John Horton Conway: the world’s most charismatic mathematician
이강기2015. 10. 13. 21:45
John Horton Conway: the world’s most charismatic
mathematician
John Horton Conway is a cross between
Archimedes, Mick Jagger and Salvador Dalí. For many years, he worried that his
obsession with playing silly games was ruining his career – until he realised
that it could lead to extraordinary
discoveries
John Horton Conway and his Leech lattice doodle.
Photograph: Hollandse Hoogte/Eyevine
On a late
September day in 1956, John Horton Conway left home with a trunk on his back. He
was a skinny 18-year-old, with long, unkempt hair – a sort of proto-hippie – and
although he generally preferred to go barefoot, on this occasion he wore strappy
Jesus sandals. He travelled by steam train from Liverpool to Cambridge, where he
was to start life as an undergraduate. During the five-hour journey, via Crewe
with a connection in Bletchley, something dawned on him: this was a chance to
reinvent himself.
In junior
school, one of Conway’s teachers had nicknamed him “Mary”. He was a delicate,
effeminate creature. Being Mary made his life absolute hell until he moved on to
secondary school, at Liverpool’s Holt High School for Boys. Soon after term
began, the headmaster called each boy into his office and asked what he planned
to do with his life. John said he wanted to read mathematics at Cambridge.
Instead of “Mary” he became known as “The Prof”. These nicknames confirmed
Conway as a terribly introverted adolescent, painfully aware of his own
suffering.
After loitering
for a time with the teenage reprobates at the back of the classroom, Conway
ultimately did well enough on the university entrance exams to receive a minor
scholarship and get his name published in the Liverpool Daily Post. As he sat on
the train to Cambridge, it dawned on him that since none of his classmates would
be joining him at university, he would be able to transform himself into a new
person: an extrovert! He wasn’t sure it would work. He worried that his
introversion might be too entrenched, but he decided to try. He would be
boisterous and witty, he would tell funny stories at parties, he would laugh at
himself – that was key.
“Roughly
speaking,” he recalled, “I was going to become the kind of person you see now.
It was a free decision.”
Now 77, John
Horton Conway is perhaps the world’s most lovable egomaniac. He is Archimedes,
Mick Jagger, Salvador Dalí, and Richard Feynman, all
rolled into one. He is one of the greatest living mathematicians, with a sly
sense of humour, a polymath’s promiscuous curiosity, and a compulsion to explain
everything about the world to everyone in it. According to Sir Michael Atiyah,
former president of the Royal Society and arbiter of mathematical fashion,
“Conway is the most magical mathematician in the world.”
For the last
quarter century Conway has held the position of Princeton’s John von Neumann
distinguished professor in applied and computational mathematics, now emeritus.
Before that, he spent three decades at Cambridge, where in the 1970s, he dived
deep into the vast ocean of mathematical symmetry. He discovered a
24-dimensional symmetry group that came to bear his name, and, with his
colleague Simon Norton, he illuminated the 196,883-dimensional Monster group
with a paper titled “Monstrous Moonshine”. Conway also discovered a new class of
numbers, infinitely large and infinitesimally small, which are now known as
“surreal numbers”. Those achievements earned him a spot as a fellow of the Royal
Society of London for Improving Natural Knowledge, the oldest scientific society
in the world. Conway likes to mention that when he was elected in 1981, he
signed the big book of fellows at the induction ceremony and was pleased to see
on previous pages the names Isaac Newton, Albert Einstein, Alan Turing, and
Bertrand Russell.
Conway’s is a
jocund and playful egomania, sweetened by self-deprecating charm. He has on many
occasions admitted: “I do have a big ego! As I often say, modesty is my only
vice. If I weren’t so modest, I’d be perfect.” That said, he is irresistibly
drawn to piddling away his days playing games, preferably silly children’s
games. While his colleagues zealously guard their vacations for uninterrupted
research time, Conway prefers to spend his summers hopping between maths camps
for students. This July, for instance, Conway is playing games at a maths camp
for teens in Bremen, Germany, and then flying over to Portland, Oregon, for a
middle-schoolers’ camp.
This lust for
the seemingly trivial has consumed a remarkable amount of Conway’s time and
energy. In addition to all the gaming, he’s also been infatuated with factoring
large numbers in his head; with reciting pi from memory to 1,111+ digits; with
calculating, nearly instantaneously, the day of the week for any given date
using what he calls his “Doomsday” algorithm. He’s invented many peculiar
algorithms—for counting stairs while you climb without actually counting, and
for how best to read through a stack of double-sided loose-leaf pages. And he’s
been known to carry on his person decks of cards, dice, ropes, pennies, coat
hangers, sometimes a Slinky, maybe a miniature toy bicycle, all props he deploys
both for explaining ideas and for his own amusement.
While there may
seem little method to this madness, curiosity-driven research is attracting
renewed attention and support as a strategy for success in the sciences, both
pure and applied, and economically for society as a whole. At the first National
Mathematics Festival
in Washington in April, the Italian economist Mario Draghi, president of the
European Central Bank and one of the keynote speakers, noted that to believe and
invest in fundamental research is to believe and invest in the future – that
with increasing constraints on demographic and natural resources, and the
impending “secular stagnation” as some call it, the countries that make
fundamental research in maths and science a high priority will be the countries
that prosper economically. Although Conway himself regards money with an
indifference verging on contempt, he is a crusading ambassador for simple
curiosity, which he considers the universal force driving discovery.
* *
*
By 1964, a couple of years longer than it
should have taken, Conway finished his PhD thesis, which explored a modest byway
of set theory. He then needed a job. This was a challenge. Not because there
weren’t jobs to be had, nor because he wasn’t qualified. The insuperable
obstacle was merely applying. As the end of his PhD funding approached, Conway
did nothing. He remembers walking down the street and bumping into Ian Cassels,
a canny Scot who for a time held the post of the Sadleirian professor of pure
mathematics, and also the position of department head. Cassels asked him, “What
have you done about a job?”
“Er, nothing,”
replied Conway.
“There’s a
position opening here, why don’t you apply?”
“How do I go
about it?”
“You write me a
letter.”
“What should I
say?”
Cassels took
pity. He offered to write the letter for Conway. He sat down at the side of the
road on a stone wall in front of King’s College, rummaged through his briefcase,
found a pen, pulled out a piece of paper, and began, “Dear Professor Cassels, I
wish to apply for …” He handed it to Conway and instructed him to sign, and
Cassels filed the letter away in his briefcase. Victory was his, Conway was
sure. A while later he got the news in the mail: “I’m terribly sorry,” Cassels
wrote. “You didn’t get the job.” But, he continued, “there is another position
coming open next year, and unless you indicate your wishes to the contrary, I
shall take your previous letter as a letter of application for that position.”
Conway succeeded in obtaining this second position. He became an assistant
lecturer.
John
Conway in his office at Princeton in 1993. Photograph: Dith Pran/The New York
Times/Red/Eyevine
The students
loved their new lecturer as much for his mind as his high jinks. He had a homely
lecturing style, discussing abstract concepts in terms of trains and cars, cats
and dogs. In lecturing on symmetry and the Platonic solids, he sometimes brought
a large turnip and a carving knife to class, transforming the vegetable one
slice at a time into an icosahedron with 20 triangular faces, eating the scraps
as he went.
For one
student, Edward Welbourne, now a software engineer in Oslo, the most memorable
was Conway’s linear algebra course – specifically, a session wherein Conway
proved that for two symmetric quadratic forms, both can be simultaneously
diagonalised (no small feat). “Doing each takes a moderately tricky piece of
computation,” said Welbourne. “To do two at the same time is thus doubly tricky,
like balancing a broom by its handle on one’s chin while juggling.” This is
exactly what Conway did, while concluding the proof. When I mentioned this to
Conway, he quibbled that in fact he had balanced a broom on his chin and
simultaneously balanced a penny on the hook of a coat hanger and then with a
centrifugal swoop spun this coat hanger contraption around like a helicopter
rotor.
Such incidents
inspired the creation of the John Conway Appreciation Society. “He was by far
the most charismatic lecturer in the faculty,” said his Cambridge colleague, Sir
Peter Swinnerton-Dyer. “I’m not sure that I can describe how charisma happens.
It just is or isn’t. And with most mathematicians it markedly isn’t.”
* *
*
Part of Conway’s charm is his talent for
spinning tales – he seems almost as expert at storytelling as he is at
discovering deep mathematical truths. A favourite in his repertoire involves
Oliver Cromwell, lord protector of the Commonwealth and fellow circa 1616 of
Sidney Sussex College, where Conway also belonged as a fellow. Working on his
biography, I heard it many times from Conway himself, and during a research trip
to Cambridge I heard it again from his first wife, Eileen.
Late one night
in the early 1960s, Conway came home and told Eileen of an odd party he’d just
attended. At the summons of the master of college, Conway and select fellows
gathered for a private dinner, together with the college chaplain and alumnus Dr
Horace Wilkinson, an anaesthetist, whose family had kept Cromwell’s head in a
velvet-lined oak box for nearly 150 years. Wilkinson donated to the college the
well-travelled skull, with the intention that it finally be laid to rest. To
hear Conway’s telling, it was a raucous night, with ample drink and a sumptuous
dinner, after which the master led a candlelit procession to the antechapel,
where the chaplain gave a brief service, followed by the burial and
consecration.
Stopping by
Sidney Sussex College to do some fact checking, I asked after Cromwell. The
porter escorted me to the antechapel and pointed to a plaque on the wall: “Near
to this place was buried on 25 March 1960 the head of Oliver Cromwell.” This
prompted me to put a few questions to Conway. Where exactly was the dinner? What
was on the menu? What was the conversation at the table? And, had he actually
seen the head? My questions were not greeted with Conway’s usual know-it-all
enthusiasm. “Yeeesss?” he said. “That is a great story, isn’t it? And I
often tell that story with myself playing a supporting role. As if I had
actually been there.”
He had made it
up – he wasn’t even a fellow at Sidney Sussex until 1964. He’d no doubt heard
rumours, and in an opportune moment, when he needed a captivating story to tell,
he claimed this tale as his own, because, well, it was a great story. The
incident revealed Conway as an accomplished fictioneer and a rather unreliable
narrator of his own life.
There is a
cartoon drawing of Conway that neatly captures this devilishness. Growing from
his head is a “horned sphere,” a topological entity classified more generally as
a “pathological example” and known for being counterintuitive and ill-behaved,
much like Conway himself. In attempting to get a better read on Conway and his
caricature, I consulted Irving Lavin, an art historian at the institute for
advanced study in Princeton. Lavin noted that Conway was in good company among
artists – Picasso, for one – who matched creativity with promiscuity, both
intellectual and interpersonal. So maybe Conway’s seeming inability to
distinguish fact from fiction correlated to his uncanny ability to see
mathematics differently, to pursue pure curiosity-driven research no matter how
superficially trivial, and to achieve his idiosyncratically original
results.
Through the
early to mid 1960s, however, Conway didn’t accomplish much. He spent the
majority of his time playing games, inventing games – such as Sprouts, with
graduate student Michael Paterson – and reinventing rules to games he found
boring, such as chess. He liked games that moved in a flash. He played
backgammon constantly, for small stakes – chalk, honour – though he never got
very good at it. By all outward appearances he was blissfully playing around,
but Conway was well aware he was doing nothing, had done nothing. He began to
worry that he didn’t deserve his job, that he was on the verge of being sacked.
He was pissing away his days playing games, though with an ever present grouping
of student disciples gathered at his knee. He oscillated between having fun and
feeling guilty and depressed. He calls this period in his life “The Black
Blank”. Inwardly he worried that his mathematical soul was withering
away.
* *
*
In August 1966, the International Congress of
Mathematicians convened at Moscow State University, and it was there, reclining
against a giant cylindrical pillar at least 5ft in diameter, that Conway turned
a crucial corner. A man approached and asked, “Are you Conway?” The interlocutor
was John McKay, then a PhD student the University of Edinburgh (now a professor
at Concordia University in Montreal).
McKay had a tip
for Conway; he suggested that it might be worthwhile exploring a mathematical
commodity that had recently attracted interest: the Leech lattice (discovered by
the University of Stirling’s John Leech) – the best lattice for a sphere packing
in 24 dimensions, with the “lattice” being a set of points derived from the
centres of the spheres.
By analogy,
consider that the best packing of circles in two dimensions is the hexagonal,
because if you connect the dots of the centres of any six circles surrounding a
central circle (pennies on a table, say), these central dots connect to form
hexagons. The arrangement of circles has 12 symmetries; it can be rotated or
reflected in 12 different ways and it looks exactly the same. By extension,
then, mathematicians suspected that the Leech lattice might contain an
exquisitely large and coveted symmetry.
The Leech
lattice intrigued Conway. He decided to go hunting for this big symmetry, for
the lattice’s “symmetry group”. Conway told his wife that were he to succeed,
this would make his name. By now he had four young daughters – he memorised his
girls’ birthdates by classifying them as “the 60-Fibs”, since they were born in
1960 plus the Fibonacci numbers, ie
1960 + 2, 3, 5, 8 = 1962, 1963, 1965, 1968. And in setting out in search of the
group, he told Susie, Rosie, Ellie and Annie that Daddy wasn’t to be disturbed.
He planned to set aside Wednesday nights from six o’clock to midnight and
Saturdays from noon to midnight, for as long as necessary. He put away the
games. He would play around with the Leech lattice instead.
Conway’s
Leech lattice doodle. Photograph: John Horton Conway
“Conway is the
rare sort of mathematician whose ability to connect his pet mathematical
interests makes one wonder if he isn’t, at some level, shaping mathematical
reality and not just exploring it,” James Propp, a professor of mathematics at
the University of Massachusetts Lowell, once told me. “The example of this that
I know best is a connection he discovered between sphere packing and games.
These were two separate areas of study that Conway had arrived at by two
different paths. So there’s no reason for them to be linked. But somehow,
through the force of his personality, and the intensity of his passion, he bent
the mathematical universe to his will.”
And he almost
seemed to do the same while looking for the Leech lattice’s symmetry group.
Conway had expected to keep to his house-arrest work ethic for weeks or months
or beyond. Locking himself away that first Saturday, he unfurled an unused roll
of wallpaper backing paper and sketched out all he knew about the problem. By
that very evening, he’d figured it out. He’d deduced the Leech lattice’s number
of symmetries. It was: 4,157,776,806,543,360,000. Or possibly double that. He
telephoned Cambridge’s John Thompson, the God of group theory, and they
determined it was the double: 8,315,553,613,086,720,000.
When I pestered
Conway for more details regarding the seminal Moscow meeting that inspired his
triumphant half-day of discovery, he begged off. He was loth to add any
“spurious precision”, as he came to refer to his embellishments, advertent or
accidental. “My memory. My memory is a liar,” he said. “It’s a good liar. It
deceives even me.”
One thing he
was willing to discuss was what precisely he was doing when he was looking for
the group. For instance, when he was working with the lattice, he wasn’t just
working with the basic (x, y) coordinates, he was working with 24-dimensional
coordinates – for example:
(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
And some of the
work was as simple as applying the Pythagorean theorem. Still Conway refused to
pull back the curtain too far. “Yes, it’s true, my calculations, technically
speaking, were using Pythagoras’ theorem,” he said. “But to concentrate on the
calculation is misleading. It’s like asking an artist, ‘Where did you paint the
person’s chin? Was it one-foot-five above the base of the picture, or
one-foot-six?’ If you’re thinking about conceptual things, the measurements
don’t matter … It’s rather unfortunate that we can’t just see these things.
Because it means that I can only appreciate the beauty of them, truly, after
I’ve have done the calculation. Since I can’t conjure up 24-dimensional space, I
use numbers to do it.
“For a time I
was thinking so geometrically about these things that I used to imagine myself
with lots and lots of arms and legs, extra limbs. Because if I have two arms and
point ’em out, then they both lie in a plane. And I’ll use a leg as well, and
now they are lying in three-dimensional space. To form an adequate idea, an
adequate geometric visualisation, of what is going on in 24 dimensions is more
or less impossible. In large dimensional space, there are large numbers of
directions to point, so you would seem to need quite a lot of arms and legs. I
distinctly remember imagining myself stuck in the middle of this space, and
waving all my arms and legs in the air, and trying to understand things, looking
up at the stars, pretending they are the lattice points, and just sort of
daydreaming.”
As tradition
dictates, Conway’s discovery of the Leech lattice’s symmetry meant that it
became known as the Conway group (which in fact contains three smaller groups,
sometimes collectively called the Conway constellation). This was the hot
mathematical news of the day and earned him invitations to lecture across the
globe.
It was at this
juncture, having found his namesake group, that Conway made what he called “The
Vow”, promising himself: “Thou shalt stop worrying and feeling guilty; thou
shalt do whatever thou pleasest.” He no longer worried that he was eroding his
mathematical soul when he indulged his curiosity and followed wherever it went,
whether towards recreation or research, or somewhere altogether nonmathematical,
such as his longing to learn the etymology of words. Conway’s fate now was to do
all the stuff that he had formerly feared his fellow mathematicians might
floccinaucinihilipilificate. “Floccinaucinihilipilification” is his favourite
word. He reckons it’s the longest word in the Oxford English Dictionary (it is
certainly in the top three), and without prompting he gives an account of its
etymology: it is a Latin-based word, invented circa 1730 at Eton as a
schoolboy’s joke. And, Conway recites nearly verbatim the OED’s definition: “the
action or habit of estimating as worthless.”
* *
*
The period of time during which Conway
discovered his group, circa 1969 – though he prefers to round it up to 1970 – he
calls his annus mirabilis. Within roughly the same 12-month period he also
discovered his surreal numbers. This came as a direct if unexpected byproduct of
playing all those games, when he noticed that big games broke down into a sum of
small games. He deconstructed the games, classifying the moves of each player,
determining who was ahead and by how much, and while doing this deconstructing,
analysing the sum of mini games within the larger game, he happened upon the
surreal numbers. Like an Escher optical illusion – say, a regular tessellation of birds morphing into fish –
Conway beheld the game, and then he saw that it embedded or contained something
else entirely: the numbers.
That same year
he also invented the Game of Life, a cellular automaton that to this day retains
cult status. It is not a game proper; Conway calls it a “no-player never-ending”
game. It is played on a grid, like tic-tac-toe and, according to three simple
rules of Conway’s devising, the cells placed on the grid proliferate, resembling
skittering micro-organisms viewed under a microscope. A cellular automaton is in
essence a little machine with groups of cells that evolve from iteration to
iteration in discrete rather than continuous time – in seconds, say, each tick
of the clock advances the next iteration, and then over time, behaving a bit
like a transformer or a shape-shifter, the cells evolve into something,
anything, everything else. As such, the Game of Life demonstrates how simplicity
generates complexity, providing an analogy for all of mathematics, and the
entire universe.
Conway
playing Game of Life, which he invented in 1970. Photograph: Kelvin Brodie/the
Sun
Conway summed
up his annus mirabilis thus: “Before, everything I touched turned to nothing.
Now I was Midas, and everything I touched turned to gold.” Nevertheless, it was
more than a decade later that the Royal Society installed him as a Fellow in
1981. Thereupon Conway went around Cambridge translating the initials FRS
(fellow of the Royal Society), telling people he was now officially a “Filthy
Rotten Swine!”
The year 1985
also proved productive for Conway – if not quite another annus mirabilis, it
came close. He had continued his sphere packing work with AT&T Labs
mathematician Neil Sloane, and that year the duo secured US Patent No.
4,507,648, “Decoding Techniques for Multi-Dimensional Codes”, applying their
sphere-packing in coding theory, figuring out how to most efficiently send
signals across telephone and fibre-optic lines. This and other papers on the
subject were recognised with a prize from the IEEE Information Theory Society;
they possessed a superior understanding of multidimensional geometry, and they
were solving crucial problems necessary for higher-dimensional
coding.
Also in 1985,
after 15 years of gestation, Conway and his coauthoring “sum chums” (Robert
Curtis, Simon Norton, Richard Parker and Robert Wilson) published the ATLAS of Finite Groups, perhaps the most important book in group theory, a realm
subsequently picked up by physicists, with “supersymmetry” offering a crucial
extension to the Standard Model of particle physics, the model explaining the basic building blocks of the
universe and the fundamental forces of nature.
The same year,
Conway accepted an invitation to speak at Princeton, which eventually led to a
job offer. He took up a full-time position in 1987. For Princeton, it was a
coup. The communications office sent out a glossy press release and the
university president, in announcing the hire, praised Conway as a “multifaceted
phenomenon … one of the most eminent mathematicians of the century”.
* *
*
In 1993, Conway attracted the attention of a
New York Times reporter. The resulting profile opened with what Conway calls his
“doomsday rule”, an algorithm by which he can calculate the day of the week for
any given date:
“Dr John H Conway sits down at his computer and
gets ready to log on. But before the computer allows him to begin work, it
quickly spews out 10 randomly selected dates from the past and the future, dates
like 3/15/2005 or 4/29/1803. Dr Conway has to mentally calculate what day of the
week each would be before his computer lets him open a file and get to work. It
is a game he has rigged up to play with himself.”
After inventing the Doomsday game of sorts in
1972, Conway had set a goal to double his speed every five years for doing 10
dates in rapid succession. Landing at Princeton did nothing to put him off
course. “Why did I want to be fast? It’s impressive,” he said. “It’s a nice
party trick. I don’t know that it ever got me any girls, but it’s the sort of
thing that might’ve done occasionally with the right girl, a certain type of
girl.”
His record was then 15.92 seconds to calculate
all 10 dates, roughly 1.5 seconds for each one. He was on track with his
doubling goal, and he informed the reporter that he was the fastest person in
the world.
The fastest, that is, until Stephen D Miller, a
19-year-old PhD student, arrived on the scene in the early 1990s. He and Conway
entered into hostile competition to see who could smack out 10 dates faster.
Conway used this as a strategy to keep his brain sharp and ward off aging, a
worry that was increasingly playing on his mind. He had always avoided mirrors,
never much liking his appearance, and as the years clicked onward he also
avoided catching sight of his reflection in shop windows.
These were turbulent times for Conway. He had
survived a difficult divorce from his second wife, Larissa (with whom he has two
boys, Alex and Oliver, both now pursuing mathematics, at Rutgers and NYU
respectively), as well as a heart attack, and attempted suicide. He had suffered
bouts of depression in the past, and after the heart attack he got depressed
again – contributing factors being the acrimony with Larissa, alienation from
his young boys, and money troubles. He ate a stash of sleeping pills like an
entrée at lunch with Larissa and her lawyer.
Following the suicide attempt he made his
comeback, so to speak – his re-entry to daily life, knowing full well that
people around town were talking – by borrowing a T-shirt belonging to his rock
climber friend Neil Sloane, and wearing it around town for days, emblazoned as
it was with the big bold letters “SUICIDE” and the tiny word “rock” beneath.
Conway thereby instituted his “Let It All Hang Out Policy”, which involved
frequently and flippantly recounting this trying chapter in his life – even to
this day, he sometimes off-handedly adds it as a chatty preface to a lecture
about maths.
Shortly following this dark period, during a
manic intellectual cliff-jumping escapade, Conway wondered what his time would
be with the help of GAD – short for “Gimme A Date!” – a computer program one of
his graduate students had designed to help Conway get even quicker. He was
nearly too scared to try. He sat down at the computer and ripped off 10 dates in
an astonishing 9.62 seconds. “I didn’t try again,” he recalled. “My heart was
pumping away like mad. I got this enormous amount of adrenaline, I actually felt
liquids pouring into my brain. And it was scary as all hell. But it was
interesting, taking the lid off and seeing how the brain works.”
In the end, not counting Conway’s manic 9.62
seconds, Steve Miller prevailed in the GAD competition – Miller calculated ten
dates in 10.66 seconds; his brain was much younger, plain and simple (he is now
a professor and vice-chair of the maths department at Rutgers). But no matter.
This routine for Conway was all part of deceiving himself into believing he was
still only five years older than his students. It was getting to the point,
however, where he wasn’t so easily fooled. “You are young, and then you are old.
And here, I’m always surrounded by brilliant young mathematicians. How do you
keep your end up?”
Keeping up with the youngsters is the gist of
what Conway calls his “Nerd’s Nightmare”: A hunchbacked centenarian, looking a
wreck, he hobbles into the Princeton maths department common room. A graduate
student asks: “Who’s the old geezer?” Her friend says: “I think that’s
what’s-his-name …? Conway!” Conway sits there wearing his Mona Lisa smile,
waiting for an opportunity to pounce. Finally, in in the course of the students’
conversation they happen to mention a date. “When were you born, again?” “April
1, 2015.” And quick as a flash Conway works it out: “THAT WAS A WEDNESDAY!” And
the students say to themselves: “Oh, there is someone in there.”
“It’s my insurance policy against old age,”
explained Conway. “This decrepit old guy snaps off a date.”
* * *
In spring 2009, three years after
he suffered a stroke that spared him intellectually but left him with a
cane and a gammy right side, Conway delivered a six-part lecture series on his
latest brainchild: The Free Will Theorem, devised with his Princeton colleague
Simon Kochen. The theorem deploys a motley combination of quantum mechanics
axioms, philosophy, and geometry. It is most simply stated as follows: If
physicists have free will while performing experiments, then elementary
particles possess free will as well, and this probably explains why and how
humans have free will in the first place.
As unlikely as it sounds, it is a line of
thinking that has an illustrious lineage, originating with John von Neumann, the
father of the modern computer. In certain quarters, the theorem is being taken
seriously, roundly debated and thoroughly discussed – with, for example, a paper
just last year in the journal Foundations of Physics, where Conway and Kochen
originally published their result in 2006, that picks up the idea and rolls it
along.
Over the course of the lectures, graduate
students in maths marvelled at how Conway and Kochen had managed to infuriate
two departments at once – trespassing on physicists’ territory in such a way as
to make philosophers’ hair stand on end. Jacob Tsimerman, another prodigious
19-year-old, was particularly interested. He’d been spending lots of time with
Conway, playing Phutball – short for Philosopher’s Football, yet another game of
Conway’s invention, using a grid board with white and black stones – and at once
debating the merits and demerits of the theorem. Tsimerman thought it was deep
and fun and puzzling. But he was more impressed with Phutball. “[Phutball] is
arguably the greatest triumph of this man,” he told me. “And I don’t mean that
condescendingly. It’s a great game.”
A few years ago, I watched Tsimerman face off
against Conway in the Princeton maths department common room, where Conway
spends all of his time because his office is such an uninhabitable tip. After
some tsk-tsking from Conway followed by a “Pfwooooah!” from Tsimerman, the
youngster enthusiastically conceded another defeat. “Your game, professor!” He
accepted a rematch, even though another game was bound to make him late for his
seminar.
Tsimerman soon suffered a setback. A few
tackles later, Conway faced trouble. He cautioned: “Reports of my death have
been greatly exaggerated!” This time, though, he was beaten at his own game, and
the victorious Tsimerman sprinted off to class. “But he’s now 15 minutes late,”
noted Conway. “That’s my real aim in getting them to play these games, to ensure
they don’t do well in maths, to destroy all these formerly promising
mathematicians.”
Tsimerman subsequently went on to Harvard, and
he’s currently an assistant professor at the Univeristy of Toronto. Conway
subsequently went on to, as ever, play more games, and engage in all manner of
nerdish delights – spending hours upon hours, for example, curing the Rubik’s cube, and
reciting pi, and playing Dots and Boxes, or Sprouts, with his 13-year-old son
Gareth, via his third wife Diana.
Usually, though, Conway can be found squatting
in the Princeton common room. Although still young at heart and head, he looks
more and more like his old friend Archimedes, increasingly bearded and
increasingly grey, with an otherworldly mien – a look that should earn him a
spot in the online quiz featuring portraits of frumpy old men under the rubric
“Prof or Hobo?” His uniform is faded chinos, stained with splotches that he
camouflages by doodling spirals or crisscrosses with his pen; and on top he
always wears a T-shirt from his infinite collection emblazoned with mathsy
messages, such as: “Are you crying? There’s no crying! THERE’S NO CRYING IN MATH
CLASS!”
For Conway it is mathematics that allows him to
clear away the clouds of reality. As he put it, “Math was always there for me.”
It is the realm where he finds solace and infinite unadulterated pleasure. He’s
retired, but he keeps on playing, and as he himself noticed, he’s now being more
productive than ever. With his Cambridge friend and collaborator Alex Ryba, now
a professor of computer science at the City University of New York’s Queens
College, he’s writing papers on magic squares, on Pascal’s theorem about a
mysterious hexagram, and on “The Extra Fibonacci Series and the Empire State
Building”. They are also finishing The Triangle Book (which Conway’s had in the
works for decades), and starting The Monster Book. Perhaps Conway’s bestselling
book ever was Winning Ways for Your Mathematical Plays (first published in
1982), a collection of wisdom about games which, in early August, is being feted
at the Museum of Mathematics in New
York City, celebrating Conway and his co-authors, UC Berkeley’s Elwyn Berlekamp
and Calgary’s Richard Guy.
As an epigram in the book advises, borrowing
from Oscar Wilde: “Life is far too important to be taken seriously.”
Siobhan Roberts is the author of Genius at
Play, The Curious Mind of John Horton Conway (Bloomsbury), out this month in the
US, and September in the UK
