American Solar Challenge 2020 Route

For fans of the American Solar Challenge in July next year, the organisers have announced the route (see map above, click to zoom). See also my updated teams list.

Route specifics:

The night-time image (see map below, click to zoom) shows how the race mostly avoids urban areas:


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.


Seven varieties of metaphysics

I was having a discussion with someone recently on metaphysics, so I thought I would blog about it. Here are seven varieties of metaphysics, describing three “layers” of reality (and yes, I am oversimplifying for brevity).

The first is Platonism. Plato believed that there was a hierarchy of Forms (Ideals), of which the highest was The One (Plato’s version of God). These Forms or Ideals were the true reality, and the physical objects we touched, saw, and tasted were only shadows of that true reality (that is the point of the allegory of the cave). The physical orange which we see and eat reflects Ideals such as “Fruit,” “Sphere,” and “Orange.” Neoplatonism continues and extends this point of view.

Saint Augustine and many later Christians held to a Christianised Platonism, in which the Ideals were thoughts in the mind of God (the Christian God, naturally). The physical objects we touched, saw, and tasted had a greater importance in Christian Platonism than they did for Plato – after all, when God created those objects, “God saw that it was good.” Much as with Platonism, the regularities that people see in the physical universe are explained by the fact that God created the universe in accordance with regularities in the Divine thoughts. However, Christian Platonism does not have the metaphysical hierarchy that Platonism or Neoplatonism have – in Christian Platonism, God makes direct contact with the physical universe.

Aristotle also reacted to Plato by increasing the importance of the bottom layer, and Aristotle’s thought was Christianised by Thomas Aquinas as Thomism. However, in Thomism the all-important bottom layer does very little except to exist, to have identity, and to have properties assigned to it. It is also not observable in any way. This can be seen in the Catholic doctrine of transubstantiation. According to the Tridentine Catechism of 1566, the bread and the wine of the Eucharist lose their bottom (“substance”) layer (“All the accidents of bread and wine we can see, but they inhere in no substance, and exist independently of any; for the substance of the bread and wine is so changed into the body and blood of our Lord that they altogether cease to be the substance of bread and wine”), while the bottom (“substance”) layer of the body and blood of Christ becomes metaphysically present instead.

Idealism denies that the physical universe exists at all. The followers of Mary Baker Eddy take this view, for example, as did George Berkeley. Only thought exists. To quote a famous movie line, “there is no spoon.” These thoughts may be independent of whatever God people believe in or, as in monistic Hinduism, they may be actually be the thoughts of God (in which case, only God exists).

The last three kinds of metaphysics deny the existence of any kind of God. In Platonist Materialism, this denial is combined with a Platonist approach to mathematics, about which I have written before. Mathematics exists independently of the physical universe, and controls the physical universe, in the sense that the physical universe follows mathematical laws. Roger Penrose is one of many scientists holding this view.

In what I am calling Extreme Materialism, the existence of an independent mathematical world is also denied, i.e. there is an empiricist approach to mathematics (mathematics simply describes observed regularities in nature). This view seems to be increasing in popularity among non-religious people, although it causes philosophical problems for mathematics.

Finally, the concept of the Mathematical Universe holds that the so-called “physical universe” is itself composed only of mathematical objects – only mathematics exists (which makes this, in fact, a kind of Idealism).


World Population

Some feedback on my last post expressed surprise that Ptolemy’s specification of the Oikoumene now holds holds 80.6% of the world’s population. Above (click to zoom), I have redrawn the classic bar charts of world population which explain this fact. Africa, Asia, and Europe contain about 86% of the world’s population. Ptolemy excluded what we now know to be Southern Africa (which only drops the total to 85%) and didn’t extend his Oikoumene quite far enough to the east.

The chart below shows the same thing, but using NASA’s image of the Earth at night. It can be seen that the spikes on the bar chart correspond to major cities.


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.

A Medieval Calendar

The beautiful image above (click to zoom) represents the month of September in the Très Riches Heures du Duc de Berry, a book of hours from the 1400s. In the background of the main picture is the Château de Saumur, with its height exaggerated (almost doubled). For comparison, below is a modern photograph of the château (by Kamel15) stretched vertically ×2:

The foreground of the main picture shows the grape harvest. At the top is a complex calendar. On the inner track, around the chariot of the sun, in red and black numerals, are the days of the month. On the outer track, in red and blue numerals, is a zodiacal calendar, showing the last days of Virgo and the beginning of Libra. Adjacent to the inner track are blue letters which relate to the 19-year Metonic cycle. Combining those letters with an appropriate table will show the phases of the moon for a given year.

The manuscript uses the Hindu-Arabic numerals first introduced to Europe by Fibonacci in his Liber Abaci of 1202. They are not quite the same as the ones we use today:

It is interesting to compare those digits with the ones in this German manuscript of 1459 by Hans Talhoffer (although Talhoffer actually mixes two different styles of 5). Then again, the letters of the alphabet have also changed since that time.