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 18^th-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.

A Century of Conflict

The European Great Powers of the eighteenth century managed to involve themselves in a great number of extensive conflicts of long duration. Here is a selected list, ignoring minor wars and those primarily against the Ottoman Empire and points further east. I have included links to the relevant Wikipedia pages for any readers who want to know more about the causes and consequences of each conflict.

1700—1721    Great Northern War

Russia, Poland, and Denmark vs. Sweden.

1701—1713    War of Spanish Succession

King of Spain dies with no heir.

England, Dutch Republic, Holy Roman Empire vs. France and Spain.

1718—1720    Quadruple Alliance

Britain, Dutch Republic, France, Austria vs. Spain.

1727—1729    Spanish-British War

Britain vs. Spain. Features blockade of Gibraltar.

1739—1748    War of Jenkins’ Ear

Britain vs. Spain. After 1742 included in next war.

1740—1748    War of Austrian Succession

Can Maria Theresa succeed to Habsburg rule?

Prussia, Bavaria, Spain and France vs. Austria, Britain, Dutch Republic, Sardinia.

1754—1763    French and Indian War

Britain vs. France. North American theater of Seven Years’ war, but it got started earlier.

1756—1763    Seven Years’ War

Britain, Prussia, Spain vs. France, Austria. Russia starts out with Austria and later switches sides.

Due to European colonies, possessions, and extensive trade routes, first global conflict.

1776—1783    American War of Independence

Colonists, France vs. Britain.

1789-1799    French Revolution

French vs. French.

1792—1815    Napoleonic Wars

Napoleon vs. Everybody.

No Mathematics!

Trouble erupted at the meeting of the Chapter House Philosophical Society in January 1785 when one of its members proposed reading a paper on astronomy. The club had been formed in 1780 to discuss ‘Natural Philosophy in its most extensive signification’, but the issue of whether ‘natural philosophy’ a.k.a. science extended as far as mathematical topics had never arisen. The Chair of the Society argued that discussion of topics that might lead to ‘mathematical disquisition’ were unconstitutional. The founding documents of the society were sent for, and finding that they did not exclude exact sciences, the chair next argued that the society should be governed by custom rather than law. Finally a resolution was introduced to ban astronomy in the future. The mathematical instrument maker George Adams Jr., who had just been elected a member of the society at the same meeting, must have wondered what kind of a club he had joined.

I thought this was interesting in light of Sorrenson‘s point about the lack of interest in mathematics at the Royal Society.

This account is taken from the delightful description of events in Millburn (2000), pp. 188-189.

References

Millburn, John R. (2000). Adams of Fleet Street. Instrument Makers to King George III. Aldershot: Ashgate.

Speaking without tongues

Henry Baker became interested in the case of Margaret Cutting who could speak clearly despite having no tongue, and he reported on the case in the Philosophical Transactions of the Royal Society. Apparently, she had a cancer of the tongue as a young child, which caused her tongue to fall out when she was about four years old. Despite this loss, she was able to talk fluently, and sing with a good voice.

Baker first heard about her from a Benjamin Boddington, Turkey Merchant of Ipswich (about whom I know nothing else). Intrigued, Baker had Boddington, accompanied by the Rev. William Notcutt, and William Hammond, apothecary of Ipswich, go to Wickham Market (about twelve miles from Ipswich) to investigate. He sent them with a list of sounds and words with which to test her. She passed all the tests and submitted to a detailed inspection of her mouth that showed indeed she had no tongue. She could also eat and drink just as normal.

In her affidavit, Margaret Cutting said she did not know exactly how old she was, but estimated around twenty-four in 1742. This would make her very close in age to Joshua Kirby, who also grew up in Wickham Market.

After the report to the Royal Society and publication in the Philosophical Transactions, the case was reported in the London newspapers, and an extract from one of the reports was reprinted in the Ipswich Journal of 15 Jan 1743.

Five years later, after lingering doubts of the truthfulness of the case were expressed by some Fellows, they had her come up to London to the Royal Society where she was subjected to a closer analysis by Dr. Milward and Dr. James Parsons MD, FRS, who related the particulars and gave a physiological explanation of why she could still talk in the Philosophical Transactions.

References

Baker, H., 1742. ‘An Account of Margaret Cutting, a Young Woman, Now Living at Wickham Market in Suffolk, Who Speaks Readily and Intelligibly, Though She Has Lost Her Tongue’, Phil. Trans. 42, 143—152.

Parsons, J., 1747. ‘A Physiological Account of the Case of Margaret Cutting, Who Speaks Distinctly, Tho’ She Has Lost the Apex and Body of Her Tongue: Addressed to the Royal Society, by James Parsons M. D. F. R. S.‘ Phil. Trans.
44, 621—626.

Henry Baker

Henry Baker, FRS (1698—1774) was an interesting person. His father, a Clerk in Chancery, died when he was young, and he was largely brought up by his grandmother. He was apprenticed as a bookseller, later declaring his apprenticeship ‘as agreeable a Part of Life as any I have ever known’. Not that he became a bookseller. At the end of his apprenticeship, he went off to visit some relatives and ended up staying for nine years. What caught his interest was the 8-year-old daughter of his host, John Forster, who had been born deaf. Baker undertook to teach Jane and her two younger siblings, also born deaf, to read, write and lip-read, a task in which he was successful and instructing the deaf became his main source of income. He charged high prices and a lucrative practice. He also swore his pupils to secrecy and never revealed the details of his procedure, although it was doubtless based on that devised by the mathematician John Wallis.

It was presumably through a shared interest in the education of the deaf that Baker met Daniel Defoe, whose youngest daughter Sophia he married. They had two sons. The elder, and more colorful one, David Erskine Baker translated Voltaire’s Metaphysics of Sir Isaac Newton into English when only seventeen, was trained as an engineer on account of his mathematical skill, and joined a troupe of travelling players. His brother Henry became a lawyer.

In his youth Baker wrote poetry. Together with Defoe he founded the Universal Spectator, and in the early 1740s he got interested in microscopes. His book on microscopes, about which we will write in a separate post, was much more successful than Benjamin Martin’s Micrographia Nova, selling out a first edition of 1000 copies in only a few months. Although primarily a popularizer rather than a researcher, he used the microscope to study both crystal growth and polyps, earning him a Fellowship in the Royal Society in 1741, and its Copley Medal in 1744.

Baker was an inveterate organizer, recorder and committee member, clearly relishing the organizational tasks involved with the Royal Society, the Society of Arts, the Society of Antiquaries, and the Society for the Encouragement of Arts, Manufactures and Commerce. With these organizations he was intersecting Kirby’s orbit as Kirby was a member of these groups, too.

Most of the information in this post comes from the delightful article on Henry Baker by Gerard L’Estrange Turner.

References

Turner, G.L’E, 1974. ‘Henry Baker, F.R.S.: Founder of the Bakerian Lecture’. Notes Rec. R. Soc. Lond. October 1, 1974 29 1 53-79.

Book Review: Benjamin Martin’s Micrographia Nova

When Benjamin Martin’s Micrographia Nova appeared in 1742, he was still an itinerant lecturer, and the book was published in Reading.

The early 1740s saw rising interest in microscopes and their use as a means of enhancing optical perception and there was an accompanying flurry of publications explaining their uses to readers and, importantly, trying to drum up sales. This was certainly the purpose of Martin’s treatise. Martin’s book contained two large plates illustrating the two types of microscope he had designed with detailed comments on their parts and usage. This portion of the book reads like an instruction manual. Oddly, the plates were engraved by Emanuel Bowen, much better known as a mapmaker.

Martin then has a section of exaggerated computation to impress upon the reader the ‘extreme minuteness of visible Animalculae’ that can be observed with the microscope. The rest of the treatise, some 40 pages or so, is devoted to a catalogue of objects worth looking at under a microscope. The catalog is impressive in its span and its testimony to Martin’s experience with the microscope if, indeed, he had observed all the items he lists, but it is short on significance. He opens with “Human hair; its bulbous Root; its long small Cylindric Form; the Substance, if black, opake; otherwise, transparent” and proceeds through parts of bodies, both human and animal with separate chapters for birds, fish, insects, and reptiles and serpents before tuning to plants and miscellaneous objects.

Martin’s descriptions can be quite vivid and colourful. Here he is on mould:

If that which we call the Vinew or Mould of any Subject be view’d, it will discover a most beautiful Scene of Vegetation of a peculiar kind; there you will discover Fields of standing Corn, i.e. Stamina, with globular Apices; and various other Plants sui Generis; and you will not rarely find those Fields and Meadows stocked with a Sort of nimble small Cattle and Herds, which skip sportively over the Lawns. You will also see their various Pursuits, Contests, and horrid Attacks and Engagements; with divers other diverting Incidents among the Inhabitants of this Terra invisa, or invisible Land.

If that isn’t enough to get you excited, Martin would have you look at snails:

Their Shells are many of them beautifully embellish’d and variegated with Colours, and curiously wrought. The Eyes of Snails are a remarkable Oddity, they are seated on the tops of their large Horns, by which means they can be drawn into the Head or thrust out at Pleasure. Their Teeth are another Microscopic Object, and it is very pretty to see ’em feed on Leaves, &c with this Instrument. This Animal is Hermaphrodite, and the parts of Generation are in the Neck, which in Coitu are easily examined by the Microscope. The Eggs of Snails are round and white, and, when hatch’d, the young tender Brood make a very pretty Scene in the Microscopic Theatre.

It is clear from the many descriptions he gives, that his aim is to encourage amateurs to explore the natural world, to revel in its complexity and to marvel at the previously hidden delights opened up by the new instrument. He does not view the microscope as a research tool. In this he is just reflecting what he does in his lectures – to instruct and delight the wealthier classes. As he says in his Preface, “I have oftentimes been requested by Gentlemen to give a Catalogue of Microscopic Objects, which I have here done, and I presume so compleat, that scarce any extraordinary Phaenomenon, which requires the Use of this Instrument, and within the Reach of a Person in private Life, will be found wanting in it”. The engraving of the microscope carries the note: “These Microscopes are Sold by J. Newbery Bookseller in Reading Berks”, emphasizing the commercial nature of the enterprise.

Of all the objects to be viewed under the microscope, Martin reserves his most fulsome praise for:

THE SEMEN; the infinitely small and numerous Animalculae in all Male Sperm are the most astonishing Spectacle, and as yet the highest Attainment of the Microscope; you cannot fail of seeing Millions of these in the smallest Quantity of the human Semen, if laid under the Microscope while warm, and view’s with the greatest Magnifier, and most strongly illuminated, by the Sun’s Light refracted and reflected upon it.

You can get your copy here.