- Hi, I'm Ana, the Ethical Systems Nerd,
with the April 4th episode of "Nerd Nodes."
(whimsical music)
Today is the birthday in 1868 of Philippa Garrett Fawcett,
who is best known for doing really well on an exam.
The exam in question was the Mathematical Tripos,
or the final exam
in a Cambridge undergraduate mathematics degree.
Fawcett, as a woman in 1890,
was permitted to attend Cambridge and to sit the exam,
but she wasn't allowed to be granted a degree,
or to be named the Senior Wrangler,
the traditional title for the man
who achieved the highest exam score in a given year.
So, when Fawcett's score on the Tripos
turned out to be 13% higher than the second highest score,
she was proclaimed to be above the senior wrangler,
to the great excitement of the assembled crowd
and to a chorus of newspaper headlines
the following morning.
The University of Cambridge would never grant her a degree,
but since her exam grade was at least officially recorded,
she was able to claim an ad eundum degree
from sister school Trinity College, Dublin
after that university started admitting women
as full members in 1904,
making her part of a group of over 700 women
known as steamboat ladies
for the means of transportation used to claim their degrees.
The Universities of Cambridge and Oxford are each made up
of many constituent colleges
and Fawcett had been an undergraduate at Newnham College,
a college for women which her mother helped to co-found
in 1871, whose students were granted the right
to sit University exams in 1881,
and which achieved full status as a college
of the university in 1948.
I attended Cambridge for a year and my college, Caius,
first admitted women in 1979, the year I was born.
Fawcett was hired as a mathematics lecturer
by Newnham after she didn't graduate,
and stayed there for 10 years, doing mathematical research
in the field of fluid dynamics.
One of her published papers deals with a theoretical shape
called an isotropic helicoid,
proposed by William Thompson or Lord Kelvin in 1871.
William Thompson, incidentally,
was Second Wrangler in his year at Cambridge.
An isotropic helicoid is any shape
which experiences an equal amount of fluid drag
no matter what its orientation is.
Thompson hypothesized that an isotropic helicoid
should spin when placed in liquid.
Recent experiments have used 3-D printers to print shapes
which should be isotropic helicoids,
but if they do spin, then it's too small to observe,
at least so far.
You can download plans to print your own isotropic helicoid
at the Thingiverse,
a website filled with 3-D printable shapes,
many of them creative commons licensed.
Another mathematician born on April 4th
was the French mathematician Edouard Lucas, born in 1842.
If you have ever committed yourself to a project
perhaps without really realizing how long it would take,
then you'll relate to Lucas who set out at the age of 15
to prove that the 39-digit Mersenne number
two to the power of 127 minus one was prime.
He would spend 19 years verifying by hand
that two to the power of 127 minus one
was in fact a Mersenne prime, proving it in 1876.
This remained the largest known prime for 75 years,
and will probably always remain
the largest prime number proven by hand.
The next two prime numbers were discovered on the same day,
January 30th 1952,
with the aid of the Standards Western Automatic Computer,
so-called because it was built
by the U.S. Bureau of Standards,
and located on the West Coast of North America
in Los Angeles, California.
A mathematician named Raphael M. Robinson
would use an improved version of Lucas' technique,
along with the computing power of the SWAC,
to find the next five Mersenne primes over the year 1952.
In addition to number theory,
Edouard Lucas also enjoyed recreational mathematics.
You have probably seen some version
of the Tower of Hanoi game,
which was invented by Lucas
and turned into a physical packaged game for sale in 1883,
with the tagline "A game brought back from Tonkin",
Tonkin being the French name for northern Vietnam,
which the French Third Republic
was in the process of invading and occupying in 1883,
an invasion which no doubt helped France
forget the humiliation of the Franco-Prussian War
and the Siege of Paris in 1870.
Lucas himself had been an artillery officer
in the French army.
So, Lucas capitalized on the orientalist Zeitgeist
and named his game the Tower of Hanoi,
giving it a fake backstory,
attributed to a fake professor at a fake university,
named using anagrams of his own name
and academic affiliation.
Lucas's boxed version of the game contained eight disks,
which need to be moved between three pegs,
following the rule that a larger disk
can never be placed on top of a smaller disk.
It turns out that the minimum number of moves to win
is two to the n minus one,
where n is the number of disks.
So at least 255 moves are required to solve
a Tower of Hanoi game with eight disks.
Lucas's fake backstory alludes to a myth that the game,
with 64 golden jewel-encrusted disks,
has been played in a Brahmin temple for many years,
and when the game is finally complete,
this will bring about the end of the world.
It's easy to imagine how Lucas,
who spent 19 years manually verifying
the primality of the 127th Mersenne number,
would have related to this story.
He offers a prize of a million francs and more
to anyone who completes the 64 disk version of the game
by hand, before announcing that it would require
18 quintillion
446 quadrillion
744 trillion
73 billion
709 million
551,615 moves,
or approximately 5 billion centuries, so rest assured
that if the game does bring about the end of the world,
it will be a long time from now.
The game has remained in use as a recreation,
as well as a psychological assessment tool,
and its mathematical underpinnings
have applications in a wide variety of fields.
It also appears in a variety of science fiction stories,
and in the 2011 movie "Rise of the Planet of the Apes",
it is aptly renamed as a Lucas Tower.
(whimsical music)