On Pebbles, Votes, Numbers, and Being Wrong

Walking Astoria #2, August 11, 2026

My jury summons.

I received a letter today: “You have been summoned for trial jury service.”

This was interesting to me because I became an American citizen relatively recently.

And last November, for the first time, I voted as an American citizen in the New York City elections.

And now I have jury duty.

Citizenship is a requirement for jury service. You have to be a United States citizen and a resident of the county in which you are summoned. And jury service is described by law not only as an opportunity for eligible citizens, but as an obligation.

The popular jury was one of the defining institutions of Athenian democracy. Large groups of ordinary citizens were selected to hear opposing arguments and decide the case. By the fourth century BCE, jurors voted secretly, by majority, and their decision was final.

So, the historical map almost draws itself: Athens, English common law, United States of America.

The citizen jury begins in Athens, passes into England, becomes part of English common law, crosses the Atlantic, and eventually I become an American citizen in Queens and receive this letter.

It is a beautiful story.

And it is wrong.

Or, at least, the arrow connecting Athens to England is something the evidence does not support.

The modern American jury does descend historically from the English jury and English common law. But the medieval English jury was not simply an Athenian institution transported through history. It emerged separately under the Norman kings, for very different purposes. Ancient Athens and medieval England are two different histories of bringing ordinary people into adjudication.

Like convergent evolution in biology.

Vertebrates and cephalopods independently evolved strikingly similar camera-type eyes: lens, iris, retina, focusing optics. Their last common ancestor did not possess this sophisticated camera-eye architecture, so the similarity is a classic case of convergence rather than inheritance from a recent common ancestor.

The connection looked obvious because I already had a map in my head.

From Athens to England to America.

And the evidence seemed to fit it.

Until it didn’t.

Among the papers that came with my jury summons, there is something called a Juror Ballot. But the word ballot is itself interesting. It comes into English from the Italian ballotta, meaning “small ball.” Small balls were used for voting, and the word later came to mean the vote or the voting paper itself.

A small object made into a political technology.

And then I remembered another one: The pebble.

The ancient Greek word for a small stone or pebble is psēphos.

But it also means a pebble used for reckoning.

A counter.

And a pebble used for voting.

A vote.

The verb psēphizomai means to cast one’s vote with a pebble.

One pebble. One vote. Psēphos means both pebble and vote.

The technology eventually became more sophisticated. Athenian jurors in the fourth century BCE were not simply picking stones from the ground. Archaeologists have recovered standardized bronze juror ballots from the Athenian Agora, including ballots inscribed psēphos dēmosia: public ballot.

And then the pebble appears in mathematics.

The Pythagorean Eurytus is reported to have arranged pebbles in order to represent numerical structures. Aristotle compares this practice to arranging pebbles into shapes such as triangles and squares.

Put four units, four pebbles, in a two-by-two arrangement, and you can form a square. To this day, we call four a square number. Number becomes something you can put on the ground. Something you can point at. Something somebody else can see. Something somebody else can rearrange and check. Something publicly demonstrable.

And in Latin, a pebble, a small stone, is called calculus. Calculus also came to mean a stone used on a counting board, and therefore reckoning or calculation. So the pebble appears again. And it could be:

Number.

Calculation.

Vote.

Judgment.

And it becomes very tempting to draw another map:

The Pythagoreans represented numbers with pebbles. The Romans called a pebble “calculus.” Calculus became the name of a branch of mathematics. Therefore, our mathematical calculus somehow descends from those Pythagorean pebbles.

Again, it sounds beautiful.

Again, I have gone too far.

We know that Pythagoreans used pebbles to represent numerical structures.

We know what the Latin word calculus meant.

We know that pebbles and similar objects were used for reckoning in the ancient world.

But that does not establish the historical chain I just constructed.

Similarity is not genealogy. Maybe this is another kind of convergence. Maybe human societies give similar solutions to similar problems.

And the answer to the question, why a pebble?

Is maybe simple: because it is cheap and everywhere.

Maybe because it is countable.

Maybe because each pebble can stand for one unit while being essentially interchangeable with another pebble.

But I have another hypothesis.

A pebble takes something abstract, something in someone’s mind, and makes it concrete and public.

A number in my head becomes a collection of objects that you can see.

A judgment in my head becomes an object that I place into an urn, and that can be counted with all the others.

One unit.

One vote.

Mathematics and democracy both require, in very different ways, that something that could remain inside an individual mind become available outside of it.

Visible.

Countable.

Public.

I do not know if there is a historical connection there.

That is my hypothesis.

And today, while walking, I received a rather good warning about hypotheses.

The Manhattan skyline under the RFK Bridge, the East River, and pebbles on its shore.

I took this picture. Look underneath the RFK Bridge: Manhattan. Obviously.

Except look more carefully.

On the left side, some of what appears to be part of the Manhattan skyline is actually still Astoria: Old Astoria and Halletts Point, with Manhattan farther behind it.

The photograph has collapsed the distance.

The objects are really there, and my eyes are working, but the map I construct from what I see can still be wrong.

And then I looked closer. Down.

Close-up of the pebbles on the East River’s shore.

There they were.

Pebbles.

Perfect.

I had spent the morning thinking about pebbles, and the shore was covered with them.

Except most of them are not pebbles.

What appeared from a distance to be pebbles turns out, up close, to be mostly pieces of glass.

Pieces of broken glass. Green. Brown. And clear.

The water had worn down their edges until they looked like small stones.

And I had done it again.

I saw something.

I interpreted it.

I constructed a plausible explanation.

And then reality complicated the story.

And in my book, I treat words, their etymologies, languages, and texts as fossils.

And examining these fossils, I will try to understand the organism.

But a fossil is not the organism.

Like, the map is not the territory.

It is evidence that the organism existed.

Something from which we try to reconstruct what was there.

The fossilized words, psēphos, calculus, ballot.

They preserve traces of practices of the past.

But it is impossible for a fossil to tell you the whole story.

And two similar fossils do not prove that one descended from the other.

Could be a case of convergent evolution.

History is messy like that.

The world is messy.

And perhaps scientific thinking begins when we become willing to say:

This is a hypothesis.

Now let us see if it survives.

Reality is the ultimate judge.

But even that relationship is not simple. We do not encounter reality without mediation. We encounter it through our senses, our instruments, our language, the questions we ask, and the maps we already carry with us. Philosophers of science have spent a great deal of time on precisely this problem: observations can test hypotheses, but observations are themselves interpreted, and a hypothesis that survives a test has not thereby been proved true.

It has only survived that test.

So far.

It may be shown wrong in the future.

And we can be wrong too.

Not only because our eyes deceive us.

My eyes did not deceive me about the buildings or the glass.

I deceived myself about what conclusions I drew from what I saw.

Our premises can be wrong.

Our inferences can be wrong.

Our historical chain can be wrong.

Our map can be wrong.

And therefore, any conclusion we draw from evidence has to remain open to revision.

There is one final irony.

I originally wanted to connect this idea directly to the Athenian jury and say, “Even the verdict can always be reopened.”

But that is wrong too.

Athenian jury verdicts were final.

Yet the larger Athenian system was remarkably open to something else: changing its laws and institutions. The Athenians regarded their capacity to modify their laws in response to changing circumstances as itself a democratic virtue.

And they were right.

And today, in these modern iterations of democracy, what was final in an Athenian court is not always final. In the United States, for example, a conviction can be challenged on appeal.

So perhaps, no matter the uncertainty, we have to do something.

A jury has to decide.

A society has to act.

A mathematician has to write the proof.

A scientist has to publish the conclusion.

A doctor has to provide a diagnosis.

A historian has to tell the story.

We cannot remain permanently undecided.

But the channel has to remain open.

Because tomorrow there may be another piece of evidence.

Another argument.

Another photograph.

Another pebble.

So, in my book, I will include what the evidence and established scholarship support.

But I will also include my own hypotheses.

Knowing that I might be wrong.