Dude, Can You Count?: Stories, Challenges, and Adventures in Mathematics

309 Pages·2009·3.33 MB·English

by  Christian Constanda (eds.)

Dude, Can You Count?
Dude, Can You Count?
Stories, Challenges,
and Adventures in Mathematics
CHRISTIAN CONSTANDA
COPERNICUSBOOKS
AnImprintofSpringerScience+BusinessMedia
Ch ristianConstanda
The Charles W. Oliphant End owed Chair
in Mathematical Sciences
The UniversityofTulsa
800SouthTucker Drive
Tulsa, Oklahoma 74104
USA
[email protected]
Disclaimer:
All characters in this book are fictitious. Any resemblance to real persons,
living, dead, or otherwise, is purely coincidental and unintentional. The book
expressestheopinionsoftheauthorandisnotintendedtomalignanyreligion,
ethnic group, organization, or individual in this or any other universe.
Published in The Netherlands by Copernicus Books,
An imprint of Springer Science+Business Media, LLC
ISBN 978-1-84882-538-3 e-ISBN 978-1-84882-539-0
Springer London Dordrecht Heidelberg New York
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Control Number: 2009939689
Mathematics Subject Classification (2010): 97A20, 97B20
© Springer-Verlag London Limited 2009
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For Lia and Dan
Preface
All that is necessary for the triumph of evil is that
good men do nothing.
1
EdmundBurke
Those who think they know everything are a great
nuisance to those of us who do.
2
Isaac Asimov
Dear Reader,
There is no doubt: the world is going to the dogs.
Moderncivilization,asweknowit,isbeingsteadilydevouredbythehungry
demons of sloth and apathy. What we inherited from the ancient Greeks and
then the Romans, the proud tradition of arts and sciences, of culture and law,
commands less and less respect as time goes by, with fewer and fewer fellow
citizenswillingtopreserveitandarrestitspassingintooblivion. Unconvinced?
Just take a look at our institutions and judge for yourself.
People monitoring the general malaise of the human species might regard
the current trends in public school education as one of its symptoms. Per-
sonally, I don’t believe so. I think they are one of its causes. At least where
mathematics is concerned, my many friends and colleagues around the world
and I see evidence of their damaging effects every year: courses need to be
watereddown, remedialclasses become a necessity,examination standardsare
lowered in line with performance expectations, grades are inflated to hide the
sad truth, and so on. Those of us who do not subscribe to such unprincipled
strategiesearnnicknameslikeDarthVader,AttilatheHun,Voldemort,orThe
Terminator. If this is the price we must pay for trying to make society under-
stand that without adequate knowledge of mathematics there is no real hope
for mankind, then so be it. In our fight against the forces of darkness, those
sobriquets become tokens of distinction and we wear them with pride.
The book in front of you is not a learned treatise based on official studies,
reports,andstatistics. Itissimplyaconversationalprimeraboutmathematics.
Morespecifically,itisasui generis,3 tongue-in-cheekdiscussionofhowmathe-
matics impinges on various aspects of human life—directly, through numeracy
skills, or indirectly, through logical reasoning—combined with an attempt to
highlight certain perceived inadequacies in our social universe that act as a
1
Irish orator, philosopher, and politician, 1729–1797.
2
American biochemist, author of science fiction and popular fiction, 1920–1992.
3
Of its own kind;unique. (Latin)
viii Preface
brake on its progress and many of which, ultimately, may be blamed on the
public’s lack of proper education.
Why write on this topic? The reason can be traced back to two incidents,
oneoldandonerecent. Thememoryoftheformerhasbeenwithmeforalong
time, nursing my desire to speak out. The latter was the final trigger.
TheoldincidentoccurredwhenIwasinsecondgrade. OneafternoonIwent
toafriend’shouseandaskedhimtocomeoutandplay. Hesaidthathewould,
butonlyifIcheckedhismathhomeworkforerrors. Sincehewenttoadifferent
school, I agreedand examined what he had scribbled in his notebook. At first
I didn’t understand anything; then, slowly, I began to grasp the enormity of
what he had done: he had taken the numbers from the wordy problem (“If 6
farmers plow 10 hectares in 3 days,....”) and added, subtracted, multiplied,
anddivided them indiscriminately until he gotthe answer givenin the backof
the book!
Atsevenyearsofage,myoptionsfordealingwiththisactofbarbarismwere
very limited: I thought I could either try to make the offender see the error
of his ways, or vent my outrage by beating the living daylights out of him. I
chose diplomacy,but my peaceful approachwas cut short with a shrug and an
indolent “Aw, forget it, it’s only math.” Only math? One word, one single
unfortunate word.... Fists erupted in all directions. Mathematical honor
was satisfied and our friendship survived, but he never asked me to check his
homeworkagain. Thiswasadefiningmomentformebecause,forthefirsttime
in my life, I discoveredhow little some people understood of mathematics and
how they misused and abused it.4
The recent incident was related to me by a colleague, whose neighbor had
asked him how he could find the volume of a rectangular room. “It’s easy,”
my colleague said. “Multiply the length and width of the floor, then multiply
the result by the height of the ceiling.” The neighbor was unhappy. “You are
telling mehow tofindthe horizontal volume,but Idon’tneedthat. I needthe
vertical one.” Lucky for the neighbor, I suppose, that my colleague was not a
seven-year-old.
The book is aimedat a wide audience. Practicallyanyonecomfortable with
polysyllabic English and logical thinking will derive some benefit from it. An
enhanced benefit level is guaranteed for students who want or have to learn
mathematics, teachers of the subject, professionals using it in their work, and
anyone else interested in the fun side of this, the most noble of all sciences.
Thecontentsareorganizedasasequenceof25SCAMs(Stories,Challenges,
andAdventures in Mathematics) that encapsulate the essence of my conversa-
tionswithanunflappablecharacterbythenameofJ.J.Moon,whomImetata
numberofconferencesaroundthecountry. ThefirsttwoSCAMs setthe scene,
introducing JJ and his modus operandi.5 The rest are constructed on a com-
4
I hasten to add that, as I grew up, both my temper and capacity for tolerance
improved considerably.
5
One’s characteristic method of work. (Latin)
Preface ix
mon template, which begins with a couple of simple yet intriguing questions
posed by JJ for students, followed by his pronouncements on an educational,
cultural, ethical, or behavioral issue and my offering of two or three brief hu-
morousstories. JJ’squestionsarethenansweredinasectiontitledNotesAfter
the Meeting. Bringing up the rear, the section A Word to the Wise comments
ona few well-knowncomputationalprinciples andlists DOs and DON’Ts that
clarify their application.
The mathematicalbits can be skipped without detriment to the free flow of
the text, which is written in everyday language, uses the word ‘like’ only with
its propermeaning,andhasno heavy(orevenlight)philosophicalundertones.
Giventhat somereadersmaybe youngandunfamiliarwith certainnames and
ideasmentionedinthe book,I erredonthe sideofcautionandprovidedlavish
details in the solutions, succinct biographical information about the people
whom I quote, and the translation of the foreign language words scattered
(sparingly) throughout.
Theproblemsandstoriesbelongtomathematicalfolkloreandarepractically
impossible to acknowledge. The best I cando in the circumstances is to thank
my friends, colleagues, and students who have brought them to my attention
by word of mouth or e-mail at one time or another, and the unknown (to me)
sources from where they came. (I would be very pleased to hear from anyone
who knows their true origin—not intermediate relays—so I could quote it in
the future.) The final selection is mine and, inevitably, reflects my personal
preferences.
A mathematics educator should teach not just scientific fact, but values as
well; hence the chatty segments, which focus irreverently on certain aspects of
the human condition and any link, solid or vague, direct or through analogy,
theymayhavewithlogicandnumbers. Oftherecreationalquestions,someaim
toshowthatnoteverysolutionisintuitivelyobvious,andsomearedesignedto
illustratehowonecanblunderintoallkindsofnonsenseifrulesarethrownout
the window. The latter should give food for thought to all those who believe
that mathematical felonies like division by zero have been decriminalized.
Do humorousstories havea placein mathematicaldiscourse? Do they ever!
According to Mark Twain,6 humor stems from sorrow and there is no humor
in heaven. He was right: humor is very much at home in the classroom,where
we systematically torture our students with lectures and exams, pretending
that we know what’s best for them. If you listen to 50 minutes of definitions,
theorems, and proofs thrown at you nonstop, your eyes will soon start glazing
over; peppered with a few amusing lines, however, that abstract talk becomes
almost bearable.
The formulas inserted at the end of the SCAMs are fundamental to correct
mathematical manipulation and writing, and should be regarded as the bare
essentialsforstudentsandsundryprofessionalswhousemathematicsasatool.
6
The pen name of Samuel Langhorne Clemens, American writer, journalist, and
humorist, 1835–1910.
x Preface
They arealsoa reminderfor schoolteachersofwhatwe requiretheir graduates
to know when they come to university. In my view, the individuals who can
recite them without hesitation when wokenup in the middle of the night have
a very good chance to achieve a state of mathematical grace.
Muchtomychagrin,insomepartsofthebookfullrigorhadtobesacrificed
to help the nonspecialist understand the gist of the argument. I apologize in
advance to those, including myself, who find this practice distasteful.
The book shines a satirical light on a lot of people and professions, but
such banter is not meant to be disparaging or offensive. I must explain that
J.J. Moon was a very trenchant and opinionated dialogue partner, the type
who does not mince words and takes no prisoners. If he sounds condescending
at times, it is because he is convinced that our way of life needs a few urgent
upgrades,andthatthequickestandmosthonestmethodtomakepeopleaware
of this is to tell them the naked, unembellished truth. JJ’s perception of the
truth,whichmaybe foundunpalatablebysome andinfuriating byothers,was
piecedtogetherfrommediareportsandeyewitnessaccounts,oftenhyperbolized
to drive the point home more forcefully. He advocates that you cannot bring
about real change unless you burst complacency bubbles and throw harpoons
atsacredcows. I triedhard,but inspite ofmy valiantefforts,he wouldnotbe
deflected from his views. Consequently, I wish to make it absolutely clear that
anything objectionable or controversial comes from JJ and has nothing to do
with me. By contrast, anything considerate and pleasant is my merit alone.
You have been warned, now start reading the book—if you dare.
Christian Constanda
Tulsa, Oklahoma, July 2009
Acknowledgements
Thewritingofthisbookhasbeenhelpedalongbymanypeople,whosesugges-
tions, comments, and assistance with software resulted in significant improve-
ments to the original draft.
Particularly deserving of my thanks are, in alphabetical order, Kimberly
Adams, John Bailey, Christopher Banerjee, Karen Bouteller, Liliana Cazacu,
James Childress, Bill Coberly, Peyton Cook, Bryce Culhane, Dan Constanda,
Dale Doty, Smaranda Galis, Tom Grasso, Matthew Hale, Brook Iwata, Kyle
Klavetter,DanielLazar,ElizabethLoew,KevinO’Neal,MauricioPapa,Shirley
Pomeranz, Eric Robison, Sujeet Shenoi, Melanie Smith, Kerry Sublette, Ian
Tweddle, David Wallace, and Charles Windass.
No book sees the light of day without proper editorial guidance and man-
agement. These have been given to me unstintingly by Karen Borthwick at
Springer–London, to whom I am grateful for keeping this project, firmly and
efficiently,onasteadycoursefrombeginningtoend. IalsowishtothankKathy
McKenzie for her very thorough copy-editing of the manuscript, and Matthew
PowerandLaurenStoneyfortheirsmoothhandlingofthe productionprocess.
My deepest gratitude, however, is reserved for my wife, Lia Constanda,
whose logical mind, sound and thoughtful advice, remarkable patience, and
unselfish support keep my fires burning bright.
Contents
Preface ..........................................................vii
Acknowledgements .............................................. xi
List of Acronyms and Abbreviations............................ xix
SCAM 1
JJ and the MICQ ................................................1
EnterJJ.Hispersona,mission,andmethod. The MICQ:anaccurate
measure of selfhood. Succinct discussion of humans with a MICQ
below the all-important mark of 50.
SCAM 2
The Mathematical Commandments...............................9
Brites and unBrites. The ten mathematical rules that underpin
numeracy and their connection with the MICQ. A matter of logic.
Baseball and cricket in an alien purgatory. How to put out a fire in
the faculty lounge. Strange algebraic goings-on.
A word to the wise about logic and human behavior.
SCAM 3
The Public School System .......................................19
Matching socks and contributing fairly to the cost of a party. The
ills of public school education. Mediocrity, dissatisfaction, classroom
discipline, and the teaching unions. A specimen test for graduating
high school students. Salary is inversely proportional to knowledge.
The wall of Jericho. Mass defection of mathematics professors to
plumbing.
A word to the wise about equality and implication.
SCAM 4
The School Mathematical Education.............................33
A cowboy’s testament. The consequences of falling in love with roy-
alty. The Principles of Least Headache, Unlimited Confidence, Con-
venient Choice, and Wishful Thinking. New Whole Math. How to
conthegovernmentoutof$5million. Themotivationalpowersofthe
‘plus’ sign. A snapshot of school mathematics through the decades.
A word to the wise about exact and approximate equalities.