On the Shoulders of Giants

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Note: this post was edited using AI.

Americans dream about taking double-decker buses to Big Ben, enjoying croissants and baguettes in the City of Love, and walking past the Trevi Fountain on the way to the Colosseum. This summer, I had the fortune of visiting London, Paris, Rome, and Sicily. Each proudly displayed its culture and history — and there was a lot of it to appreciate, as even the most storied cities in the United States don't have the thousands of years people have been living and building in these places. Between the British, French, and Roman Empires, these countries have left a profound impact everywhere from Romania and French Polynesia to New England and British Columbia. The work of scientists like Isaac Newton, Marie Curie, and Galileo Galilei continues to shape lives worldwide.

How just a few countries in Western Europe came to influence so much of the world is a subject that has been addressed by many historians. I am no historian, but as a student of science and technology, I wanted to write about how learning this history on my trip made me think about my role as a technical person in a highly uncertain 21st century. Witnessing a rich legacy of science, and of honoring scientists, was inspiring. Meanwhile, I also thought about mistakes these countries made in their technological and economic hubris at the height of their power.

Thinking Big

While in Rome, I visited an interesting exhibit on Leonardo da Vinci. Leonardo is the archetypical Renaissance man. In addition to painting the Mona Lisa, probably the most famous work of art in the world, he experimented with anatomy and all kinds of flying machines that were far ahead of his time. This is exemplified by a famous quote which he probably never said:[]

“Once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return.”

For me, Leonardo da Vinci is a model for thinking big. He had extensive knowledge across a wide range of subjects, and was eager to learn more and make his mark. Instead of settling for improving horse-drawn carriages, he wanted humans to thoroughly understand their own bodies and fly like birds for the first time. He was always curious, and he was in the right place for that: Florence was the unparalleled center of the Renaissance.

Despite his genius, history would not remember Leonardo in the same way if he had turned his attention to improving horse-drawn carriages. This is partly because better carriages are less interesting than flying machines or diving suits, but it is also because big and imaginative ideas capture the soul in a way incremental steps cannot. Smaller steps are no doubt important, but if we focused solely on improving planes, we would not have stumbled upon a moon landing so quickly. We needed a literal moonshot and a grand vision to convince the public that landing on the moon was possible (though very difficult) and worth doing.

In modern science, the pursuit of disruptive moonshot ideas has become less common. While the 20th century witnessed countless scientific revolutions that changed our view of the world, from general relativity to the double helix, the pace of progress has seemingly slowed despite the increase in funding. This is often attributed to a “low hanging fruit” scenario: thought experiments may have been enough to spark the development of special relativity, but even Einstein could not find a theory of everything by just thinking about it if he lived today. Modern day disruptive ideas demand substantial funding and large teams. The belief is that most of the less costly disruptive ideas have already been discovered.

However, Park et al. [] challenge this “low hanging fruit” theory. They observe this decline across scientific fields and contend that it is unlikely for all fields to find their “low hanging fruit” at the same time. Instead, they claim that part of the reason for the decline is that researchers focus on very narrow fields, often citing older familiar works or even their own works rather than reading more broadly. This is an idea that Leonardo would approve of: his art and science informed each other, especially as his artistic hand enabled him to represent human anatomy more accurately, and his studies of anatomy in turn informed the realism in his artistic creations. Embracing the Renaissance man ideal can serve as a model to think broadly and find disruptive ideas, especially in a 21st century in need of such ideas.

Unfortunately, Leonardo is also an example of why thinking big is so hard. Many of his inventions simply were not feasible with the technology of the time. This meant that although he had great ideas, he often kept them to himself and his notebooks rather than implementing them in the real world, so they failed to influence others as much as they could have.

Archimedes was more successful in this regard. He is best known for his observation while taking a bath and watching the water rise. This supposedly led him to realize how buoyancy works and run naked through the streets of Syracuse, Sicily shouting “eureka!” (These are the same streets I saw when I stayed in Syracuse.) But this was far from his only big idea. Another famous work of his is The Sand Reckoner, in which he works with very large numbers in an attempt to estimate the number of grains of sand needed to fill the universe. His final estimate (8 × 10⁶³ []) was wildly inaccurate, but even thousands of years later we respect his bold calculations despite his numerical answer.

While much of Leonardo's thoughts were hidden in his notebooks, Archimedes let everyone know his big ideas. His thoughts were disseminated through the Mediterranean of antiquity and have influenced scientists and mathematicians for generations. Leonardo has also inspired many scientists and mathematicians, but often not until long after his death. One of his notebooks was written around 1508, but was not discovered until 1690.[]

Today, however, both Leonardo and Archimedes are honored for their novel ways of thinking in science and have served as role models ever since. Paying homage to great minds from long ago is a fun way to feel connected to history, as I did in Rome and Syracuse, but it also has more direct and practical purposes that I hadn't thought much about before this trip. It is by standing on the shoulders of giants that warring visions of the world may claim legitimacy and pick up where previous generations left off.

Shoulders of Giants

One thing I was impressed by in England and France was the extent to which they honor their scientists. The single most famous landmark of Paris is the Eiffel Tower, which is mostly unadorned except for the names of famous French scientists painted in gold along each side. Lavoisier (conservation of mass), Ampere (relationship between electric current and magnetic fields), Coulomb (law of electric forces), all those familiar names from high school chemistry and physics are there.

The second most famous landmark of Paris is the Notre Dame, which is a cathedral and does not display the names of scientists. But the Westminster Abbey church in London actually does. Along with various kings and queens, the abbey contains the graves of such prominent names as Isaac Newton, Charles Darwin, and Stephen Hawking.

It was a little surprising to see an atheist physicist and the agnostic father of evolution buried in the same church where the British monarch takes the throne and vows to serve God. But this shows the central role of science in the British national narrative. Science and technology have historically been one of the United Kingdom's chief exports to the world. It was this development in science that was a core piece of Britain's becoming the first industrialized nation and then the largest empire in history. In France, too, great French scientists were part of what made France a significant economic and imperial power.

These British and French scientists have always served as giants on whose shoulders others may stand on, in their own countries and elsewhere. But not all who stood on those shoulders saw further. The massive British and French empires were also known for their exploitation of colonies, a feat made more efficient by their access to technology. They got better weapons, better transport, and better communications, all of which were vital in their expanding colonial empires. Steamships let them get to the colonies quickly, trains helped them get around the colonies, and telegraphs connected colonial administrations across vast distances.[] What is it that led to such rapid technological progress in Europe?

Innovative Ideas

Galileo Galilei was a central figure of the Italian Renaissance, meaning he inherited the legacy of a period of relative stagnation in Europe. After the fall of Rome, Europe entered what some call the “Dark Ages”. But this was not the only legacy he inherited. He also inherited the legacy of Christian civilization in Europe, and was part of a movement reviving the legacy of Greco-Roman civilization. Greco-Roman civilization itself was formed when after conquering Greece, Rome absorbed the elements of Greek civilization it found inspiring instead of rejecting them as altogether foreign. So Galileo inherited the legacies of at least three civilizations: Christianity, Rome, and Greece. Europe also borrowed some of Islamic civilization due to translations of famous Arabic works such as al-Khwarizmi's Al-Jabr.

Far from popping out of nowhere, the Renaissance had up to four prior intellectual traditions on which it could draw. What distinguished it from the Middle Ages is that the Middle Ages were dominated by just one intellectual tradition: Christianity. Not that Christianity was irrelevant to the Renaissance: many great Renaissance works such as David and The Last Supper take direct inspiration from the Bible. But the Renaissance also revived classical Greek and Roman ideas alongside the Christian ones, such as a reengagement with Hellenistic science, Socratic philosophy, and Cicero's literature alike. Even David is in the style of Greek sculpture. The Renaissance was also open to new Islamic ideas: Al-Jabr was the main mathematics textbook in European universities all the way up to the 16th century.[] The combination of all these ideas from disparate sources led to an unprecedented rate of intellectual progress in Europe.

Galileo died in 1642. Shah Jahan completed the Taj Mahal mausoleum in 1648, when Newton was a small child. At the time, the Mughal Empire in India was reaching its zenith. Although it was an Islamic empire, the majority of its population was Hindu. Did the Mughal Empire embrace diverse intellectual traditions like its contemporary in Renaissance Europe?

Shah Jahan's grandfather, the Mughal emperor Akbar, was surprisingly open to diverse traditions. He encouraged dialogue between the various faiths of his empire, had Sanskrit classics translated into Persian, and incorporated local Indian traditions into his architecture. He was impressed by the realism and perspective developed in art samples from the European Renaissance brought by Jesuit missionaries, and incorporated these into Mughal art as well.[]

However, science does not make the list of the great Mughal advances. As one of the gunpowder empires, the Mughals did make guns, but that does not rank as an inspiring and innovative development. Perhaps this is because Akbar was just one emperor, and was not educated in science, so it is understandable that there would not be a scientific revolution in his empire. Euclid's Elements was not translated into Sanskrit until 1719.[] Another reason is that the Mughals did not draw on older traditions to the maximum extent possible: mathematicians in the Islamic Golden Age prior to the Mughals were already familiar with the Elements,[] but the Mughals themselves were not.

When cultures and ideas are in deeper and more meaningful contact, scientific revolution becomes more likely. The scientific achievements of the Hellenistic age such as those of Archimedes and Euclid followed a period of interaction between Greek culture and Egyptian, Persian, and Mesopotamian cultures. This influenced India as well, leading almost immediately to the Mauryan empire and then to great scientific achievements like the mathematics of negative numbers and new ideas in astronomy under the Gupta empire. Both India and the Hellenistic age influenced the Islamic Golden Age, which in turn impacted the Renaissance along with Christian and revived Greco-Roman traditions. Finally, this led to the scientific revolution in Europe.

Is this an infallible rule? You could point to the Song Dynasty in China as an example of great scientific advancement (gunpowder, compass, woodblock printing) with relatively little external cultural interaction. But even China has a long history of competing philosophical schools, especially Confucianism, Taoism, Buddhism, and Legalism. So perhaps it is not cultural contact for its own sake that stimulates new science and creative thinking; rather, it is a diversity of ideas that tends to follow from the mingling of traditions. If everyone thinks the same way in all walks of life, they will be conformists in science, too.

Takeaways

As I grow in my career in science and technology, I want to keep an eye on my little place in history in addition to my technical skills. I aspire to leverage this understanding to help me pick meaningful issues to work on and contribute positively to the world. This means I have to read, experience, and most importantly reflect on history. From my Europe trip, here's what I learned from a scientific perspective:

• From Leonardo da Vinci, I learned to think big. I aspire to be strong enough to risk failure, bold enough to try things that were previously impossible, and curious enough to constantly search for new avenues of thought.
• From Archimedes, I learned to ground my big thinking. In order to have an impact, I need to not only think big but also effectively communicate my ideas. I know not all my ideas can succeed, so I should have humility in acknowledging when I am uncertain or just plain wrong.
• From the Eiffel Tower and Westminster Abbey, I learned to stand on the shoulders of giants. Building on previous scientific achievements is a force strong enough to create massive industrialized empires. I am certainly not into imperial domination myself, but at least I can try to make cool stuff.
• From the broader history of science and technology in Europe and the world, I learned to be open to diverse ideas. This means being open to ideas of people from different cultures and backgrounds, not for the sake of some amorphous diversity, but because intellectual diversity is a genuinely crucial component of creative thinking.

In my future travels I want to continue thinking about the history of each place I see and what I can learn from it. After all, one more thing I learned from Leonardo da Vinci is to be a Renaissance man: just as Leonardo synthesized the arts and sciences in his work, my studies in history will lead me to more exciting paths in science and technology.

References

1. The famous quote that da Vinci never said (Dave English, Air Facts, 2020) ^
2. Papers and patents are becoming less disruptive over time (M. Park, E. Leahey, & R.J. Funk, Nature, 2023) ^
3. The Sand Reckoner (Weber State University) ^
4. Da Vinci notebook sells for over $5M (History, 2009) ^
5. Al-Khwarizmi (Shawn Overbay, Jimmy Schorer, and Heather Conger, University of Kentucky) ^
6. Akbar (Encyclopædia Brittanica) ^
7. Jagannātha Samrāṭ (McGill University) ^
8. Industrial Imperialism, the “New” Imperialism (Khan Academy) ^
9. Mathematical Treasure: Early Translations of Euclid's Elements into Arabic (Frank J. Swetz, Mathematical Association of America, 2020) ^