Lewis Carroll

1
Lewis Carroll

• A man of science and mathematics
• who also happened to write nonsense

Jamie Gilbertson October 25, 2005 Math 471
2
Fast Facts about Lewis Carroll

• Born Charles Lutwidge Dodgson
• Birthday January 27, 1832
• Birthplace Daresbury in Cheshire, England
• Number Three out of Eleven Children
• Father Charles
• His father was an Anglican Clergymen
• Along with his father, he suffered
• from a stutter his whole life
• Mother Frances

3
School Days

• At 11 years old Richmond Boarding School
• Teacher James Tate
• Potential in Mathematics was formed
• 14th Birthday enrolled at Rugby for 3 years
• Began entertaining family with
• Poems
• Stories
• Drawings

4
Who is Alice?

• 1850 Entered Christ Church College in Oxford
• Henry Liddell was Dean at Christ Church College
• Henry Liddell had four Children
• Harry
• Lorina Charlotte
• Alice
• Edith

Photo Taken by Dodgson of Alice Liddell
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Honors

• Finished at Christ Church with First Class Honors
  in Mathematics
• 1855-1881 Mathematical Lecturer at
• Christ Church College

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Hello, my name is Lewis Carroll

• Published two mathematical textbooks in 1860
• By February 1861
• completed another text
• Was working on four more
• Wrote for The Train magazine where he needed a
  penname
• Lutwidge Ludovicus Lewis
• Charles Carolus Carroll

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Off to Wonderland

• July 4, 1862 Alice Stories were born
• Dodgson was traveling with the Liddell children
• February 1863, the stories were written down
• Given the name
• Alices Adventures in Wonderland
• June 1868 Began moving onto
• Through the Looking Glass

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Mathematical Works

• At this time he wrote numerous mathematical
  texts
• A syllabus of plane algebraical geometry (1860)
• Two Books of Euclid (1860)
• The Formulae of Plane Trigonometry (1861)
• Condensation of Determinants (1866)
• Elementary Treatise on Determinants (1867)
• Examples in Arithmetic (1874)
• Euclid and His Modern Rivals (1879)
• The Game of Logic (1887)
• Curiosa Mathematica, Part I A New Theory of
  Parallels (1888)
• Curiosa Mathematica, Part II Pillow Problems
  thought out during Sleepless Nights (1893)
• Symbolic Logic Part I (1896)

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Contributions to Mathematics

• Enjoyed increasing understanding by viewing
  things as a game.
• Some portions of his works were missing.
• Many feel he should be credited with
• Mechanical Test for validity of logical terms
• Truth Tables
• Method of trees for determining
• validity

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Areas of Study

• Recreational Logic
• Determinants
• Geometry
• the mathematics behind tournaments and elections
• Many other puzzles of various sorts

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Determinants
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Determinants

• Used a square matrix to compute the determinant
• Known as condensation
• Condensation is also known as the method of
  contractants

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Review of Determinants

• To find the determinant of a matrix
• For a 2x2 Matrix

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Condensation

• Example Begin with 3x3 matrix
• The first condensation yields

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Condensation

• The second condensation yields
• This is the determinant of the original matrix
• Simplifying the result produces

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Truth Tables
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Review of Truth Tables

• Terminology

 
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Review of Truth Tables
 
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Example Problem

• Use a truth table to determine if
• (PQ) P V Q
• Yes, they are equivalent because the P column and
  the columns of (PQ) and P V Q are the same

 
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A Day for Any Date
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A Day for Any Date

• Developed an algorithm to determine the day of
  the week on which any date falls.

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A Day for Any Date Century

• The Century Item
• Take the Century Item and divide by Four
• Take remainder from three
• Multiply remainder by two

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A Day for Any Date Year

• The Year Item
• Add together the number of dozens, the remainder,
  and the number of fours in the remainder

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A Day for Any Date Month

• The Month Item
• If it begins or ends with a vowel, subtract the
  number denoting its place in the year, from 10.
• This, plus its number of days, gives the item for
  the following month.
• Had a flaw in the Month Number System
• Table has since been developed

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A Day for Any Date Day

• The Day Item
• Use the day of the Month
• Sum the results of each part together
• Divide the answer by seven.
• Use the remainder to determine your day.
• The remainder gives the day of the week

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Four Color Map Problem
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Four Color Map Problem

• Game for Two Players
• Topological Problem of designating
• regions on a map by colors.

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Four Color Map Problem

• Player A draws a map divided into countries
• Player B is to color it using as few colors as
  possible
• Two adjacent countries must have
• different colors
• The object is to force Player B
• to use as many colors as possible

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Four Color Map Problem

• Example

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Doublets
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Doublets

• Created the Doublets Puzzles
• Every step in the word ladder differs by one
  letter and must formulate a new word.
• Example PIG ? STY
• PIG
• WIG
• WAG
• WAY
• SAY
• STY

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A Tiny Bit of Nonsense
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An Unanswered Question

• Why is a raven like a writing-desk?
• The Mad Hatter never answers his riddle
• in Alice's Adventure In Wonderland

The Hatter opened his eyes very wide on hearing
this but all he said was, "Why is a raven like
a writing-desk?"..."Have you guessed the riddle
yet?" the Hatter said, turning to Alice
again."No, I give it up," Alice replied. "What's
the answer?""I haven't the slightest idea," said
the Hatter.
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Finally an Answer

• Carroll's answer
• "Because it can produce a few notes, tho they are
  very flat and it is nevar put with the wrong end
  in front!"
• Note the clever misspelling
• of nevar so it is "raven"
• spelled backwards.

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Other Nonsense Contributions

• From the Poem, Jabberwocky
• "And hast thou slain the Jabberwock? Come to
  my arms, my beamish boy! O frabjous day!
  Callooh! Callay!" He chortled in his joy.
• The word chortle
• Combine the words chuckle and snort
• chortle (chôr tl) n.
• A snorting, joyful laugh or chuckle

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In the End

• Contracted a cold in January 1898
• Breathing became more difficult
• Died at 230pm on January 14, 1898 of a bronchial
  infection
• He was never married

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Special Thanks To

• Cameron Newhams Lewis Carroll Website
• www.lewiscarroll.org
• The Lewis Carroll Homepage
• www.lewiscarroll.com
• Joc/Efr
• www-history.mcs.st-andrews.ac.uk/Mathematicians/
  Dodgson.html
• Math World
• http//mathworld.wolfram.com/Condensation.html
• Sundance Software Technologies
• John Fischers The Magic of Lewis Carroll