This highlights a point that I keep coming back to in discussions about technique. A car’s tires are its sole interface with the ground. Everything that the car does in relation to making it move has to go through those tires. At a defensive driving course that I did once, the point was made over and over again that putting the best tires that you can afford on your car (and having the correct tire pressure) was the most effective way to make your car safer. And so is the case in running, as well as speed skating that the point at which ALL technical analysis must begin is the point where your foot, or your blade (in the case of speed skating) comes in contact with the ground.

The reason I say this is that, in my new role as a coach, I have had a chance to interact with a lot of other coaches and hear a lot of opinions on things related to elite sports performance. I’ve been an elite athlete long enough to know that very good coaches are extremely rare, although I did expect a slightly higher standard. What I am really trying to say is that I have heard a great deal of nonsense.

Even after a lifetime of experience, no coach can be “perfect”, and that is the rub.

Of course, nobody can or should expect a coach to be “perfect” right out of the box, nor should anyone expect such perfection after many years. Even after a lifetime of experience, no coach can be “perfect”, and that is the rub. An ideal coach’s attitude (as it should be for an athlete) is to always be improving, and to always seek it out. Now if everyone in the world were genetically identical, then it is conceivable that such perfection could be attainable, at least in theory. But people are not identical, conditions are different everywhere, and sports themselves evolve over time.

World records should be evidence enough of this. Take a sport like running – humans have been running for millions of years, our bodies are designed to do it. People have been competing in running races for at least a few thousand years (possibly more), yet world records are still being broken. Why? There are always very small refinements in technique, as well as technology, such as the clothes and shoes that runners wear. There are also constant developments in training methodology, and the pool of eligible athletes is always expanding.

The sum of all those complex parts is a gradual improvement in the overall standard of the sport, and an indicator of that is the fall of world records. So it shouldn’t surprise anyone that it angers me when I hear a coach say something along the lines of “if you want to do this time, then this is what you need to do” where “this” is usually a very specific set of instructions and technique where the athlete is basically a machine simply in need of having certain buttons pressed.

I like to take a more first-principles approach to coaching. Luckily there has been a lot of good research on the subject which allows me to stand on the shoulders of giants. It still surprises me how much the literature obviously isn’t being used by everyone. More esoteric still is the approach to technique.

Running is pretty much the only sport where you can tell an athlete to “just run a lot and what you feel to be the best technique will be it” and expect good results. Even then, most runners can benefit from small adjustments to their running technique, especially sprinters. This is because running is a very natural thing to do, and evolution has tuned our bodies quite well to do it. Just about every other sport must come up with what is necessarily “artificial” technique.

Strangely enough, the history of technique development in most sports indicates that the approach described above for running has been the one applied. Technique development has been a haphazard mix of trial-and-error (mostly error), and chance innovation, usually by sportspeople who train in isolation, or who come from other sports.That doesn’t mean that every sport other than running has rubbish technique, far from it. Those who have innovated have usually been the very best elite athletes, and they have often been very coordinated and possessed good natural biomechanics, which allows them to better feel when their own bodies are acting efficiently or not.

However, many example exist where technique has taken a very sudden leap forward because someone, usually a coach, stopped for a moment and thought about a movement, and how it could be different. The Fosbury Flop is a good example – there’s no way anyone decides that jumping backwards over a pole is a natural way to jump high, but Dick Fosbury realized that the arching of the back allowed a high jumper’s center of mass to be lower than the bar as it was being jumped over. Planting the front foot in a discus throw to get a little extra speed from the “whip” at the end of the spin, and kicking the front foot prior to throwing a javelin in order to take advantage of tendon-tension across the front of the body are two more subtle examples of deliberate technique development which yielded results.

there’s no way anyone decides that jumping backwards over a pole is a natural way to jump high

Not surprisingly now, I turn my attention to speed skating technique. I previously did a preliminary breakdown of skating technique in an attempt to understand the differences between ice and inline skating technique. In that article I concluded that the main reason that differences existed was because of the differences in the way ice blades and inline wheels behave when subjected to changes in force, and changes in angle (relative to the ground).

So you have these points on the ground. Actually they’re curvy lines and they aren’t very big. They provide lateral resistance and are effectively frictionless along their direction of motion. We push against these points in order to move forwards. We begin by simply pushing against them while they’re not moving (i.e. in a standing start), but doing this limits our speed to how fast our muscles can move. Then we start to use the lateral resistance and directional flow, but even this has limitations. Eventually, we use the curve of the blade to generate centrifugal force to give us extra force in our push. This is discussed in a previous post to some extent.

But what are those forces? Perhaps more importantly, what forces are required? Well, anecdotally, since us speedskaters are always being told to feel for “pressure” in the push (that pressure is the angular acceleration perpendicular to the direction of motion of a blade describing a curve on the ice) I will use the most obvious place where we find this “pressure” to come up with a suitable starting number – the corner. The corner radius in a long track is anywhere between 25m and 31m depending on which track you’re skating on, and which lane you’re in. Unsurprisingly, maximum pressure is found in a corner of the smallest radius, so we’ll take 25m.

Next we need some speed. The fastest skaters can skate a lap of a 400m oval in about 24 seconds, which comes to 60km/h or m/s. The cornering force that the skater must overcome is given by:

a skater skating a 24 second lap would be pulling 1.13 ‘g’s around the inner corner

This gives F to be 11.1ish (actually ) multiplied by the skater’s mass in kilograms. Just to give you a sense of scale for these forces, the force of gravity is about 9.8N per Kg of mass, so a skater skating a 24 second lap would be pulling 1.13 ‘g’s around the inner corner. Just for reference, you have to skate a 25.55 second lap to be pulling exactly 1g. This is significant because the lean you need to get in a corner to overcome a 1g cornering force is exactly 45 degrees.

As you can see, 45 degrees is actually quite a steep lean, and a 24 second lap would require even more. Just how much more is a matter of  remembering our sine and cosine rules.

Why is determining the angle important? Because it allows us to calculate the forces acting on the skater. We already have the force of gravity (9.8N) and and the centrifugal force (11.1N), but as you can see from the diagram, a skater doesn’t push directly down, or directly to the outside of the corner. A skater necessarily pushes along a line from the point of the center of mass to the point where the blade comes into contact with the ice, and this is where that angle becomes important. For the 25.55 second lap, when the cornering force and the force of gravity are equal (and the angle is 45 degrees) we simply add and which is about 13.86N per kilogram of bodyweight. When we go a little faster  we have to add and which comes to 14.52N per kilogram of bodyweight.

In other words, that extra 1.55 seconds of speed is worth just short of one extra newton of cornering force per kilogram of bodyweight. If you weigh 70kg, then that’s the difference between 970.2 newtons (the equivalent of lifting 100kg) of cornering force and 1016.4 newtons (the equivalent of lifting 104kg). Not forgetting, of course, that you’re doing this “lifting” with one leg while balanced on a sliver of metal 1.1mm thick, and travelling at 60km an hour. I’m sure anyone who’s ever done a 1-rep max test can tell you how much difference just a few kilograms can make when you’re right on the limit.

don’t forget that you’re doing this “lifting” with one leg while balanced on a sliver of metal 1.1mm thick, and travelling at 60km an hour

Of course, this is not the whole story, it is only the starting point. This is only a force requirement. Ultimately, we would like to calculate the “work” requirement (force distance), and the “power” requirement (the rate of work, or more precisely ). If you’ve been paying attention, you will realize that the force requirement says nothing about movement (which is, sadly, a rather inescapable element of speed skating). I weigh 72kg, so 14.52N per kilogram of bodymass is equivalent to the force that a 107kg weight would exert on me. I’m pretty sure I can’t do a 107kg one-legged-squat, but if I stand up straight, I can probably hold much more weight. Of course, if I skated with my legs straight, or close to it, I wouldn’t go very fast because there are other forces to overcome than cornering forces.

There is also air resistance. I covered this aspect of the sport briefly in this post, mostly to highlight what I perceived to be incorrect decisions regarding selection, which were impacted by not taking into account the importance of the altitude at which times were skated. In short, altitude makes a difference to air resistance, and air resistance is such a significant factor in speed skating (some say as high as 80%) that even small difference in air resistance can have a measurable impact on times. In that previous post, I introduced this equation:

is the force, is the air density is velocity is area is drag coefficient and is a direction vector for the velocity. Using some fairly simple mathematics, I was able to show that going from sea level to 1400m (the elevation of the Utah Olympic Oval) reduces aerodynamic drag by about 15%. I say “simple” because at no point did I actually have to calculate the force, I only needed to calculate the difference between two forces. But now that we are trying to calculate force requirements, it is time to get our hands dirty.

I thought a skier was a reasonably good aerodynamic approximation to a speed skater so I used their wind tunnel data

Let us begin at a typical indoor oval at sea level with favourable conditions of about 5 degrees ambient temperature. The air density would be 1.269kg per cubic meter. For velocity, we’ll take our 24 second lap (60km/h), for frontal area I’ve ripped off some approximate numbers from journal articles that variously discuss skiers and cyclists who have gone through the trouble of wind tunnel testing. For frontal area, I’m using 0.45 square meters, and for drag coefficient I’m going to use 0.6. When you plug all these numbers into the formula you get 47.59N. That may not seem like much, but when you consider that it is the force required simply to stay at a constant speed, it is significant. Look at it another way, in a frictionless vacuum, 47.59N of constant force would push a 72kg mass (me) in a straight line to 60km/h in just over 25 seconds and do it in just over 200m.

Which brings me nicely to my final point of this post (which seems to have ballooned out into something much bigger than I anticipated). The force required for a skater to actually accelerate. Without exception, all individual skating distances begin with a standing start. So far this analysis has only looked at the forces required to maintain a speed of roughly 60km/h (which is certainly at the high end of what is currently possible in the skating world). Getting there is another matter entirely.

all skating distances begin with a standing start – this analysis has only looked at forces required to maintain speed – getting there is another matter entirely

When calculating the acceleration required, we encounter a strange dilemma. The very best sprinters in the world can skate a standing 100m in about 9.5 seconds. We’ll round up to 10. Assuming constant acceleration over that 10 seconds (which would carry the requirement of the least amount of force), a skater would have to accelerate at 2 meters per second, per second (i.e. at the end of the first second, they would be traveling at 2m/s, at the end of the second second, the would be traveling at 4m/s etc.) This gives exactly 10 seconds for 100m, and the force required to achieve this is exactly 2m (so for a 72kg mass, a force of 144N is required (which is the same force as a 14.7kg mass exerts due to gravity). This doesn’t seem like such a big deal until you realize that acceleration isn’t constant because, for reasons explained above and in previous articles, there are technical limitations. Also, a 2 meter per second per second constant acceleration leaves you traveling at 20 meters per second (72km/h), well above the top speed of any skater.

Luckily, we have an easy way out of this. We know that our 60km/h-capable skater can exert a force of 14.52N per kg of body mass which is the same as saying that our skater apply force to accelerate at 14.52 meters per second per second which can take us up to 16.6 meters per second in well under two seconds, and since you only have to travel at 16 meters per second for 6.25 seconds to cover 100m, we have easily solved our original dilemma, and are now left with the question of why standing 100m splits are so slow, given that fast skaters can apply so much force. After all, if you can accelerate at 14.52 meters per second per second, it takes you 1.15 seconds to reach 60km/h. Assuming this is your top speed, you would only have to skate at this speed for another 5.7 seconds to cover 100m – that’s a standing 100m in 6.85 seconds!

so many things are wrong with this graph!

Obviously the curves are much smoother, and the fact that force isn’t the only variable to consider comes into play. Remember that our figure of 14.52 is the force required to keep everything in balance at a certain speed, as soon as your body moves, the numbers will be different because there are physical limitations to the rate of work you can do (power), and even if there weren’t there are physical limitations to how fast you can move parts of your body.

Ultimately, the answer lies in biomechanics, which I hope to cover in a later post.

This thought spawned a little dinner table discussion with some friends and the question was put to the table “if our perception of time decreases like this, then when are you truly half way?”. Well, obviously if one takes the average age to be, say 80 years, then halfway wouldn’t be at 40, but at some point before then, but when? This spawned a simple but interesting back-of-the-envelope (actually, it was scribbled on my new ipad) calculation with a slightly counterintuitive result.

We begin at the beginning. Your first day/week/month/year of your life represents 100% of your life experience, and your second represents a half, and so on. One quickly realizes that we are forming a harmonic series.

So we have a few results already, because of what we know about the harmonic series. First, we know that, even though the individual terms converge to zero, the sum does not converge at all. So the sum of your perceived life experience doesn’t converge to a number, but really does depend on how long you live for (which, frankly, is a relief). From this, it is an easy deduction that the halfway point in this “perceived experience measure” also depends on the length of life we select for our calculations, and it must be finite.

So we have the graph of which should be familiar to anyone who has passed high school maths. We need to find the area under the graph between 1 and some number (the life expectancy age) to determine the total “experience”, then we divide that number by 2 and find some number (the perceived-life-experience halfway point) for which the area under the graph between 1 and is that number. So first:

which just turns out to be . Half of that is simply . So all we have to do is rearrange the equation:

so…

Which is not what you expect… In fact, I almost put an exclamation mark at the end of that result, except in mathematics, that would have an actual meaning (factorial). So this basically means that if you expect to live to a hundred, then your “percieved life experience” halfway point is actually when you’re 10, which is considerably lower than 50. So much so that I keep thinking that I have the wrong result.

Obviously, this doesn’t account at all for the fact that we tend to forget things that happened when we were very young, and recent memories are slightly stronger and so on, but even so (assuming that I haven’t made a mistake in my working) this is an interesting result.

I’d like to hear people’s thoughts on this…

You sweat over this for a few weeks until one of your interns suggests a solution to you while spilling your coffee on the photocopier. She suggests that you allow every female of the population to continue having children until they have a male child. Once they’ve given birth to a male child, then they are required by law to stop.

You ponder this for a while. Obviously, allowing everyone to have a male child will be very popular with the electorate, but can we really simply allow everyone to keep trying until they get one? Surely this would result in some kind of population explosion. Worse yet, wouldn’t it result in some kind of huge imbalance in the male-female ratio?

Actually no. The ratio remains at exactly 1:1, and the birth rate is exactly 2 – zero growth.

The mathematics is not particularly difficult. One can easily write out a table of all the probabilities and the required figures (the birth rate and the gender ratio) can be found by way of summing infinite geometric series. But how are you going to convince the electorate of this rather counter-intuitive result?¹

Let’s start by drawing a box.

A box

This box represents the first child. Let’s say it’s of unit-size, representing one child. I’ve coloured half of the box black and the other half white indicating that the probability that the child is a boy is one half, and the probability that the child is a girl is also a half.

Of course, if the child is a girl, we get to try again. That box should only be a half the width of the original because there’s only a half the chance that the event it represents will happen. The length of the box should still be one though, because given that it does happen, it still represents one child. The colour scheme is identical to the first box. We can repeat this as many times as we want, but I will stop at four.

four kids

What this is really representing, is that the probability of having exactly one boy is a half, the probability of having exactly one girl and one boy is a quarter, the probability of having exactly two girls and one boy is an eighth, and so on. The diagram however, allows you to very easily see why the gender ratio stays exactly balanced – when you sum all the probabilities, you’re still going to get the same ratio of boys to girls. In fact, using the rule suggested by the intern will preserve a gender ratio reflective of the probability of having a boy or a girl, which we have assumed to be 50:50.

The question of population growth is slightly more tricky. Below is the same diagram, except with one of the cases highlighted.

girl girl boy is highlighted

We could think through every single one of these cases and add them up. And it’s not even a very difficult thing to do. But if you’re a government minister, you’re probably too lazy even for that. So what about…

another way of stacking

All I’ve done is stack the boxes differently. If we continue stacking the progressively smaller boxes on top of each other, you will get a gap of etc., until you eventually end up with a gap at the top of which equals zero (in an asymptotic sense) and voila! You have a box that is one by two, giving your expected value of births per mother to be two.

This is a good way to control overpopulation because the birth rate should be about 2.1 for a steady population (because not all babies will live long enough to reproduce) and 2 is significantly lower than 2.1. (Things like twins don’t have much of an effect, as they only account for 2% of live births)

Just quietly, I don’t believe that implementing a policy like this would be an easy thing to do. Despite the obviousness of the mathematics, there is no doubt in my mind that many will cry foul and drum up all manner of absurd conspiracy theories accusing the government of taking away freedom and the like. That, of course, will all be a smoke screen for the real problem which is, despite the public school system, not too many people appreciate the absolute truth of mathematics, and will sooner accept a better-sounding and more intuitive dogma, handed down by a loud radio show host, than actually bother to listen to reason.

It came right down to the wire. I was still writing at 4pm… while the earlier pages of my thesis were simultaneously being printed. Despite the mad rush approaching 5pm, I actually managed to get the thesis in on time. Some of the other honours students got caught up with binder difficulties, but not me. My dexterity and ability not to flail and crack the shits when a binding machine was being stupid held me in good stead. With a sweaty brow and steely nerves, I bound both copies of my thesis in record time and submitted them before the due date (which is unusual for me).

For those who are interested, i have provided a copy of my thesis here (PDF 489KB). It is written in a way as to be easily understood (at least to those who understand it). I would recommend at least 2nd year algebra although 3rd year algebra would be an ideal base for being able to comprehend what I have written. It is 60 pages long so you might want to grab a drink. Its not particularly good.

Important note to those who read my thesis (my thesis examiner’s excepted, of course): If you spot a mistake, typo, badly-drawn picture I DON’T WANT TO KNOW!

Every year about 90 countries send teams of their six best high school students to participate in the International Mathematical Olympiad, a grueling mathematics competition in which contestants sit two exams of four and a half hours each over two days solving a total of six problems. Needless to say, these problems are of an exceedingly high level of difficulty and coming up with solutions requires exceptional ingenuity and mathematical ability.

In this issue we speak to a young mathematician with an enviable reputation in the IMO. In 2001 Peter McNamara became the first Australian to ever win two gold medals in IMO competitions. He is one of the select few who have been to three IMOs (he obtained a bronze medal in his first appearance). In this issue of Paradox, we interview Peter to find out what makes him tick.

Peter enjoys a game of table tennis in the MIT basement at 2am

got some time for an interview for paradox?

For the record, what is your full name?

Peter James McNamara

Is there any significance to your name?

..like were you named after anyone famous?

Not that I know of.

What is your favourite colour?

I don’t have a favourite colour. It used to be red because I was in red faction at primary school.

So… Peter… tell us… why are you in Melbourne?

A Holiday? I have to physically be somewhere don’t I?

Are you enjoying this holiday?

Yes, Melbourne is a nice city to be in, even if it can get a little cold at times.

Ok… moving right along… Tell us about your educational background

Well I finished a science degree with honours in Mathematics at the University of Sydney in 2005. Prior to that, I was at school in Perth.

Ok, while you were growing up, did you have any heroes? Y’know, somone who you really looked up to and who inspired you?

I don’t think I ever really looked up to any heroes.

what was primary and secondary school like for you? Did you find it very easy or very difficult?

I usually found myself on top of things at school, there weren’t many difficulties. I don’t know if that says more about me or about the educational system though.

well then, I know that you know that I know this, but tell the loyal readers of paradox – what are your plans for the immediate future? (education-wise)

Many readers of paradox will also already know this, but I’m off to MIT to pursue a PhD in pure mathematics, starting Septermber 2006.

Ah… what exactly made you pick MIT?

Well, they are a good university. Being in close proximity to Harvard was also an attracting factor, since the two universities have arrangements where you can do classes at either, and even be supervised by faculty members from the other university. It also helps that I have a couple of friends in Boston too.

sounds like a good deal, what are your plans (if indeed you have any) for when you return to Australia (if indeed you plan to do so)?

I don’t actually have any plans for that time, it is currently a long way into the future and I’m sure a lot will happen between now and then.

I won’t forget about the readers of Paradox though.

Ok, now for people who are considering a similar course of study, was the process of getting into and organising to go to MIT a difficult one? Are there any common pitfalls that one should avoid?

I can only speak about entry into US universities, but if someone wants to go to the united states to study, they’re going to have to start seriously looking into the entire application procedure a good twelve months in advance. The actual applications are due in about 8-9 months in advance, and there are some required tests which must be completed prior to that.

Make sure you’re organised and know all the key dates.

ok… now onto the topic which I think all of our readers really want to hear about… the IMO. Tell us about your first experience at the IMO

Well the IMO was a big event. I guess the first experience was arriving off the plane in Romania and meeting our guide, if I want to be pedantic.

, Alina.

was she hot?

Trust you to ask that Daniel. I’ve only got pictures in Perth, so I can’t get you to judge for yourself.

oh well… moving right along…

Do any IMOs stand out as your ‘favourites’?

Well being in Romania was really enjoyable. It was well organised, all the students were staying in the one building, which is best for the social side of things, and Europe is a great place to visit.

Do you have any stand-out memorable moments from any of the IMOs? interesting games or pranks?

In Romania we managed to steal a stuffed kiwi from the New Zealanders, which was their mascot, and ended up going to the room above them (occupied by the neutral swiss) and hanging (with our best approximation to a noose) the unfortunate flightless bird from their window to dangle outside the Kiwi’s.

I guess with Cheeseman around in Romania, that is the most likely time for pranks

we all know that you were the first australian to ever win two gold medals at the IMO… when you found out that you had won your second, did you have any special feelings of exhiliration… or was it just “oh yeah, that’s pretty cool”?

Well it was a good feeling to have done so well. I knew I had done well in the exam and was looking at a gold medal that year so it wasn’t really a suprise when I eventually heard the results. It still was great to have managed to be the first from this country to achieve such a feat.

did you ever feel alot of pressure… representing Australia and all?

I don’t remember feeling under much pressure. It was a fun time, and yes there were nerves around but I tended to cope with those allright. Perhaps the chant of “Aussie Aussie Aussie, Oi Oi Oi” we made before each exam helped calm the nerves.

I’ve heard that after your third IMO’s closing ceremony you got to meet another famous past Australian IMO representative – Terry Tao. What was that like?

It was a bit like “um, I don’t really know what to say”. All I can really remember is shaking his hand and getting my photo taken with him.

what do you feel is the most important thing you took out of the IMO?

Oh, that’s a hard question. The sort of things that one takes out are generally intangible things, such as appreciation of mathematics and culture, memories and friendships. On the tangible side, that is where the game of gluck got introduced into MUMS circles from.

Ok, lightening up a little… Has your mathematical reputation and/or ability ever been useful in a real-life situation such as picking up at a nightclub? getting good seats at the football?

Us mathematicians unfortunately don’t get the rock star treatment at night clubs, or the corporate connections to get good tickets to the footy, though it’s probably about time that we did!

I have come across people knowing about my mathematical feats before i knew them though.

now, on the flip side of that, have you ever felt the need (for social reasons or otherwise) to conceal your mathematical abilities?

Well I’m not really that good at maths anyway. My differential geometry is terrible. I don’t go around shouting out that I’m a good mathematician though, that would be a case of hubris.

while we’re on the topic of maths… do you have a favourite theorem or lemma?

I don’t have a favourite theorem or lemma. It’s more the beautiful proofs that attract my appreciation.

any particularly beautiful proofs which stand out?

off the top of my head, I can think of a couple of number theoretic proofs which stand out – a topological proof of the infinity of primes, and a bizarre involution proof of the two squares theorem, both of which are in “proofs from the book” incidentally.

where do you see yourself in 10 years time?

apart from having a phd, given that i couldn’t say anything about what i’d do after that, i guess all i can restrict myself to is that i shall be somewhere on the surface of this planet.

have you ever felt pressured to pursue mathematics at uni and/or as a career, or have your choices so far in that regard been entirely your own?

I’ve always chosen myself what I’ve wanted to study and pursue.

Do you have any regrets, mathematical or otherwise?

I don’t think it is possible to live a life without having any regrets at all.

so can you pinpoint one or two which stand out in your mind?

I don’t really know if I could give a fully honest answer to a question like that. Maybe when I am an old codger and it no longer matters to me what reaction I get when leaking information then I’d open up more.

I did make an elementary mistake in the inaugural final of the PI chess tournament which I never recovered from

If you weren’t about to go to MIT to do a PhD, what do you think you would be doing instead?

If I wasn’t doing maths, then I don’t know what I’d be doing. If I still was doing maths, then I’d be doing a PhD at either Melbourne Uni or ANU. Probably after an overseas holiday.

tell us about your interests and hobbies outside of maths

I’m a keen follower and player of cricket and football, probably a better footballer than cricketer, despite my size. I haven’t been able to play cricket for a couple of years though because of frequent summer interstate travel. I guess that is a sacrifice of living interstate.

I also enjoy playing good games; pool, diplomacy, bartog, chess (when I’m not in the mood that it is a mathematically trivial deterministic game), gluck to name a few.

what is your favourite board game?

diplomacy, by a fair margin.

If you knew that the world was going to end in exactly 48 hours and there was nothing you could do about it, what would you do with the remaining time you had?

Well I’d have to work really hard to prove the Riemann Hypothesis then. If I had any spare time, then it would be off to work on the Birch and Swinnerton-Dyer conjecture.

Do you have a favourite band?

It changes over time. I’ve actually tended to like bands from Western Australia, such as Jebediah, Eskimo Joe, Little Birdy and Fourth Floor Collapse. Oh, and there is that recent discovery of mine, The Klein Four.

Favourite food?

Cake

Preferably a chocolatey cake, with a dash of liqueur

do you have a favourite TV show?

I like Coupling (the first three seasons) and Family Guy. Being part of the Simpsons generation, the early Simpsons episodes can never be discounted either. I don’t actually watch that many shows on TV though.

favourite film(s)?

Not sure if there is a standout there, but I’ll throw up a few names to be a good sport. The Ring, Kill Bill 1.

now one for the ladies out there reading this interview – are you single?

Isn’t that well known around MUMS? The answer is no. Actually the readership of Paradox would be predominantly male, so in a bid to attract more female readers, perhaps consideration could be given to interviewing some eligible mathematical bachelors for future issues.

…and finally, what is the air speed velocity of an unladen swallow?

A European or an African swallow?

I don’t know that!

ok, thanks very much for the interview Peter, lastly… do you have any questions for me?

No worries mate,

Shouldn’t you have been hurled into an abyss with that last statement though?

how do you know I wasn’t?

I can see you.

D’oh… [interview ends]

620-311 Metric Spaces is a third-year mathematics subject at the University of Melbourne taught by Kris Wysocki. The Staff Student Liaison Committee (SSLC) conducts surveys and provides feedback to the department to help improve teaching. The report is typically read aloud to the class near the end of semester.

Question 1, oh what fun, I’ll try and keep this short
The average, it was two point five, its here in my report
I s’pose that means the pace of this subject is too quick
But not by much, no not at all, just slow it down a tick

Now question 2 posed the point, are lectures clear or not?
Many people ticked box three, how many? I forgot
But, in the end, three was the mean, when all was tallied up
So spot on Kris, keep it up with balls and inf and sup

Question 3, it was about the hardness of this stuff
And as in 1, the class all thought it was a little tough
The mean it was, when all was summed, a meagre two point six
So don’t fret Kris, you’re not far off, just a little bit to fix

So on we go to question 4, the tutes this was about
The av’rage, it was higher now, but don’t all stand and shout
‘twas only point one seven greater than the number three
that’s good I guess, it means the tutes are found useful-ly

So now to five we find out now, if you were stimulated
The answer’s ‘yes’, at least it seemed, when all was tabulated
A quarter and a four again did maketh up the mean
How int’resting I thought when I, this result did glean

Question 6, as we move on, sit tight we’re nearly there
This question asked us how much for the tutes we did prepare
Some said alot, some said not much, but most were quick to scribble
‘cause three’s the mean, so once again, we’re left right in the middle

So last we have question 7, but wait there’s more to come
This one begged us calculate our tute attendance sum
The mean on this, a little low, it came to two point four
But that’s not bad, considering there’d just been four before

Tutes that is, but now we end, on a funny note
There was no question 8 prescribed at least not one I wrote
But low behold there was a chap who managed such a feat
To answer “two” to question 8, for this comedic treat

So now, to sum and finalize, we’re going pretty swell
A little quick, a little hard, but int’resting as well
I hope you liked my short report, attached the numbers are
So if you’d like to see them all, come and see me.

This is the speech that I delivered when I ran for the position of president of the Melbourne University Mathematics and Statistics Society (MUMS). I was unsuccessful. I was, instead, elected to the position of Education Officer.

Hello everyone, how are we all today? My name is Daniel Yeow, I’m currently in the 6th year of a 5 year BA/BSc double degree, in my previous term I was third year rep and I am here to tell you why I would make a good MUMS president.

I am a man of many talents. I can move my ears, I can solve a rubik’s cube in under a minute and I can make an inappropriate sexual innuendo out of almost any sentence in almost any situation. But THAT is not why you should vote for me to be the president of MUMS. Sure, these talents are very useful, sure it is true that past presidents of MUMS have generally been very talented individuals, but what is it really that an organisation requires, needs – no demands from its president. It demands leadership.

Like the Alexanders, Caesars and Churchills before me I do not aim to be merely a good leader. I wish to be a great leader, and like all great leaders who have been before, I wish to lead by example. Julius Caesar fought in the front lines of his infantry and I have been inspired to do likewise. I plan to not only talk the talk, but also to walk the walk. I’m a doer, and those of you who know me well, will know that I will not shy away from hard work, when hard work is what’s required.

Sure, I may not be the most capable mathematician running for president, or the MUMS committee for that matter, but my academic record betrays a more important trait, I believe – an indomitable will. A will that will not give up at the first sign of failure (or the second in some cases). I believe that my ‘average’ abilities in mathematics will enable me to better relate to the vast majority of people in MUMS. We can’t all be math Olympiad medallists or academic prize winners after all.

The MUMS committee has, in the past, been accused of being cliquey. There is a perception that we are just a bunch of know-it-alls with our in-jokes in paradox and that we are out of touch with the general population. I wish to change all that. I wish to preside over a MUMS which is more approachable, more user-friendly, all the while without loosing our real aim – to make maths fun for everyone, not just a select talented few.

I’ve been president of Amnesty International, I’ve been president of the Eltham Roller Skating Club and I’ve had a little bit of experience organising the odd event here and there. I will bring my own unique brand of direction and leadership to MUMS. I will marry my experience with my expertise in the field of leadership. I love maths and it is my vision to share that love with everyone.

THAT is what I am all about. I may or may not be the most obvious choice for a MUMS president. I may not have all the academic credentials of a typical MUMS president. What I CAN promise is leadership with a sense of flair and imagination. Now I leave it in your capable hands. I trust you will make the right decision. Thank you.

This poem was written for the Melbourne University Mathematics and Statistic Society’s magazine, Paradox. It is about an experience that I experienced as a first-year (freshman) at Melbourne University.

When I started maths and stats
I also did philosophy
in that we studied brains in vats
and Descartes’ dual-lology

My study habits weren’t the best
I did not always go
To lectures, tutes and even tests
My learning curve was slow

One day in June, I learned my lesson
its one that you must know
it happened in an exam-session
I was a daft mo-fo

On thursday was my maths exam
but phyics was on tuesday
on monday I had planned to cram
for only stuff the next day

So Tuesday came, so starts the fable
but something wasn’t proper
I sat and stared but on the table
there lay a quaint heart-stopper

The maths exam was sitting there
and quite to my surprise
I looked around and to be fair
could not believe my eyes

I couldn’t believe I’d muddled up
the dates of my exams
but I never, never, never give up
so I came up with a plan

I’d work from basics, from the ground
first principles they were known
Whitehead and Russell knew it was sound
as Principia Mathematica has shown

Alas my mind had not the will
nor ability that day
to finish all, to crush, to kill
the shock and the dismay

But greater shock there was to come
for when results came out
that subject’s final score would sum
to fifty percent

p.s. the moral of this story is 620-211 is an easy subject

p.p.s. at Melbourne University your grade is a number between 0 and 100. 50 is the pass mark.