The triboelectric effect was discovered 2600 years ago by Thales of Miletus. When items in this illustrated (incomplete) list are rubbed together, the low-numbered item gains a positive charge, and the high-numbered item gains a negative charge.

For example, glass rubbed with silk (or, even better, polyester) gains a positive charge, once called “vitreous electricity.” Amber rubbed with wool gains a negative charge, once called “resinous electricity.” Indeed, our word “electron” comes from the Greek ἤλεκτρον, meaning “amber.”

Infinitesimal by Amir Alexander: a book review

Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander (2014)

I recently read Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander. This book concentrates on the “indivisibles” of Bonaventura Cavalieri and the “infinitesimals” of John Wallis (the man who introduced the ∞ symbol). As a history of pre-calculus, that’s rather incomplete. There are also some errors, noted by Judith Grabiner in her review for the MAA.

Alexander portrays the Jesuits as the “bad guys,” suppressing the idea of “indivisibles,” even though interesting and useful mathematical results can be obtained by using them. However, Alexander does not fully explain the Jesuits’ actions. There is not a word about their struggle with the Dominicans for intellectual leadership of the Catholic Church (although this played a major part in the Galileo saga). Nor does he explain the link between defending Aristotle and defending the doctrine of Transubstantiation. And, of course, the critics of Cavalieri and Wallis were actually quite correct. “Infinitely small numbers” greater than zero do not exist, and calculus did not have a rigorous foundation until the work of Cauchy and Weierstrass in the 1800s.

I was left rather disappointed with this book. GoodReads rates it 3.83, but I’m only giving it two stars.

Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander: 2 stars

Looking back: 1987

In 1987, my PhD work at the University of Tasmania was beginning to take shape, and I produced a technical report with some preliminary results. I also started a side-project on functional programming language implementation which was to result in the design of a novel computer (a computer, sadly, that was never actually built, although many people joined in on the hardware aspects).

Also in that year, Supernova 1987A became visible within the Large Magellanic Cloud (picture above taken by the Kuiper Airborne Observatory). The programming language Perl also appeared on the scene, and Per Bak, Chao Tang, and Kurt Wiesenfeld coined the term “self-organized criticality.” Prompted by a discovery in 1986, physicists held a conference session on high-temperature superconductivity, billed as the “Woodstock of physics.” The immediate benefits were somewhat over-hyped, however.

The usual list of new species described in 1987 includes Fleay’s barred frog from northern New South Wales and south-eastern Queensland (picture below taken by “Froggydarb”).

In the world of books, James Gleick popularised chaos theory with his Chaos: Making a New Science, Allan Bloom wrote The Closing of the American Mind (which Camille Paglia called “the first shot in the culture wars”), and Donald Trump co-wrote Trump: The Art of the Deal (nobody imagined that he would be President one day).

Horror writer Stephen King had a good year, with The Tommyknockers and several other novels being published. The term “steampunk” was coined in 1987, and Orson Scott Card’s Speaker for the Dead, the sequel to Ender’s Game, won the Hugo Award for best science fiction or fantasy novel (it also won the Nebula Award in 1986, the year it was published).

In music, The Alan Parsons Project released their album Gaudi (which included the single below), U2 released The Joshua Tree, and Linda Ronstadt, Emmylou Harris, and Dolly Parton released Trio. The Billboard top song for 1987 was the rather silly 1986 single “Walk Like an Egyptian.”

Films of 1987 included 84 Charing Cross Road (based on the wonderful 1970 book by Helene Hanff), Bernardo Bertolucci’s The Last Emperor, Japanese hit A Taxing Woman (マルサの女), sci-fi action film Predator, Australian film The Year My Voice Broke and, of course, the cult classic The Princess Bride (based on the 1973 novel by William Goldman).

In this series: 1978, 1980, 1982, 1984, 1987, 1989, 1991, 1994, 2000, 2004, 2006, 2009.

The fascination of large stones

There is a perennial interest in the megaliths (large stones) used in ancient construction. Sometimes the interest is driven by conspiracy theories. But what are the facts?

Stonehenge (click to zoom, photo by Adrian Pingstone – link)

Around 2580 BC, construction of the Great Pyramid of Giza began, using stones of up to 50 metric tonnes in weight. At about the same time, stones of similar weight were being erected at Stonehenge. Somewhat later, in 1350 BC, the Colossi of Memnon (650-tonne statues) were erected in Egypt

The Western Stone, Jerusalem (photo by David Shankbone – link)

The Western Stone is a large stone block at the base of the Western Wall in Jerusalem. It formed part of the Jewish Temple built by Herod the Great. Herodian architecture was characterised by large closely-fitting chiselled stone blocks, and the Western Stone is one of the largest, weighing about 500 metric tonnes.

Stone of the Pregnant Woman, Baalbek

At about the same time, construction of the Temple of Jupiter began in what is now Baalbek, Lebanon. Stones of up to 800 metric tonnes were used in the foundations. The quarry was 900 metres away, and still contains the 1,000-tonne Stone of the Pregnant Woman, which was not completely separated from the surrounding rock, and was never used. This stone was quarried at an angle, in order to allow it to be easily dropped onto rollers or a sledge.

Later centuries saw the Moai statues of Easter Island and the walls of Cuzco, although these involved weights far less than those of Roman construction.

The Russian Thunder Stone, during transport and in final form (photo on right by Andrew Shiva – link)

The Thunder Stone was a large granite boulder (of about 1,500 metric tonnes) discovered in Russia and transported to Saint Petersburg to be used (after some shaping) as the base of a statue of Peter the Great. Transport took about nine months, being completed in 1770. On land, a sledge was used, pulled by 400 men and rolling over bronze spheres. A special barge was used at sea. This boulder represents the pinnacle of megalith construction. For comparison, its weight was a little over the maximum capacity of a modern mobile crane, such as the Liebherr LTM 11200-9.1.

Construction of the Mussolini Obelisk, Rome

One of the most recent examples is the Mussolini Obelisk in Rome, constructed in 1929 during the fascist regime of Benito Mussolini. Carved from Carrara marble, it weighed around 300 metric tonnes, and was transported on land using a sledge running over planks lubricated with soap. The sledge was pulled by 36 pairs of oxen in Tuscany, and by a tractor in Rome. As with the Thunder Stone, a barge was used at sea. This was perhaps the last example of megalith construction using primarily ancient techniques. Since then, there have been more impressive examples of construction, but using smaller components, newer techniques, and more modern materials. The days of using large stones are over!

The chart below summarises the megaliths we have listed here.

The Oikoumene of Ptolemy

I was reading recently about the Geographia of Ptolemy (written around 150 AD). This classic book applied Greek mathematical skills to mapping and map projection – and if there was one thing the Greeks were good at, it was mathematics. According to Neugebauer, Ptolemy believed the Oikoumene, the inhabited portion of the world, to range from Thule (63° North) to 16°25′ South, and 90 degrees East and West of Syene in Egypt.

The map above illustrates this Oikoumene, with a modern population overlay in red (data from SEDAC). Ptolemy was not too far wrong – today this region holds 80.6% of the world’s population, and the percentage would have been greater in antiquity.

Also shown on the map are some of the many cities listed in the Geographia. Open circles show Ptolemy’s coordinates (from here, adjusted to a Syene meridian), and filled circles show true positions. Ptolemy had reasonably good latitude values (an average error of 1.2° for the sample shown on the map), but much worse longitude values (an average error of 6.8°). The longitude error is mostly systemic – Ptolemy’s estimate of 18,000 miles or 29,000 km for the circumference of the earth was only 72% of the true value (several centuries earlier, Eratosthenes had come up with a much better estimate). If Ptolemy’s longitudes are adjusted for this, the average error is only 1.5°.

However, Ptolemy’s book deserves considerable respect – it is not surprising that it was used for more than a thousand years.