Bryan Bunch's Blog: S.T.E.M. History Update

When I was planning Before Eureka! , I wanted from the beginning to contrast purely rational thinking—on the part of Archimedes—with mystical experiences. Once reason was that I noticed that books for young readers these days often have a strong fantasy component, and I wanted to be at least a little bit trendy; but I also had wanted to write for a long time about how what we observe can often be viewed either as part of the natural order or as some supernatural intervention.

When I looked for a god to embody the supernatural, it was easy to think of Artemis. First of all, I knew that Archimedes was killed as a direct result of a festival for Artemis in Syracuse. The citizens got drunk during the celebration and the Roman general Marcellus took advantage of the situation to complete his invasion of the city. And, as I began to research Syracuse, one of the first things I encountered was the story of how Artemis had turned the nymph Arethusa into the fresh-water fountain that encouraged the formation of a Greek colony on the site. Later I also learned that in some versions of the legend, Artemis and her twin brother, Apollo, were born in what later became Syracuse.

While writing Before Eureka! , I read all of a good modern translation of both the Odyssey, and the Iliad<, I knew the stories fairly well from summaries and excerpts and many references in literature, but I had not read the originals from start to finish. In both, but especially in the Odyssey, I found how the Greeks saw the gods interacting with humans. It was not clear why Athena favored Odysseus so strongly, but she just did. When she appeared to help him, she usually showed up disguised as a human that he might otherwise know. I took a similar path with Artemis and Archimedes in my novel. Artemis favors Archimedes and intervenes in his life by appearing in human form (and also appears to Archimedes’ friend Phyllis in dreams).

Choosing Artemis might have seemed like a small thing, but ultimately it affected the entire plot of the novel. I did not have much in mind for the character of Phyllis; I just pictured a thin, tomboy who would be a friend of Archimedes, partly because I had personally had some friends in my childhood who were girls, about as many as close friends who were boys. To make Archimedes more rational, I choose to have his family be Pythagoreans, which had the added benefit that the Pythagoreans not only did not believe in Greek gods and revered number instead, but also they had been persecuted by other Greeks, so that could be a motivation for a villain. I had no idea originally that Artemis would control the story of my book, but then I know that She works in ways that are not always visible to us humans.

When I was planning Before Eureka! , I wanted from the beginning to contrast purely rational thinking—on the part of Archimedes—with mystical experiences. Once reason was that I noticed that books for young readers these days often have a strong fantasy component, and I wanted to be at least a little bit trendy; but I also had wanted to write for a long time about how what we observe can often be viewed either as part of the natural order or as some supernatural intervention.

When I looked for a god to embody the supernatural, it was easy to think of Artemis. First of all, I knew that Archimedes was killed as a direct result of a festival for Artemis in Syracuse. The citizens got drunk during the celebration and the Roman general Marcellus took advantage of the situation to complete his invasion of the city. And, as I began to research Syracuse, one of the first things I encountered was the story of how Artemis had turned the nymph Arethusa into the fresh-water fountain that encouraged the formation of a Greek colony on the site. Later I also learned that in some versions of the legend, Artemis and her twin brother, Apollo, were born in what later became Syracuse.

While writing Before Eureka! I read all of a good modern translation of both the Odyssey and the Iliad. I knew the stories fairly well from summaries and excerpts and many references in literature, but I had not read the originals from start to finish. In both, but especially in the Odyssey, I found how the Greeks saw the gods interacting with humans. It was not clear why Athena favored Odysseus so strongly, but she just did. When she appeared to help him, she usually showed up disguised as a human that he might otherwise know. I took a similar path with Artemis and Archimedes in my novel. Artemis favors Archimedes and intervenes in his life by appearing in human form (and also appears to Archimedes’ friend Phyllis in dreams).

Choosing Artemis might have seemed like a small thing, but ultimately it affected the entire plot of the novel. I did not have much in mind for the character of Phyllis; I just pictured a thin, tomboy who would be a friend of Archimedes, partly because I had personally had some friends in my childhood who were girls, about as many as close friends who were boys. To make Archimedes more rational, I choose to have his family be Pythagoreans, which had the added benefit that the Pythagoreans not only did not believe in Greek gods and revered number instead, but also they had been persecuted by other Greeks, so that could be a motivation for a villain. I had no idea originally that Artemis would control the story of my book, but then I know that She works in ways that are not always visible to us humans.

When the literary level of the books and poems I read rose as I grew older, and partly because some words once little used become fashionable, I began to encounter the word palimpsest. At first, as was my habit as a young man, I ignored a word whose meaning I did not know and plowed ahead, but eventually curiosity overwhelmed me and I looked up the odd word. In the broadest sense, palimpsest means “used for a second purpose,” although from the contexts in which I encountered it, the meaning was more that of something partly hidden, partly known. The word derives from Greek and later Latin for a thing that has been “scratched over,” probably referring to a wax-covered tablet of the type Romans used in which previously written words could be scratched over with a new message. Book collectors, however, restrict the meaning of palimpsest to a parchment that has had the original writing in ink scraped off and new written text covering the parchment, although there may be a shadow of the original still visible. Parchment, made from sheepskin, is expensive, so many surviving documents from the middle ages are palimpsests.

In 1229 CE the scribe Joannes Myronas created what is now considered the greatest palimpsest we know. He did it by writing prayers over several books of the earliest known copies of works by Archimedes. The palimpsest was recognized in 1907 as containing the (mostly hidden) work of Archimedes. What could be read by eyesight alone was published early in the twentieth century, but the wars of that century caused the actual artifact to be moved about and essentially lost until 1960. Finally in 1999 it was turned over to William Noel, a curator of the Walters Art Museum in Baltimore, who was able to arrange for modern scientific and linguistic techniques to uncover the text and drawings of Archimedes.

I started writing Before Eureka! The Adventures of Young Archimedes in 2003, so I soon learned of the now famous palimpsest. In 2007, The Archimedes Codex by Reviel Netz and William Noel was published, which told the history of the document and gave an account of its contents, a book that became one of several touchstones for my novel, which was completed in 2014. More recently, scientists have trained even more powerful x-rays on the pages, clarifying more of Archimedes’original text. We may never know all of what Archimedes wrote, because Joannes Myronas scrambled books, using parts but not all of some and interspersing the pages with other scraped parchments. But the palimpsest provides the first known Archimedes text with drawings, essential for understanding some of the arguments, and several writings not known from any other source.

One of the problems in trying to keep Before Eureka! The Adventures of Young Archimedes historically correct was trying to determine which inventions attributed to Archimedes were really his. At one time or another Archimedes has been credited with the compound pulley, the odometer, the ship’s propeller, a mechanical “computer” that showed the motions of the planets and Moon, and a mirror that could set ships on fire. One of the most intriguing questions is whether he invented the common screw, which began to be used about the time he lived [287 to 212 BC].

The common screw is a simple machine that is exceptionally versatile. Essentially a helical (three-dimensional spiral) coil, it changes rotational motion to linear motion. It is used to hold together two pieces of wood, tighten a lid onto a jar, remove a cork from a bottle, connect a light bulb to a lamp, attach a hubcap to a tire. In each case, the screw changes rotational motion to linear motion. Some suggest the ancient Greek mathematician Archytas of Tarentum, who lived about a century before Archimedes, invented the common screw, but there is little evidence for this.

A similar device for lifting a fluid to a higher level, known as the Archimedean Screw, is almost always attributed to Archimedes. When the lower end of the device is placed in water and the screw is rotated, water slowly rises in the tube. For many centuries the device was commonly used to raise water from one level to another—for irrigating fields, pumping out ships, and so on. It is still used to raise oil in some modern engines.

The Archimedean screw is based on the same principal as the common screw—changing rotation into linear motion—and the timing seems right. Also, Archimedes is known to have studied the spiral—the two-dimensional cousin of the helix—using it to create constructions for trisecting angles or squaring circles. So it seems plausible that he investigated practical ways to use spirals and helices. But Archimedes is said to have placed no value on his inventions, preferring to be known for mathematics. He never described in writing his inventions. And so, a mystery remains.

While making the following entry for 300 BCE in my forthcoming book S.T.E.M. Chronicle about a recently recognized ancient solar observatory, I was taken back to an personal spiritual adventure, visiting Castlerigg near Kenwick in England’s Lake Country. Here is the new entry for S.T.E.M. Chronicle:

The Thirteen Towers solar observatory is constructed at Chankillo in Peru. The Sun’s motion from solstice to solstice can be tracked by viewing the towers at sunrise from one location and at sunset from another.

Castlerigg, about 700 years older than the Thirteen Towers, is not a series of towers, but a henge, or stone circle—in this case, flattened at one end. There is a rectangle of stone in the middle. As you stand in the rectangle, you can see clefts between the nearby hills that appear to be sight lines for viewing the Sun as it stand still at the solstice—or perhaps the Sun appearing in the notch would signal one of the equinoxes, heralding spring or foretelling the coming winter.

Alas for science, but hooray for mystery. Apparently scientists who have studied Castlerigg can locate no solar alignments at all. No one today knows what purpose the henge was.

All I know, what that I felt some spiritual peace just being there, even more than I had found some years earlier at Stonehenge (before it was off bounds to casual visitors). That might be purpose enough.

As is the case with all persons from ancient times, we know little about their lives directly, but have to extrapolate from whatever clues we can find, so the writer of the biography or an historical novel about a famous person from the distant past has to be somewhat of a detective. One of the few clues to the personality of Archimedes is a practice attributed to him by Plutarch, whose description of Archimedes as part of the life of Marcellus is the most extensive account of his life from ancient times: Plutarch says “”he used to trace geometrical figures in the ashes of the fires and diagrams in the oil on his body” and that he forgot to bathe because he was preoccupied thinking about mathematics.
When I was writing Before Eureka! The Adventures of Young Archimedes, I followed Plutarch and brought this behavior into his boyhood, making it the basis of other boys derisively calling Archimedes by the nickname “Figures.” Plutarch’s Archimedes appeared to interact with his own thoughts better than with what society expected of him.
Although I did not start out with this idea—indeed, I didn’t even recognize it until the novel was written—my young Archimedes would today be diagnosed as having Asperger’s Syndrome, one of the lower rungs of the autistic spectrum. I finally understood this when a friend who has Asperger’s and has written two books about it spoke at a meeting I attended. My friend’s experiences described in the talk all seemed like the kind of difficulties with personality that my version of young Archimedes had. Furthermore, the obsession with a particular topic and great skill in dealing with that topic is typical of the autistic spectrum. Archimedes total focus on mathematics, as described by Plutarch, fits that autistic pattern as well.

I saw the movie The Imitation Game the other day. In one of the early scenes the actor playing Alan Turing says that he is needed for a code-breaking task in World War II because he is the greatest mathematician in Britain. I wondered if it was true.

Aside from proving in 1936 that no method can calculate all true results in mathematics (which hardly seems helpful), it would appear to the nonmathematician that before World War II Turing was not doing what we normally think of as mathematics at all. His main result was independently proved in the same year by the American mathematician Alonzo Church [1903-1995], who is barely known outside mathematical circles. This theorem, despite its negative aspect, remains one of the bases of a branch of mathematics called “foundations”—so it counts as mathematics. But Turing’s fame comes more from his work with computers than from his mathematics per se. Here are some of the relevant entries from my book The History of Science and Technology.

Alan Mathison Turing
[b. London, June 23, 1912, d. Wilmslow, Cheshire, England, June 7, 1954]
Before World War II, Turing showed that an idealized machine (a universal Turing machine) using a few simple operations can calculate the values of all functions that a mathematician can compute. Despite this, Turing proved that some mathematical results remain beyond calculation. During the war Turing was instrumental in building a machine that decoded enemy messages, a prototype for electronic computers. After the war Turing developed such computers. Turing's 1952 study of the mathematics of fluid interactions helped biologists show how organisms develop and chemists analyze fluids with periodic properties.

In August of 1936, Alan Turing's paper "On Computable Numbers with an Application to the Entscheidungsproblem" describes the "Turing machine," an imaginary machine that can solve all problems that are computable. In fact, the definition of "computable" is that the problem can be solved by a Turing machine. This paper solves Hilbert's 23rd, the decidability problem or Entscheidungsproblem, by showing that it is not possible to devise a method for determining the truth or falsity of all statements that can be made in a part of formal logic called the predicate calculus. Therefore, there is no single way to prove or disprove all logical statements. Alonzo Church [b. Washington DC, June 14, 1903, d. Hudson, OH, August 11, 1995], independently of Alan Turing, shows that there is no single method for determining whether or not a statement in mathematics is provable or even true (Church's Theorem). See also 1900 MATH.

In 1943: A team headed by Alan Turing develops Colossus at Bletchley Park in England. The Colossus, designed by Thomas Flowers and Maxwell Herman Alexander Newman [b. London, February 7, 1897, d. Comberton, England, February 22, 1984], is the first all-electronic calculating device (it uses 1500 vacuum tubes). Unlike a general-purpose computer, however, Colossus is dedicated to cracking German codes--and is very good at it, possibly influencing the course of World War II.

Most of the famous mathematicians of the 1930s also worked in the foundations branch of mathematics and also produced important theorems, but they were Austrian, Russian, or German, so Turing’s claim of being the greatest British mathematician is justified.

I found this accidentally and wonder where it came from--it does not seem to be from ancient writings. Aldous Huxley is given a credit, but as someone who quoted it. If anyone knows, please let me find out.

A Quote by Archimedes on charm, day, discovery, losing, mind, and spirit:

Spoken of the young Archimedes: . . . [he] was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.

Archimedes (c.. 287 - 212 BC)

Source: quoted by Aldous Huxley
Contributed by: Zaady

When I started writing Before Eureka! The Adventures of Young Archimedes I thought I would begin with some very easy mathematics. The Greek numeration system had no symbol greater than the one for 10,000, which they called a myriad, but Archimedes needed much larger numbers, so he invented a system for writing them. My idea was to have the young boy think about the number of stars and, although there are only about 6,000 stars visible to the naked eye, recognize a need for representing numbers greater than a myriad. We know from one sentence in Archimedes’ writings that his father, Phidias, was an astronomer, so in the first scene I wrote for the book Phidias is instructing his son about the constellations. As a bonus, I knew that the Greek goddess Artemis was said to have created Orion and Scorpio by flinging Earth creatures into the sky; I had already chosen Artemis as a supernatural influence on events because She had a close association with Syracuse and also was indirectly involved in the events that led to Archimedes death.
There are several versions in Greek mythology of what happened to the handsome hunter Orion. I chose the one in which Orion tried to seduce the virgin Artemis (glossed over in my account) so she had him killed by a scorpion. The constellations Orion and Scorpios end up on different sides of the sky because the starry Orion wants to keep as far away from the scorpion constellation as he can.
I needed Phidias and the young Archimedes placed somewhere high so that they could see both constellations at once. Having visited Syracuse to get ideas for the book, I remembered the ruins of an ancient fort that were high above the city, so I set the scene there. To make it logical for the two to visit the fort to observe the stars, it seemed like a good idea to have the family home nearby, which put it in Epipolae.
Then I worried that since Orion dips below the horizon during the summer and Scorpio is in the summer sky, how could Phidias show Archimedes both on the same evening. A friend had a computer program that shows the position of the stars for any latitude for any day in the past or present, so I put him on the case. After considerable computer time, he determined that mid-December in Syracuse would work.
So now I had the season and location for the scene, which would determine much else. And this all occurred because I wanted to include some easy mathematics.

When I started writing Before Eureka! The Adventures of Young Archimedes I thought I would begin with some very easy mathematics. The Greek numeration system had no symbol greater than the one for 10,000, which they called a myriad, but Archimedes needed much larger numbers, so he invented a system for writing them. My idea was to have the young boy think about the number of stars and, although there are only about 6,000 stars visible to the naked eye, recognize a need for representing numbers greater than a myriad. We know from one sentence in Archimedes’ writings that his father, Phidias, was an astronomer, so in the first scene I wrote for the book Phidias is instructing his son about the constellations. As a bonus, I knew that the Greek goddess Artemis was said to have created Orion and Scorpio by flinging Earth creatures into the sky; I had already chosen Artemis as a supernatural influence on events because She had a close association with Syracuse and also was indirectly involved in the events that led to Archimedes death.
There are several versions in Greek mythology of what happened to the handsome hunter Orion. I chose the one in which Orion tried to seduce the virgin Artemis (glossed over in my account) so she had him killed by a scorpion. The constellations Orion and Scorpios end up on different sides of the sky because the starry Orion wants to keep as far away from the scorpion constellation as he can.
I needed Phidias and the young Archimedes placed somewhere high so that they could see both constellations at once. Having visited Syracuse to get ideas for the book, I remembered the ruins of an ancient fort that were high above the city, so I set the scene there. To make it logical for the two to visit the fort to observe the stars, it seemed like a good idea to have the family home nearby, which put it in Epipolae.
Then I worried that since Orion dips below the horizon during the summer and Scorpio is in the summer sky, how could Phidias show Archimedes both on the same evening. A friend had a computer program that shows the position of the stars for any latitude for any day in the past or present, so I put him on the case. After considerable computer time, he determined that mid-December in Syracuse would work.
So now I had the season and location for the scene, which would determine much else. And this all occurred because I wanted to include some easy mathematics.