Category Archives: Education

Of Tartary

The Universal Pocket Companion (3rd edition, 1760), mostly comprises ready-reckoner type tables as well as information on weights, measures, and currencies, and a lengthy listing of London merchants.  All good practical information.


The book also includes brief summaries of history and geography. Here we see what those who were commoditizing information felt should be part of the mental furniture of the mildly-educated mid-eighteenth century Londoner.  From the geography section, here is the one-paragraph summary of Tartary.

OF TARTARY—The Air of this Country is very different by Reason of its vast Extent from North to South: The most Southern Parts having the same Latitude with the middle Provinces of Spain and the most Northern reaching beyond the arctick polar Circle. The longest Day in the North is about two Months, and the shortest in the South nine Hours and three Quarters.  The Manners of the People are very rude and barbarous; their ordinary Food is Horse-Flesh, and they live in Tents and open Fields. The Religion is Paganism in the North and towards the South Mahometism prevails.  The Great Cham of Tartar is an absolute Monarch, and assumes such a proud Superiority over his Subjects as never to be spoke to but upon their Knee with their Faces towards the Ground. His Subjects stile him the Shadow of God; he looks upon himself as the Monarch of the whole World; and every Day after he has dined, he causes the Trumpets to sound, thereby giving Leave to all the Kings and Princes of the Earth to go to Dinner. The chief Commodities of this Country are Sable, Martins, Silk, Camblets, Flax, Musk, Cinnamon, and great Quantities of Rhubarb.

Now you know all that it was deemed necessary for you to know about Tartary.

Back in the day, this book would have set you back three shillings.  If you missed your chance at the time, you can now get a look at it free with an internet connection through the magic of Google Books.


Categories of Argument

John Tillotson (1630—1694) was an interesting person.  Born in Yorkshire in 1630, son of a Puritan clothier, he went up to Cambridge in 1647, graduating BA in 1650, MA in 1654, and becoming a fellow of Clare College.  Tillotson married the stepdaughter of John Wilkins (incidentally, Oliver Cromwell’s niece) and Wilkins and Tillotson became very close.  Wilkins got Tillotson elected Fellow of the Royal Society, and Tillotson was appointed Wilkins’ literary executor after Wilkins’ death in 1672. Meanwhile, Tillotson was marching up the ranks of the Church of England collecting plum positions and ending up as the Archbishop of Canterbury.

Tillotson published a number of his sermons during has lifetime and after his death, both previously published and unpublished sermons were collected, edited, and published in numerous editions, typically running around 12 or 14 volumes. They were extremely popular among both clergy and lay-people and circulated widely for over a century. In the first sermon in the collected editions (this quote is from the 1748 Edinburgh edition), he lays out a four-fold system of argument, breaking knowledge into mathematical, natural philosophical, and moral realms, as well as matters of fact, in which I think he gives a very clear exposition of epistemology in the late 17th century (he disclaims originality in the classification, but gives a good exposition).

Mathematical things, being of an abstracted nature, are capable of the clearest and strictest demonstration: but conclusions in natural philosophy, are capable of proof by an induction of experiments; things of a moral nature, by moral arguments; and matters of fact, by credible testimony. And though none of these be capable of that strict kind of demonstration which mathematical matters are; yet have we an undoubted assurance of them, when they are proved by the best arguments that things of that kind will bear. No man can demonstrate to me, unless we will call every argument that is fit to convince a wise man a demonstration, that there is such an island in America as Jamaica: yet, upon the testimony of credible persons who have seen it, and authors who have written of it, I am as free from all doubt concerning it, as I am from doubting of the clearest mathematical demonstration. So that this is to be entertained as a form principle, by all those who pretend to be certain of any thing at all, That when any thing, in any of these kinds, is proved by as good arguments as a thing of that kind is capable of, and we have as great assurance that it is, as we could possibly have supposing it were, we ought not in reason to make any doubt of the existence of that thing.

There’s more. In fact there are 254 more sermons, and this one alone runs 55 pages. Enjoy.

George Washington’s Mathematics

Fred Rickey has recently posted on his Academia page a nice joint paper with Theodore Crackel and Joel Silverberg on George Washington’s early mathematics education.

In the 18th-century, students would copy extracts from books and copies of carefully worked computations into their own copy-books that they could then use for study and reference.

Some of George Washington’s original copy or cypher-books are known and the authors work backwards to discover his sources. They show that George Washington learned decimals and some work with logarithms and trigonometry. They also show that he did not use this theory in his surveying problems, relying on measurement of accurate scale drawings rather than computations to find sides of triangles. In a nice turn of phrase, they say Washington “encountered” mathematics, setting aside the questions of how much he understood, let alone used.