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Year 1688

The so-called 'Glorious Revolution' in England in 1688 was a pivotal event in the country's history. It also began a train of events leading to almost twenty years of war in Europe and the emergence of Britain as a major power. This is why elsewhere I cover the life of Thomas Pitt who, living from 1653 to 1726, straddled this period of rapid social and economic change in Europe and the world.

Wills, 1688: a global history

To take an overview of the deepening connections between parts of the world, I will often go back to a short but highly interesting book, John Wills' global history of the year 1688. He speculates that: In 1688 a full sense of the variety of the world's places and peoples, of their separations and their connections, was confined to a few, referring to the small number of travellers as well as the literate …

Transmission of mathematical ideas

A few notes here from G.G.Joseph's excellent book, The Crest of the Peacock, specifically looking at evidence for transmission of mathematical knowledge and number systems.

Babylonian origins

See p.111 for first example of Diophantine technique used by Babylonians.

The second example is a cuneiform tablet, catalogued as Plimpton 322. It is not a trigonometrical table but is evidence for the methodical production of Pythagorean triples. We are all familiar with the (3,4,5) triangle and its properties, (that 3²+4²=5²), but not everybody will be aware that there are many more such combinations, infinitely many in fact. They are known as Pythagorean triples. Examples include (7,24,25) and (96,110,146).

With the help of some fairly elementary algebra, it is possible to generate triples using a formula.

This method of generating integral Pythagorean triples is usually attributed to Diophantus (c …

Size of Earth and the Antipodes

In his thesis The origins of antipodal theory (see below for details), Schiöth gives a useful summary of the history of measuring the earth's size.

Calculating the size of the earth

The first known calculation in the extant literature of the circumference of the earth might be derived from Eudoxus. In On the Heavens (298b), Aristotle attributes the figure of 400,000 stades for the circumference of the earth, to unknown 'mathematicians.' Due to Eudoxus’s known influence on Aristotle’s astronomy, some scholars have pointed out that in this passage Aristotle might be referring to Eudoxus.

Value of the stade: The stade (στάδιον or stadion) was an ancient Greek unit of measurement, ‘in origin the distance covered by a plow in a single draft, consisted of 600 Greek feet; but the length of a foot was subject to some local variation in the Greek world’ (Harley & Woodard, 1987, p …

The Greek geographical tradition

Notes

For the ancient Greeks, geography was synonymous with cartography

Examples include Eratosthenes and Ptolemy.

The Greek geographers traced their tradition back to the ancient poets, Homer and Hesiod, followed by Anaximander, "then Democritus and Eudoxus and Dicaearchus, Ephorus and a large number of others; and again, their successors, Eratosthenes, Polybius and Posidonius", as Schiöth abbreviates the list given by Strabo.

Both Homer and Hesiod depicted the earth as a flat circular disc surrounded by the river Oceanus, and Anaximander is credited with the first attempt at a world map on this basis, although lost. It is reconstructed in this example from WM Commons. (FP Note: the dividing lines between continents differ from those accepted later - here the Nile divides Africa from Asia and the Phasis (modern-day Rioni in Georgia) divides Europe from Asia.):

Hecataeus is said to have improved upon Anaximander’s map. Fragments of his Circuit of the …

The difficulty of measuring space and time

Notes

In antiquity, the positions of the stars could be measured, albeit crudely. Observations had shown that when one travelled north or south, the stars visible on any night of the year change. Further north, stars within a broad circle around the Pole Star are visible at all seasons, that is, they never set below the horizon. As you go south, this circle shrinks, but a greater number of equatorial stars become visible only sometimes and at some seasons. Contrastingly, when travelling east and west it was found that the same stars were visible at all locations along what could thus be defined as a line (really a circle) of latitude.

Similarly, measurements of the shadow cast by a gnonom – an upright stick in full sun – would give different results at different latitudes. By travelling up the River Nile past Aswan, one entered the tropical region, where the summer sun …