\section{Thales and Co.}
\label{thalesandco.}

This is my favorite part of the Greek story. As complicated as Greek history and philosophy can be, it's astonishing that they basically appeared at a single time and at the hands of a single man. And, since before Plato we've known who that person was: the inventor of philosophy, and by extension, physics. A First can happen only one time.

When I write a scientific paper, I do so, with other people and usually devote many pages to the bibliography. I would have no luck submitting a paper for publication without reference to previous work. Now. Take out a blank sheet of paper. What you would be holding is a replica of the bibliography for all of the work of Thales of Melitus. Nobody before him thought like him. Now everyone in the West thinks like him. He had no tradition to guide him and no predecessors. In fact, the intellectual climate into which he was born was totally unlike the tradition that he left. Astonishing.

He's thought to have lived still before the stabilization of Greek writing, so only stories about his words and actions survive through the work of later Greeks. They specifically name him and tell nearly consistent stories about him. He's thought to have lived from around $-620$ until about $-550$. We can check the approximate time using modern, but straightforward astrophysical mechanical calculations. Two of Thales' many talents were those of practical geometer and astronomer, which tells us that he was probably well-traveled. Indeed, he was thought to have learned geometry in Egypt where it was a part of the everyday real-estate and architectural practice of carefully recalculating land areas after annual Nile flooding. Also, the Babylonians had for centuries been the world's master astronomical observers, while also being the world's most {\itshape unimaginative} astronomers. They took data, extensive data over so long a time, that they were able to mechanically predict repeating astronomical events like solar and lunar eclipses. They did nothing with those data, except log them. 

Our hero must have learned their techniques because, as a famous Thales-story goes, he predicted an eclipse of the sun---a big event, this prediction. Horodotus later wrote, ``On one occasion [the Medes and the Lydians] had an unexpected battle in the dark, an event which occurred after five years of indecisive warfare: the two armies had already engaged and the fight was in progress, when day was suddenly turned into night. This change from daylight to darkness had been foretold to the Ionians by Thales of Miletus, who fixed the date for it within the limits of the year in which it did, in fact, take place.'' By turning the crank backwards, the date of such a moon-sun conjunction, calculated for complete darkness at the location of the battlefield site can be precisely determined to be May 28, $-585$, consistent with the stories and right during Thales' mature adulthood.
Other stories abound, among them a story suggestive of Thales as a typically fuzzy academic. Plato and others tell that while walking, he was concentrating so hard that he fell into a well. I can relate to that. A passing young girl (in some versions, old woman) chided him for having his head so far in the clouds that he was unable to see where he was walking. 

So, a thick-headed -7th century loser? Well, he also correctly predicted favorable meteorological conditions for olives, bought up all of the presses in Melitus and Chios and then made a fortune leasing them out. So, one gets the impression of a clever, if focused guy.

But, what's important about Thales was that in addition to serving as a respected teacher and well-traveled mathematician (he was supposed to have been responsible for some geometrical demonstrations) he asked questions that apparently nobody had asked before. 
Look around you. Everything is different, one object to the other, and events, from one time to the next. Weather is different; people have different reactions to the same stimuli; of course seasons repeat, but spring plants are not identical each year; winter storms are random and varying; and so on. The world is more full of dissimilarities, than it is of similarities. 

It's not hard to understand why causes of events would be attributed to the capriciousness of that meddling group of Greek gods. And they were: the gods were responsible for all events that were not understood, and most which were. But, instead of accepting arbitrariness or whim, for some reason Thales asked what was the {\itshape same about the world}. He argued that underlying the seeming accidental nature of the world was a universe which a) \textbf{{\itshape has a consistent, uniform structure}} and b) is \textbf{{\itshape knowable}}. Two remarkable, new ideas.

This pair of notions: that there is a consistency to the universe and that we can comprehend it are the two most important commitments to which every scientist subscribes. If there is anything like a Faith in science, it is embodied in these two ideas. There had been many very sophisticated cultures in the millennia before the 7th century BC, but it was on the western shore of Turkey during precisely this time that Western Philosophy and Science was born in the questions of one man.

He went further. He declared that there was a common substance to all of reality. Water. All life depends on it, the weather either dumps it down, or sucks it up. It's hard to find anything natural that's not somehow related to water, and of course for a Greek, water was their their highway, their Minoan-inspired, claim to fame. 

This is a modern idea. A single substance, responsible for all life and all existence. So, three important ideas: 
\begin{enumerate}
\item the universe is consistent, 
\item it's knowable, and 
\item it is derived from a single, common substance.
\end{enumerate}One can build a science on those ideas.


\subsection{His Students}
\label{hisstudents}

For whatever reason, indeed, these ideas caught on among Thales' contemporaries and students. We know of only a handful, but in all likelihood there were many. Like all teachers who imagine that one or two will stand out among the rest, he had a couple who are in the history books. The topics which concerned them differed in the details, but the Research Programme\footnote{The British spelling will be understood after our interlude on Scientific Knowledge.} was common: a project to understand the common causes which were responsible for the world being the way it is, and not otherwise\footnote{a phrase of Johannes Kepler, a hero our ours heavily influenced by Greek ideas}. This was the basis of what became known as the Ionian School of Philosophy.

The Ionian philosophers were largely secular, which was an important requirement in order for them to make progress. As we'll see also, they tended to just Pronounce Things without what we would tend to think of as scientific assertion. But, that's what happens when you're inventing a new way of thinking---it comes slowly as you learn to speak in a new way.

The student probably closest to Thales was Anaximaner (circa $-610$ - $-546$), about whose life we know very little. We have reason to believe that he wrote extensively on various subjects, among them astronomy and cosmology, but also geography--he is thought to have been the first to make a map of the whole (known) world. So, he must have been a famous Ionian citizen and a practical thinker.

But, he was also deep and in the finest tradition of student-teacher relations, he didn't agree with his mentor. But, the disagreement was in the specifics---he was committed as well to the three, new Thales ideas. He was sympathetic to the idea of a common, underlying substance, but believed it to be a more esoteric substance than water, what he called the apeiron, or ``boundless.'' I mean, where did water come from? Something more fundamental, a substance which would come prior to all. Further, Anaximander had a notion of some sort of dynamics, important balances, tensions between pairs of opposites. Water is opposite and in a healthy way, balanced with dry. Hot is balanced against cold and so on. If one gets out of balance, there is a penalty and so a desire to restore that balance.

This too is a non-trivial, influential notion. With this kind of thinking we begin to develop the idea of unity based on balanced tension{\ldots}a concept fruitfully used in Greek philosophy, but also in later religious thought: the tension between good and evil; heaven and hell; temptation and resistance, etc. In physics, indeed, we have these tensions and tend to also think in terms of balance. The most obvious of these is positive and negative electricity, but also heat and cold, north and south magnetic poles, particles and antiparticles{\ldots}Many dualities are involved in conservation laws as we'll see. 

The other of the two most famous ``A'' students of Thales was Anaximenes of Miletus. For him, water was still worth considering for Fundamental Substance, but he imagined again some sort of dynamic among the various phases of water: invisible vapor, condensation in clouds and mist, liquid water, rocks (yep, he wouldn't have known ice). Further rarified water{\ldots}well, that's fire. But, the point was that the fullness of existence was described by the passage of one form of the single substance into another in a regular and repeatable way and that the differences among the forms were quantitative. 

From Anaximenes, we can see a further retreat from the mystical as he considered seriously the formation of rainbows. Prior, the rainbow was a kind of ephemeral thing, always in the distance, never to be captured, but nonetheless undeniably{\ldots}there. Clearly, magic. Anaximenes argued for a rational explanation. The rainbow was some interaction among light rays, compact air, and water. The rainbow's solution would wait until the 17th century and would tax the most talented geometers, but the Rainbow as a Research Project was initiated by Anaximenes.



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%There is a particularly poignant story of a slightly older and more established mathematician named Gottlob Frege who was similarly pursuing a logical derivation of mathematics. Russell's discovery of the paradox ruined Frege's life work. In reply to Russell's respectful letter informing him of the difficulty, Frege wrote back, ``Your discovery of the contradiction has surprised me beyond words, and I should like to say, left me thunderstruck because it has rocked the ground on which I meant to build arithmetic...I must give some further thought to the matter.'' Later, Russell took pains to highlight Frege's many contributions to mathematics, but the older man never was able to rebuild his system in light of the Russell Paradox.
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