The Alexandrian–nay, Gaussian–Solution

Carl Friedrich Gauss

A year ago, I wrote about “the Alexandrian solution” to the Gordian Knot. I saw this as a metaphor for all instances in which genius lies in espying the simplicity hiding in a complex situation.

It just occurred to me that Carl Friedrich Gauss was, at the age of 10, just such an Alexander the Great. (Alexander was young, too, of course. In espying simplicity, it seems to help to be young — ie, intellectually daring, unspoiled by the complexity of life, et cetera.)

In about 1787, the young Carl Friedrich sat in class when the teacher told the kids to find the sum of the numbers 1 through 100. In other words:

1 + 2 + 3 … + 100 = ?

Think of this as the Gordian Knot. The teacher assumed that the kids would be busy for a long time, practicing their addition skills. Gauss reacted just as Alexander would have (I take poetic license):

This is too f***ing boring. There must be a simpler way.

Did Gauss get nervous as the other kids pulled ahead adding numbers, while he was still at 1, searching for simplicity? I don’t know. But he found it:

He realized that the numbers came in pairs:

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101

(and so on until:)

50 + 51 = 101

So the sum of the numbers is simply (simply!)

50 x 101, or 5,050

You might, if you’re a regular on The Hannibal Blog, be guessing that I’m much less interested in sums of numbers than in, shall we say, Gordian Knots and Alexandrian Solutions in general — meaning in other, preferably surprising, walks of life.

If you can think of any instances in which daring simplicity blasted through mind-numbing complexity, drop me a line.

What Mendel tells us about thinking

Find quietude. Observe whatever is around you. If it seems banal, discover it to be fascinating and mysterious. Ignore distractions, otherwise known as ‘everybody else’. Ask simple questions that puzzle you. Be patient in pondering them.

That is how I imagine Gregor Mendel might answer us today if we asked him: How  — I mean how! — did you achieve your stunning intellectual breakthroughs, on which we today base our understanding of biology?

Put differently: Let’s pretend that Gregor Mendel were alive today instead of in the 19th century, and that he were not an Augustinian monk in the former Austrian Empire but a wired and connected, über-productive modern man with an iPhone, a Twitter account, cable television, a job with bosses who email him on the weekend, etc etc.

Would this modern Mendel be able to achieve his own breakthrough in those circumstances?

So far in my rather long-running thread about the greatest thinkers in history, I’ve featured mostly philosophers and historians, with the odd scientist and even one yogi. But it occurred to me that Mendel belongs into that pantheon — not only for his thought but also for his thinking. I think he offers us a timely life-style lesson, an insight that fits the Zeitgeist of our hectic age.

So: First, a brief recap of his breakthrough. Then my interpretation how his life style and thought process made that breakthrough possible (and why ours might make such breakthroughs harder).

1) Mendelian genetics

Mendel was an Augustinian monk in what used to the Austrian Empire (and what is now the Czech Republic). He had an open and inquisitive mind and, as a monk, wasn’t all that busy, so he had plenty of spare time. He liked to breed bees. Then he began breeding peas. That’s right. Peas.

Peas intrigued him. (Would they intrigue you? What else does not intrigue you?) He found peas interesting because they had flowers that were either white or purple and never anything else. (Would you find that interesting?)

Mendel contemplated what peas could therefore teach him about how parents pass on traits to their offspring, ie what we would call genetics.

At the time, conventional wisdom held that the traits of parents are somehow mixed in their children. If parents were paint buckets, say, then a yellow dad and a blue mom would make a green baby bucket, and so on. (It’s interesting that nobody spotted how implausible this was: After several generations every bucket, ie every living thing, would have to end up mud-brown. Every creature would look the same. Instead, nature is constantly getting more colorfol, more diverse, with more and stranger new species.)

So Mendel, in the late 1850s and early 1860s, started playing with his peas. Pea plants fertilize themselves, so Mendel cut off the stamens of some so that they could no longer do that. Then he used a little brush and fertilized the castrated pea plant with pollen from some other pea plant. He thereby had total control over who was dad and who was mom.

He was now able to cross-breed the peas with purple flowers and the peas with white flowers. So he did. Then he waited.

Surprise #1:

Already in the next generation, Mendel could rule out the prevailing “paint-bucket-mixing” theory. No baby pea plants had lighter purple (or striped or dotted) flowers. Instead they all had purple flowers.

So he took those new purple-flowered pea plants and cross-bred them again. And again, he waited.

Surprise #2:

In the next generation, most pea plants again had purple flowers. But some now had white flowers. Wow! How did that happen?

Moreover, the ratio in this generation between purple and white flowers was exactly 3:1. Hmm.

Mendel kept doing these experiments, and kept thinking, and then inferred the simple but shocking conclusion:

  1. Each parent had to be contributing its version of a given trait (white vs purple, say) to the offspring.
  2. Each baby thus had to have both versions of every trait, but showed in its own appearance only one version, which had to be dominant.
  3. The other (“recessive“) version, however, did not go away, and when these pea plants had sex again, they shuffled the two versions and randomly passed one on to their offspring (with the other coming from the other parent), so that their baby again had two versions.

This looks as follows:

In the second generation, every pea plant has a purple (red, in this picture) and a white version, one from each parent, but since the purple is dominant, every flower looks purple.

In the next generation,

  • one fourth will have a purple from dad and a purple from mom (and look purple),
  • one fourth will have a purple from dad and a white from mom (and still look purple),
  • one fourth will have a white from dad and a purple from mom (and still look purple), and
  • one fourth will have a white from dad and a white from mom (and look white).

The rest, you might say, is history. With all our amazing breakthroughs in biology in the 20th century, we merely elaborated on his insights, in the process explaining the mechanism of evolution (Darwin, coming up with that idea at the same exact time, had no knowledge of Mendel’s breakthrough.)

In today’s language, Mendel

  • showed the difference between genotype and phenotype. (Your genotype might be white/purple, for example, but your phenotype would be purple.)
  • understood the basic idea of meiosis (the division of a cell into two haploid gametes — a sperm cell or egg with half of the mother cell’s chromosomes, randomly chosen),
  • described how two gametes then merge sexually to form a diploid zygote (ie, a cell with all chromosome paired up again, one member of each pair coming from each parent),
  • explained how some versions of the gene pairs, called alleles (such as purple or white), are expressed and some not, even as those not expressed can re-emerge in the phenotype in the next generation.

DNA, RNA, ribosomes and all that were merely detail.

2) How was it possible?

Let’s make ourselves aware, first, of what it must have been like for Mendel during these years (this is purely conjecture):

  • He got up.
  • He prayed.
  • Had breakfast.
  • Went into the garden.
  • Looked at the pea flowers for a long time.
  • Watered them.
  • Took a break.
  • Watched the peas some more.
  • Thought about them.
  • Dozed off for a nap.
  • Woke up and had an idea, still inchoate in his mind.
  • Went to bed.
  • Thought about it some more….

You get the idea. Not exactly stressful. Few interruptions. Lots of waiting (how long is one generation of peas anyway?).

He was, we would say, switched off. He was not multi-tasking, he did not have adrenaline coursing through his veins as he answered a text message while watching a video stream while writing a Powerpoint …

Compare his time with his pea plants to Einstein‘s time at the Bern patent office, where he was utterly underemployed and could easily have been bored, but instead did thought experiments and had his “miracle year”.

Or compare it to Isaac Newton‘s time after had to leave the action of Cambridge (because plague broke out) and returned to the isolation of his family farm with nothing to do except watch apples drop from trees….

Or compare it to the time when Gautama Siddhartha (aka the Buddha) withdrew from all action and sat, just sat, under a tree, with the birds pooping on his head until there was a pile of guano on his hair, with his flesh melting from his bones because he was too deep in concentration to eat…..

Lesson #1:

Good stuff can happen during downtime (even if you didn’t volunteer for it).

Corollary: Can good stuff happen during uptime? You may have to take time out to be creative.

Lesson #2:

Be amazed.

Corollary: Don’t assume the things and people in your daily life are boring.

Lesson #3:

Turn the devices off.

Corollary: Distraction not only kills people, it also kills thought.

Lesson #4:

Be patient.

Corollary: You can’t breed peas in internet time. Nor novels, scripts, songs, paintings…

Lesson #5:

Look for the simple.

Corollary: The more bewildering the complexity observed, the simpler the solution.

(See also: Gordian knot.)

Lesson #6:

It doesn’t have to be complete to be original.

Corollary: It took us a century to explain the process Mendel grasped; an idea is good even if it “merely” starts something.

(See also: Incompleteness theorem. Mr Crotchety’s favorite — need I say more?)

Lesson #7:

Don’t expect the world to get it right away.

Corollary: If it took us a century to understand Mendel’s breakthrough, we might take a while even for yours. 😉

The case for Alexander Hamilton (II)

Alexander Hamilton came from a different background than the other Founding Fathers, one that gave him a different worldview and philosophy of governance and freedom.

It is a philosophy that was bitterly contested at the time — and still is today, especially in this “Tea-Party” year. But overall, Hamilton’s vision is the one that prevailed. We today are, to a surprising extent, living in Hamilton’s America. So what was that vision?

  1. In the previous post, I looked at Hamilton as a man, at his character, life and background.
  2. In this post, I try to describe the ideas that such a character, life and background produced, and their timeless (but, as you’ll see, tragic) legacy.

Balance in government

Recall from the previous post that Hamilton, illegitimate and foreign-born, felt like an outsider in America, felt vulnerable as result, and had reason to be pessimistic about human nature, for he had seen, in the West Indies and in revolutionary America, atrocious human acts.

In particular, he had seen how dangerous mobs could be.

Recall also that he was a superb intellect, deeply versed in the classics.

It was therefore natural that he should appreciate an ancient concept, dating all the way back to Polybius and Aristotle: that balance is necessary to preserve liberty.

The government that best reflects human nature, in this view, blends the elements of

  • monarchy,
  • aristocracy (which literally means rule of the best) and
  • democracy.

But they have to stay in balance, because an excess or corruption of any one of these elements will destroy liberty, by becoming, respectively,

  • tyranny,
  • oligarchy or
  • mob rule.

Thus, for example, Aristotle and Polybius considered Carthage and Rome balanced, but Athens during the time of Socrates to be too democratic to be stable. In Hamilton’s own day, the French Revolution might illustrate the point even better: tyranny and oligarchy (the ancien régime) gave way to mob rule (the guillotine), which gave way to another tyranny (Napoleon), without any intervening liberty in more than motto.

In particular, Hamilton and several other important Founding Fathers, especially James Madison, shared with the classical philosophers an admiration of Rome. When they wrote public treatises, such as The Federalist Papers (discussed below), they adopted Roman pen names. Hamilton, for instance, was Publius (after Publius Valerius, the first consul of Republican Rome).


Early in their careers, Hamilton and Madison were intellectual allies in this respect. They wanted a republic, not a democracy. They feared tyrannical minorities and majorities equally. Thus they became the most important individuals in the creation and passing of America’s Constitution.

Madison had more intellectual input into the actual document, and was the note-taker during the Constitutional Convention. But Hamilton and Madison then collaborated in campaigning for that Constitution to be ratified by the states. (The document, much as we esteem it today, was very controversial and ratification was a close call.)

The Federalist Papers

This meant above all explaining and interpreting the proposed Constitution, which Hamilton and Madison, along with John Jay, later the first Chief Justice, did with one of the most impressive literary achievements in history: The Federalist Papers.

The Federalist Papers are a collection of 85 essays, of which 51 are attributed to Hamilton, 29 to Madison and 5 to Jay (so Hamilton was clearly the main author). The essays amount to about 175,000 words. And they wrote them in the space of only seven months, in their spare time (!), for they were still pursuing their main vocations during office hours — Hamilton as a lawyer.

Here is a measure of how important The Federalist Papers continue to be: By the year 2000, they had been quoted 291 times in Supreme Court opinions, with the frequency of citations rising with the years. (p. 261 in Ron Chernow’s biography of Hamilton)

And in these Federalist Papers, we see Hamiltonian values — meaning the ancient values of balance — on display. Hamilton envisioned:

  • a strong executive, (≈ monarchy)
  • a strong legislature (≈ democracy), and
  • an independent judiciary that could and should, if necessary, overrule the “popular will” if it destroyed liberty. (≈ aristocracy)

Judicial Review (and Prop 8 )

That this last bit is the “aristocratic element” might take a bit of explaining. To be sure, it is not the only aristocratic element in America’s overall structure. The electoral college originally had actual powers to select the president. Members of the upper chamber of the legislature — called the Senate, in direct allusion to Rome — were elected by state legislatures rather than the voters (an idea that many in the Tea Party want to bring back). And so on.

But the judiciary seems to me to be the most important aristocratic check on both potential tyranny and mob rule. In Federalist Nr 78, Hamilton wrote that

no legislative act … contrary to the constitution can be valid.

This sounds simple and obvious now, but it is not actually in the Constitution. In effect, Hamilton said that the Supreme Court (ie, a meritocratic elite) must be able to overturn legislation (ie, the popular will). Hamilton thus prepared the way for a later Supreme Court decision (Marbury v Madison, 1803) that established the concept of judicial review.

And that, of course, is what we have today. If you want to see the inherent and eternal tension that Hamilton foresaw, look, for instance, to the controversy about California’s “Prop 8“:

  • it is a ballot measure (ie, an expression of the popular will),
  • in which a majority voted to restrict a right (marriage) of a minority (gays and lesbians),
  • before a federal court overturned that vote.

Each side in the Prop 8 debate is screaming “tyranny” at the other, but Hamilton’s notion of balance will prevail. Hamilton, in the 18th century, would certainly have been surprised by the context (gay marriage) but not by the principle involved.

Center and periphery: “enumerated” and “implied” powers

That example of Prop 8, in which a federal judge has overturned a state ballot measure, also shows another aspect of Hamilton’s vision: there also had to be a balance between the core and the periphery, between central government and state government.

Recall the previous post again: Hamilton was actively fighting — as George Washington’s chief of staff, mostly — in the Revolutionary War, whereas some of the other Founding Fathers, and specifically Hamilton’s future enemies (I will get to them in a minute), remained in the comfort of their plantations or with the Continental Congress in Philadelphia, with its bustling dinner-party circuit.

What vantage point did that give Hamilton on the fledgling nation?

He saw that the nation was not viable as such. If the United States then has an equivalent today, it would be the United Nations.

America was fighting a professional army and navy (the Brits) with a ragtag force of militiamen who had no uniforms, and often no shoes and weapons. These Americans enlisted for a year at a time, which meant that Washington feared that his entire fighting force might literally disintegrate and vanish at the end of each enlistment period.

The nation, such as it was, had no powers of taxation. At all. So it had no money to pay its soldiers. And it could not issue debt. It relied on the individual states both for money and for soldiers. On occasion, the American troops mutinied, once even marching on Philadelphia and sending Congress to flee from its own soldiers.

This was not an abstract matter for Hamilton or Washington: They were starving and freezing with their soldiers at, for instance, Valley Forge, a miserable plateau in Pennsylvania where the Americans wintered in 1778-9.

The painting above (of Washington and Lafayette on horseback, with perhaps Hamilton as the rider behind them?) does not really do the misery justice. According to Chernow’s new biography of Washington, the Americans (unlike the soldier in the picture) had no shoes, no coats, sometimes no shirts, and were dying of cold, disease and starvation.

So Hamilton and Washington formed a vision of a strong center, one that could feed and clothe its soldiers and hold the states together. For the center to be strong, it would have to have a professional army, and powers of taxation and borrowing (“Aha,” say the Tea Partiers of 2010…).

When opponents later charged that the Constitution did not explicitly mention the things necessary to build such a strong central government (for example a Central Bank), Hamilton replied that

it is not denied that there are implied as well as express powers.

And thus Hamilton, almost en passant, submitted another evergreen argument into American politics, which you hear debated this year by Tea Partiers parsing “enumerated” and “implied” powers.

But Hamilton was not for a Leviathan (I believe he would be shocked by the bloat of our federal government today). He definitely envisioned the central government, though strong, as sitting atop states that remained otherwise sovereign in their daily affairs. Hence the “federalist” nature of the new country, and the name Hamiltonians called themselves: Federalists.

The federal balance that Hamilton conceived was so stable that Switzerland, in 1848, imported it wholesale and Germany, a century later, in large part.

The first American Capitalist

Alexander Hamilton was the only Founding Father who grasped not just one but both revolutions occurring in his time:

  1. the political revolution in governance and
  2. the industrial revolution.

For background: America was an agrarian society. The colonies were dependent on Britain for manufactures. There were no companies as such (both the legal form and the accounting systems did not exist in any form recognizable to us). Banks as such did not exist. Stock exchanges did not exist.

Hamilton’s enemies, primarily Thomas Jefferson, wanted to keep it that way. To Jefferson, an agrarian America was more “pure” than an industrial America. Here, arguably, likes the origin of America’s schizophrenia regarding “Main Street” versus “Wall Street”. But let’s remember (recall once again the previous post) that the agrarian “purity” of which Jefferson talked was based on slave plantations such as his own in Virginia. It was pre-capitalist, yes, but in a feudal, illiberal, dehumanizing way.

Hamilton, on the other hand, wanted to abolish slavery and looked ahead to a capitalist era. He read Adam Smith’s (then new) Wealth of Nations. He grasped modern concepts of finance. He wanted America to manufacture things, and to finance this new economy with banks and securities.

So he entered the most fruitful period of his career, as the first Treasury Secretary. Washington was president, and the only two other members of the cabinet were Thomas Jefferson as Secretary of State and Henry Knox as Secretary of War. But neither Jefferson nor Knox had much to do, whereas Hamilton became a de facto prime minister to Washington in putting the new country together. Within a few years, Knox had a dozen civilian employees in War, Jefferson had six at State, and Hamilton had … more than 500 at the Treasury. Knox was a jovial nature and didn’t care. But Jefferson was seething.

Hamilton was too busy to care. Within a few years, he created:

  • a central bank,
  • a monetary policy and paper currency to go with it,
  • a stock exchange,
  • a coast guard and customs service to collect the tariffs that were to finance the government (there was no income tax).

In short, he seeded the modern American economy.

The tragic lesson: American inversion of reality

You may agree by now that Hamilton was a genius and that, yes, his vision, more than any other Founding Father’s, created the nation we know. But I personally have learned more from the tragic aspect of his career.

The tragedy has to do with the political inversion of reality that was threatening to undo Hamilton’s career when he died so prematurely in his duel.

And that, too, may be the Founding Fathers’ legacy to us.

What am I talking about?

Opposition to Hamilton and his ideas started early. Some compatriots always found something sinister in his charm and success and genius, in his foreign origins and cosmopolitan attitudes, and in specific opinions such as Hamilton’s abolitionism.

For example, during the struggle in the states to ratify the Constitution, the anti-federalists began posing as populists, even though the most prominent of them were rich slave owners. Patrick Henry of Virginia — the very same Henry who famously said “Give me Liberty or give me Death!” — argued against the Constitution by telling delegates that

They’ll free your niggers.

Others, less blunt than Henry, wrapped their scorn in the emerging meme of the day, which painted Hamilton as a closet monarchist or aristocrat, whereas the (slave-owning) agrarians were the true democrats.

George Washington, who usually kept a dignified distance from the political swamp but reliably sided with Hamilton, wryly observed the irony:

It is a little strange that the men of large property in the South should be more afraid that the Constitution will produce an aristocracy or a monarchy than the genuine, democratical people of the East.

By the “people of the East” he meant the mostly northern farmers, merchants and industrialists in Hamilton’s circles.

Hamilton himself also deployed his irony. In a newspaper piece in 1791, referring to Madison and Jefferson, he wrote (Chernow, p. 307):

As to the negroes, you must be tender upon the subject … Who talk most about liberty and equality …? Is it not those who hold the bill of rights in one hand and a whip for affrighted slaves in the other?

But irony rarely wins in America. Then as now, the most effective political strategy in American politics is relentlessly repetitive attack until reality becomes what the attacker wants it to be. Jefferson was the worst offender, but Madison, Hamilton’s erstwhile soulmate, was just as bad after he split from Hamilton and went over to the “Republican” side.

And let’s reflect on that label the Jeffersonians chose, for a moment. Why call yourself “Republican” if not to imply that your opponents are un-republican? Everything you’ve read in this post so far tells you that Hamilton was a true republican, and yet Jefferson and his cronies now campaigned to make people think the opposite.

And cronies they had plenty. (Both sides did, to be fair). The Fox News of the day was the National Gazette, first published in 1791, a newspaper that served as the mouthpiece for Jeffersonian attacks branding Hamilton as a monarchist, tyrant and what not.

And thus it was that

  • the future presidents Jefferson and Madison, the patrician owners of slaves and plantations, became known and remembered for generations as the folksy democrats who were close to the land and people, whereas
  • Hamilton, the illegitimate quasi-orphan from the Caribbean who had worked his way to success with sheer talent and grit and who wanted to free the slaves, became the elitist aristocrat.

I have, in the paragraphs above, suggested several modern analogs to the issues raised in this post. But I will leave you to ponder this last subject on your own. And I will end, very much as Hamilton might, on that note of pessimism.

The case for Alexander Hamilton (I)

Alexander Hamilton is “my favorite” Founding Father, as I’ve hinted several times before. But I’ve never actually explained what I meant by that.

In this and the next post, I will try to unravel which aspects of this complex, visionary and soulful man (just look at that portrait above!) so resonate with me.

  • In this first post, I’ll sketch the man, his temperament, his journey and philosophy about people and life.
  • In the next post, I’ll describe his intellectual contribution to American governance and political philosophy.

You’ll see after the second post that the man can’t be separated from his ideas, nor the ideas from the man. And you’ll see (I hope) how timeless — meaning: relevant today — Hamilton is.

I will give you my interpretation, but my main source is Ron Chernow’s excellent biography of Hamilton. (I am now reading Chernow’s new biography of George Washington as well.)

Now, to Hamilton, the man:

1) He was an outsider who ended up on the inside

Hamilton was the only Founding Father born outside of what became the United States. He was born in a Caribbean hellhole (called Nevis, in the West Indies) that seemed to specialize in tropical diseases, random violence and the slave trade.

And he was born as an ‘outsider’ in another way: he was illegitimate. His mother was not married to his ostensible father, James Hamilton, and even James Hamilton was probably not his biological father (instead, that seems to have been a gentleman by the name of Thomas Stevens).

His childhood was rough. When Hamilton was a teenager, in the space of a few years,

  • his mother died,
  • his father vanished,
  • his aunt and uncle and grandmother also died,
  • his cousin committed suicide, and
  • Alexander and his brother were disinherited and left penniless orphans.

As Chernow puts it:

that this fatherless adolescent could have ended up a founding father of a country he had not yet even seen seems little short of miraculous.

2) He had an open mind

This experience might mark him as, yes, an American archetype: The Immigrant Who Reinvents Himself.

Reinvent himself he certainly would — several times throughout his short life, and in a unique, and uniquely compelling, way.

He began by getting himself to America. Through savvy, wit, charm, chutzpah, and luck, Hamilton found himself on a trading ship to New York, with an allowance from an older mentor and a job that gave him a bottom-up view of international commerce, shipping and smuggling. (Much later, this expertise would serve him well, when he founded the US customs service and Coast Guard.)

Already his mind was expansive, open to new worlds, both of experiences and ideas. Coming from the Caribbean, he was bilingual in English and French (although, unlike Franklin, Jefferson and Adams, he would never set foot in that superpower of the day).

He was, in a word, cosmopolitan. And this would, yet again, mark him as an outsider in America. For America has always had, and continues to have, an ambivalent — nay, schizophrenic — relationship with cosmopolitan types. Yes, Americans sometimes admire and appreciate them and their perspective. But they also distrust cosmopolitans and are ready to exclude them at a whim — by calling them elitist, for example, or insinuating that they are not real Americans.

Hamilton was also unapologetically erudite, immersing himself into the classics, and in particular in Plutarch, one of my favorites. Among the Founding Fathers he was in good company in this respect, for they all valued intellect and learning. But in America at large this erudition would — yet again — make him potentially suspect, for America has always had, and continues to have, the same ambivalence toward intellectuals that it has toward cosmopolitans.

3) He had a romantic sense of honor

His illegitimate and Caribbean background, and his cosmopolitan style, made him vulnerable to attacks on his reputation. Understandably enough, Hamilton was therefore unusually touchy about his good name, and fiercely keen about defending it. He was an Enlightenment man who believe in reason and law, but he simultaneously retained an older, classical, romantic, even Homeric sense of honor.

His thirst to earn and defend his honor — and specifically his American and patriotic honor — made him demand to be in battle, in the line of actual fire. So he fought with extra valor in the war and came to the attention of George Washington. Hamilton was 22 and Washington 43 when the general made the young man his protégé and chief of staff, giving Hamilton not only a perfect view into American history as it unfolded but a role in shaping it.

Washington was tall, imposing, dignified, laconic and kept his emotions bottled up. Hamilton was five foot seven, slim and athletic, elegant, gave his emotions free reign and was so articulate that he talked himself into trouble as much as out of it. The two men, so different and yet like father and son, would form one of the most important relationships in history.

Hamilton yearned to be more than chief of staff. He wanted to become a war hero, by commanding troops and risking his life. At Yorktown, Washington gave him that command and Hamilton became that hero, after fighting as though driven by a death wish.

In this respect, Hamilton was certainly very different than those Founding Fathers who would become his enemies — above all Jefferson, who somehow always found himself where there was no physical danger, and in one case (when he was governor of Virginia) actually fled on horseback from fighting, for which he was accused of dereliction of duty.

(Remember this when we get to the next post, and the hyper-partisan fight between Jeffersonians and Hamiltonians.)

4) He was ethical but all-too-human

The biggest ethical issue of the day was, of course, slavery. And how did Hamilton regard this institution?

As despicable and evil. He was unambiguous and clear about it. He was the first and staunchest abolitionist among the Founding Fathers.

To us this is a no-brainer, but to Americans at the time it was not. Washington, Jefferson, Madison and all the Southern Founding Fathers owned, bought and sold slaves. They may have had qualms, but never enough to free their slaves or to push for abolition (Washington was the only one of them to emancipate his slaves after his death). This, of course, is the founding irony at the heart of the American idea: Thomas Jefferson owned human beings at the very instant in which he wrote the words “… life, liberty and the pursuit of happiness.”

So Hamilton was unusual in that he was ethically on the right side of this issue. Which would make it all the more ironic — in that inevitable American way — that his political enemies, including some of the aforementioned slave owners, would later try to paint him as immoral.

How? The way one does this in America: with a sex scandal. Hamilton, stupidly and unnecessarily, allowed himself to be seduced. It was America’s first public and politicized bimbo eruption, a sort of proto-Lewinsky affair. It is of no interest or consequence to us, but it was in its day.

Hamilton was certainly a charmer and flirt. That episode aside, however, Hamilton was also a devoted husband and father, perhaps because he had never had a father. He and his wife had an intimate bond. And his eight children meant everything to him. When his oldest son, handsome and also sensitive about his honor, died in a duel, Hamilton went to pieces in grief.

5) He had a nuanced grasp of human nature

From his reading of history and the classics, and his own upbringing in the West Indies, Hamilton developed a sophisticated worldview that was somewhat pessimistic about human nature, at least in comparison to the — then as now — reflexive and simplistic optimism that usually wins arguments in America.

Thus he saw the potential evil of tyranny — which, of course, he was actively fighting with Washington in the war against the British crown — but he also saw the potential evil of mobs, of anarchy. There was a lot of violence in those days, much of it directed at Tories or loyalists, who might easily end up tarred-and-feathered or even lynched. But Hamilton, even though he fought for the republic, always remained humane towards individuals on the other side — and wary of mobs on any side.

Our countrymen have all the folly of the ass and all the passiveness of the sheep in their compositions,

he once said. And that would lead him to say things such as this:

We should blend the advantages of a monarchy and of a republic in a happy and beneficial union.

But that will be the segue to the next post.

6) He died as he lived, but too young

But before I hand over to that next post, just one final anecdote that gives a glimpse into his character. Because he guarded his reputation and honor so jealously, he had, on occasion, to duel. He certainly saw the folly of dueling as he got older. He must even have hated it after he lost his beloved son in a duel.

But when, in the ordinary course of bitter partisan politics, certain things were said between him and a vulgar mediocrity named Aaron Burr, Hamilton picked up the very pistols his son had used, rowed across the Hudson to New Jersey (duelling was illegal in New York), and met his challenger in a clearing by the river.

It appears that Hamilton shot first, but “threw his shot away”, in the parlance. In other words, he deliberately missed by firing into air, thus signaling that both parties had satisfied the requirements of honor and could end this business without shedding blood.

Then it was Burr’s turn. But Burr had a different sense of chivalry. He aimed at Hamilton and found his target.

Hamilton, in convulsions, was rowed back to New York, where he died many agonizing hours later, as his family and city grieved over the loss of a great man, who, aged about 47, had already changed the world in ways that would only fully become clear generations later.

Greatest thinkers: Greeks or Germans?

The Hannibal Blog has featured many thinkers — in the threads on Socrates and Great Thinkers among others.

Inevitably, Greeks and Germans have been somewhat disproportionately represented.

So it is time to revisit the most scientific and conclusive confrontation between Greeks and Germans to date.

Not new but timeless:

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How Muhammad created Europe

Historians are still arguing about why and how (and even when) the Roman Empire fell — and by extension why, how and when the “Middle Ages” and “Europe” (ie, northwestern Europe as we understand it) began.

One theory is that the answer is to be found, somewhat surprisingly, not in northwestern Europe but on the opposite side of the former Roman Empire. This story-line involves Muhammad, Islam and the Arab conquests in the century after Muhammad’s death in 632. The stages of those conquests you see in the map above.

In this post, I want to introduce that thesis to you and the one it tried to replace.

I do this not in order to endorse either thesis, but in order to celebrate the elegant and imaginative beauty of the thought processes of the two historians who produced them.

These two thinkers are

  • Edward Gibbon and
  • Henri Pirenne,

and I am hereby including them into my pantheon of the world’s greatest thinkers.

(Which reminds me: Scientists and philosophers are currently over-represented on my list, so I am also retroactively including the historians Herodotus, Polybius, Livy and Plutarch. Thucydides is already on the list.)

And at the end of the post, I’ll ponder what this eternal debate about Rome tells us about intellectual theorizing in general.

My source, besides the books of Gibbon and Pirenne, is Philip Daileader’s excellent lecture series on the Early Middle Ages.

I) Edward Gibbon

Edward Gibbon

Gibbon was a typical specimen of the Enlightenment. He hung out with Voltaire, considered religion (and especially Christianity) a load of superstitious poppycock, trusted in human reason and was enamored by the classics.

Being a man of independent means, he was able to devote all his time and energies to investigating what he considered the great mystery of antiquity. Why did the Roman Empire fall?

The result was an epic work of beautifully written English prose called The Decline and Fall of the Roman Empire. The first of its six volumes came out in the year of America’s Declaration of Independence.

The book was so powerful that its thesis turned into what we would call a meme. Ask any semi-literate person today why the Roman Empire fell and he is likely to answer something like this:

Barbarians invaded → Rome fell

Gibbon’s thesis in more detail


In brief, Gibbon believed that the Roman Empire was

  1. in part a victim of its own success, having prospered so much that its citizens had become soft, and
  2. in part a victim of Christianization, which replaced the pagan warrior ethic with an unbecoming concern for the hereafter.

As Gibbon famously said, Rome’s

last remains of military spirit were buried in the cloister.

This corrosion of morals or values, according to Gibbon, left the Western Roman Empire (Diocletian had divided it into two halves, east and west, for administrative purposes) vulnerable to the blonde hordes from the north.

And thus, federations of Germanic tribes crossed the Rhine and Danube and ransacked the Roman Empire, eventually sacking Rome itself and deposing the last (Western) Roman emperor in 476.

The Ostrogoths and Lombards took Italy, the Visigoths took Spain and the Franks took Gaul (→ Francia, France).

Within a few generations, one Frankish family, the Carolingians, seized power. Under Charlemagne (= Carolus Magnus, Karl der Grosse, Charles the Great), the Carolingians then united much of western Europe, an area that happens to overlap almost perfectly with the founding members of the European Union.

In the nice round year of 800, Charlemagne, the king of Francia, became a new Emperor. He sparked a small cultural and economic recovery (the “Carolingian Renaissance”), but his descendants bickered about inheritance, and the Carolingian empire split into what would become France, the Low Countries and Germany.

And there we have it: “Europe”.

II) Henri Pirenne

Henri Pirenne

Like Gibbon, Henri Pirenne was a man of his time. But that time was the late nineteenth and early twentieth century. Historians now felt that “moral” explanations of history were a bit woolly and preferred to think in terms of impersonal, and primarily economic, forces rather than great individuals or events.

And this led Pirenne, a Belgian (and thus a Carolingian heir), to a very different, and extremely original, thesis. The title of his monumental book, Mohammed and Charlemagne, essentially says it all.

The Pirenne thesis begins with a view that, first of all, nothing noteworthy “fell” in 476. Who cares if an emperor named, ironically and aptly, “little Augustus” (Romulus Augustulus) was deposed in that year? Roman civilization went on exactly as before. To most Europeans, nothing whatsoever changed.

That civilization was

  1. urban
  2. Mediterranean and
  3. Latin in the West

The Germanic tribes in fact came not to destroy but to join this civilization. They had entered the Roman Empire long before 476 to live there in peace, but were forced repeatedly to move and fight. When they eventually deposed the Romans, the Barbarians settled in the Roman cities and gradually adopted Latin (which was by this time, and partially as a result, branching into dialects that would become Catalan, Spanish, French etc).

Most importantly, the Mediterranean (medius = middle, terra = land) remained the center of this world, and trade across its waters enriched and fed all shores, north and south, east and west.

So what changed?

What changed was that Muhammad founded Islam, united the Arabs and then died. Suddenly, the Arabs poured out of the desert and conquered everything they encountered.

Look again at the map at the very top. In effect, the Arabs conquered the entire southern arc of the former Roman Empire until Charles Martel (Charlemagne’s grandfather) stopped them near Poitiers in France.

The Arabs thus split the Mediterranean in two. Suddenly, the “Mediterranean” was no longer the center of the world, but a dividing line between two worlds.

Ingeniously, Pirenne then inferred the rest of his thesis from archaeological finds: In the years after the Arab conquests, papyrus (from Egypt) disappeared from northwestern Europe, forcing the northerners to write on animal hides. Locally minted coins disappeared, too. Gone, in fact, was everything that was traded as opposed to produced locally.

The Arabs, Pirenne concluded, had blockaded and cut off northern Europe from the rest of the world. Europe thus became a poor, benighted and involuntarily autarkic  backwater.

This, finally, amounts to the “fall” of Roman civilization in northwestern Europe. Roman cities, administration and customs disintegrated. Europe becomes a small and isolated corner of the world.

It is within this then-forgettable corner that the Carolingians rise and create “Europe”. As Pirenne famously said:

Without Islam, the Frankish Empire would have probably never existed, and Charlemagne, without Muhammad, would be inconceivable.

III) So who was right?

I promised to ponder what this debate might say about intellectual theorizing in general. Well, here goes:

1) Nobody needs to be wrong

As it happens, neither Gibbon nor Pirenne have ever fallen out of favor. Both are still considered to have got much of their interpretation right. The caveat is merely that their theses are considered … incomplete.

We encountered such a situation when talking about Newton and Einstein. Einstein in effect proved Newton “wrong”, and yet we have never discarded Newton, just as we won’t discard Einstein when somebody shows his thinking to have been incomplete.

2) Progress = making something less incomplete

Although both Gibbon’s and Pirenne’s theses were incomplete, they add up to an understanding that is less incomplete, so that others can make it even less incomplete.

This, in fact, is what has been happening. Subsequent historians have wondered why, if their theories were true in the West, the Eastern Roman (ie, Byzantine) Empire did not fall for another millennium.

Regarding Gibbon: The East, too, faced Barbarian invasions (from the same tribes). And the East was even more Christian than the West. So something must be missing in Gibbon’s explanation.

Regarding Pirenne: The East, too, was cut off from the south by the Arab conquests (though perhaps not as much).

IV) One possible omission: depopulation

So, even though both Gibbon and Pirenne, may well have been right, that there had to be at least one more factor: disease.

Perhaps it was smallpox arriving from China, and later plague. Perhaps it was something else. (The theory of massive lead poisoning is now discredited. Again: They had lead pipes in the East and the West.)

Whatever the disease(s), the population of the Roman Empire collapsed. And the West, which had fewer people than the East to begin with, became largely empty.

Its cities were deserted. Rome’s population was 1 million during the reign of Augustus but 20,000 by the time of Charlemagne. People used the Roman baths of northern cities as caves. New city walls were built with smaller circumferences than older city walls.

Fields and land lay fallow, too. We know this because taxes were levied on land (not labor), and tax revenues fell due to agri deserti, “abandoned fields”.

Viewed this way, both the Germanic invasions that Gibbon focussed on and the Arab invasions that Pirenne focussed on were perhaps not a cause but a symptom of the fall of Rome. It seems likely that the Germans and Arabs showed up because there were few people blocking their way, and conquered for that same reason.

If we ever find out the complete answer, it will be because Gibbon and Pirenne pointed us in the right direction.

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The “heart” of the Western Tradition: Dante


Nudged by Cheri, I’m re-reading Dante’s Inferno right now on my Kindle. Reading Dante is always a good idea.

The Inferno, or Hell, is the most gripping of the three parts of Dante’s epic Divine Comedy–the more boring parts being Purgatory and Paradise. (And isn’t that interesting, by the way: As every journalist and writer knows, the awful makes for an infinitely better story than the hunky-dory.)

But in this post I want to make a different, more historical, point about Dante: He may just be the single best illustration of a metaphor I told you about last year to explain–really, really explain–the entire Western Tradition.

To recap that post very briefly: You can think of “Western culture” as a human body.

  • The left leg is ancient Athens and Rome, Socrates and Aristotle;
  • the right leg is Jerusalem and the Bible, Moses and Jesus;
  • the crotch is the end of the Roman empire when the two “legs” met;
  • the torso is the Middle Ages, when the two traditions became one;
  • the left arm is the Renaissance;
  • the right arm is the Reformation;
  • the neck is the Enlightenment; and
  • the head is us, ie modernity.

(The metaphor, which comes from Professor Phillip Cary, is more subtle, so please read the older post.)

So where does Dante fit in?

Well, he was a product of the Middle Ages, located in the “torso” just below the left arm pit, where the Renaissance was to begin. The Renaissance, or “left arm”, in this analogy, was to be Petrarch, a fellow Tuscan and co-founder, with Dante, of the “Italian” language.

You see this all through the Inferno: the surprising and constant mixture of Athens/Rome and Jerusalem, of the (pagan) classics and the Judeo-Christian, Bible-thumping fire and brimstone, so that the two legacies merge to form a new and distinct tradition, as two haploid gametes unite to make a new, diploid human being.

The overall structure, both narrative and psychological, is, of course, Biblical: We are in Hell, after all. (The ancients did not have Hell, a place where we are punished for our sins. They only had a boring and gloomy place named Hades.)

But look who guides Dante through this Hell: It is Virgil, the greatest of the Roman poets, who told of brave Aeneas surviving the sack of Troy and founding the Roman nation. Dante can think of no one nobler, and yet Virgil is a pagan, so Dante meets him, along with Homer, Horace and the other ancient greats, in the first circle of Hell. Relatively un-dreadful, this circle is the limbo where those hang out who were unlucky enough to live before there was a Christianity to be baptized into.

Together, Virgil and Dante then descend deeper and deeper, from one circle to the next, to witness the torments of the sinners increasing with the vileness of their sin. But again, look whom they encounter:

  • Cerberus, the three-headed dog who guarded Hades (although Dante describes him slightly differently),
  • Charon, the ferryman who brought the dead souls across the river Styx for their final destination in Hades,
  • Centaurs, half men and half horses, who caused mischief in the Greek myths,
  • even historical characters such as Alexander the Great, whom we meet boiling in a river of blood in return for the blood that he spilled. (Hannibal must have been floating nearby.)

On and on. Virgil and Dante casually discuss things such as “your ethics”, which is assumed to mean Aristotle’s Ethics (the only text on ethics that the medievals had recourse too).

This, then, was the torso just before Petrarch emphasized its left (humanist, classical) side, thus launching the Renaissance and eventually provoking others to raise the right (Protestant, then counter-Reformationist) arm.

Located just below the left arm pit of the Western Tradition, Dante was thus … its heart!

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The veil of ignorance: great thought experiment

John Rawls

John Rawls

What if we could get together to form a new kind of society … and we did not even know who we would be in that society?

This is a famous thought experiment, proposed by the Harvard philosopher John Rawls in his 1971 book, Theory of Justice.

Rawls was trying to justify democracy as fair as opposed to merely utilitarian (ie, “the greatest good of the greatest number”). How would we go about deciding what is fair? By imagining a situation that has never existed, and indeed can never exist.

Rawls called that situation the “original position”:

No one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like. I shall even assume that the parties do not know their conceptions of the good or their special psychological propensities. The principles of justice are chosen behind a veil of ignorance.

You have probably already grasped the power of the experiment. Normally, we think of justice with ourselves in mind. A single black mom in a public-housing project will have a very different view than a start-up entrepreneur in Silicon Valley or a trustafarian in prep school or a prisoner or …. you get the point.

But if we don’t know whether we will be tall or short, male or female, smart or dumb, lazy or ambitious and all the rest of it, we have to test every principle against the possibility that we might be the least advantaged member of society with respect to it.

A simple example: Slavery in 19th-century America.

Slave owners considered America free and fair and were prepared to go to war for that “freedom”. That’s because the slave owners assumed that they were, well, slave owners. Using purely utilitarian reasoning, they might have concluded that slavery produced the maximum pleasure of the greatest number of people (ie, the white majority) and was therefore right.

But if they had played Rawls’ thought experiment, they would have had to imagine that they might instead be slaves. Suddenly, slavery no longer looks so good.

Getting liberté, egalité, fraternité onto one flag


Now, some of you might remember that, back in April, I tried to figure out whether freedom and equality could ever coexist, as the naked-boobed Marianne (pictured) was clearly hoping. In that post, I was thinking about biology. But perhaps the answer lies in Rawls’ thought experiment.

As we imagine a society without knowing what role we have in it, we will certainly agree that it should be free, and that we should not sacrifice that freedom by forcing everybody to be equal.

But that leaves us having to imagine inequality, and, thanks to our veil of ignorance, we might be the ones ending up with the least (wealth, opportunity, beauty, power…). So how can we agree to inequality that is fair?

The answer is

  • First, that inequality must benefit even the least advantaged member of society (though obviously not in the same proportion). So we do not mind that the Sergey and Larry at Google get astronomically rich because even a single black mom in a public-housing project can now google where to get her baby a flu shot.
  • Second, that the cushy positions in society must be open to all.

Intelligence and talent, for those playing the thought experiment rigorously, would thus cease being mere boons for the individuals that are lucky to have them and instead become social resources that help even those who don’t have them.

I can immediately think of lots of things that we still would not agree on–inheritance taxes, say. But Rawls’ thought experiment definitely introduces even a certain amount of fraternité into the equation. Marianne would love him. For the power of this experiment, I’m hereby including Rawls in my pantheon of great thinkers.

Beyond arousal and control: “Flow”


I really like this visual depiction of flow.

Some of you might remember that I am fascinated with the concept of flow, and the Positive Psychology that is based on it.

Flow is a state of effortless and complete absorption into whatever we are doing, a state in which we are and feel at our best and most creative, when we achieve harmony and mastery, when we forget time and feel good.

Flow does not come easily, of course. They say that it takes ten years of training at something–soccer, violin, writing, you name it–before you become able to slip into flow.

Which brings me to this diagram. It is by Mihaly Csikszentmihalyi, an unpronouncable Hungarian psychologist who might just belong into my growing pantheon of great thinkers. Indeed, quite a few people consider him a great thinker, and he has even received an award called Thinker of the Year.

You can view the diagram the following way:

Most of us spend most of our time hanging out somewhere near the bottom left:

  • We are apathetic because we are not challenged and have not applied ourselves to mastery of anything, or
  • we have taken up a challenge unprepared and are floundering, which causes us to worry, or
  • we are good at something but not challenged, so we become bored.

The way out is two sweep either clockwise or counterclockwise in the diagram:

  • Challenge yourself, by finding something you want to master. If your skill level is low, at least you will feel aroused, which is a good first step toward learning and flow.


  • Keep learning, practicing, mastering, refining. Even if you are not challenged yet, you will become relaxed and feel in control, which builds confidence and is also a great step toward flow.

This is, of course, nothing but the self-help manual of the Samurai and Zen disciples through the centuries.

It’s also a great reminder for us parents and teachers (especially those public-school bureaucrats in America): You must, you must, you must challenge a child to “educate” (ex-ducare = lead out) him or her from apathy.

Watch Csikszentmihalyi’s TED talk:

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A Republic, not a Democracy: James Madison


I have been researching James Madison for a little project that I am not yet entirely at liberty to disclose. And my research is reminding me to be extremely impressed–so impressed that he may just be my favorite founding father. He certainly belongs into my pantheon of the world’s greatest thinkers.

Madison, of course, was not only the fourth president but also, and more importantly, the “father” of the US Constitution. He was the one who took the official notes in the sweltering summer heat of Philadelphia in 1787, and the one whose “Virginia Plan” (which was delivered by the other Virginian delegate but conceived by Madison) formed the basis of the subsequent compromises that led to our constitution. He was 36 years old at the time, and as physically short as he was intellectually giant. Wouldst that America had a man of his ilk today.

I am about to sketch out his vision of freedom as succinctly as I can, but let me just say that if you have been reading the Hannibal Blog for a while, you won’t be at all surprised that I admire the man. Madison fits perfectly my tastes for:

Since it is that last point that is most likely to be misunderstood, let me drill into that part of Madison’s thinking. Here is how I understand his views on the matter:

Madison originally preferred to use the word republic to describe the new America they were building, as opposed to the word democracy.


Republic comes from the Latin res publica, which means ‘public thing’–in other words a country ‘owned’ by its people rather than by a monarch. Deriving from Latin, the word reminded educated men such as Madison of republican Rome (ie, Rome before its civil wars), which was so remarkably stable and moderate, and which so impressed Polybius.

Being a public thing, a republic implicitly contains the element that we would call democracy, but it is understood that this is a representative democracy, in which the people choose representatives who in turn decide the issues of the day in competition with other branches of the government. Governance, in other words, has a basis in the people but is removed from the mob.

Most importantly for Madison, minorities in this republic are protected from majorities. He recognized that the tyranny of majorities is perhaps the greatest threat to freedom (which liberal thinking is all about, after all).

Put differently and in modern lingo, Madison was the opposite of a ‘populist‘. If he were around today, certain ‘real-America’ Alaskans would attack him with demagogic effect for being elitist.


Democracy, by contrast, comes from the Greek and means ‘rule of the people‘. The connotation to educated men such as Madison was therefore ancient Athens, during the Periclean era of the Peloponnesian War, which had a direct democracy as opposed to the balanced representative one.

As part of another project that I’m not totally at liberty to disclose yet, I am also looking into that Athenian democracy right now. And allow me to state clearly that it ended in chaos and failure, in pre-emptive wars (Sicily) that should never have happened and mob-mad injustices such as the trial of Socrates.

Direct democracy is of course alive and well today in western states including California. In a mindlessly populist culture, it is a popular idea. (Stuck in a debate? Just say “let the people decide!”) What that leads to I have described in The Economist.