Lives In Mathematics Practical Theology kiwiconnexion
David Bell: Hey, welcome along everyone to
Live On Air this Sunday evening, 12 February 2017. We’re kicking off again for the Trinity-
at-Waiake eLearning centre, and Kiwi Connexion which services the whole thing. Welcome to
this particular broadcast. Peter Davies and David Erasmus; I’ve known both of these guys
for quite a long time indeed, but they have one common area that interests me a very great
deal, and that is that they’re both highly trained and capable mathematicians. So, tonight’s
topic is about living a life in mathematics, and I thought I’d get each of them to briefly
introduce themselves by saying where they studied mathematics first of all. So, maybe
Peter Davies; could we start with you please? Peter Davies: Yes, David. Thank you. Effectively
mathematics is my career; I’m an actuary by profession. My children – one of them is in
their 30s – they still don’t actually know what I do for a living, but I’ll just briefly
explain that I’m effectively an insurance mathematician. So, every insurance company
you come across will have an actuary. Some of them have a lot of actuaries. The bigger
ones will have many. The smaller ones maybe use a consultant.
I’m an external actuary to probably 20 or so of New Zealand’s smaller insurance companies,
and they all by law have to have an actuary so that their premiums and their reserving
and so on – so they can all pay their claims. Maths was one of my favourite subjects at
school, and then I trained at the University of Cape Town, doing a degree in actuarial
science which had a very good maths and statistics base, and then I did professional exams after
that. You do the professional exams through one of the professional bodies. I did mine
through the London Institute, so qualified as an actuary through the Institute of Actuaries
in London. It’s a very good career. It’s a very good way of making a career in mathematics.
David Bell: Peter, I didn’t know that at the University of Cape Town, and I guess this
must be the case in numerous universities, that you could actually do your first degree
in actuarial science. Peter Davies: Yes, there are a number of universities
around the world who work closely with the examining bodies. So the University of Cape
Town invested some significant time and effort in linking a particular course. It was through
the Faculty of Commerce. With the Institute of Actuaries in London they made sure the
syllabus was in line with the UK professional [syllabus 3:19]. The deal was that if you
passed particular subjects with an upper second or above, then you could get exempted from
some of the initial professional exams. We all still had to do the final professional
exams, but by doing a degree you could cover the initial technical subjects. There’s I
think three universities in Australia who do that. They’ve linked up with the Australian
Professional Institute. So, yeah it’s a very good way of reducing the length of time of
part-time study that you have to do by combining it with your university studies.
David Bell: That’s fascinating. That’s a great introduction. David Erasmus; you too have
made a career out of mathematics. Where did you study?
David Erasmus: Coincidentally from the same university; also the University of Cape Town
in South Africa. I grew up partly in the UK, partly in South Africa and I’ve spent the
last 20 years in New Zealand. My direction was more pure mathematics. University of Cape
Town pure mathematics has a bit of a focus on topology which is rather fun. For myself
though, I particularly like things like calculus, analysis, computer graphics and that kind
of thing. I’ve basically a large part of my life focussing on those topics as I developed
software for simulating models and teaching mathematics.
David Bell: The two of you have got this incredibly rich background that uses the mathematics
that you studies at university in your every day working lives. So, I’m picking from that,
that you both still continue to enjoy the subject of mathematics as a whole, even though
you’re focussed in very particular areas. Do you still like mathematics?
Peter Davies: Briefly – I don’t know if it’s a Chinese proverb, but along the lines of,
if you do a job you enjoy you’ll never work another day in your life; I’m very much in
that category. David Erasmus: Yes, and I think I’d echo that;
I really enjoy what I do. I don’t like everything in mathematics. In fact, things like statistical
analysis don’t excite me particularly – number crunching, but there’s a lot of things in
mathematics I really love and enjoy doing. David Bell: Both of you have also got really
interesting stories to tell about a kind of emphasis on education, and somehow your mathematics
got you involved in different sorts of educational activities. Peter, you started what is one
of the most successful private schools in New Zealand. This is when I first got to know
you; you had just a couple of years before got a prefabricated classroom onto a site
in what was the rural Albany. Would you like to just tell us a little bit about that story?
It’s quite fascinating. Peter Davies: I didn’t think you were going
to bring that up. Anyway, yes if I just go back a step; I was very fortunate to go to
a very good school in Johannesburg. It was a church school. We were poor, but we went
by virtue of my father being an Anglican minister. It was a school founded very much on people
who had no desire to be wealthy, but who gave their lives to build up the school. It’s a
magnificent school on Houghton Ridge, if anybody knows Johannesburg. Coupled with that upbringing,
and a desire to see the best education for my children, when we got to Auckland we basically
set up a pioneer school, and it had to be on a non-profit basis.
So everything about it has been non-profit; everyone involved in the board is a volunteer.
So it started with 34 children, and it’s up to about 800 students now. So that really
came from a combination of two things; wanting to have a facility that delivered the values
and education that I had been privileged to enjoy, and to give some sort of legacy back
in a different sort of way. For all the luxuries we’ve got, we’ve had none of the hardships
that the Christian brothers of – it was The Community of the Resurrection was the name
of the community who basically started the school. That’s the story there.
David Bell: It’s a magnificent achievement in terms of what you’ve done within Auckland,
New Zealand. David, you’ve got an equally interesting tale – a peripatetic mathematician
– did I pronounce that incorrectly? I’m not sure of it. You decided to go wondering, I
think after you graduated. David Erasmus: Well, I can actually tell you
quite a similar story; I was asked by some nuns running a church school in Soweto in
South Africa. They had the situation that they wanted to teach mathematics but they
had no maths teachers – nobody qualified to teach mathematics. So they’d been donated
all these computers by IBM and they asked if I could help. So I developed some software
for them to try to excite children with simulations and animations and stuff like that, to try
to get the students enthusiastic about mathematics, which worked so well, that a few years later
some of those students took part in maths Olympiads and did very well in the end. I
did it on the basis that I would do it freely for them if I could sell the software outside,
and that’s of course been financially very lucrative for me because that mathematics
software I developed has been sold around the world.
David Bell: Your suite of programmes for teaching children number skills, is it at about…
David Erasmus: It does the full range of mathematics, right up to things like calculus, analysis,
integration; that kind of thing. David Bell: You taught mathematics. Did you
teach it in a high school, or you taught some other things as well?
David Erasmus: Yes. Actually I was wondering if you were going to ask that. I did teach
mathematics a little, but I taught physics a lot more. My personal feeling is it’s hard
to teach a subject that you really love and know very well. It’s sometimes better to teach
a subject you know slightly less well, like physics. So I think I was a more successful
physics teacher than mathematics teacher, because I made fewer assumptions talking to
the students. David Bell: That’s a really interesting observation.
Does that ring any bells you, Peter Davies? Peter Davies: Not really. I have lectured
from time to time. Maybe for the reasons David’s outlined I wasn’t a good lecturer. I find
it difficult to slow down the pace and appreciate how long it takes everyone, including me,
to absorb new facts. The teachers have to move very carefully and continually check
that their students are grasping each step of the way, and I had difficulty with – once
I understand something I go at breakneck speeds in my thoughts, but to teach that concept
to someone else, you have to slow it down by a factor of 100, and I have difficulty.
My brain has difficulty doing that. So, teaching is a very special skill. My wife teaches new
entrance, or junior – teaching the junior primary school, and the patience and skill
to teach that level is just phenomenal. I was not a good teacher of university students
studying financial mathematics, so my chance of surviving in the primary school would be
zero. David Bell: I taught maths in high school
for a few years – five years I think – four or five years, and what it did for me was
confirm that I wanted to somehow base my life on mathematics, because I’d been so grasped
– excited by some of the things that I’ve learned, that I did want to communicate those
ideas to others, but perhaps a little bit like David Erasmus, and maybe a little bit
like you, Peter; I didn’t find it all that easy. Because maths is compulsory in the curriculum,
I didn’t necessarily find it all that easy to get some concepts across at all levels,
from the junior high school to the senior. I did try my hand a little bit at teaching
physics which was an absolute disaster, because I’m not a physicist. That’s the reality.
Probably the thing that I enjoyed teaching the most was art, which I did for a term when
a particular high school didn’t have an art teacher for what was regarded as the most
difficult class of – they were then Form 4 boys – they had very little academic skill.
That was the kind of turning point at which I realised something that David Erasmus had
said; that because I wasn’t an artist, and I had no training in art or design or anything
like that, but I did want to somehow communicate a skill and an enthusiasm to those kids. It
was the fact that I didn’t have any knowledge whatsoever that enabled some really good interactions
to take place. I wonder, for both of you, we’ve all done high level mathematics; is
there one subject area that interests you and excites you?
Peter Davies: David was fortunate that he could handle and enjoy pure mathematics. I
struggled with the pure mathematics. I really enjoyed anything to do with programming, and
I guess in my work, probability; probability in terms of applying concepts in my work,
and programming which isn’t really mathematics, but it’s kind of an extension of the logical
train of thought. Working with logic; that was what I enjoyed the most I would say. From
second year onwards I struggled with the more theoretical side of pure maths. I liked calculus
too, by the way. David Erasmus: Yes, and for myself I’d say
the same; things that I didn’t like would be things like statistics and that kind of
thing – number crunching. I think the solution to the – what’s that called? The four colour
maps – the current map I think is a dreadful solution, because there’s too much involved
with number crunching. I like pure mathematics. I like notation. I love things like calculus
and the notation of partial differential equations, integrals; that kind of thing.
David Bell: I struggled more with complex analysis than real analysis. I really enjoyed
the kinds of theorems that were generated on the real number line, but I suppose the
area that I most enjoyed was actually in philosophy where we doing the meta-theory of mathematics;
the sort of Bertrand Russell kind of thing; how do you make mathematics? I think the crucial
theorem that I learned and certainly had to reproduce in exams was the proposition that
not every well-formed formula is provable. I think in foundations of mathematics that
is one of the most significant theorems that came out of the 20th Century, and it was actually
round about the time that the Copenhagen interpretation of quantum physics was getting really developed
n the late �20s, early �30s. So that’s the area for me; mathematical logic I suppose.
When it came to trying to explain it to my daughters, they really weren’t very interested.
I found that very few people were interested. I wonder whether there’s a kind of parallel
there to a Christina faith. Sometime I’d be really interested in what you guys have got
to say about this. Sometimes when I’m talking about Christian faith, my thoughts race ahead
because I’ve got a bit of background knowledge in it and I get the impression perhaps that
other people don’t get onboard as quickly. How is it for you? Both of you have what I’d
call a spiritual outlook on life; does mathematics somehow impinge on that, and how do you communicate
it? Peter Davies: You go first, David.
David Erasmus: Oh okay. I don’t know how easy that is to answer. I think what I would say
is having a strong feeling for mathematics might be represented by a belief in a universal
truth, rather than opinion. I’d say one big difference between mathematics – certainly
mathematics is based on a number of assumptions of course, but the idea is that there is a
universal single answer to any question which would seem to be almost a religious perspective
and very different from any other subject. I don’t know what you think about that.
David Bell: I’ve got to spend some time thinking about that. Peter, what about for you? Has
mathematics in any way got a kind of spiritual component for you?
Peter Davies: As far as mathematics goes, and my involvement with it; I’m quite a fundamentalist.
You described how interesting you found a particular hypothesis; to me I enjoy mathematics
for the ultimate absolute answers that it produces. In that regard, David referred to
integration; integration is a part of calculus where you’re effectively working backwards
using a variety of techniques, some of which are quite complex using square root of negative
one to solve a differential equation or something. A lot of these you can verify by going back
the other way. So you can verify an integration by then differentiating. So, a lot of my work
can always be cross-checked. All my programming work can always be cross-checked.
So I’m very deterministic in my mathematical field, and not at all – maths itself to me
isn’t spiritual; what maths gives to me is tools to address practical problems, but in
that regard, for example if I just use one example of the theory of creation versus evolution,
there’s a theorem called the infinite monkey theorem, which you may have heard of, however
you want to express it. The theory goes along the lines of if you put a million monkeys,
and let them tap away at a million computers for a million years, all the great works of
Shakespeare will be written. That kind of is where some evolutionists come from; the
argument that because life is always changing, and you put millions of years in front of
it anything is explainable as a random outcome. I’m not mentioning this as one example; what
that million monkey theorem tells you is that that’s rubbish.
You can work out deterministically that if you did put a million monkeys on a million
typewriters for a million years, and they actually typed all the time and didn’t take
five minute monkey smoke breaks or what have you, you might get one twinkle twinkle little
star – just those words – twinkle twinkle little star with no spaces. If you introduce
spaces it becomes even more impossible. So what that gives you is a tool for realising
that there’s nothing random about evolution; the complexity of what’s evolved can’t have
happened randomly. Whatever form life arrived on earth at, it
didn’t start here just from an accident. It came here from somewhere and it has purpose.
It’s too complex to have come here by random. I guess you could say that’s one example of
my thinking. What probability teaches you is when people say things like a million monkeys
on a million typewriters will write all the works of Shakespeare; you know that’s false,
and it’s absolutely impossibly false, and the same for the complexity of life. So that’s
just one example. David Bell: It’s an interesting example. I
did a little video on this very thing a few months ago. Richard Dawkins had tried to say
a long time ago back when he wrote the Selfish Gene, so that’s I think about 30+ years ago;
what he tried to say was if you had essentially not a universe, but multiple universes – an
infinite number of universes, then you would get it. What he did was use a phrase; he said,
this is the means of dissolving astronomically impossible odds. Of course, I think you’re
much more on the right track; you can’t dissolve these astronomically impossible odds. Dawkins
and that sort of Darwinist approach, I think does try to subvert what I think are fairly
sound mathematical principles. In opposition to Dawkins, the great cosmologist Fred Hoyle,
who was the proponent of the steady stake theory in the �60s I guess, he wanted also
to dissolve those astronomical odds. So he proposed a continuous creation out of nothing.
When eventually the scientific evidence stacked up more towards a particular beginning – a
big bang, a moment in time as it were, Hoyle looked at what are called the cosmological
constants, and when he looked at all the cosmological constants he arrived at the conclusion that
this could not have been the result of mere chance. He gave a famous quotation, and I’m
not going to try and quote it exactly but it went along the lines that all the evidence
stacks up for the evidence of some kind of mind or purpose at work. That was a major
shift for one of the stars of evolving universe theories. David, you studied some of this
quite a few years ago at a symposium in Oxford or Cambridge?
David Erasmus: It was a course at Oxford; very enjoyable but tough. We did two weeks
of a philosophy course which basically constructed all the basic philosophical theory and went
into quite deep things about God and the existence and that kind of things; started very basic
things and built up right up to things like the philosophical implications of things like
Einstein’s Theory of Relativity. Although I’d sort of made my way carefully through
the mathematics of his theory, I’d never actually thought about the philosophical implications.
It was a very tough course and quite interesting – very mind-stretching I could say and introducing
me to a lot of topics that I hadn’t thought about before, in terms of quite similar things
about the probability about the universe being accidental and that kind of thing.
Peter Davies: From my perspective, yes I’m quite sure that some entity – God, for want
of a better word, that we don’t understand, and the more that – and I love reading science
and all the – I read a lot of scientific journals on genetic – just advance in medicine. Everything
we learn makes it clear just how more complex everything is than we previously understood.
I think there’s a Greek proverb about it; the more you learn, the more you realise you
don’t know. So, no it’s certainly having an analytical mind and ability to understand
probabilities has helped me become certain that we’re not just a random accident.
David Erasmus: Yes, and I think if you would like me to follow-on David, similarly I would
say that thinking about things like that is definitely influenced by your mathematical
logic, and I think which I wish a little bit more was taught in schools; mathematical logic,
probabilities and things like that, in a way which is understandable so people can relate
to questions like that. David Bell: In both of your instances then,
maths has ended up strengthening your faith? Do you think you would have had a weaker faith
belief if you hadn’t had mathematics as a background?
David Erasmus: Hard to say. Possibly. Peter Davies: I think maths is just part of
the enquiring mind. I was interested that you taught art, David. I’m impressed. For
me, everything I’ve found interesting has been analytical, and certainly in an analytical
approach to not just maths but to history, to biology, to physics, to chemistry, to evolution;
all lead you down a path to a purpose in life. David Bell: Peter, I taught just one fraction
of a class for one fraction of the time in the art, but it did have a profound effect.
Mathematics has certainly strengthened my faith. I would even go so far as to say my
view of mathematics is what the philosophers and foundational mathematicians would call
the platonic view. I believe in Plato’s theory of ideal forms in the universe. I don’t believe
in it in quite the same way that Plato was on about, but I do think that mathematics
is as close as you can possibly get to an expression of what God might be on about.
So, there are a couple of books on my shelves; Is God a Mathematician, done by some very
lively physicists and mathematicians. The last question I’d like to ask you is related,
and it is both of you are extremely talented musicians. Just tell us something about your
instruments and what you do. Peter Davies: You go first, David.
David Erasmus: I’m a self-taught player of an instrument called the balalaika. It’s a
Russian three-stringed instrument. When I taught myself to play it in South Africa,
there wasn’t one available, so I had to make one with very sparse information. One of the
things I found interesting when I was making it, is of course that the frets are placed
according to a logarithmic scale. So this is one of the many instances in my life where
I find that magically mathematics was the toolbox which provided the answers to the
questions I had. It helped me space those frets correctly on the neck of the balalaika
that I made. David Bell: You’ve busked your way around
the world on that balalaika, haven’t you? David Erasmus: Indeed. That was a wonderful
experience, yes; travelled around Europe playing the balalaika. We did extremely well and enjoyed
it enormously. David Bell: You are pretty ably supported
by your good lady… David Erasmus: Yes [32:28].
David Bell: Peter, when I first went to Trinity at Waiaki, I think within the first six months
of discovering your talents, did we have you playing one of – was it a Beethoven Appassionata?
I can’t remember, but you certainly did it at one of our fundraising dinners for the
new building, and it was absolutely superb. You’re a talented singer and piano player.
Peter Davies: I would say that in the actuary profession it is well-known that there is
a common link between mathematical ability – a love of maths and a love of musical, and
some musical ability. From a young age I sang in my father’s choir and always enjoyed it.
I also did piano lessons, so got my Grade 8 at school, but of the two – I’ve got a brother
who really is talented at both – he can improvise, he can sight-read. I love singing. I always
have, always will; four part harmony with the melody, the odd change of key is just
so uplifting – spiritually, personally – everything. Piano; I was more a technician rather than
a talented person, I would say. Very comments, thank you David.
David Bell: Last question before the wrap-up; I’m curious to know if you could possibly
name a favourite composer, who would that be?
Peter Davies: Schubert. No, Chopin. David Erasmus: Tchaikovsky.
Peter Bell: Tchaikovsky. Schubert must be somewhere in there, and for me…
Peter Davies: I’ll go with Chopin. Peter Bell: Okay, you’re going with Chopin
– you’re going with Tchaikovsky. For me it’s sort of [34:31], probably Shostakovich. So
maybe our musical – we’re drawn to music that somehow reflects the areas of mathematics
that interested us. I don’t know. May I say on behalf of the congregation at Trinity at
Waiaki, the group that run the e-Learning Centre, how very appreciative we all are of
your coming in to this first Live On Air for 2017. It’s been an absolute privilege to be
able to talk to the two of you. I’ll say at this point, thank you very much, and good
evening. Peter Davies: Thanks everyone. Thanks David. Lives in Mathematics Practical Theology Kiwiconnexion