Math-Frolic Interview #10
"
Ultimately, what I found myself
learning about undermined all of my previous ideas about what
mathematics IS (or, more particularly, what the system of natural
numbers is). I felt compelled to share this awareness as widely as
possible."
-- Matthew Watkins
It was an absolute thrill to be in touch with, and 'interview,' someone as prominent as Keith Devlin. Today I have a thrill exactly for the opposite reason... the thorough delight of getting to learn more about someone I don't know at all, but found intriguing from the one book of his I've read.
Mathematician Matthew Watkins is the author of "
The Mystery of the Prime Numbers," a beautifully-produced, self-published book out of Britain that has little presence in the math landscape, and yet as I said in my Devlin interview, is "
one of the most fascinating/extraordinary math books for a mass audience I've ever read" (AND, it is just the first volume of a trilogy!)
Dr. Watkins is, as you'll see, a rather independent, eclectic sort, 'doing his own thing,' but doing it fascinatingly!
He currently holds "an honorary research position at Exeter University's School of Engineering, Computing, and Mathematics," and his homepage is here: http://empslocal.ex.ac.uk/people/staff/mrwatkin/index.htm
Below, are his lengthy and interesting responses to my questions (once again, I've bolded a few bits here and there of particular interest). ...Enjoy!
(And, if you're interested in prime numbers and number theory, I strongly recommend getting hold of his book!)
***********************************
1) Most of the folks I'm interviewing here at
Math-Frolic are math bloggers… you are not, but are a math author who I
chose because your volume, "The Mystery of Prime Numbers" is so
fascinating. But first, let me ask if, besides your home pages, you
have any social Web presences (Twitter, Facebook, Google+, etc.) that we
should know about?
No. I'm generally quite distrustful of these
new social media. I have a particular aversion to Facebook. I can see
some possible advantages of using Twitter, but also how it could become a
terrible distraction. As a self-publishing author trying to promote my
work, I do realize that these media are generally considered
indispensable, but I'd rather sell less books than get caught up in
these worlds which I want no part of. Encouraging people to "like" me
or "follow" me would just seem pathetic and distasteful.
[I can relate to this, as I also am very Facebook-averse and use social media rather minimally. I love Twitter, but yes, it's a huge distraction!]
2) How did your interest in mathematics originally come about, and when did you know you wanted to pursue it professionally?
It
was something I naturally excelled at from my earliest schooldays,
presumably just something to do with the way my brain works. And not
being very good at athletic or artistic pursuits, being a slightly
weird-looking, awkward kid, I naturally identified with the thing I was
good at. At that stage, I liked it because I was good at it, as simple
as that. I think that's probably quite a common backstory for adult
male mathematicians.
My family moved from England to the USA when I was
9, and because of the relative backwardness of the school system I
arrived into, I began to REALLY excel at mathematics. They ran out of
work to give me and my 6th grade teacher bought me a big algebra book
from which I taught myself how to factor polynomials, etc. I was the
weird brainy English kid at the back of the classroom! From there I
went on to teach myself calculus. By my mid-teens I was determined to
return to the UK, and the most realistic strategy was to secure a place
at a university here. Because a US high school certificate is worth
almost nothing in that context, I somehow managed to squeeze in 34
mathematics credits at the local campus (the whole of a 'major' at that
time) while finishing high school, thinking that this might just get me a
place. It paid off, as the University of Kent put me straight into
their second year (of a three year course). I was extremely focused and
confident as a student, and two years later, I was given a fully-funded
opportunity to do a Ph.D.
But by my mid-teens, I had become far
more passionate about the arts, philosophical ideas, cultural and
political movements, etc. than I was about mathematics. If I'd have
been able to, I probably would have done a degree in the humanities. So
the fact I ended up with a maths PhD was more the result of following a
path of least resistance than following my abiding interests.
It
was only halfway into my PhD that
I suddenly awoke to the beauty,
wonder and sheer 'otherness' of mathematics, something I'd been entirely
blind to up to that point. But I was also becoming rapidly
disillusioned with the over-specialisation and competitive nature of
academia, so I was destined to leave that path behind.
3) A
quote from one of your Webpages reads: "...we can confidently say that
nothing like this book has been created before. It's not just another
'popular science' book about prime numbers (neither is it a book of
woolly New Age number mysticism!) – rather, the issue of prime numbers
acts as a gateway into some truly strange philosophical territory whose
relevance extends well beyond abstract mathematics and which is
genuinely worthy of the word 'mystery.' "
Can you briefly describe
what you are attempting to accomplish with your interesting "trilogy" of
books that relate to number theory, especially as different from what
other books on the subject have done before? And where did the idea for
your books originate -- has it slowly evolved over time, or did you
pretty much know from the start what your approach and content would be?
Originally
it was going to be one book, but when Matt Tweed (illustrator) and I
sat down to formulate a plan, it became apparent that it would end up
being an intimidatingly fat tome. Hence the idea of a more manageable
trilogy. The original book has been brewing since the late 90's,
really. I had dropped out of academia to pursue other interests after a
year's post-doc research in Belgium, but before too long I became drawn
back in to mathematics, albeit in a very different way.
A strange chain
of events led me to consider the philosophical implications of the
irregular distribution of prime numbers, which led to my becoming aware
of some very strange, unexpected work (mostly post-70s) applying ideas
from number theory to physics, and vice versa. I hadn't specialized in
number theory and my knowledge of physics was fairly patchy, so there
was a lot to learn (and still is). But this led to my "
Number Theory and
Physics Web-archive" [
http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/physics.htm],
my attempt to encourage some dialogue between the number theory and
physics communities about what this might all mean.
Many active
mathematicians still express surprise that number theory has any
physical applications (beyond cryptography), but the fact that
physicists might shed light on the inner workings of the number system
is profoundly weird, even to me after years of thinking about this
stuff. It suggests a very different kind of relationship between the
numerical and physical worlds than has previously been put forward, and
quite possibly will end up informing the ongoing philosophical debate
concerning the "mind-body problem" (more accurately the relationship
between psyche and matter).
Ultimately, what I found myself
learning about undermined all of my previous ideas about what
mathematics IS (or, more particularly, what the system of natural
numbers is). I felt compelled to share this awareness as widely as
possible. Philosophers and 'generalists' should be discussing these
matters, I feel, but they're currently the domain of a relatively tiny
group of specialists in the mathematical sciences. In my attempts to
explain my interests to my friends (none of whom has any mathematical
background),
I developed a repertoire of metaphors, analogies,
visualizations and other techniques to convey key ideas. Developing the
Web-archive was taking up a lot of my time, and was entirely unfunded,
so people started to suggest that I put together a book version. There
were a number of false starts, due to the sheer size of the undertaking
and the problem of trying to write for such a broad range of
mathematical abilities, and the project was almost completely abandoned
at least twice. But once Matt Tweed got hold of a rough draft, his
enthusiasm and sense of wonderment were so encouraging that we decided
to just go for it, regardless of commercial considerations.
4)
Your books are self-published, which means they are not readily
available in American bookstores. Nor do I see much discussion of them
among mathematicians/teachers here which seems a shame. Are your books
better known and distributed in your own country of Britain? And were
you unable to get a traditional publisher for the volumes, or did you
deliberately choose self-publishing for some other reason?
No, my
books aren't in bookshops in Britain either. It's practically
impossible to get self-published works into stores on either side of the
Atlantic. It's hard enough to even get reviews. Publications that
feature book reviews tend to use the publishing industry as a "filter" -
if it's not been conventionally published, the thinking goes, then it
probably isn't worth reviewing. But in my case, I decided from the
outset to bypass traditional publishing and do everything myself. I'd
read enough about the publishing industry to have become horrified, and I
just wasn't prepared to compromise in the way that I almost certainly
would have had to in order to make the book(s) more marketable on their
terms. What I learned basically told me that my books would be
"unpublishable," but for whatever reason I decided to just go ahead and
publish them anyway.
Despite this, we've had a few good reviews,
mostly on blogs, but also Prof. Brian Josephson's (he's the Nobel
physics laureate from Trinity College, Cambridge) in the Times Higher
Education. For that esteemed organ to review a self-published work was
almost unprecedented. It led to a spike in sales for a couple of weeks,
but they dropped off again quite soon after. People are just bombarded
by so much media these days, that to promote something you just have to
get out there in the marketplace and shout louder than everyone else
(or employ someone else to). This doesn't come naturally to me. But
I'm patient, and have much faith in the value of what we're doing. Most
importantly, the core content of these books will remain valid
indefinitely, as it's not subject to social or cultural trends.
My
attitude has been to let the books prove themselves on our own terms,
and then if a traditional publisher wants to license them (without
making any substantial changes) and handle the distribution/promotion,
that would be great - unless it was Rupert Murdoch's HarperCollins or
some other dubious corporate entity. That's the other problem with the
publishing industry - like the music industry, small independents are
rapidly being subsumed into corporate behemoths which are increasingly
impersonal, homogeneous and entirely profit-driven, and I'd rather not
get involved in that!
This is the first time in the history of
books that it's possible for someone like me, with almost no capital and
no business premises, to distribute a professionally printed and bound
book worldwide. That in itself I find exciting. My sales have been in
the 100s rather than the 1000s, but with every copy that gets sent out
to Japan, Brazil, Canada or Finland, I feel a small sense of victory.
5)
I've only read (and enjoyed) your first volume thus far... can you give a hint of where the final (third) volume will
eventually lead readers? (what sorts of ideas/conclusions)
As I
hinted in an earlier answer, my aim is to convince readers that the
number system is something very different than what they had previously
thought, that we just don't know what we're dealing
with. The physics side of things comes in quite heavily in
Volume 3 (it took the first two volumes to get to a point where that can
meaningfully happen), as well as some of my own
philosophical/cultural/psychological insights into "what it all might
mean" - although I'm being very careful to avoid any kind of ideology or
dogma.
The subtle relationships between number, matter and psyche are
what interest me more than the technical details of maths and physics,
hence "
Prime Numbers, Quantum Physics, and a Journey to the Centre of
Your Mind" [Vol. 3]. But I don't want to give too much away, you'll just have to
wait and see!
6) Can you tell us some of your own favorite
math books that you like reading for enjoyment, and also any additional
math books that you'd especially recommend to lay people?
The
honest truth is that I don't read mathematical books for enjoyment. I
read a lot, but almost entirely in other subjects. Years ago, I read an
Ian Stewart book where he outlined a number of major unsolved
mathematical problems (I can't recall the title) - that was quite useful
for me at the time, to get a general overview of areas of the subject
which I was unfamiliar with. And I read four popular books on the
Riemann Hypothesis as part of the research for the SoC trilogy (Sabbagh,
du Sautoy, Derbyshire, Rockmore) - that was mainly to be sure that I
wasn't duplicating anything of those authors too closely. Those are all
worthy books in their various ways, but
I find a lot of the 'popular
mathematics' literature has an unspoken ideology built into it which I
instinctively rebel against -- it's that narrative of "Great Men" with
their "Great Ideas" ascending some kind of mountain of technical
progress, a sort of self-congratulatory conquest. I don't buy into the
Western myth of "Progress". Also,
there's a subtle matter of denying the
"shadow" side of mathematical thinking, which troubles me. Mathematics
has allowed humanity to reshape the world faster than our wisdom can
keep up, and this isn't being addressed. It's presented as something
which solves our problems, but almost never as
something which can also create them. Yes, it has
led to some cool little gadgets... but who exactly chose to reshape
society so that practically everyone you see in a public environment
these days is semi-permanently distracted by some kind of screen? Who
decided that we should all be plugged into a global economy at the mercy
of wholly selfish derivatives traders employing complex algorithms,
wreaking havoc on whole populations? Electronic surveillance? Drone
warfare?
One book which that analysis
doesn't
apply to is Douglas Hofstadter's incredible "
Godel, Escher,
Bach," although it's not exactly an easy read (it was the only
existing book I could initially compare the SoC trilogy to when I was
still considering dealing with conventional publishers). I read that as a
teenager and it definitely influenced me.
If I had to recommend a
book for lay people, it would be quite an unusual one: Michael S.
Schneider's
"A Beginner's Guide To Constructing The
Universe" (1995) which takes what I'd consider to be a more
healthy, holistic approach to number-related issues. Also, just the
other day I saw a copy of Keith Critchlow's
"The Hidden Geometry
of Flowers" (2011), which although not purely mathematical, I
would strongly recommend to people seeking to get some insight into the
underlying mathematical layers of physical reality. Some of Clifford
Pickover's books which I've leafed through look quite engaging (although
some are a bit too "recreational mathematics" for my liking). And
having seen some of Martin Gardner's articles, I suspect his books are
probably worth checking out - there's one called
"Meta-mathematical Themas" which was once recommended
to me.
[Actually the title is "Metamagical Themas" and it's another Hofstadter book, not Gardner. It IS a FABULOUS volume, but not a lot of math. Hofstadter, by the way, has a new book to look forward to, due out this year, "Surfaces and Essences."]
7) I almost get a sense that you are kind of 'doing
your own thing' out on the math sidelines… I've often commented that
Britain produces a lot of great math writers and communicators… have you
worked with or collaborated much with any names we might recognize, or
are you indeed sort of out there in your own arena?
I'm afraid
I'm out on my own! I did send promo copies of Volume 1 to Ian Stewart
and Marcus du Sautoy, just to see what reaction I'd get. Ian Stewart
was very encouraging, really liked it and said it "deserves to sell a
lot of copies." But he also warned me of the difficulties of getting
any traction with self-publishing, and gave me some helpful promotional
advice. Marcus du Sautoy never responded (I sent him Volume 2 as
well). No doubt he's very busy, but I was mildly disappointed, as he's
currently "Simonyi Professor for the Public Understanding of Science" at
Oxford (having taken over Richard Dawkins' post), so I thought he might
recognize the value of what we're doing. Perhaps he sees it as
competition for his "
Music of the Primes" (although they're wildly
different books in tone and content). We met briefly at a random matrix
theory conference in 2001. A few of us were standing around, slightly
awkwardly, as mathematicians at conferences tend to do, and he started
enthusing about my web-archive, without realizing I was responsible for
it! That felt very encouraging at the time (this was before I'd decided
to do the book thing). Shortly after that, at his request, I helped him
out with a few little bibliographic references for his book, but he
didn't acknowledge that either. He must be very busy.
8) To round yourself out a bit, when you're not doing mathy things, what are some of your main interests/hobbies/activities?
Since
1994 I've been playing a seven-stringed Turkish instrument called a
saz. I've never learned the traditional Turkish style, but it's a very
versatile instrument, and I've done an awful lot of writing and playing
and jamming in a lot of different styles with people I've met over the
years. I've been involved in quite a bit of free improvisation (I
helped to found the Exeter improv collective '
Children of the Drone',
still going after a decade, see
http://www.childrenofthedrone.net).
Playing "free" music is one of the only situations where my
rational/analytical mind shuts down and allows the more
intuitive/creative side some airtime. So that's very important to me. I
also blog about my musical adventures and about various music I
discover, both the current, vibrant scene in Canterbury where I'm
currently based, as well as a great diversity sounds from all times and
places. And I've been curating a series of monthly podcasts about the
so-called 'Canterbury scene' of the late 60's and 70's (a sprawling
amalgam of psychedelia, progressive rock, minimalism, experimentalism
and jazz fusion) [
http://canterburysoundwaves.blogspot.co.uk]
I
do a lot of walking, exploring the nooks and crannies of the English
countryside, visiting megalithic sites and old churches, etc. I read a
lot (as widely as possible), and love helping out with other people's
gardening (although sadly I'm not a natural gardener -- I need to be told
what to do!).
Generally,
I'd say, I'm interested in
"everything, and how it all joins together." I'm a generalist. Reality
is fascinating! Analytic number theory just happens to be the area
I've focused on in recent years.
9) Any parting words, not covered above, you'd care to pass along to a math-oriented audience?
How about this:
"what we don't know is hugely more significant than what we do know"?
That
sounds appropriately meaningful! I just think we should humble
ourselves and recognize that in previous eras where the levels of
mathematical/scientific knowledge now appear laughably inadequate,
people at the time still imagined themselves to be at the cutting edge,
having almost explained everything (rather like the dominant stance
these days). We'll always just be dipping our toes into the vast Ocean
of the Unknown, and we'd probably do ourselves a big favour to recognize
that, rather than continually congratulate ourselves on how "advanced"
we supposedly are.
***********************************
Wow, this has been a fascinating set of responses from someone a bit off the normal beaten path of math. And I'll reiterate that I believe Dr. Watkins' first book is a wonderful read -- I ordered it through
Amazon and received it in short order... hope word of it spreads.
Thanks for participating here, Matthew!
ADDENDUM: Sol Lederman at "Wild About Math" blog just announced he'll be doing a podcast with Dr. Watkins in the future. Something to look forward to. Sol (very) favorably reviewed Matthew's first book well over a year ago:
http://wildaboutmath.com/2010/09/24/review-the-mystery-of-the-prime-numbers/
Sol Lederman's podcast with British mathematician Dr. Matthew Watkins (author of "The Mystery of the Prime Numbers") is now up:
