CSULB - Science Colloquium Jim Stein

[ BACKGROUND TALKING ]
>> LAURA: THIS IS A GREAT TIME TO GET TOGETHER.
THIS IS OUR ACTUALLY SEVENTH [INAUDIBLE] BREAKFAST.
SO WE'VE BEEN ENJOYING THESE FOR LAST YEAR AND THIS YEAR.
WE HAVE SIX DEPARTMENTS IN OUR COLLEGE, SO WE'VE GONE
THROUGH ALL SIX DEPARTMENTS AND ARE
ON OUR SECOND CYCLE BACK TO MATH AGAIN.
SO IT'S KIND OF FUN AND EXCITING TO DO THIS.
I LOOK FORWARD TO THESE EACH TIME.
IT'S REALLY FUN TO, TO HEAR FACULTY TALKING
ABOUT THE THINGS THEY DO, AND THEIR EXCITEMENT
ABOUT DOING THEIR RESEARCH AND,
AND MOST OF THEM WHAT THEY'RE DOING WITH THEIR STUDENTS
AND THE HIGH-RANKING STUDENT WORK,
AND THAT'S JUST REALLY FUN TO SEE.
WE STARTED THIS FELLOWS PROGRAM AS A WAY TO GET FRIENDS
AND ALUMNI TOGETHER BECAUSE WE WANTED TO GET PEOPLE
TO KNOW MORE ABOUT OUR COLLEGE AND WHAT WE'RE DOING HERE
AT CAL STATE - LONG BEACH.
WE HAVE GREAT ALUMNI IN THE COMMUNITY, AND WE HAVE A LOT
OF FRIENDS WE'VE MADE, COLLABORATORS.
AND SO THIS IS AN OPPORTUNITY TO BRING PEOPLE TOGETHER,
TO GET TO KNOW EACH OTHER BETTER, TO LEARN MORE
ABOUT WHAT WE'RE DOING.
AND SO THAT'S WHY WE HIGHLIGHT A DEPARTMENT EACH TIME
TO HIGHLIGHT THE RESEARCH OF A FACULTY MEMBER, AND WHAT'S GOING
ON IN THAT DEPARTMENT JUST SO YOU CAN GET A BETTER SENSE
OF SOME OF THE THINGS THAT WE'RE DOING.
AND WE'RE REALLY PLEASED TODAY TO HIGHLIGHT DR. JIM STEIN
FROM THE DEPARTMENT OF MATHEMATICS AND STATISTICS,
AND WE'LL HEAR MORE ABOUT HIM LATER FROM HIS DEPARTMENT CHAIR,
AND LET ROBERT INTRODUCE HIM.
HERE AT CAL STATE - LONG BEACH, WE'RE ALL ABOUT STUDENTS.
THAT'S WHAT WE'RE HERE FOR IS TO EDUCATE OUR STUDENTS.
AND THE MISSION AT OUR COLLEGE IS TO REALLY DO OUR BEST
TO PREPARE AND TRAIN OUR STUDENTS IN A WAY
SO THAT THEY'RE VERY HIGHLY PREPARED TO GO
OUT INTO GRADUATE PROGRAMS, PROFESSIONAL PROGRAMS,
AND OUT INTO THE WORKFORCE.
OUR STUDENTS GO INTO GOVERNMENT, ACADEMIA,
EDUCATION, [INAUDIBLE].
THEY GO INTO INDUSTRY IN ALL AREAS.
AND SO WE FEEL IT'S REALLY IMPORTANT
THAT WE TRAIN OUR STUDENTS WELL
SO THAT THEY ARE HIGHLY COMPETITIVE THAT WILL ALLOW THEM
TO TAKE THEIR PLACE IN THE COMMUNITY.
AND BECAUSE WE'RE HIGHLIGHTING THE DEPARTMENT OF MATHEMATICS
AND STATISTICS TODAY, I'D JUST
LIKE TO EMPHASIZE WHAT THIS DEPARTMENT DOES IN THE WAY
OF PREPARING OUR STUDENTS.
EVERY STUDENT WHO COMES INTO THIS UNIVERSITY HAS TO TAKE
AT LEAST ONE MATH CLASS, AND THIS RANGES ANYWHERE
FROM PRE-BACCALAUREATE CLASSES, BECAUSE WE DO HAVE STUDENTS
WHO COME WHO ARE NOT READY
TO ACTUALLY START COLLEGE-LEVEL COURSES YET, ALL THE WAY TO,
YOU KNOW, MASTER'S LEVEL MATHEMATICS COURSES.
AND THAT'S AN AWESOME RESPONSIBILITY
FOR A DEPARTMENT TO BE.
THINK ABOUT IT.
YOU HAVE TO BE RESPONSIBLE FOR THE MATH OF EVERY STUDENT
IN THIS UNIVERSITY, AND WE HAVE, LIKE, 38,000 STUDENTS,
SO THAT'S QUITE A BIG JOB.
YOU KNOW, I JUST WANT TO COMMEND DR. ROBERT [INAUDIBLE],
HE'S THE CHAIRMAN OF THE DEPARTMENT.
HE JUST DOES THIS SUPERB JOB OF MAKING SURE WE HAVE WHAT WE NEED
FOR THE STUDENTS AND [INAUDIBLE]
[ APPLAUSE ]
>> LAURA: AND IN ADDITION TO, YOU KNOW, PREPARING MATH MAJORS
AND MATH TEACHERS,
THAT DEPARTMENT SUPPLIES ALL THE MATH COURSES FOR ALL THE SCIENCE
AND ENGINEERING STUDENTS.
SO THAT'S A BIG RESPONSIBILITY TOO, YOU KNOW,
IN PREPARING OUR STUDENTS TO GO
OUT INTO [INAUDIBLE] CAREERS AND THE WORKFORCE.
WE HAVE A NATIONAL PROBLEM OF NOT HAVING ENOUGH PEOPLE
WHO HAVE [INAUDIBLE] WORKFORCE AND SO IT'S ONE OF OUR MISSION,
PART OF OUR MISSION IS TO MAKE SURE WE ARE PREPARING MORE
AND MORE STUDENTS FOR THAT
AND THAT THEY ARE BETTER PREPARED AND,
AND THE MATH DEPARTMENT CERTAINLY HELPS
TREMENDOUSLY THERE.
I THINK WE HAVE A NUMBER OF MAJORS
THAT WE ARE DOING WELL IN, IN WHAT WE DO HERE IN THE COLLEGE.
OUR STUDENTS REALLY DO GO OFF TO TOP-NOTCH GRADUATE PROGRAMS.
YOU KNOW, THE STANFORDS AND THE HARVARDS
AND ALL THE TOP-NOTCH SCHOOLS.
OUR STUDENTS GET THERE.
YOU KNOW, PH.D PROGRAMS, M.B. PROGRAMS.
THEY GET INTO PROFESSIONAL PROGRAMS
AT REALLY TOP-NOTCH SCHOOLS, AND OUR STUDENTS ARE IN DEMAND
IN THE WORKFORCE OUT THERE.
WE HAVE PEOPLE WHO CALL AND SAY THEY WANT OUR STUDENTS,
AND WE'VE TALKED TO PEOPLE THAT ARE IN THE INDUSTRY.
THEY REALLY DO LIKE HOW WE PREPARE OUR STUDENTS,
AND THAT'S REALLY GREAT TO HEAR.
WE ALSO HEAR FROM OUR ALUMNI WHO COME BACK
AND TELL US WHAT A GREAT EXPERIENCE THEY HAD HERE,
AND OFTENTIMES IT'S THAT ONE CLASS OR THAT ONE FACULTY MEMBER
OR THAT RESEARCH EXPERIENCE THAT WAS CAREER OR LIFE CHANGING
FOR THEM IN MANY CASES.
THERE ARE PEOPLE WHO ARE STRUGGLING,
AND THAT ONE FACULTY MEMBER JUST MADE A REAL DIFFERENCE FOR THEM.
AND I'M REALLY PROUD OF OUR FACULTY, AND YOU KNOW, THAT'S,
THAT'S WHAT IT'S ABOUT.
THEIR JOB HERE.
THEY LOVE STUDENTS.
THEY CARE ABOUT STUDENTS.
YOU KNOW, THEY MAKE A DIFFERENCE IN THE LIVES OF OUR STUDENTS,
AND IT'S ALWAYS GREAT TO HEAR OUR ALUMNI.
MARYANN HEARS THIS OFTEN WHEN SHE'S OUT TALKING TO OUR ALUMNI,
AND IT'S REALLY GREAT TO HEAR HOW MUCH THEY APPRECIATE OUR
FACULTY HERE AND EXPERIENCES HERE AT CAL STATE - LONG BEACH.
WE ALSO HAVE A LOT OF COLLABORATIONS IN THE COMMUNITY
THAT WE'RE REALLY PROUD OF AND TO BE A PART OF IT,
AND THESE INCLUDE OTHER COLLEGES WITHIN CAL STATE - LONG BEACH.
THIS ALSO INCLUDES OUR COMMUNITY COLLEGES,
SERIDOS [ASSUMED SPELLING] AND LONG BEACH CITY,
AND WE HAVE A NUMBER OF COLLEAGUES FROM SERIDOS TODAY.
YOU WANT TO WAVE YOUR HANDS OVER THERE.
ANYBODY FROM SERIDOS?
[ APPLAUSE ]
>> LAURA: WE REALLY APPRECIATE THE COLLABORATIONS THEY DO
WITH US, PARTICULARLY IN THE MATH
AND SCIENCE TEACHER PREPARATION.
IT'S JUST A WONDERFUL WORKING RELATIONSHIP WE HAVE WITH THEM,
BUT WE HAVE A LOT OF OTHER WONDERFUL COLLABORATIONS.
I MEAN, WE'RE WORKING WITH SOME DEVELOPERS OF A PCH
IN [INAUDIBLE] WHERE WE MAY HAVE A SCIENCE LEARNING CENTER
DOWN THERE.
WE'RE WORKING WITH [INAUDIBLE] L.A. ON MOVING ONE
OF OUR GREEN FACILITIES OVER THERE TO HAVE A NEW
AND EXPANDED GREEN THING.
SO WE DO A LOT OF THINGS IN OUR COMMUNITY AS WELL AS OUR ALUMNI,
AND WE'RE REALLY PLEASED AND PROUD
TO HAVE THOSE KINDS OF RELATIONSHIPS.
IT'S IMPORTANT THAT WE MAINTAIN THOSE COLLABORATIONS.
YOU KNOW, THAT'S HOW WE CAN BEST SERVE OUR STUDENTS.
THAT THEY HAVE THESE KINDS OF OPPORTUNITIES.
SO, AGAIN, THIS IS WHY IT'S SO IMPORTANT TO HAVE YOU HERE TODAY
TO LEARN MORE ABOUT US.
TO BUILD THOSE COLLABORATIONS WITHIN OUR COMMUNITY.
SO THANK YOU FOR COMING.
WE REALLY APPRECIATE THE PART THAT YOU PLAY
IN THE LIVES OF OUR STUDENTS.
I'D LIKE TO HAVE YOU GET A FEW UPDATES
ABOUT WHAT'S GOING ON IN OUR COLLEGE.
I HAD ANNOUNCED LAST FALL THAT WE HAVE FIVE SEARCHES GOING
TO TENURE-TRACK FACULTY MEMBERS, AND THESE ARE
IN INORGANIC CHEMISTRY, MATH EDUCATION, THEORETICAL PHYSICS,
EXPERIMENTAL PHYSICS, AND SYSTEMS PHYSIOLOGY.
AND AT THE TIME, I SAID WITH THE BUDGET, WE'RE HOPING
THAT WE CAN GO FORWARD WITH ALL OF THESE SEARCHES.
WELL, IN JANUARY, OUR CHANCELLOR ANNOUNCED THAT WE HAVE A FREEZE
OF ALL HIRING WITHIN THE CSU SYSTEM,
AND THAT ONLY HIRING WOULD GO FORWARD FOR THOSE CASES
OF EXCEPTIONS FOR CRITICAL NEEDS.
WELL, FORTUNATELY, THE DAY BEFORE,
WE HAD SENT OUT TO ONE PERSON
FOR THE INORGANIC CHEMISTRY A POSITION, AND SO I'M PLEASED
TO ANNOUNCE THAT WE HAVE DR. SHAHA DARACKSHA [ASSUMED
SPELLING], WHO WILL BE OUR NEW INORGANIC CHEMIST COMING
IN THE FALL.
SO WE'RE PLEASED TO HAVE THAT POSITION ACTUALLY FILLED.
BUT WE HAVE A PROVOST HERE WHO ALSO REALLY HAS A VISION
AND LOOKING FORWARD, AND I'M REALLY PLEASED THAT SHE FELT
THAT WE STILL NEED TO GO FORWARD AND HIRE A TENURE-TRACK FACULTY.
SO SHE DID APPROVE OUR OTHER FOUR SEARCHES AS EXCEPTIONS.
SHE SAW THE NEED WE HAVE HERE, AND SHE BASED THAT NEED
ON THINGS LIKE WE HAVE BOTTLENECK COURSES
WHERE WE REALLY NEED TO HIRE NEW, MORE FACULTY
TO HELP STUDENTS GET THROUGH.
WE'VE HAD CRITICAL COURSES WHERE THEY COULDN'T BE TAUGHT
BECAUSE WE DIDN'T HAVE FACULTY, AND OUR STUDENTS NEED THEM.
SHE WAS LOOKING ALSO TO MAKE SURE
THAT WE HAVE HIGH-QUALITY CANDIDATES, AND IN OUR SEARCHES
AND OUR POOLS, WE HAD THAT.
AND WE HAVE THOSE NEEDS SO SHE DID APPROVE THE EXCEPTIONS
FOR THOSE FOUR OTHER SEARCHES.
SO WE'VE COMPLETED THE INTERVIEWS
FOR THE THEORETICAL AND, AND EXPERIMENTAL PHYSICS,
AND I ANTICIPATE MAKING SOME OFFERS PROBABLY
BY THE END OF NEXT WEEK.
THEN WE ALSO HAVE THE MATH EDUCATION MOVING WELL ALONG
THROUGH THE CANDIDATES, AND WE'LL KNOW MORE NEXT WEEK.
I ANTICIPATE WE'LL MAKE AN OFFER.
REALLY GREAT CANDIDATES IN ALL THESE SEARCHES.
THE SYSTEMS PHYSIOLOGY ONE IS NOT AS FAR ALONG.
WE ACTUALLY DO TELEPHONE INTERVIEWS HOPEFULLY SOON SO.
BUT WE HOPE TO HIRE IN ALL THESE POSITIONS, AND IT'S GOING
TO MAKE A REAL DIFFERENCE IN BRINGING IN NEW FACULTY,
THE EXCITEMENT THEY BRING, THE RESEARCH THEY BRING,
AND WORKING WITH OUR STUDENTS IN FILLING CRITICAL NEEDS
THAT WE DO HAVE WITHIN OUR COLLEGE.
FOR ANY OF YOU WHO HAVE WALKED PAST THE CONSTRUCTION SITE
FOR OUR NEW HALL OF SCIENCE,
WE'RE GOING TO BE [INAUDIBLE] [LAUGHS].
YOU'LL KNOW THAT THAT BUILDING CONSTRUCTION WAS PUT ON HOLD,
AND WE HAVE A BIG HOLE OUT THERE.
WITH THE RAIN, IT'S TURNED
INTO A MEGA SIZE OLYMPIC SWIMMING POOL, [LAUGHS]
BUT IT WILL DRY OUT, AND THE BUDGET WILL GET BETTER,
AND WE WILL COMMENCE THE BUILDING
OF OUR SCIENCE BUILDING.
WE'RE NOT SURE WHEN WE'LL BE ABLE TO GET IT STARTED AGAIN,
BUT WE'RE VERY OPTIMISTIC THAT IT WILL HAPPEN HOPEFULLY SOON.
AND I JUST WANT TO REMIND YOU
THAT WE DO HAVE SOME GREAT NAMING OPPORTUNITIES
IN THAT BUILDING THAT WILL MAKE A REAL DIFFERENCE
FOR OUR STUDENTS.
SO IF ANY OF YOU HAVE AN INTEREST IN A NAMING OPPORTUNITY
OR INTERESTED IN HELPING OUR STUDENTS,
PLEASE SEE MARYANN PARTNER [ASSUMED SPELLING].
MARYANN, YOU WANT TO RAISE YOUR HAND.
[LAUGHS] MARYANN LOVES TO TALK
TO PEOPLE [INAUDIBLE] OF OUR STUDENTS.
AND DESPITE THE BUDGET CUTS, YOU KNOW,
GREAT THINGS ARE HAPPENING.
AND YOU KNOW, I HAVE SUCH AN OPTIMISTIC AND WONDERFUL FEELING
ABOUT WHAT'S GOING ON NOW.
I GO, WHY IS THAT BECAUSE THE BUDGET IS SO BAD, BUT YOU KNOW,
I THINK IT'S BECAUSE EVERYBODY'S JUST COMING TOGETHER.
YOU KNOW, THEY REALIZE THAT, YOU KNOW, THAT WE HAVE TO DO
WITH LESS IN SOME AREAS, BUT THEY'RE JUST SO EXCITED
ABOUT WORKING WITH STUDENTS AND DOING THINGS.
AND I DON'T HAVE TIME TO TALK ABOUT ALL THE THINGS,
BUT I DO WANT TO SHARE SOME REALLY EXCITING NEWS WE JUST
GOT RECENTLY.
DR. JEAN LE BOU [ASSUMED SPELLING] AND THE DEPARTMENT
OF CHEMISTRY AND BIOCHEMISTRY,
AND DR. THOMAS REDDICK [ASSUMED SPELLING] IN THE DEPARTMENT
OF ASTRONO, PHYSICS AND ASTRONOMY JUST RECEIVED NEWS
IN THE LAST COUPLE OF WEEKS
THAT THEY'RE GETTING MSF CAREER AWARDS.
NOW, FOR THOSE OF YOU WHO DON'T KNOW ABOUT IT,
MSF CAREER AWARDS, THIS IS REALLY EXCITING.
THESE ARE HIGHLY-COMPETITIVE, VERY PRESTIGIOUS AWARDS
FOR FACULTY WHO ARE EARLY IN THEIR CAREERS.
DR. BOU IS IN HER SIXTH YEAR HERE, AND DR. REDDICK IS
IN HIS SECOND YEAR HERE.
SO TO GET THESE KINDS OF AWARDS AT THIS POINT
IN THEIR CAREER IS JUST FANTASTIC, AND THEY HAVE,
THESE ARE FIVE-YEAR AWARDS.
DR. BOU IS, IS FOR ABOUT $600,000,
AND DR. REDDICK IS ABOUT $450,000.
SO THESE ARE MAJOR AWARDS, AND THEIR BUDGETS INCLUDE SUPPORT
FOR UNDERGRADUATE AND GRADUATE STUDENTS TO WORK
WITHIN THEIR RESEARCH SO THAT'S THE EXCITING PART TOO.
DR. REDDICK WAS TELLING ME THAT WHEN HE LOOKED
AT THE MSF WEBSITE, ABOUT 35 AWARDS WERE BEING NATIONALLY,
AND WE HAVE NOT JUST ONE, BUT WE HAVE TWO OF THOSE HERE
AT CAL STATE - LONG BEACH.
I THINK THAT TELLS YOU THE QUALITY
OF OUR FACULTY WE HAVE HERE, AND THIS IS JUST REALLY EXCITING.
I MEAN, WE'RE REALLY PROUD OF THOSE TWO AS WELL
AS ALL OF OUR FACULTY.
IF YOU HAPPEN TO SEE THEM, TELL THEM CONGRATULATIONS.
>> ROBERT: IN A RECENT ARTICLE IN THE "WALL STREET JOURNAL,"
THEY RANKED THE 200 PROFESSIONS BASED ON FIVE INGREDIENTS.
ENVIRONMENT, INCOME, EMPLOYMENT OUTLOOK,
PHYSICAL DEMAND, AND STRESS.
[LAUGHTER] LUMBERJACKS CAME IN 200.
DAIRY WORKER, 199.
TAXI DRIVER, 198.
AT THE OTHER END, IN THIRD PLACE WAS STATISTICIANS.
SECOND, ACTUARIES.
AND NUMBER ONE WAS MATHEMATICIANS.
DO NERDS RULE?
[LAUGHTER] [INAUDIBLE] SOME AMONG YOU HAVE HEARD ME
ON THE KING, TALK ABOUT THE [INAUDIBLE] OF THE NERVES.
THE DEPARTMENT OF MATHEMATICS
AND STATISTICS IS A VERY LARGE DEPARTMENT
AS LAURA HAS JUST SAID.
LAST FALL, THE DEPARTMENT HAD 39 TENURE, TENURE-TRACK FACULTY,
42 LECTURERS, 22 TEACHING ASSISTANTS,
AND 14 GRADUATE ASSISTANTS.
IT TAUGHT OVER 41 PERCENT OF THE UNITS OF THE COLLEGE FOR A TOTAL
OF 1,842 FULL-TIME STUDENTS.
THAT'S A SMALL UNIVERSITY.
ALMOST SIX PERCENT OF THE UNITS OF THE WHOLE UNIVERSITY.
8,625 STUDENTS TOOK CLASSES FROM US,
OF WHICH 430 ARE UNDERGRADUATE MAJORS AND MORE
THAN 165 ARE GRADUATE STUDENTS IN FOUR PROGRAMS.
APPLIED MATHEMATICS, APPLIED STATISTICS,
MATHEMATICS EDUCATION, AND PURE MATHEMATICS.
OUR MAJORS, BOTH GRADUATE AND UNDERGRADUATE,
GO ONTO A VARIETY OF PROFESSIONS.
SOME WORK IN BUSINESS AND INDUSTRY
SUCH AS INSURANCE COMPANIES OR MANUFACTURING
OR HEALTH CARE COMPANIES DOING ANALYSIS OR ACTUARIAL WORK.
SOME GO ONTO GOVERNMENT WORKING DOING NUMBER CRUNCHING.
MANY BECOME TEACHERS AT THE HIGH-SCHOOL LEVEL IN LONG BEACH
AND L.A. AND ORANGE COUNTIES.
FEW, BUT STILL A SIGNIFICANT NUMBER, AS SEVERAL OF HERE,
ARE HERE,
BECOME COMMUNITY-COLLEGE TEACHERS THROUGHOUT THE CITY,
THE STATE, AND THE COUNTRY, AND A SELECT FEW GO
TO EARN PH.D'S AND TAKE OVER MY JOB.
[LAUGHTER] RECENTLY, I WAS ASKED WHAT DOES BEACH PRIDE MEAN
TO YOU?
MY ANSWER WAS AS FOLLOWS.
THAT AT LEAST THREE [INAUDIBLE] WITHOUT PRIDE.
I'M PROUD ABOUT THE DEPARTMENT
BECAUSE I BELIEVE WE SERVE OUR STUDENTS WELL.
INDEED, A FEW OF THE MAJORS, BOTH UNDERGRADUATE AND GRADUATE,
ARE BETTER SERVED HERE THAN AT MANY OTHER
INSTITUTIONS [INAUDIBLE].
SECOND, I'M PROUD OF OUR STUDENTS.
WITH US [INAUDIBLE] FACING MANY OBSTACLES GO ON AND CONTRIBUTE
TO SOCIETY IN MANY WAYS.
FOR RAPHAEL, WHO IS A SUCCESSFUL TEACHER IN A TOP HIGH SCHOOL
IN L.A., TO JOHNNY, WHO'S A PROFESSOR
IN APPLIED MATHEMATICS AT BROWN UNIVERSITY.
FINALLY, MY PRO LIFE CONSISTS OF BEING SURROUNDED
BY FACULTY AS COLLEAGUES.
ONE OF THEM SPENDS MANY WEEKENDS EVERY YEAR
WITH HIGH SCHOOL STUDENTS SOLVING HARD PROBLEMS.
MANY OF THOSE HIGH STUDENTS,
HIGH SCHOOL STUDENTS LATER CHOOSE MATHEMATICS
AS THEIR CAREER, BUT IN ANY CASE,
THEY TREASURE THE EXPERIENCE THEY HAVE
AS YOUNG MEN AND WOMEN.
AND THE SAME COLLEAGUE THAT DIRECTS MATH DAY AT THE BEACH,
WHICH IS A GREAT EVENT COMING UP ON [INAUDIBLE].
A RESTRAIN TO WHICH MANY OTHER FACULTY AND STUDENTS COMPETE.
ANOTHER COLLEAGUE IS A NATIONALLY-RECOGNIZED AUTHOR
OF MATHEMATICS TEXTBOOKS WHO IS ALSO AN INCREDIBLE TEACHER,
AND ANOTHER ONE WHO BESIDES BEING A MASTERFUL JUGGLER IS
ALSO A GREAT TEACHER.
AND THE LIST GOES ON.
AND, INDEED, YOU ARE IN FOR A TREAT FROM ONE
OF THOSE FINE COLLEAGUES.
JIM STEIN HAS BEEN WITH US FOREVER.
[LAUGHTER] A VERY WELL-LIKED TEACHER, GREAT MENTOR
AND ADVISOR, RESPECTED COLLEAGUE,
WELL-KNOWN RESEARCHER, BRILLIANT CONVERSATIONALIST AND LECTURER.
HE'S A NERD THAT MAKES US NERDS PROUD.
ALAS, HIS LOVELY WIFE HAS CHOSEN TO SIMPLIFY HIS LIFE
SINCE HE'S CURRENTLY WRITING TWO OTHER BOOKS
SO HE WILL SEMI-RETIRE NEXT YEAR.
I WAS VERY SAD THAT HE'S PARTIALLY LEAVING US,
BUT JIM WILL ALWAYS BE WELCOME IN THE DEPARTMENT,
AND SO I ASK YOU TO DO THE SAME AND WELCOME JIM STEIN.
[ APPLAUSE ]
>> JIM STEIN: FIRST OF ALL, I'D LIKE TO THANK ROBERT
FOR THAT NICE INTRODUCTION, AND SECOND OF ALL,
I'D LIKE TO THANK WHOEVER IT WAS THAT HAD THE IDEA TO INVITE ME
TO DO THIS BECAUSE I JUST LOVE TALKING TO LARGE GATHERINGS,
AND FINALLY, I'D LIKE TO THANK YOU ALL FOR COMING
AND SUPPORTING THE UNIVERSITY
AS YOU HAVE BOTH NOW AND IN THE PAST.
MILLENNIA ONLY COME AROUND ONCE A THOUSAND YEARS,
AND SO MY IDEA WAS THAT WHAT THEY SHOULD HAVE HAD WAS A MAN
OF THE MILLENNIUM.
AND I KNOW WHO I WOULD HAVE NOMINATED
AS MAN OF THE MILLENNIUM.
I WOULD HAVE NOMINATED ISAAC NEWTON
BECAUSE ISAAC NEWTON MADE THE WORLD BASICALLY THE WAY IT WAS,
THE WAY IT IS TODAY.
NOT ONLY WAS NEWTON A FABULOUS MATHEMATICIAN AND PHYSICIST,
NEWTON ESSENTIALLY CHANGED THE WAY THAT WE LOOK AT THE WORLD.
PRIOR TO NEWTON, THE UNIVERSE WAS A UNIVERSE OF MYSTERY.
AFTER THAT, IT WAS A UNIVERSE OF PROBLEMS THAT COULD BE SOLVED.
AND NEWTON USHERED IN A SPIRIT
OF WHAT MIGHT BE CALLED INTELLECTUAL OPTIMISM.
AND IT REACHED ITS CULMINATION WITH THE FOLLOWING QUOTE
FROM PIERRE-SIMON DA LAPLACE.
I USED TO BE ABLE TO MEMORIZE THESE THINGS WHEN I WAS YOUNGER,
BUT REMEMBER, I CAME HERE JUST BEFORE NIXON LEFT OFFICE.
SO MY MEMORY IS FADING.
AND ALSO, BECAUSE LAPLACE WAS FRENCH, THEY, THEY ARE GIVEN
TO RUN-ON SENTENCES SO YOU'LL EXCUSE ME
IF I BREATHE OCCASIONALLY IN THIS.
"GIVEN FOR ONE INSTANCE AN INTELLIGENCE
WHICH WOULD COMPREHEND ALL THE FORCES
BY WHICH NATURE IS ANIMATED AND THE RESPECTIVE POSITIONS
OF THE BEINGS WHICH COMPOSE IT.
IF, MOREOVER, THE INTELLIGENCE WERE VAST ENOUGH
TO SUBMIT THESE DATA TO ANALYSIS, IT WOULD EMBRACE
IN THE SAME FORMULA BOTH THE MOVEMENTS OF THE LARGEST BODIES
IN THE UNIVERSE AND THOSE OF THE LIGHTEST ATOM.
TO WIT, NOTHING WOULD BE UNCERTAIN, AND THE FUTURE
AS THE PAST WOULD BE AS THE PRESENT TO ITS EYES."
A BEAUTIFUL STATEMENT, BUT ONE OF THE THINGS
THAT YOU CAN BE PRETTY SURE ABOUT LAPLACE IS HE NEVER HAD
TO DO WHAT I HAVE TO DO FRIDAY.
I HAVE TO TAKE MY CAR INTO THE GARAGE
TO GET THE BRAKES CHECKED.
AND ONE OF THE THINGS THAT WHEN YOU TAKE YOUR CAR
INTO A GARAGE IS THEY HAVE A VERY ANNOYING HABIT
OF WHEN YOU CALL UP AND SAY, "CAN I PICK UP THE CAR?",
THEY SAY, "SORRY, IT ISN'T READY YET."
AND THERE'S ACTUALLY A VERY GOOD REASON
THAT THEY HAVE SO MUCH DIFFICULTY.
IT'S BECAUSE THEY ARE FACING A REALLY DIFFICULT PROBLEM.
NAMELY, THE PROBLEM OF SCHEDULING REPAIRS FOR THE CARS
THAT COME INTO THE GARAGE.
AND TO GIVE YOU AN EXAMPLE
OF WHY SCHEDULING IS A MORE COMPLEX PROBLEM
THAN OTHER PROBLEMS YOU MIGHT ENCOUNTER, LET ME TAKE A COUPLE
OF OTHERS THAT HAPPEN TO US IN ORDINARY, EVERYDAY LIFE.
FIRST OF ALL, LET'S SUPPOSE THAT YOU HAVE TO MAKE OUT THE,
YOU HAVE TO WRITE THE CHECKS FOR THE MONTH.
I DON'T KNOW ABOUT YOU, BUT WHEN THE FIRST COMES AROUND,
I JUST WRITE OUT ALL MY MONTHLY CHECKS.
OK. YOU HAVE A STACK OF BILLS.
YOU HAVE YOUR CHECKBOOK.
YOU WRITE OUT A CHECK.
YOU PUT IT IN THE ENVELOPE.
YOU SEAL IT.
DO ANOTHER ONE, AND YOU CAN SEE THE STACK OF BILLS GO DOWN
AND THE ENVELOPES INCREASE, AND YOU CAN GET A PRETTY GOOD IDEA
OF WHEN THIS TASK IS GOING TO BE FINISHED.
AND IT TAKES YOU ABOUT AS LONG TO WRITE THE RENT CHECK
AS IT DOES TO WRITE THE CHECK
FOR THE CABLE COMPANY EVEN THOUGH THE RENT CHECK IS A
LARGER NUMBER, IT'S ABOUT THE SAME AMOUNT OF TIME.
NOW, ANOTHER, BUT MORE COMPLICATED TASK IS
IF YOU HAPPEN TO HAVE A ROLODEX AND DROP IT ON THE FLOOR
AND HAVE TO PUT ALL THE CARDS BACK IN ORDER,
IN ALPHABETICAL ORDER.
YOU START THIS TASK BY, YOU KNOW, WE'VE ALL PUT THINGS
IN ALPHABETICAL ORDER, AND IT'S VERY EASY
TO DO THE FIRST FEW CARDS IN THE DECK, BUT AS YOU GET MORE
AND MORE CARDS, IT BECOMES HARDER AND HARDER TO,
TO FIND THE APPROPRIATE PLACE FOR THE CARD SIMPLY
BECAUSE THE DECK OF ALL-READY SORTED CARDS HAS GOTTEN
MUCH LARGER.
SO THIS IS A MORE COMPLEX TASK
IN THAT EVEN THOUGH YOU CAN SEE THE FINISH LINE,
EVERY CARD YOU ADD TO THE DECK GETS YOU CLOSER
AND CLOSER TO THE FINISH LINE.
WHAT HAPPENS WITH THIS PROBLEM IS THAT THE CARDS GET HARDER
AND HARDER TO SORT AT THE END.
UNLIKE, IT TAKES JUST AS LONG TO WRITE THE LAST CHECK
AS IT DID THE FIRST, BUT THE LAST CARD TAKES MUCH LONGER
TO SORT UNLESS IT EITHER ENDS WITH ZZZZ OR BEGINS WITH A,
IN WHICH CASE YOU CAN SLAM IT ON THE BACK OF THE DECK
OR THE FRONT OF THE DECK.
NOW, LET'S LOOK AT THE PROBLEM THAT THE GARAGE FACES.
THE GARAGE HAS TO DO A VERY COMPLICATED SCHEDULING PROBLEM
BECAUSE TASKS AT THE GARAGE SOMETIMES HAVE
TO BE PERFORMED IN SEQUENTIAL ORDER.
I WISH MY COLLEAGUE,
SELENE WATSON [ASSUMED SPELLING] HAD BEEN THERE FOR ME TO TALK
TO BECAUSE HE'S AN EXPERT IN AUTO REPAIR,
BUT MY IMPRESSION IS THAT IF YOU'RE GOING
TO REPLACE THE SHOCKS, FOR INSTANCE, OR CHECK THE BRAKES,
WHAT YOU HAVE TO DO IS YOU HAVE TO PUT THE CAR
UP ON THE HYDRAULIC LIFT.
AND BEFORE YOU CHECK THE, BEFORE YOU REPLACE THE SHOCKS
OR CHECK THE BRAKE, AND ALSO WHAT MIGHT HAPPEN IS YOU MIGHT
HAVE MECHANICS OF VARYING DEGREES OF SKILL.
SOME CAN CHANGE THE OIL, BUT IF THEY HAVE TO DO COMPLICATED JOBS
LIKE REPLACE THE TIMING BELT, THINGS LIKE THIS,
ONLY CERTAIN MECHANICS CAN DO CERTAIN JOBS.
AND SO WHAT MIGHT HAPPEN AT THE GARAGE IS YOU'RE MAKING
OUT A SCHEDULE, AND IT LOOKS LIKE YOU'RE THROUGH,
AND ALL OF A SUDDEN YOU REALIZE THAT ALL FOUR CARS
IN THE GARAGE NEED THE HYDRAULIC LIFT AT EXACTLY THE SAME TIME.
SO WHAT ARE YOU GOING TO DO?
EITHER YOU BACKTRACK
ON RECONSTRUCTING THE SCHEDULE SOMEWHAT, OR, AND TRY AGAIN,
OR YOU REALIZE IT'S JUST TOO MUCH
OF A MESS, AND YOU START OVER.
SO THIS IS A REALLY, REALLY DIFFICULT PROBLEM,
AND IT'S SUBSTANTIALLY MORE DIFFICULT
THAN THE OTHER PROBLEMS THAT WEREN'T,
THAT WE PREVIOUSLY ENCOUNTERED,
BUT WHAT CHARACTERIZES THE 20TH CENTURY IS FOR THE 20TH CENTURY,
MATHEMATICS WAS BROUGHT INTO THE PICTURE IN ORDER TO SHOW
THAT THERE WERE CERTAIN PROBLEMS THAT WERE NOT ONLY DIFFICULT,
THEY WERE OUTRIGHTLY IMPOSSIBLE.
AND THEY COME FROM THREE DIFFERENT AREAS.
ONE COMES FROM OUR UNDERSTANDING OF THE PHYSICAL UNIVERSE.
ONE COMES FROM MATHEMATICS, AND ONE COMES
FROM THE SOCIAL UNIVERSE, AND SO LET'S PUT THIS ON HERE.
LET'S SEE IF EVERYBODY CAN SEE THIS.
OK. I'VE STATED THESE, THE IDEAS FAIRLY QUICKLY, BUT IN PHYSICS,
MOST PEOPLE HAVE HEARD, ESPECIALLY AT A GATHERING
LIKE THIS, HAVE HEARD
OF HEIZENBURG'S UNCERTAINTY PRINCIPLE,
WHICH SAYS THAT IT'S IMPOSSIBLE
TO SIMULTANEOUSLY DETERMINE BOTH POSITION AND VELOCITY.
NOW, THERE'S AN AWFUL LOT OF QUANTUM MECHANICS GOING ON HERE,
AND A LOT OF PHYSICISTS HAVE DONE A MUCH BETTER JOB
OF EXPLAINING THIS THAN I POSSIBLY COULD
SO THE LECTURE ISN'T GOING TO INVOLVE THIS.
[ INAUDIBLE AUDIENCE RESPONSE ]
>> JIM STEIN: WELL, I COULD HAVE USED.
IT'S TRUE.
I COULD HAVE USED MOMENTUM.
I COULD HAVE PUT MOMENTUM THERE,
BUT I WASN'T SURE EVERYBODY KNEW WHAT MOMENTUM WAS,
AND THEY'RE PRETTY CLEAR ON VELOCITY.
OK. SO, WITH MATHEMATICS,
YOU HAVE GODEL'S INCOMPLETENESS THEOREM.
AND THIS WAS AN ASTOUNDING RESULT PROVED
BY THE AUSTRIAN LOGICIAN, KURT GODEL, IN WHICH HE SHOWED
THAT THERE WERE TRUE MATHEMATICAL PROPOSITIONS
WHICH LOGIC CANNOT ESTABLISH.
THAT'S, WHEN YOU STOP TO THINK ABOUT IT,
THAT'S AN AMAZING RESULT FROM A PHILOSOPHICAL AS WELL
AS A MATHEMATICAL STANDPOINT BECAUSE PRIOR TO THAT,
MATHEMATICIANS HAD THOUGHT, "OK.
IF YOU TAKE A MATHEMATICAL PROPOSITION,
EITHER THERE'S A COUNTER EXAMPLE TO IT,
OR THERE'S A PROOF FOR IT."
AND GODEL SHOWED THAT THIS WAS NOT THE CASE.
AND FINALLY, IN THE SOCIAL UNIVERSE,
THERE'S ARROW'S IMPOSSIBILITY THEOREM IN WHICH HE SHOWED
THAT THERE WERE LIMITATIONS TO TRANSLATING THE PREFERENCES
OF THE INDIVIDUALS IN A GROUP TO THE PREFERENCES OF THE GROUP.
THAT'S WHAT WE DO WHEN WE VOTE.
AND THAT'S WHAT I'M GOING TO DISCUSS TODAY.
AND IN ORDER TO START THE DISCUSSION,
WE GO BACK A LITTLE BEFORE THE FRENCH REVOLUTION
TO SOMEONE NAMED LE MARQUIS DE CONDORCET.
AND CONDORCET ORIGINALLY STARTED OUT AS A MATHEMATICIAN.
IN FACT, HIS DOCTORIAL THESIS WAS SO GOOD THAT ONE
OF THE PREEMINENT MATHEMATICIANS AT THE TIME SAID, "HEY,
THIS GUY REALLY HAS PROMISE AND SHOULD GO MUCH FURTHER."
BUT CONDORCET GOT INTERESTED IN ECONOMICS AND POLITICS, AND,
UNFORTUNATELY, COME THE FRENCH REVOLUTION,
HE MADE A WRONG CHOICE OF WHO TO ALLY HIMSELF WITH.
ENDED UP IN THE BASTILLE.
TWO DAYS LATER, HE WAS DEAD.
THAT'S ONE OF THE REASONS, INCIDENTALLY,
THAT I HAVEN'T ABANDONED MATHEMATICS FOR POLITICS.
SEEMS DANGEROUS.
[LAUGHTER] BUT ANYWAY,
WHAT CONDORCET STARTED DOING WAS HE STARTED INVESTIGATING
VOTING SYSTEMS.
AND WHEN ALL YOU'VE GOT IS A DICTATOR OR ONE OF THE LOUISES
WHO WERE THE KINGS OF FRANCE AT THE TIME,
YOU DON'T HAVE MUCH VOTING TO DO BECAUSE THAT'S THE GUY.
THAT'S ALL THERE IS.
IN A LESS COMPLICATED, IN AN ELECTION,
BUT ONE THAT'S FAIRLY STRAIGHTFORWARD IS ONE
IN WHICH YOU ONLY HAVE TWO CANDIDATES.
WHAT YOU DO IS YOU VOTE FOR YOUR CHOICE.
WHOEVER GETS THE MOST VOICE WINS, VOTES WINS.
BUT WHAT IF YOU HAVE THREE OR MORE CANDIDATES?
AS WE OFTEN DO IN AMERICAN ELECTIONS.
THIS CAUSES PROBLEMS.
JUST GO BACK TO 2000, AND YOU CAN SEE WHAT HAPPENED
WHEN NADER MANAGED TO FOUL UP THE 2000 ELECTION
TO SUCH AN EXTENT THAT THE ELECTION FINALLY HAD
TO BE DECIDED BY THE SUPREME COURT.
NOW, IF YOU TAKE A LOOK AT THE PROBLEMS THAT ONE ENCOUNTERS
WHEN YOU HAVE THREE PEOPLE IN AN ELECTION, THERE ARE ALL SORTS
OF DIFFERENT SYSTEMS THAT YOU CAN USE.
FOR INSTANCE, MANY, MANY ELECTORAL AREAS USE RUNOFF
BETWEEN THE TOP TWO CANDIDATES.
WHAT THEY DO IS THEY HAVE TWO, THEY HAVE AN INITIAL ELECTION.
THEY TAKE THE TOP TWO CANDIDATES.
THOSE TWO HAVE A RUNOFF.
THE PROBLEM HERE IS THAT THIS IS EXPENSIVE.
YOU HAVE MULTIPLE, YOU HAVE SEVERAL DIFFERENT ELECTIONS.
[PHONE RINGING]
AND WHEN YOU HAVE, WHEN YOU HAVE MULTIPLE ELECTIONS, THERE'S,
AS I SAY, MORE EXPENSE, MORE TIME CONSUMING.
SO ONE WAY OF GETTING AROUND THIS IS A METHOD WHICH IS USED
IN SEVERAL COUNTRIES, AUSTRALIA IS ONE, AND IS ALSO USED
IN A BUNCH OF LOCAL ELECTIONS IN THE UNITED STATES, AND IT'S,
IT'S CALLED, IT'S CALLED IRV.
WHEN, WHAT YOU DO IN IRV IS YOU RANK ALL THE CANDIDATES.
EVERY PERSON HAS A BALLOT.
YOU RANK THE CANDIDATES, HOWEVER MANY THERE ARE.
YOUR FIRST CHOICE, YOUR SECOND CHOICE, AND YOUR THIRD CHOICE,
AND WHAT YOU DO IS SOMETHING AKIN TO WHAT THEY DO
ON THE TELEVISION SHOW "SURVIVOR".
WHAT HAPPENS WITH "SURVIVOR" IS THAT THE PERSON
WHO GETS THE LEAST FIRST-PLACE VOTES GETS VOTED OFF THE ISLAND.
YOU SEE WHO'S LEFT.
WHO GOT THE LEAST FIRST-PLACE NOW, VOTES NOW.
YOU GET THEM OFF THE ISLAND, AND, FINALLY,
YOU'RE DOWN TO TWO CANDIDATES, AND IT'S A NORMAL ELECTION.
SO THE ADVANTAGE OF IRV, WHICH I THINK STANDS
FOR INDEPENDENT RUNOFF VOTING,
MEANS THAT YOU NO LONGER HAVE TO,
HAVE TO CONDUCT TWO DIFFERENT ELECTIONS.
YOU CAN DO IT ALL AT ONCE, AND SEVERAL PLACES HAVE DECIDED
THAT THIS IS A GOOD WAY TO GO.
BUT THE MARQUIS DE CONDORCET, IN STUDYING VOTING SYSTEMS,
LEARNED THAT THERE WERE PROBLEMS
WHEN ONE HAD MORE THAN TWO CANDIDATES.
AND ONE OF THE PROBLEMS CAN BE ILLUSTRATED BY A CHART
THAT I'M ABOUT TO PUT UP.
BUT THE MARQUIS DE CONDORCET WAS INVESTIGATING A PROPERTY
THAT MATHEMATICIANS CALLED TRANSITIVITY.
IT'S VERY EASY TO UNDERSTAND WHAT TRANSITIVITY IS BY LOOKING
AT NUMERICAL COMPARISON.
BILL GATES HAS MORE MONEY THAN ARNOLD SCHWARZENEGGER.
ARNOLD SCHWARZENEGGER HAS MORE MONEY THAN ME.
THEREFORE, BILL GATES HAS MORE MONEY THAN I DO.
TRANSITIVITY WORKS GREAT FOR NUMERICAL COMPARISONS.
ON THE OTHER HAND, IT DOESN'T WORK SO GOOD FOR FRIENDS.
FOR INSTANCE, MY WIFE IS A FRIEND OF MINE,
OR AT LEAST SHE WAS WHEN I LEFT THIS MORNING,
AND MY WIFE HAS A BUNCH OF FRIENDS,
SOME OF WHICH ARE FRIENDS OF MINE, SOME AREN'T.
SO FRIENDSHIP ISN'T TRANSITIVE.
EVERYBODY HAS FRIENDS WHOSE FRIENDS ARE NOT FRIENDS
OF YOURS.
SO FRIENDSHIP IS NOT A TRANSITIVE IDEA,
BUT WHAT THE MARQUIS DE CONDORCET NOTICED IS
THAT EVEN THOUGH INDIVIDUAL PREFERENCE IN A,
IN AN ELECTION IS TRANSITIVE.
GO BACK TO JUST A VERY SHORT PERIOD OF TIME.
IF YOU PREFERRED OBAMA TO CLINTON,
AND YOU PREFERRED CLINTON TO MCCAIN, WHEN THE TIME CAME
TO PULL A LEVER BETWEEN OBAMA AND MCCAIN,
YOU WEREN'T PULLING THE RED ONE.
YOU WERE PULLING THE, YOU WERE PULLING THE OBAMA,
THE OBAMA LEVER BECAUSE IF YOU PREFER OBAMA TO CLINTON
AND CLINTON TO MCCAIN,
YOU OBVIOUSLY PREFER OBAMA TO MCCAIN.
THAT'S TRANSITIVITY FOR INDIVIDUAL PREFERENCE,
BUT WHAT CONDORCET NOTICED IS THAT TRANSITIVITY IS NOT,
OR RATHER MAJORITY PREFERENCE IS NOT TRANSITIVE.
AND TO DO THAT, I'D LIKE YOU TO LOOK AT THIS CHART.
WHAT THIS CHART IS, WE HAVE AN ELECTORAL GROUP OF 100 PEOPLE.
FORTY PLUS THIRTY-FIVE IS SEVENTY-FIVE,
TWENTY-FIVE IS A HUNDRED.
AND EACH OF THE 100 PEOPLE MARKED A BALLOT
BETWEEN THREE CANDIDATES, A, B,
AND C. AND THEY INDICATED THEIR FIRST CHOICE,
SECOND CHOICE, AND THIRD CHOICE.
AND IF YOU TAKE A LOOK, THERE ARE,
TAKE A LOOK AT HOW MANY PEOPLE PREFER A TO B. FORTY
IN THE FIRST ROW, TWENTY-FIVE IN THE SECOND.
SO 65 PEOPLE, A MAJORITY, PREFER A TO B. AND IF YOU TAKE A LOOK
AT HOW MANY PEOPLE PREFER B TO C, WELL,
IN THE FIRST ROW 40 PREFER B TO C, IN THE SECOND ROW 35 PREFER B
TO C. THAT'S A TOTAL OF 75.
A MAJORITY PREFER B TO C.
SO IF MAJORITY PREFERENCE WERE TRANSITIVE,
A MAJORITY WOULD PREFER A TO C. AND IF YOU TAKE A LOOK,
UNFORTUNATELY, THAT'S NOT THE CASE BECAUSE IF YOU LOOK
AT ROWS TWO AND THREE, 35 PEOPLE PREFER C TO A IN ROW TWO,
25 PEOPLE PREFER C TO A IN ROW THREE.
SO A MAJORITY PREFER C TO A. THE FACT THAT,
THE FACT THAT MAJORITY PREFERENCE IS NOT TRANSITIVE,
AND SO IT'S NOT LIKE INDIVIDUAL PREFERENCE,
IS KNOWN AS CONDORCET'S PARADOX.
AND IT TURNS OUT THAT THIS IS, I LOVE GREAT EXAMPLES
BECAUSE GREAT EXAMPLES FULFILL SEVERAL DIFFERENT ROLES AT ONCE.
AND ONE OF THE THINGS THAT HAPPENED
IN THE 1940'S WAS THEY STARTED INVESTIGATING WHETHER
OR NOT THERE WAS AN IDEAL WAY TO IMPLEMENT A DEMOCRATIC SYSTEM.
AND OF COURSE, THIS HAPPENED RIGHT AFTER WORLD WAR II
WHEN ALL THE DICTATORSHIPS HAD COLLAPSED, DEMOCRACY WAS
ON THE RISE, AND PEOPLE WERE LOOKING FOR WAYS
TO RESOLVE THIS PROBLEM.
AND EVERYBODY KNOWS THAT IF YOU HAVE AN ELECTION,
AND THE WINNER DIES, YOU'VE GOT A PROBLEM.
I'M, BUT WHAT HAPPENS
IF YOU HAVE AN ELECTION, AND THE LOSER DIES.
YOU WOULDN'T THINK THERE WOULD BE A PROBLEM,
BUT WATCH WHAT HAPPENS IN THIS CASE.
NOW, THIS IS WHY THIS IS, YOU KNOW, A LOVELY EXAMPLE
BECAUSE I ONLY HAVE TO USE ONE TRANSPARENCY.
LET'S SUPPOSE THAT YOU HAVE SAVING THE UNIVERSITY MONEY,
REMEMBER THAT ARNOLD.
OK. LET'S SUPPOSE THAT YOU HAVE AN ELECTORAL SYSTEM
THAT YOU'VE GOT THESE BALLOTS,
AND WHATEVER THE ELECTORAL SYSTEM IS,
YOU'VE DECIDED THAT A IS THE WINNER.
NOW, B DIES.
REMOVE B FROM THE PICTURE.
SO YOU HAVE 40 PEOPLE PREFER A TO C, BUT IN THESE TWO ROWS,
75 PEOPLE PREFER C TO A. SO, YOUR ORIGINALS,
YOUR ORIGINAL WINNER WAS A. B DIES.
YOU COUNT THE BALLOTS AGAIN.
C IS THE WINNER.
OK. LET'S SUPPOSE THAT B WON THE ELECTION, AND C DIES.
ELIMINATE C, LET'S SEE NOW.
I THINK I CAN PROBABLY DO THIS BY DOING IT THIS WAY.
OK. B WAS THE ORIGINAL WINNER, C DIES, AND IF YOU TAKE A LOOK
IN ROW ONE AND ROW THREE,
65 PEOPLE PREFERRED A, A TO B. NEW WINNER.
AND FINALLY YOU CAN SORT OF SEE WHAT'S COMING.
SUPPOSE C WINS THE ELECTION BY WHATEVER METHOD YOU'RE PROVING,
YOU'RE USING, AND A DIES.
WELL, IF A DIES, IF YOU LOOK AT THE FIRST TWO ROWS,
75 PEOPLE PREFER B TO C. AGAIN, YOU HAVE A NEW WINNER.
NOW, THIS MAY STRIKE YOU AS PERHAPS, OK,
IT'S SORT OF A WEIRD THING ABOUT ELECTIONS,
BUT I THINK I CAN BRING IT HOME
IN A LITTLE MORE GRAPHICAL OF FASHION.
LET'S SUPPOSE THAT 100 PEOPLE ARE GOING OUT TO DINNER,
AND THEY HAVE A CHOICE OF THREE DIFFERENT, THEY HAVE A CHOICE
OF THREE DIFFERENT ITEMS ON THE MENU.
THEY CAN EITHER HAVE CHICKEN, OR THEY CAN HAVE FISH,
OR THEY CAN HAVE PASTA.
AND SO, WHAT HAPPENS IS, THEY CALL UP THE RESTAURANT,
AND THEY SAY, THE RESTAURANT SAYS THAT'S TOO COMPLICATED.
CAN YOU DO, WE, ALL WE CAN DO IS IF WE'RE GOING
TO PREPARE 100 ORDERS, ALL WE CAN DO IS PREPARE ONE DISH.
TELL US, TELL YOU WHAT WE'LL DO.
WE'LL GIVE YOU A GOOD PRICE,
BUT YOU GOT TO COME UP WITH ONE DISH.
SO WHAT THE ORGANIZATION DOES IS IT SUBMITS BALLOTS TO ALL,
YOU KNOW, IT SUBMITS BALLOTS TO ALL THE PEOPLE WITH A, B,
AND C REPRESENTING CHICKEN, FISH, AND PASTA.
AND WHATEVER HAPPENS, THE GROUP, SOMEBODY COUNTS THE BALLOTS,
AND THEY SAY, "OK, CHICKEN'S THE WINNER."
SO THEY CALL UP THE RESTAURANT,
AND THE GUY SAYS, "WE'D LIKE CHICKEN."
AND THE CHEF SAYS, "YOU KNOW, I'M SORRY TO TELL YOU THIS,
BUT WE'RE OUT OF FISH."
OK. WE'LL SWITCH TO PASTA.
[LAUGHTER] WEIRD.
THINK ABOUT IT.
THAT'S ESSENTIALLY ONE OF THE PROBLEMS,
ONE OF THE PROBLEMS THAT, THAT HAPPENS WITH VOTING SYSTEMS.
AND WHAT HAPPENED IN THE LATE 1940'S WAS KENNETH ARROW,
WHO WAS A GRADUATE STUDENT AT STANFORD AT THE TIME,
STARTED INVESTIGATING SITUATIONS LIKE THIS.
AND WHAT HE DISCOVERED WAS WHAT I QUOTED
AS "ARROW'S IMPOSSIBILITY THEOREM", AND HE DISCOVERED
THAT THERE WERE A BUNCH OF SITUATIONS THAT IF YOU ASK THEM
TO OCCUR SIMULTANEOUSLY,
YOU COULDN'T FIND A VOTING SYSTEM THAT SATISFIED THIS.
YOU CANNOT FIND A VOTING SYSTEM,
WHICH SATISFIES TRANSITIVITY OF GROUP PREFERENCE.
IN OTHER WORDS, IF THE GROUP PREFERS A TO B,
AND THE GROUP PREFERS B TO C, THEN THE GROUP MUST PREFER A
TO C. YOU CAN'T HAVE IT SATISFIED THE DEAD
LOSER CONDITION.
YOU CAN'T HAVE A DICTATOR IN IT
BECAUSE IF YOU HAVE THE DICTATOR,
ONE PERSON JUST CHOOSES WHAT HAPPENS,
AND THEN THERE ARE NO REMAINING PROBLEMS.
AND FINALLY, IF EVERYBODY IN THE GROUP PREFERS A TO B,
THEN THE GROUP PREFERENCE SHOULD PREFER A TO B. THESE ALL SEEM
LIKE REASONABLE CONDITIONS,
BUT THEY SIMPLY COULDN'T HAPPEN SIMULTANEOUSLY.
AND WHEN THIS WAS PUBLISHED,
THIS WAS PUBLISHED IN THE EARLY 1950'S.
TON OF RESEARCH DONE IN THIS AREA.
ARROW WON THE NOBEL PRIZE IN 1972 FOR THIS WORK.
AND WHAT HAPPENS WITH MATHEMATICIANS IS
WHEN SOMEBODY COMES UP WITH A NOVEL RESULT,
OTHER MATHEMATICIANS THINK TO THEMSELVES,
"REMINDS ME OF A PROBLEM ON WHICH I'D BEEN WORKING."
AND THAT'S WHAT HAPPENED TO VARIOUS OTHER PEOPLE
WHO WERE LOOKING AT THE PROBLEM OF REPRESENTATION.
NOW, REPRESENTATION IN A DEMOCRACY IS A MAJOR PROBLEM.
THE PROBLEM OF CONSTRUCTING THE HOUSE OF REPRESENTATIVES.
HOW MANY REPRESENTATIVES EACH STATE SHOULD GET WAS
SUCH AN IMPORTANT PROBLEM
THAT WASHINGTON SUBMITTED A SUGGESTED WAY OF DOING IT.
JEFFERSON SUGGESTED A SUBMITTED, SUBMITTED A WAY TO DO THIS.
BUT THE ONE THAT WAS ORIGINALLY DECIDED ON WAS DEVISED
BY ALEXANDER HAMILTON.
I THINK HE WAS THE FIRST SECRETARY OF THE TREASURY,
AND I'M PRETTY SURE HE DID THIS BEFORE THE DUAL WITH AARON BURR.
BUT IN ANY WAY, TO GET AN IDEA OF HOW THIS,
HOW THIS PARTICULAR METHOD KNOWN AS THE HAMILTON METHOD WORKS.
WHAT I'VE DONE IS IF YOU TAKE A LOOK AT THE CALIFORNIA COUNTIES.
CALIFORNIA IS, WE ALL KNOW CALIFORNIA IS A WEIRD STATE,
BUT THERE'S NO OTHER STATE WHICH HAS FOUR TWO SYLLABLE,
I'M SORRY, THREE TWO SYLLABLE, FOUR-LETTER WORD COUNTIES ALL
OF WHICH END IN O. INYO COUNTY, MONO COUNTY, AND YOLO COUNTY.
SO LET'S SUPPOSE THAT THESE PEOPLE GET TOGETHER
TO FORM INMOYO [ASSUMED SPELLING], FIRST TWO LETTERS
OF EACH, AND INMOYO IS AN ORGANIZATION WHICH IS GOING
TO HAVE 13 REPRESENTATIVES FROM THE COUNTIES.
AND IF YOU LOOK AT THE POPULATION.
I MADE UP THESE NUMBERS SO,
SO I DON'T KNOW WHAT THE APPROPRIATE NUMBERS ARE,
BUT I MADE THEM UP TO ILLUSTRATE THE IDEA.
I ASSUME THAT INYO HAD 45 PERCENT OF THE POPULATION,
MONO HAD 40 PERCENT OF THE POPULATION, YOLO HAD 15 PERCENT
OF THE POPULATION, AND WHAT YOU CAN DO
FOR EACH COUNTY IS DETERMINE A QUOTA.
AND THE QUOTA IS VERY EASY.
WHAT YOU DO IS YOU MULTIPLY, YOU TAKE TO DETERMINE THE QUOTA
THAT INYO COUNTY GETS.
YOU SIMPLY TAKE 45 PERCENT OF 13.
SO INYO COUNTY IS ENTITLED TO 5.85 REPRESENTATIVES,
AND MONO COUNTY IS ENTITLED TO 5.20 REPRESENTATIVES.
THAT'S 40 PERCENT OF 13.
THAT'S THE EASY ONE.
AND THAT YOU DON'T NEED THE CALCULATOR FOR.
AND YOLO IS ENTITLED TO 1.95 REPRESENTATIVES.
SO HOW ARE YOU GOING TO GIVE EACH
OF THE COUNTIES A WHOLE NUMBER OF REPRESENTATIVES?
HERE'S THE HAMILTON METHOD.
WHAT YOU DO IS, AND I'VE WRITTEN THAT IN THE SECOND,
IN THE SECOND GROUP OF NUMBERS.
WHAT YOU DO IS YOU START WITH A QUOTA,
AND YOU MAKE AN INITIAL ASSIGNMENT CONSISTING
OF THE INTEGER PART OF EACH ONE OF THE NUMBERS.
SO, OF THAT, INYO IS INITIALLY ENTITLED TO FIVE,
MONO IS INITIALLY ENTITLED TO GIVE,
AND YOLO IS INITIALLY ENTITLED TO ONE.
NOW, YOU LOOK AT THE LEFT OVER FRACTION, WHICH FOR INYO IS .85,
FOR MONO IS .20, AND FOR YOLO IS .95.
INITIALLY, YOU'VE ASSIGNED 11 OF THE 13 REPRESENTATIVES.
SO THAT MEANS YOU'VE GOT TWO STILL THAT YOU HAVE TO ASSIGN.
AND SO WHAT YOU DO IS YOU LOOK AT THE FRACTIONAL PART,
AND BECAUSE YOU HAVE TWO TO ASSIGN,
YOU TAKE THE TWO LARGEST FRACTIONAL PARTS.
IN THIS CASE, YOLO WITH, YOLO AND INYO HAD THE TWO LARGEST
OF THE THREE FRACTIONAL PARTS.
THERE ARE STILL TWO REPRESENTATIVES TO ASSIGN.
SO I PUT AN ASTERISK HERE, AND SO INYO ENDS UP WITH SIX,
YOLO ENDS UP WITH TWO, AND MONO ENDS UP WITH 5.
AND THIS IS THE HAMILTON METHOD, AND IT WAS USED
AND USED PRETTY MUCH SUCCESSFULLY
WITH NO REAL PROBLEMS UNTIL 1880.
NOW, I DON'T KNOW WHY ALL THE, THE PEOPLE WHO GO INTO SCIENCE
OR MATHEMATICS GO INTO IT, BUT I WENT INTO IT PARTIALLY BECAUSE,
YOU KNOW, I HAD A KNACK FOR IT, BUT ALSO PARTIALLY
BECAUSE THERE'S A THRILL OF DISCOVERY.
WHEN YOU STUMBLE ON SOMETHING NEW
THAT NOBODY HAS EVER SEEN BEFORE,
OR NOBODY HAS EVER EXPLAINED BEFORE
THAT IS AN EXPERIENCE LIKE NO OTHER.
GALILEO EXPERIENCED IT WHEN HE SAW THE MOONS OF JUPITER.
DARWIN, WHOSE 200TH BIRTHDAY JUST OCCURRED A FEW DAYS AGO,
HE EXPERIENCED IT WHEN HE DEVISED THE ORIGIN OF SPECIES,
BUT IT'S SUBTLER IF YOU'RE A MATHEMATICIAN BECAUSE, YOU KNOW,
WE DON'T DEAL WITH THESE REAL, PHYSICAL IDEALS
THAT THE OTHER SCIENCES DEAL WITH.
AND SO THE, THE THRILL OF DISCOVERY IS SOMEWHAT SUBTLER.
AND IT OCCURRED TO AN INDIVIDUAL NAMED CHARLES SEATON IN 1880.
CHARLES SEATON WAS THE CHIEF CLERK OF THE U.S. CENSUS BACK
IN 1880, AND BACK THEN, THE WORD COMPUTER MEANT, HEY,
THAT'S WHAT I DO FOR A LIVING.
I MULTIPLE, ADD, SUBTRACT, AND DIVIDE AND COMPUTE THINGS,
AND BEFORE THEY INVENTED THESE WONDERFUL LITTLE BOXES,
A COMPUTER WAS ACTUALLY A JOB PROFESSION.
AND MOST OF THE PEOPLE
IN THE CENSUS DEPARTMENT WERE COMPUTERS.
AND 1880 WAS A CENSUS.
AND SEATON DID NOT KNOW HOW MANY REPRESENTATIVES WERE GOING
TO BE AWARDED TO EACH OF THE VARIOUS DIFFERENT STATES.
SO WHAT HE DECIDED TO DO WAS HE TOOK THE RESULTS OF THE CENSUS
OF 1880 AND CONSTRUCTED VIA THE HAMILTON METHOD THE
REPRESENTATIVE ASSIGNMENT FOR ANY NUMBER OF REPRESENTATIVES
IN THE HOUSE OF REPRESENTATIVES FROM 275 UP TO 350.
NOW, IF I WERE TO GIVE YOU AN, AN EXCEL SPREADSHEET
AND 20 MINUTES, YOU COULD WRITE THE PROGRAM AND DO IT.
BUT THINK OF THE DIFFICULTY OF DOING THIS BACK IN 1880
WHEN YOU HAD NO CALCULATIONAL [PHONETIC] DEVICES LIKE THIS.
YOU HAD POPULATIONS LIKE 8., 8,341,919.
YOU HAD TO FIGURE OUT WHAT FRACTION THAT WAS
OF THE ENTIRE POPULATION DOING ONLY LONG DIVISION.
JUST AN ABSOLUTELY BACKBREAKING TASK,
BUT WHAT HAPPENED WAS SEATON DISCOVERED SOMETHING GENUINELY
INTERESTING WHEN HE DISCOVER, WHEN HE STARTED DOING THIS.
WHAT HE DISCOVERED WAS SOMETHING CALLED THE ALABAMA PARADOX.
NOW, IF HE WERE A MATHEMATICIAN,
IT WOULD BE CALLED SEATON'S PARADOX.
SO HE SORT OF WENT INTO THE WRONG BUSINESS.
BUT HERE'S THE ALABAMA PARADOX, WHICH AROSE IN 1880.
IF YOU LOOKED AT A HOUSE OF REPRESENTATIVES,
WHICH HAD 299 SEATS, THE STATE OF ALABAMA GOT 8 SEATS.
IF YOU INCREASED THE NUMBER OF REPRESENTATIVES IN THE HOUSE,
IN THE HOUSE OF REPRESENTATIVES FROM 299 TO 300
AND USED THE HAMILTON METHOD, ALABAMA'S REPRESENTATION GOES
DOWN FROM 8 SEATS TO 7 SEATS.
NOW, REMEMBER WHAT I SAID.
DISCOVERY IN MATHEMATICS IS A LITTLE MORE SUBTLE.
BUT YOU LOOK AT NUMBERS LIKE THIS, AND YOUR EYES POP
BECAUSE YOU WOULD EXPECT THAT IF THERE ARE MORE REPRESENTATIVES
IN THE HOUSE OF REPRESENTATIVES, WELL,
EACH STATE SHOULD EITHER HAVE THE SAME NUMBER
OF REPRESENTATIVES AS BEFORE, MAYBE ONE OF THEM GOES UP ONE,
BUT YOU WOULD NOT EXPECT ONE OF THE REPRESENT, ONE OF THE STATES
TO GO DOWN IN REPRESENTATION.
SO THIS WAS CERTAINLY A GLITCH IN THE HAMILTON METHOD
OF DETERMINING REPRESENTATIVES.
AND SO, THEY DECIDED THEY'D LIVE WITH THIS FOR AWHILE,
AND THEY LIVED WITH THIS UNTIL 1900 WHEN THEY ENCOUNTERED,
IN ANOTHER CENSUS,
THEY ENCOUNTERED THE POPULATION PARADOX.
NOW, THE POPULATION PARADOX IS NOT SO WEIRD A THING BECAUSE AT
THAT TIME, VIRGINIA WAS GROWING MORE RAPIDLY THAN MAINE,
BUT MAINE GAINED A SEAT
IN THE HOUSE WHILE VIRGINIA LOST A SEAT.
NOW, YOU WOULD THINK THAT IF ONE,
IF ONE STATE IS GROWING MORE RAPIDLY THAN ANOTHER STATE,
IT WOULD GAIN REPRESENTATIVES AT THE EXPENSE MAYBE
OF THE OTHER STATE, BUT IF YOU THINK ABOUT IT, OK,
IF YOU TAKE A REALLY LARGE STATE THAT'S GROWING MORE SLOWLY
THAN A REALLY SMALL STATE,
YOU COULD STILL SEE HOW THIS MIGHT HAPPEN.
SO I'M NOT EXACTLY SURE THAT THIS QUALIFIES
AS A PARADOX THE WAY THE ALABAMA PARADOX DOES,
BUT IT'S CALLED THE POPULATION PARADOX.
AND SO THE REPRESENTATIVES HUNG ON TO THE HAMILTON METHOD
UNTIL 1907 WHEN WE HIT THE NEW STATES PARADOX.
THE WAY THEY HANDLED CHANGING THE HOUSE OF REPRESENTATIVES
WHEN A NEW STATE WAS ADDED TO THE UNION, IN 1907,
OKLAHOMA WAS ADDED TO THE UNION.
AND WHAT THEY DID WAS THAT THEY'D LOOKED
AT THE CURRENT NUMBER OF SEATS IN THE HOUSE OF REPRESENTATIVES,
AND THEY'D LOOK AT THE PERCENTAGE
OF THE CURRENT POPULATION THAT THE NEW STATE HAD.
AND IF THE NEW STATE HAD TEN PERCENT
OF THE CURRENT POPULATION,
THEY WOULD JUST ADD TEN PERCENT MORE REPRESENTATIVES
TO THE HOUSE OF REPRESENTATIVES.
SAY, TAKING IT UP FROM 300 TO 330,
AND THEN DO THE HAMILTON METHOD ALL OVER AGAIN.
WELL, WHEN THEY USED THE HAMILTON METHOD AGAIN,
OKLAHOMA ENTERED THE UNION ADDING SEATS TO THE HOUSE
TO ACCOMMODATE OKLAHOMA, BUT MAINE GAINED A SEAT
IN THE HOUSE WHILE NEW YORK LOST A SEAT.
MAINE SEEMS TO BE THE VILLAIN IN BOTH THE POPULATION PARADOXES
AND THE NEW STATES PARADOX, BUT I THINK IT WAS JUST COINCIDENCE.
ANYWAY, SO WHAT HAPPENED?
THIS WAS MORE THAN THEY COULD TOLERATE.
AND SO AFTER SCRATCHING THEIR HEADS,
THEY WENT TO A MORE SOPHISTICATED SYSTEM
OF ASSIGNING REPRESENTATIVES.
IT'S THE ONE THAT'S CURRENTLY IN USE TODAY,
THE HUNTINGTON HALE [ASSUMED SPELLING] METHOD,
BUT THE HUNTINGTON HALE METHOD IS NOT PERFECT.
AND, REMEMBER WHAT I SAID ABOUT MATHEMATICIANS SAYING
THAT REMINDS ME OF A PROBLEM THAT I WAS WORKING ON?
WELL, TWO MATHEMATICIANS, BALINKSY AND YOUNG, WERE LOOKING
AT ARROWS' THEOREM, AND THEY SAID MAYBE SOME
OF THE IDEAS HERE CAN BE ADOPTED TO REPRESENTATION.
AND WHAT THEY DISCOVERED WAS THAT IF YOU HAVE A QUOTA METHOD.
NOW, WHAT DISTINGUISHES A QUOTA METHOD IS THAT IF YOU LOOK
AT SOMEONE'S QUOTA ASSIGNMENT OF 5.85,
YOU HAVE TO GIVE THEM EITHER FIVE REPRESENTATIVES
OR SIX REPRESENTATIVES.
YOU DON'T HAVE A CHOICE OF GIVING THEM 3 OR 19 OR WHATEVER
BECAUSE THESE ARE THE TWO INTEGERS THAT ARE THAT CLOSEST.
THAT'S WHAT A QUOTA METHOD IS.
THEY LOOKED AT, THEY, THEY MANAGED TO PROVE
IN MUCH THE SAME SPIRIT, ALTHOUGH NOT THE SAME WAY,
THAT ARROW HAD PROVED
THAT A CERTAIN ELECTORAL SYSTEM WAS IMPOSSIBLE.
WAS THAT IT WAS NOT POSSIBLE TO CONSTRUCT A QUOTA METHOD
WHICH SIMULTANEOUSLY AVOIDED THE ALABAMA PARADOX
AND THE POPULATION PARADOX.
SO, WHAT'S HAPPENED IN THE 20TH CENTURY IS YOU HAVE,
YOU HAVE MATHEMATICS SHOWING THAT THE UNIVERSE
IN MANY DIFFERENT AREAS HAS LIMITATIONS.
NOW, I KNOW WE STARTED A LITTLE LATE.
I DON'T KNOW WHETHER I HAVE TIME FOR ONE MORE EXAMPLE,
OR WHETHER YOU WANT ME TO WRAP IT UP?
>> GO AHEAD.
>> JIM STEIN: OK.
I WANTED TO DO A BRIEF DISCUSSION OF GODEL'S,
OF GODEL'S THEOREM SIMPLY BECAUSE IT'S ONE OF THE GREAT,
IT'S ONE OF THE GREAT RESULTS IN MATHEMATICS.
AND IN ORDER TO GIVE YOU A FLAVOR OF THIS, WHEN WE THINK
OF PROPOSITIONS IN MATHEMATICS, SOME OF THEM ARE, YOU KNOW,
SOME OF THEM ARE PRETTY STRAIGHTFORWARD,
BUT MATHEMATICS IS ABOUT PATTERNS.
AND HERE'S ONE, HERE'S A PATTERN
THAT I'VE ALWAYS FOUND VERY ATTRACTIVE.
MOST MATHEMATICIANS WILL TOO.
IF YOU ADD UP THE ODD NUMBERS, THERE'S SQUARES.
ONE IS ONE TIMES ONE.
ONE PLUS THREE IS TWO TIMES TWO.
ONE PLUS THREE PLUS FIVE IS THREE TIMES THREE.
ONE PLUS THREE PLUS FIVE PLUS SEVEN IS FOUR TIMES FOUR.
NOW, IF YOU'RE A MATHEMATICIAN, YOU WONDER WHETHER
OR NOT THIS PATTERN GOES THROUGHOUT ALL THE INTEGERS.
AND THERE ARE TWO DIFFERENT WAYS
THAT YOU MIGHT DECIDE TO GO ABOUT THIS.
ONE WAY IS TO CHECK ALL THE INTEGERS ONE AT A TIME
UNTIL YOU EITHER FIND A COUNTER EXAMPLE,
AN INTEGER FOR WHICH IT DOESN'T WORK, OR YOU MANAGE TO SHOW
THAT THEY'RE ALL TRUE.
THERE'S A PROBLEM WITH THAT.
IF YOU DON'T FIND A COUNTER EXAMPLE,
IT'S GOING TO TAKE YOU FOREVER TO GET
THROUGH CHECKING ALL THE SINGLE CASES
BECAUSE THERE ARE AN INFINITE NUMBER OF INTEGERS.
THAT'S PROBABLY THE REASON THAT THE IDEA
OF MATHEMATICAL PROOF AROSE BECAUSE THERE ARE THINGS
THAT YOU WANT TO SAY THAT THERE'RE ALWAYS TRUE SO YOU LOOK
FOR MATHEMATICAL PROOF.
NOW, THERE ARE LOTS OF WAYS THAT MATHEMATICIANS PROVE THINGS,
BUT WHAT I'D LIKE TO DO IS INSTEAD OF SHOWING YOU A PROOF
BY INDUCTION, WHICH CAN BE DONE FOR THIS, OR A PROOF BY ALGEBRA,
I'D JUST LIKE TO SHOW YOU SOME PICTURES.
SO, WHAT I'M GOING TO DO IS I'M GOING TO DRAW THE BLACK DOTS IN,
LET ME SHOW YOU THE TWO DIFFERENT THINGS.
THE WHITE DOTS ARE WHAT YOU PREVIOUSLY HAD,
OR THE WHITE DOT IN THIS INSTANCE.
THE BLACK DOTS ARE THE LAST NUMBER TO BE ADDED.
SO, YOU CAN SEE HERE THAT WHEN YOU START WITH THE ONE WHITE DOT
FROM THE PREVIOUS CASE, AND YOU ADD THREE BLACK DOTS.
YOU GET A TWO BY TWO SQUARE.
SO NOW WHAT I'M GOING TO DO IS I'M GOING
TO COLOR ALL THESE DOTS WHITE
AND ADD FIVE MORE AROUND THE EDGES.
YOU GET A THREE BY THREE SQUARE.
COLOR ALL THESE THREE BY THREE DOTS WHITE, ADD SEVEN DOTS
AROUND THE EDGES, YOU GET A SQUARE.
MAYBE NOT A FORMAL MATHEMATICAL PROOF THAT YOU COULD WRITE
UP IN A JOURNAL, BUT YOU SHOW IT TO ANY MATHEMATICIAN,
AND THEY SAY, YEAH, IT'S COOL.
WE'VE PROVED IT.
AND THE AMAZING THING THAT GODEL DID WAS HE SHOWED
THAT THERE ARE PROPOSITIONS, AND TO THIS DATE, THE,
THE PROBLEM WITH WHAT GODEL DID IS HE SHOWED THAT A PROPOSITION
WHICH REALLY DIDN'T HAVE ANY MATHEMATICAL SIGNIFICANCE
WHATSOEVER, IT WASN'T SOMETHING
LIKE IT'S A BEAUTIFUL PATTERN LIKE THIS.
IT'S A VERY AWKWARD AND ARTIFICIAL TYPE OF PROPOSITION,
BUT HE SHOWED THAT THERE WAS A PROPOSITION INVOLVING THE
INTEGERS THAT YOU COULD NEITHER FIND A PROOF FOR IT LOGICALLY
OR PROVE THAT THERE ARE DISCOVER OR CALENDAR EXAMPLE.
SO THIS WAS ALL OF A SUDDEN, THIS WAS IN A HAZY, NEVER,
NEVERLAND THAT MATHEMATICS HAD NEVER SUSPECTED EXISTED BEFORE.
THAT THERE ARE PROPOSITIONS WHICH ARE TRUE,
BUT THE MATHEMATICS CANNOT PROVE.
AND THIS NOT ONLY CHANGED MATHEMATICS,
BUT IT ALSO CHANGED PHILOSOPHY.
THERE ARE ENTIRE BRANCHES OF PHILOSOPHY WHICH ARE BUILT
UP ON THE LOGICAL SYSTEMS THAT GODEL WORKED
WITH EXTENDING THE LOGICAL SYSTEMS,
SEEING WHAT THE LIMITATIONS OF THESE LOGICAL SYSTEMS ARE.
AND IF YOU LOOK AT WHAT HAS HAPPENED IN THE 20TH CENTURY,
THERE ARE SOME PEOPLE, YOU KNOW, WE'RE LIVING IN A TIME
OF BUDGET PROBLEMS, AND PEOPLE ARE GLOOMY BECAUSE OF THEM,
BUT LAURA STRUCK A VERY OPTIMISTIC NOTE.
AND IT, SOME OF THE SAME THING HAPPENS WHEN YOU FIND THAT THEY,
YOU KNOW, THAT MIGHT HAPPEN WHEN YOU SEE A DEAD END
IN MATHEMATICS OR SCIENCE.
YOU SAY, OK, WE'VE HIT THE WALL.
BUT IF YOU LOOK AT SOME OF THE THINGS THAT HAPPEN
WHEN YOU HIT THE WALL, ISAAC NEWTON SPENT TEN YEARS
OF HIS LIFE ON ALCHEMY.
WENT NOWHERE.
IN FACT, IT WENT SO NOWHERE THAT HE BURIED HIS NOTES
FOR 300 YEARS AND SAID NOBODY'S TO LOOK AT THIS FOR 300 YEARS.
AND WHEN THEY UNEARTHED IT,
THERE WERE NO GREAT TRUTHS THERE.
I WAS, I COULD SEE A GREAT ROBERT LUDLUM NOVEL ONCE THEY,
YOU KNOW, [LAUGHTER].
DIDN'T HAPPEN.
THERE WAS REALLY NOTHING OF INTEREST
BECAUSE HE WAS PURSUING ALCHEMY WITHOUT THE BASIC UNDERSTANDING
OF THE ATOMIC THEORY, WHICH RENDERED ANY CONCEPT
SUCH AS THE DISCOVERY OF THE PHILOSOPHER'S STONE,
WHICH WOULD TRANSMUTE BASE METALS INTO GOLD.
YOU CAN'T DO THAT.
AND IF NEWTON HAD KNOWN THAT,
HE PROBABLY WOULDN'T HAVE WORKED ON ALCHEMY.
HE WOULD HAVE DONE MORE PHYSICS AND MATHEMATICS,
OR HE MIGHT HAVE BEEN WORKING IN CHEMISTRY.
AND IF YOU LOOK AT WHAT HAPPENED TO ALCHEMY,
ALCHEMY'S A DEAD END EXCEPT FOR WRITING HARRY POTTER NOVELS
OR WHATEVER, BUT IF YOU LOOK AT IT,
ALCHEMY MORPHED INTO CHEMISTRY.
AND THE WORLD THAT WE HAVE TODAY IS THE OUTGROWTH, YOU KNOW.
IF I WERE TO ASK, IF I WERE
TO ASK MOST PEOPLE WHAT'S THE MOST IMPORTANT OF THE SCIENCES
IN THEIR LIVES, HOW IT MOST IMPACTS THEIR LIVES,
MY FEELING IS IT'S PROBABLY CHEMISTRY.
IT'S A TOSS UP BETWEEN THAT AND, AND MAYBE PHYSICS.
THE ONLY REASON THAT BIOLOGY IS A LITTLE BEHIND IT IS
BECAUSE BIOLOGY WAS THE LAST OF THE SCIENCES TO REALLY COME
UNDER SYSTEMATIC SCRUTINY.
IT TOOK, IT TOOK AWHILE TO OVERCOME SOME OF THE PREJUDICES
THAT WERE INVOLVED IN LOOKING AT BIOLOGICAL STRUCTURES,
AND IT TOOK A LONGER TIME TO WORK WITH THE COMPLEX STRUCTURES
THAT BIOLOGY DEALS WITH.
BIOLOGY DEALS WITH MUCH MORE COMPLEX STRUCTURES
THAN EITHER CHEMISTRY OR MATHEMATICS OR PHYSICS,
AND THE MORE COMPLEX THE STRUCTURE,
THE MORE DIFFICULT THE PROBLEM.
WE GET BACK TO THE GARAGE.
THEY HAVE THE MORE COMPLICATED THINGS TOO.
SO I'D LIKE TO CLOSE JUST BY SAYING THAT I FEEL
THAT IT'S IMPORTANT TO LOOK FOR THE DEAD ENDS AS WELL
AS WHAT YOU CAN DO BECAUSE THE DEAD ENDS SHOW YOU WHAT YOU
CAN'T DO, AND THEN MAYBE YOU KNOW HOW
TO ALLOCATE YOUR RESOURCES A LITTLE BETTER.
AND HEY, THOSE OF YOU LEGISLATORS THAT ARE LOCKED
UP IN THE CAPITOL IN SACRAMENTO,
YOU MIGHT PAY A LITTLE ATTENTION TO THAT.
[LAUGHTER] THANK YOU VERY MUCH.
AS BEETHOVEN WOULD HAVE HEARD THEM, AS HE PROGRESSED
THROUGH HIS CAREER, AND YOU COULD HEAR THAT, YOU KNOW, THE,
THE FIRST, THE FIRST FEW SYMPHONIES,
HE HEARD PERFECTLY FINE.
BUT YOU COULD HEAR THE QUALITY OF THE HEARING GET WORSE,
AND BY THE END, I DON'T THINK HE WAS TOTALLY DEAF
FOR THE 9TH CENTURY, FOR THE 9TH SYMPHONY.
HE COULD, HE COULD HEAR SOUNDS.
HE COULD, HE COULD HEAR VOLUMES AND CERTAIN TONES,
BUT HE CERTAINLY COULDN'T HEAR THE DEPTH OF THE MUSIC
THAT HE HAD CREATED, BUT NONETHELESS, IT'S LIKE THE,
IT'S LIKE THE BLIND GEOMETERS.
THAT HE WASN'T DEAF FROM BIRTH.
I, YOU KNOW, IT'S TO ME, IT'S JUST AS IMPOSSIBLE
TO IMAGE HOW ONE COULD COMPOSE MUSIC IF ONE WERE DEAF
FROM BIRTH AS IT IS TO DO GEOMETRY IF ONE IS BLIND
FROM BIRTH, BUT THERE IS A DIFFERENCE
BECAUSE MUSIC IS A PURELY SENSUAL EXPERIENCE
OR PURELY SENSORY EXPERIENCE WHEREAS GEOMETRY IS AN
INTELLECTUAL ONE.
IT'S POSSIBLE TO SET UP AN AXIOM SYSTEM FOR ANYONE
OF THE GEOMETRIES AND DESCRIBE IT ABSTRACTLY
WITHOUT EVER SEEING THE STRUCTURES
THAT YOU ARE DISCUSSING.
YOU CAN SAY WHAT A TRIANGLE IS.
WHAT A LINE SEGMENT IS.
YOU CAN GIVE THE PROPERTIES AND THE THEOREMS
WITHOUT EVER DRAWING A TRIANGLES AND LINE SEGMENTS.
AM I RIGHT, ROBERT?
>> ROBERT: YEAH, YOU CAN.
>> JIM STEIN: YEAH.
YEAH. I MEAN, YOU WOULDN'T, OF COURSE, [LAUGHTER],
YOU WOULDN'T, OF COURSE, IN A GEOMETRY COURSE
BECAUSE YOU GET THE IDEAS FROM THE PICTURES, BUT THAT,
YOU KNOW, THAT ILLUSTRATES ONE OF THE IDEAS THAT A LOT
OF THE MATHEMATICIANS HAVE LOOKED AT.
THE IDEAS OF MODELS OF MATHEMATICAL STRUCTURES,
AND THAT WAS, OK, HATE, I HATE TO GIVE PLUGS,
I HATE TO PLUG A BOOK BECAUSE I JUST FEEL, YOU KNOW,
I SORT OF FEEL LIKE A SHILL, BUT ONE OF THE THINGS
THAT I WAS INVESTIGATING AND LOOKED
AT FOR THE BOOK WAS THE IDEA OF DIFFERENT MODELS
FOR VARIOUS AXIOMATIC STRUCTURES.
AND THERE WAS A TREMENDOUSLY INTERESTING QUESTION
IN THE 19TH CENTURY THAT WAS TACKLED
BY SEVERAL MATHEMATICIANS.
IS THE EUCLIDEAN PLANE AS WE KNOW IT THE ONLY MODEL
FOR THE AXIOMS OF THE EUCLIDEAN, I CAN DRAW SOMETHING.
LOVE IT. OK.
IF YOU LEARN EUCLIDEAN GEOMETRY THE WAY I DID,
HERE'S A LINE L. HERE'S A POINT P. AND ONE OF THE AXIOMS
IN EUCLIDEAN GEOMETRY IS THROUGH EVERY LINE, I'M SORRY,
THROUGH EVERY POINT OFF A GIVEN LINE, THERE'S ONE
AND ONLY ONE LINE PARALLEL TO THE ORIGINAL ONE.
AND MATHEMATICIANS HAD WONDERED FOR GENERATIONS WHETHER
OR NOT THIS AXIOM WAS REALLY NECESSARY.
IT'S CALLED THE PARALLEL AXIOM.
COULD IT BE PROVEN FROM THE OTHER AXIOMS,
AND IF IT WERE NECESSARY, IS IT THE, IS THE PLANE THE ONLY MODEL
IN WHICH THIS IS TRUE?
AND IN THE 19TH CENTURY,
A COUPLE OF DIFFERENT MATHEMATICIANS MANAGED TO SHOW
THAT THIS IS NOT THE ONLY, THE PLANE IS NOT THE ONLY MODEL.
IN FACT, WHAT YOU CAN DO IS YOU CAN DRAW MODELS
IN WHICH THERE ARE NO PARALLEL LINES THROUGH A POINT,
GET TO A GIVEN LINE, AND WHERE THERE ARE INFINITELY MANY LINES
THROUGH A POINT.
THERE ARE DIFFERENT SURFACES.
THEY'RE NOT ON A FLAT PLANE.
THEY'RE SORT OF ON BIZARRELY-SHAPED SURFACES,
BUT NONETHELESS, THIS IS THE WAY THAT MATHEMATICS DEVELOPS.
MATHEMATICS LOOKS AT QUESTIONS IN THE ABSTRACT,
POSES QUESTIONS, AND ONE OF THE TRUE JOYS FOR, AT LEAST FOR ME,
PROBABLY THE HIGH POINT
OF MY MATHEMATICAL CAREER WAS I WROTE A PAPER BACK
IN 1972 OR 1973.
IT WAS VERY ABSTRACT.
GOT WRITTEN UP IN A JOURNAL.
FIVE PEOPLE ORDERED REPRINTS OF IT OR ASKED ME FOR REPRINTS.
SO I HAD 45 LEFT, BECAUSE THE JOURNALS ALWAYS SEND YOU 50,
SITTING ON A SHELF.
EIGHT YEARS GO BY.
ALL OF A SUDDEN, I GET A FLOOD OF REQUESTS FOR THIS ARTICLE
FROM ELECTRICAL ENGINEERS.
FROM ALL OVER THE WORLD, AND I RAN OUT OF COPIES.
AND SO I WONDERED WHAT THE HELL WAS HAPPENING.
AND SOMEBODY HAD TAKEN THE STUFF THAT I DID,
WHICH WAS PURELY ABSTRACT MATHEMATICS AND ADAPTED IT
TO SHOWING THAT IT HAD PRACTICAL USE
IN SOMETHING CALLED SIGNAL PROCESSORS.
SIGNAL PROCESSORS ARE DEVICES FROM ELECTRICAL ENGINEERING,
WHICH, NOT SURPRISINGLY, ARE USED TO PROCESS SIGNALS.
AND WHAT THE MATHEMATIC, I'M SURE MANY
OF YOU HAVE HAD THE FOLLOWING EXPERIENCE.
YOU'VE TURNED ON SOMETHING LIKE YOUR AMPLIFIER OR ON A PIECE
OF AUDITORY EQUIPMENT, AND YOU HEAR THE SQUEAL, YOU KNOW, THAT,
THAT JUST DESTROYS YOUR EARS?
MY THEOREM TELLS YOU WHEN AND WHEN NOT
THAT THEOREM, THAT SQUEAL OCCURS.
OK. NOT A GOOD, [LAUGHTER] NOT UP THERE WITH NEWTON,
BUT NONETHELESS, I LOOK AT IT THIS WAY.
SOMETHING THAT I DID THAT WAS TRULY ABSTRACT,
AND I'VE SPENT ALL MY LIFE IN ABSTRACT MATHEMATICS,
IT'S SOMETHING, AND IT'S ONE OF THE PLEASURES OF MATHEMATICS
THAT ACTUALLY GETS USED FOR PRACTICAL PURPOSES.
AND THIS HAS HAPPENED TIME AND AGAIN.
THIS IS THE STORY OF MATHEMATICS.
THE ITALIAN G, DIFFERENTIAL GEOMETERS
OF THE LATE 19TH CENTURY WORKING OUT THE MATHEMATICS
OF THESE OBSCURE SURFACE.
NOBODY CARES.
AND THEN ALL OF A SUDDEN EINSTEIN COMES ALONG,
AND HE SHOWS THAT THIS IS THE MATHEMATICS
THAT DESCRIBES THE UNIVERSE AND THE THEORY OF RELATIVITY.
AND THIS IS ONE OF THE, YOU KNOW, ONE OF THE PLEASURES
OF MATHEMATICS IS THAT IT HAS SO MANY DIFFERENT APPLICATIONS
AND OCCURS IN SO MANY DIFFERENT AREAS.
WHO WOULD HAVE BELIEVED THAT IT WOULD SHOW YOU
THAT THERE ARE PROBLEMS THAT YOU CAN'T IMPLEMENT THE PERFECT
DEMOCRACY, OR YOU CAN'T COME UP WITH A GOOD WAY,
A REALLY PERFECT WAY
OF STRUCTURING THE HOUSE OF REPRESENTATIVES?
IT'S FASCINATING.