no harm should befall him.  Archimedes was to be treated with the respect accorded to a man of his stature. Yet, fate had a different outcome for our noble Archimedes.  The Roman officer, who discovered Archimedes busily drawing circles and making calculations in his sand tray, had not received Marcellus’s orders. When Archimedes shouted, “Please do not disturb my calculations,” the officer was in no mood to obey an old, foolish man.  When Archimedes insisted on finishing his calculations, the soldier ended his life.

The death of Archimedes is a poignant reminder that whatever ideas, thoughts, calculations that remain locked in a human mind, is forever lost to the world.  Unless, there is a record!  In 1906, the philologist J.L. Heiberg discovered a palimpsest, also known as a scroll in which the original writing has been partially erased to be repurposed for new text.  Miraculously, beneath the Greek orthodox scriptures, were hidden copies of assorted key works by Archimedes. The Arab mathematicians safeguarded his work through the Dark Ages until it could be swept into the seventeenth century scientific revolution.

But that is another story…

“Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.” 




“Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.”



King Heiron had another problem.  Who else should he turn to but his old friend, Archimedes, who recently helped him out of a rather embarrassing situation involving the launch of the Syracusia. This time, the King believed he was a victim of fraud.  He gave his goldsmith a generous amount of gold with instructions to make him a wreath befitting of his royal personage. When King Heiron examined the finished product, he suspected that his cunning goldsmith had somehow devised a way to keep some of the gold by substituting it with an inferior metal.  He was in a quandary. The wreath weighed the same amount as the gold that had been entrusted to the goldsmith.   There was no proof of deception.

Sudden, almost miraculous, realizations happen in the oddest moments, engendered by a movement or a fleeting thought.  Archimedes came to his brilliant conclusion when he was taking a bath.  He noticed how the water level rose as he sunk deeper into the water.  Legend has it that he leaped straight out of his bath and ran unclothed through the streets to the king, shouting with enthusiastic gusto, “Eureka! Eureka!” which means, “I’ve got it! I’ve got it!”

The answer was elegant and profoundly transformational.  Archimedes first immersed a piece of gold that weighed the same as the royal wreath and noted the rise in the water level.  He then immersed the actual wreath and noted the water level was higher than the gold.  This meant that the wreath must be a greater volume than the gold, even if it was the same weight.  Mystery solved.

Whether or not there is any truth to this legend, it does give insight into Archimedes’ scientific methodology.  He used small, everyday problems as a starting point for crucial theoretical advancements.  Perhaps Eureka was the genesis for his groundbreaking work on how things float – hydrostatics.

“Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.”

Godfrey Harold Hardy, A Mathematician’s Apology, (1940)

I Will Move The Earth


“Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.”


The Ocean

The Syracusia, a luxurious ship weighing in at 4,064 tons, sat uselessly on shore, a beached monstrosity. “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” Archimedes boldly proclaimed to King Heiron II of Syracuse in Sicily around 260 BC.  Impervious to the pressures that an impatient king and a skeptical crowd could bring to bear, Archimedes single-handedly launched the Syracusia, one of the largest vessels of the ancient world. His ingenious arrangement of levers and pulleys did what huge teams of men pulling ropes could not accomplish.

Archimedes was a legend in his own life and is considered, in our age, to be the greatest inventor of ancient times. Sir Isaac Newton was known to be in awe of him.  The inventor of the pulleys and levers that could launch a ship also designed the first water pump, called an Archimedes screw which is still used today. He created a planetarium to show the motions of all the planets.  When Syracuse was besieged by the Roman fleet, Archimedes used his skill to protect his beloved city. He constructed catapults to bombard the ships with boulders, grappling devices to throw down scaling ladders, and even a hook and crane to lift massive enemy boats out of the water and tip them over.  Even so, in many respects, his inventions were the least of his achievements.

Archimedes was the world’s first great Scientist.  He went beyond the study of scientific subjects by thinking about problems in the scientific way that we now take for granted. But that is for another post…

“If I have seen further than others, it is by standing up the shoulders of giants.”

Sir Isaac Newton