Today is the birthday (1832) of Charles Lutwidge Dodgson, better known by his pen name Lewis Carroll, an English writer, mathematician, logician, Anglican deacon, and photographer. His most famous works are Alice’s Adventures in Wonderland, and its sequel Through the Looking-Glass, but his work in mathematics and logic, though limited in scope and much less well known, is of enduring value.
I’ve had a hard time appreciating the Alice books all of my life. When I was 4 years old my father read me the first chapter of Wonderland as a bedtime story, and that night I had a nightmare that I still remember vividly—everything in the world swirling in a kaleidoscopic jumble. For decades thereafter I could not hear or read the tales, see the classic illustrations, or watch depictions in films without recoiling in horror. I’m a little better now. In fact I managed to control my infantile fears long enough to write a post on the Mad Hatter here 3 years ago: http://www.bookofdaystales.com/mad-hatter-day/ For the moment I’ll pass over these books and return a little later. Meanwhile, a little about his personal life, then his mathematics and photography, plus minor quirks.
During his early youth, Dodgson was educated at home in Croft-on-Tees in North Yorkshire. His reading lists preserved in the family archives testify to a precocious intellect: at the age of seven, he was reading books such as The Pilgrim’s Progress. He also suffered from a stammer – a condition shared by most of his siblings – that often influenced his social life throughout his years. At the age of twelve, he was sent to Richmond Grammar School (now part of Richmond School) in nearby Richmond.
In 1846, Dodgson entered Rugby School where he was evidently unhappy, as he wrote some years after leaving:
I cannot say … that any earthly considerations would induce me to go through my three years again … I can honestly say that if I could have been … secure from annoyance at night, the hardships of the daily life would have been comparative trifles to bear.
Scholastically, though, he excelled with apparent ease. “I have not had a more promising boy at his age since I came to Rugby”, observed mathematics master R. B. Mayor.
He left Rugby at the end of 1849 and entered Oxford University in May 1850 as a member of his father’s old college, Christ Church. He had been at Oxford only two days when he received a summons home. His mother had died of “inflammation of the brain” – perhaps meningitis or a stroke – at the age of 47. His early academic career wavered between high promise and irresistible distraction. He did not always work hard, but was exceptionally talented in mathematics and achievement came easily to him. In 1852, he was awarded first-class honours in Mathematics Moderations, and was shortly thereafter nominated to a Studentship by his father’s old friend Canon Edward Pusey. In 1854, he obtained first-class honours in the Final Honours School of Mathematics, placing first on the schools list. He remained at Christ Church studying and teaching, but the next year he failed an important scholarship through his self-confessed inability to apply himself to study. Even so, his talent as a mathematician won him the Christ Church Mathematical Lectureship in 1855, which he continued to hold for the next twenty-six years. Despite early unhappiness, Dodgson was to remain at Christ Church, in various capacities, until his death.
Traces of Dodgson (and Alice) can be found all around Christ Church to this day. For example, almost opposite opposite Christ Church is Alice’s Shop on St Aldate’s. It was formerly frequented in Victorian times by Alice Liddell, the inspiration for Alice’s Adventures in Wonderland and Through the Looking-Glass and What Alice Found There, who used to buy sweets there. She lived at Christ Church with her father Henry Liddell, who was Dean of the College and Cathedral.
The shop was featured as the Old Sheep Shop in Through the Looking-Glass. One of the original John Tenniel illustrations shows the inside of the shop. It was used as a setting in Chapter 5 of the book (Wool and Water) and is owned by a sheep in the story:
She looked at the Queen, who seemed to have suddenly wrapped herself up in wool. Alice rubbed her eyes, and looked again. She couldn’t make out what had happened at all. Was she in a shop? And was that really — was it really a sheep that was sitting on the other side of the counter? Rub as she could, she could make nothing more of it: she was in a little dark shop, leaning with her elbows on the counter, and opposite to her was an old Sheep, sitting in an arm-chair knitting, and every now and then leaving off to look at her through a great pair of spectacles.
The shop is characteristic of the dream-like qualities within the Looking-Glass world, in that every time Alice tries to focus on a specific object on its many shelves it changes shape and shifts to another shelf. At another point the shop itself vanishes and Alice finds herself outside with the sheep in a boat, having been given a pair of knitting needles which turn into oars in her hands. The sheep herself continues to be make scornful, personal remarks and then finally, on appearing back in the shop, sells Alice an egg, which promptly turns into Humpty Dumpty.
The overwhelming commercial success of the first Alice book changed Dodgson’s life in many ways. The fame of his alter ego “Lewis Carroll” soon spread around the world. He was inundated with fan mail and with sometimes unwanted attention. According to one popular, but almost certainly apocryphal, story, Queen Victoria herself enjoyed Alice In Wonderland so much that she commanded that he dedicate his next book to her, and was accordingly presented with his next work, a scholarly mathematical volume entitled An Elementary Treatise on Determinants. Dodgson himself vehemently denied this story, commenting “… It is utterly false in every particular: nothing even resembling it has occurred”; and it is unlikely for other reasons. As T.B. Strong comments in a Times article, “It would have been clean contrary to all his practice to identify [the] author of Alice with the author of his mathematical works.” He also began earning quite substantial sums of money, but continued with his post at Christ Church even though he disliked teaching.
In 1856, Dodgson took up the new art form of photography under the influence first of his uncle Skeffington Lutwidge, and later of his Oxford friend Reginald Southey. He soon excelled at the art and became a well-known gentleman-photographer, and he seems even to have toyed with the idea of making a living out of it in his very early years.
A study by Roger Taylor and Edward Wakeling exhaustively lists every surviving print, and Taylor calculates that just over half of his surviving work depicts young girls, though about 60% of his original photographic portfolio is now missing. Dodgson also made many studies of men, women, boys, and landscapes; his subjects also include skeletons, dolls, dogs, statues, paintings, and trees. His pictures of children were taken with a parent in attendance and many of the pictures were taken in the Liddell garden because natural sunlight was required for good exposures.
He also found photography to be a useful entrée into higher social circles. During the most productive part of his career, he made portraits of notable sitters such as John Everett Millais, Ellen Terry, Dante Gabriel Rossetti, Julia Margaret Cameron, Michael Faraday, Lord Salisbury, and Alfred, Lord Tennyson.
By the time that Dodgson abruptly ceased photography (1880), he had established his own studio on the roof of Tom Quad at Christ Church, created around 3,000 images, and was a master of the medium, though fewer than 1,000 images have survived time and deliberate destruction. Dodgson reported that he stopped taking photographs because keeping his studio working was too time-consuming. He used the wet collodion process which required considerable skill and experience.
Controversy continues to surround Dodgson’s interest in Alice and other girls as photographic models. I honestly cannot make up my mind as to whether his interest was prurient, or simply part of a common Victorian aesthetic. For me, chronocentrism is as intriguing and troublesome as ethnocentrism. It’s impossible for me to put myself into the mind of a Victorian mathematician, or in the moral milieu of the time.
Dodgson invented a writing tablet called the nyctograph that allowed note-taking in the dark, thus eliminating the need to get out of bed and strike a light when one woke with an idea. I find this so incredibly personal; I have never had the urge to wake in the middle of the night and write my ideas down. The device consisted of a gridded card with sixteen squares and system of symbols representing an alphabet of Dodgson’s design, using letter shapes similar to the Graffiti writing system on a Palm device.
He also devised a number of games, including an early version of what today is known as Scrabble. He appears to have invented — or at least certainly popularized — the “doublet” (word ladder), a form of brain-teaser that is still popular today, changing one word into another by altering one letter at a time, each successive change always resulting in a genuine word. For instance, CAT is transformed into DOG by the following steps: CAT, COT, DOT, DOG.
Within the academic discipline of mathematics, Dodgson worked primarily in the fields of geometry, linear and matrix algebra, mathematical logic, and recreational mathematics, producing nearly a dozen books under his real name. Dodgson also developed new ideas in linear algebra (e.g., the first printed proof of the Kronecker-Capelli theorem), probability, and the study of elections (e.g., Dodgson’s method) and committees; some of this work was not published until well after his death.
His mathematical work attracted renewed interest in the late 20th century. Martin Gardner’s book on logic machines and diagrams, and William Warren Bartley’s posthumous publication of the second part of Carroll’s symbolic logic book have sparked a reevaluation of Carroll’s contributions to symbolic logic. Robbins’ and Rumsey’s investigation of Dodgson condensation, a method of evaluating determinants, led them to the Alternating Sign Matrix conjecture, now a theorem. The discovery in the 1990s of additional ciphers that Carroll had constructed, in addition to his “Memoria Technica”, showed that he had employed sophisticated mathematical ideas in their creation.
Dodgson’s life remained little changed over the last twenty years of his life, throughout his growing wealth and fame. He continued to teach at Christ Church until 1881, and remained in residence there until his death. He died of pneumonia following influenza on 14 January 1898 at his sisters’ home, “The Chestnuts” in Guildford. He was two weeks away from turning 66 years old. He is buried in Guildford at the Mount Cemetery.
Here’s a few favorite quotations:
It’s no use going back to yesterday, because I was a different person then.
She generally gave herself very good advice, (though she very seldom followed it).
“But I don’t want to go among mad people,” Alice remarked.
“Oh, you can’t help that,” said the Cat: “we’re all mad here. I’m mad. You’re mad.”
“How do you know I’m mad?” said Alice.
“You must be,” said the Cat, “or you wouldn’t have come here.”
“Begin at the beginning,” the King said, very gravely, “and go on till you come to the end: then stop.”
“Would you tell me, please, which way I ought to go from here?”
“That depends a good deal on where you want to get to.”
“I don’t much care where –”
“Then it doesn’t matter which way you go.”
“I wonder if the snow loves the trees and fields, that it kisses them so gently? And then it covers them up snug, you know, with a white quilt; and perhaps it says “Go to sleep, darlings, till the summer comes again.”
One of the deep secrets of life is that all that is really worth the doing is what we do for others.
If everybody minded their own business, the world would go around a great deal faster than it does.
“Alice laughed. ‘There’s no use trying,’ she said. ‘One can’t believe impossible things.’
I daresay you haven’t had much practice,’ said the Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.
I’m not strange, weird, off, nor crazy, my reality is just different from yours.
If you drink much from a bottle marked ‘poison’ it is certain to disagree with you sooner or later.
In Hints for Etiquette: Or, Dining Out Made Easy, Dodgson mocks dining habits of his era:
As caterers for the public taste, we can conscientiously recommend this book to all diners-out who are perfectly unacquainted with the usages of society. However we may regret that our author has confined himself to warning rather than advice, we are bound in justice to say that nothing here stated will be found to contradict the habits of the best circles. The following examples exhibit a depth of penetration and a fullness of experience rarely met with:
In proceeding to the dining-room, the gentleman gives one arm to the lady he escorts– it is unusual to offer both.
The practice of taking soup with the next gentleman but one is now wisely discontinued; but the custom of asking your host his opinion of the weather immediately on the removal of the first course still prevails.
To use a fork with your soup, intimating at the same time to your hostess that you are reserving the spoon for beefsteaks, is a practice wholly exploded.
On meat being placed before you, there is no possible objection to your eating it, if so disposed; still in all such delicate cases, be guided entirely by the conduct of those around you.
It is always allowable to ask for artichoke jelly with your boiled venison; however there are houses where this is not supplied.
The method of helping roast turkey with two carving-forks is praticable, but deficient in grace.
I am so thoroughly reminded of Mrs Beeton’s rules and admonitions by this parody. Here she is on oysters – tribute to the Walrus and the Carpenter:
- INGREDIENTS.—3 dozen oysters, 2 oz. butter, 1 tablespoonful of ketchup, a little chopped lemon-peel, 1/2 teaspoonful of chopped parsley.
Mode.—Boil the oysters for 1 minute in their own liquor, and drain them; fry them with the butter, ketchup, lemon-peel, and parsley; lay them on a dish, and garnish with fried potatoes, toasted sippets, and parsley. This is a delicious delicacy, and is a favourite Italian dish.
Time.—5 minutes. Average cost for this quantity, 1s. 9d.
Seasonable from September to April.
Sufficient for 4 persons.
THE EDIBLE OYSTER:—This shell-fish is almost universally distributed near the shores of seas in all latitudes, and they especially abound on the coasts of France and Britain. The coasts most celebrated, in England, for them, are those of Essex and Suffolk. Here they are dredged up by means of a net with an iron scraper at the mouth, that is dragged by a rope from a boat over the beds. As soon as taken from their native beds, they are stored in pits, formed for the purpose, furnished with sluices, through which, at the spring tides, the water is suffered to flow. This water, being stagnant, soon becomes green in warm weather; and, in a few days afterwards, the oysters acquire the same tinge, which increases their value in the market. They do not, however, attain their perfection and become fit for sale till the end of six or eight weeks. Oysters are not considered proper for the table till they are about a year and a half old; so that the brood of one spring are not to be taken for sale, till, at least, the September twelvemonth afterwards.
INGREDIENTS.—Oysters, say 1 pint, 1 oz. butter, flour, 2 tablespoonfuls of white stock, 2 tablespoonfuls of cream; pepper and salt to taste; bread crumbs, oiled butter.
Mode.—Scald the oysters in their own liquor, take them out, beard them, and strain the liquor free from grit. Put 1 oz. of batter into a stewpan; when melted, dredge in sufficient flour to dry it up; add the stock, cream, and strained liquor, and give one boil. Put in the oysters and seasoning; let them gradually heat through, but not boil. Have ready the scallop-shells buttered; lay in the oysters, and as much of the liquid as they will hold; cover them over with bread crumbs, over which drop a little oiled butter. Brown them in the oven, or before the fire, and serve quickly, and very hot.
Time.—Altogether, 1/4 hour.
Average cost for this quantity, 3s. 6d.
Sufficient for 5 or 6 persons.
Prepare the oysters as in the preceding recipe, and put them in a scallop-shell or saucer, and between each layer sprinkle over a few bread crumbs, pepper, salt, and grated nutmeg; place small pieces of butter over, and bake before the fire in a Dutch oven. Put sufficient bread crumbs on the top to make a smooth surface, as the oysters should not be seen.
Time.—About 1/4 hour.
Average cost, 3s. 2d.
Seasonable from September to April.
- INGREDIENTS.—1 pint of oysters, 1 oz. of butter, flour, 1/3 pint of cream; cayenne and salt to taste; 1 blade of pounded mace.
Mode.—Scald the oysters in their own liquor, take them out, beard them, and strain the liquor; put the butter into a stewpan, dredge in sufficient flour to dry it up, add the oyster-liquor and mace, and stir it over a sharp fire with a wooden spoon; when it comes to a boil, add the cream, oysters, and seasoning. Let all simmer for 1 or 2 minutes, but not longer, or the oysters would harden. Serve on a hot dish, and garnish with croutons, or toasted sippets of bread. A small piece of lemon-peel boiled with the oyster-liquor, and taken out before the cream is added, will be found an improvement.
Time.—Altogether 15 minutes.
Average cost for this quantity, 3s. 6d.
Seasonable from September to April.
Sufficient for 6 persons.
THE OYSTER AND THE SCALLOP.—The oyster is described as a bivalve shell-fish, having the valves generally unequal. The hinge is without teeth, but furnished with a somewhat oval cavity, and mostly with lateral transverse grooves. From a similarity in the structure of the hinge, oysters and scallops have been classified as one tribe; but they differ very essentially both in their external appearance and their habits. Oysters adhere to rocks, or, as in two or three species, to roots of trees on the shore; while the scallops are always detached, and usually lurk in the sand.
OYSTER PATTIES (an Entree).
289. INGREDIENTS.—2 dozen oysters, 2 oz. butter, 3 tablespoonfuls of cream, a little lemon-juice, 1 blade of pounded mace; cayenne to taste.
Mode.—Scald the oysters in their own liquor, beard them, and cut each one into 3 pieces. Put the butter into a stewpan, dredge in sufficient flour to dry it up; add the strained oyster-liquor with the other ingredients; put in the oysters, and let them heat gradually, but not boil fast. Make the patty-cases as directed for lobster patties, No. 277: fill with the oyster mixture, and replace the covers.
Time.—2 minutes for the oysters to simmer in the mixture.
Average cost, exclusive of the patty-cases, 1s. 1d.
Seasonable from September to April.
THE OYSTER FISHERY.—The oyster fishery in Britain is esteemed of so much importance, that it is regulated by a Court of Admiralty. In the month of May, the fishermen are allowed to take the oysters, in order to separate the spawn from the cultch, the latter of which is thrown in again, to preserve the bed for the future. After this month, it is felony to carry away the cultch, and otherwise punishable to take any oyster, between the shells of which, when closed, a shilling will rattle.
TO KEEP OYSTERS.
- Put them in a tub, and cover them with salt and water. Let them remain for 12 hours, when they are to be taken out, and allowed to stand for another 12 hours without water. If left without water every alternate 12 hours, they will be much better than if constantly kept in it. Never put the same water twice to them.
OYSTERS FRIED IN BATTER.
INGREDIENTS.—1/2 pint of oysters, 2 eggs, 1/2 pint of milk, sufficient flour to make the batter; pepper and salt to taste; when liked, a little nutmeg; hot lard.
Mode.—Scald the oysters in their own liquor, beard them, and lay them on a cloth, to drain thoroughly. Break the eggs into a basin, mix the flour with them, add the milk gradually, with nutmeg and seasoning, and put the oysters in the batter. Make some lard hot in a deep frying-pan, put in the oysters, one at a time; when done, take them up with a sharp-pointed skewer, and dish them on a napkin. Fried oysters are frequently used for garnishing boiled fish, and then a few bread crumbs should be added to the flour.
Time.—5 or 6 minutes.
Average cost for this quantity, 1s. 10d.
Seasonable from September to April.
Sufficient for 3 persons.
EXCELLENCE OF THE ENGLISH OYSTER.—The French assert that the English oysters, which are esteemed the best in Europe, were originally procured from Cancalle Bay, near St. Malo; but they assign no proof for this. It is a fact, however, that the oysters eaten in ancient Rome were nourished in the channel which then parted the Isle of Thanet from England, and which has since been filled up, and converted into meadows.
“O Oysters,” said the Carpenter,
“You’ve had a pleasant run!
Shall we be trotting home again?’
But answer came there none–
And this was scarcely odd, because
They’d eaten every one.