Lewis Carroll in Numberland

His Fantastical Mathematical Logical Life

Robin Wilson

Lewis CarrollMathematical Lecturer

1855 - 1881

What I look like when I’m lecturing

… there’s something grand in the expression of the brow and in the action of the hand.

Letter to Margaret Cunnynghame, 1868

Alice and the Mock Turtle…

The different branches of arithmetic – ambition, distraction, uglification, and derision…

How many hours a day did you do lessons?

Ten hours the first day, nine hours the next, and so on…

Alice and the Two Queens

What’s one and one and one and one and one and one and one and one and one and one?

Take nine from eight…

Divide a loaf by a knife…

The Hunting of the Snark

Two added to one – if that could be done…

( )( )7 10 1000 817

93

392

+ + -=-

Map Making

What do you consider the largest map that would be really useful?

About six inches to the mile.

Only six inches!...

Revd. Charles Dodgson

Croft Rectory

Some problems from Francis Walkingame’s arithmetic text

• What is the cube root of 673373097125? Ans. 8765.

• If from London to York be accounted 50 leagues; I demand how many miles, yards, feet, inches, and barleycorns? Ans. 150 miles, 264000 yards, 792000 feet, 9504000 inches, 28512000 barleycorns.

• What sum did that gentleman receive in dowry with his wife, whose fortune was her wedding-suit: her petticoat having two rows of furbelows, each furbelow 87 quills, and each quill 21 guineas? Ans. £3836: 14s.

Some problems from Francis Walkingame’s arithmetic text

• A gentleman going into a garden, meets with some ladies, and says to them, Good morning to you, 10 fair maids. Sir, you mistake, answered one of them, we are not 10; but if we were twice as many more as we are, we should be as many above 10 as we are now under –how many were they? Ans. 5

• The spectators’ club of fat people, though it consisted of 15 members, is said to have weighed no less than 3 tons – how much, at an equality, was that per man? Ans. 4 cwt.

An Oxford ‘viva voce’ examination

Responsions, 1851

Letter to Louisa, June 1851

Bartholomew ‘Bat’ Price Twinkle, twinkle, little bat…

Oxford Finals Class List, 1854

Letter to Mary Dodgson, December 1854

My dear Sister,

I have just been to Mr. Price to see how I did in the papers, and the result will I hope be gratifying to you. The following were the sum total of the marks for each in the First Class:

Dodgson . . . . . 279 Bosanquet . . . . 261 Cookson . . . . . 254 Fowler . . . . . . . 225 Ranken . . . . . . 213

He also said he never remembered so good a set of men in. All this is very satisfactory.

Christ Church, Oxford

Hiawatha’s Photographing

Lewis Carroll on the Pythagorean Theorem

It is as dazzlingly beautiful now as it was in the day when Pythagoras first discovered it, and celebrated the event, it is said, by sacrificing a hecatomb of oxen [100 oxen] – a method of doing honour to Science that has always seemed to me slightly exaggerated and uncalled-for.

One can imagine oneself, even in these degenerate days, marking the epoch of some brilliant scientific discovery by inviting a convivial friend or two, to join one in a beefsteak and a bottle of wine. But a hecatomb of oxen! It would produce a quite inconvenient supply of beef.

Euclid’s ‘Elements’

• Written c. 300 B.C.

• Most printed book after the Bible

• Used for teaching for 2000 years

• 13 books on geometry, arithmetic, etc.

• Axiomatic and hierarchial

• Widely used in Victorian times

• Strongly supported by Dodgsonbut not by everyone – many ‘modern rivals’

Dodgson’s versions of Euclid

A plane angle is the inclination of two straight lines to one another, which meet together, but which are not in the same direction.

Plain anger is the inclination of two voters to one another, who meet together, but whose views are not in the same direction.

When a line, meeting another line, makes the angles on one side equal to that on the other, the angle on each side is called a right angle.

When a Proctor, meeting another Proctor, makes the votes on one side equal to those on the other, the feeling entertained by each side is called right anger.

Euclid

Euclid

Dodgson

Dodgson

Dodgson’s versions of Euclid

Euclid

Dodgson

An obtuse angle is one which is greater than a right angle.

Obtuse anger is that which is greater than right anger.

Dynamics of a Parti-cle

WEG = Gladstone

WH = William Heathcote

GH = Gathome-Hardy

An Algebraic FallacyLetter to Wilton Rix (1885):

If x and y are each equal to 1, it is plain that

And also that

Hence

Now divide each side of this equation by . Then

But

So that

( )2 22 0x y- - =

( )5 0x y- - =

( ) ( )2 22 5x y x y- - = - -( )x y-

( )2 5x y- + =

( ) ( )1 1 , i.e. 2x y+ = + =

2 × 2 = 5

Alice’s Adventures

Underground

Queen Victoria :‘Send me the next book Mr. Carroll produces.’

1867

She was not amused.

A Tangled Tale

Excelsior…

To My PupilBeloved Pupil! Tamed by thee,

Addish-, Subtrac-, Multiplica–tion,

Division, Fractions, Rule of Three,

Attest thy deft manipulation!

Then onward! Let the voice of Fame

From age to age repeat thy story,

Till thou hast won thyself a name

Exceeding even Euclid’s glory.

A Tangled Tale (1885)

An addition sum

(reverse)

(subtract)

(reverse)

(add)

£ 9 16 s 5 d

£ 5 16 s 9 d

£ 3 19 s 8 d

£ 8 19 s 3 d

£ 12 18 s 11 d

(reverse)

(reverse)

(subtract)

(add)

________________

________________

______

______

763

367

396

693

1089

That’s logic.

4 red (yes), 5 grey (no) counters

(1) Babies are illogical.

(2) Nobody is despised who can manage a crocodile.

(3) Illogical persons are despised.

=> Babies cannot manage crocodiles.

(1) No kitten that loves fish is unteachable.

(2) No kitten without a tail will play with a gorilla.

(3) Kittens with whiskers always love fish.

(4) No teachable kitten has green eyes.

(5) No kittens have tails unless they have whiskers.

=> No kitten with green eyes will play with a gorilla.

Charles Dodgson(Lewis Carroll)

(1832 - 1898)