Remember Leonhard Euler from the Satan’s Arithmetic post? Of course you do. Now behold Euler’s Disc – probably the most hypnotic thing ever.

Look into the eyes, look into the eyes, not around the eyes… and you’re under…

The physics behind this “scientific toy” can be found here, but basically, it comes down to this:

A spinning/rolling disk ultimately comes to rest; and it does so quite abruptly, the final stage of motion being accompanied by a whirring sound of rapidly increasing frequency. As the disk rolls, the point P of rolling contact describes a circle that oscillates with a constant angular velocity w. If the motion is non-dissipative, w is constant and the motion persists forever, contrary to observation (since w is not constant in real life situations). In fact, precession rate of the axis of symmetry approaches a finite-time singularity modeled by a power law with exponent approximately -1/3 (depending on specific conditions).

So there you have it. Obviously, it’s important that you remember that rolling friction is the primary mechanism for kinetic energy dissipation in this scenario and not air resistance.

From Frederick Schoeman of Cape Town on Friday’s Cape Times letters page:

Satan’s Arithmetic

I believe that a couple of centuries ago, two mathematicians were demonstrating their numerical skills to the French monarchy when one of them stunned his opponent and the audience by reciting an algebraic formula and claiming it to be proof that “God lives”. Could I borrow a leaf out of that man’s book and claim that, since the graph of world population growth over the past 1700 years looks like a serpent trying to slither up a wall, Satan is alive and thriving on human lust?

I’ve been doing some extensive research into Fred’s story, but the best that I could come up with was the the story of Leonhard Euler, who was a mathematician, but was Swiss, not French, and his presentation of an algebraic formula, claiming to be the proof that God lives. This presentation was made to another individual, Denis Diderot who was French, but was better known for his philosophical musing, rather than his mathematical prowess. In addition, this presentation was made in St Petersburg in 1774, in front of the Russian Empress Catherine II, rather than any French monarch. Wikipedia tells us:

There is a famous anecdote inspired by Euler’s arguments with secular philosophers over religion, which is set during Euler’s second stint at the St. Petersburg academy. The French philosopher Denis Diderot was visiting Russia on Catherine the Great’s invitation. However, the Empress was alarmed that the philosopher’s arguments for atheism were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was later informed that a learned mathematician had produced a proof of the existence of God: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, “Monsieur! (a+b)^n/n = x, donc Dieu existe, répondez!”.

This roughly translates as:

Listen mate, a plus b to the power n, over n, equals x. That means God exists. What do you say to that then, huh? HUH?!?

Allegedly, Denis failed to provide an immediate answer. Or indeed any answer:

Diderot, to whom (says the story) all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress.

This sudden stage fright could have been due to Euler’s sheer mathematical brilliance. Or, conversely, it may have been caused by Diderot’s incredulity that some Swiss bloke had successfully baffled him with bullshit by spouting some maths at him and pretending that it meant something that it actually didn’t. Why not try something similar at your local supermarket this weekend? At the Deli counter, ask for some ham. When the lady asks how much you’d like, exclaim loudly (remembering to use a tone of perfect conviction): “Madam! a x squared, multiplied by b x, plus c, equals zero, therefore I’m off to the jams and spreads aisle. What say you to that?”. See if she can find an immediate answer.

When she can’t, she must ask her boss’s permission to leave the country and go back to France.

Either way, there’s a whole lot more detail, including eye witness accounts, right here.

Of course, the formula didn’t prove that God exists at all, although it later proved invaluable in predicting how long one would have to wait for the next bus to the St Petersburg city centre. Nice work, Leonhard.

So, the first of Fred’s paragraphs proven wholly misguided, yet almost slightly true, we move on to his second. The bit about the snake.

But before that, at this point that I’d like us all to stop and consider some stuff for just a second. Firstly, put yourself in Fred’s shoes. At some moment in time, Fred actually felt that there was a connection between his 18th century algebraic French monarchy court presentation story and a graph of world population growth over the last 1700 years. Personally, I can’t see it. It’s like me taking an excerpt from a book on the dinosaurs and somehow linking it to the recent downturn in Malaysian rubber production. But I digress. The important point here is that Fred saw this relationship. Secondly (and still in Fred’s shoes), Fred sat down and wrote to the Cape Times about it. That is, not only did he feel that the connection was a valid one, he felt it was worth sharing – not just with his friends (although I have no idea if he put it on his Facebook wall) – but with the general population of Cape Town and surrounds. While he was typing (or writing – who knows?) away, he still thought it was a good idea to sent it through to the letters page. When he addressed the envelope or entered the email address ([email protected]), he remained under the impression that the not only did his observation make complete sense, but that it was so important that 268,000 readers should be informed of it. And then, once his thoughts arrived at the Cape Times office, at a time when sharks, rugby, racial issues, politics and cellphone masts (What? – Ed.) are at the forefront of all of our minds, Fred’s letter was one of the seven best that was received by the local rag that day.

Yes. Really.

But onto the serpent thing. I had a good luck around on the internet and the best graph I could come up with to illustrate Fred’s serpent against a wall thing was this one:

Obviously, you can ignore the bit before 311 AD, as Fred didn’t consider that when making his serpentine comparison. Personally, I felt that it was a bit of a stretch, but then I’m no expert on what exactly a serpent trying to slither up a wall looks like. That’s why I searched for “a serpent trying to slither up a wall” on google images.

This was the best that I could find:

Which seems to suggest that human population exploded upwards, remained almost static while traveling back and then forward again in time, before increasing almost exponentially, peaking and then dropping off to the current number. That aside, we shouldn’t overlook that fact that

…it’s gripping onto that brickwork because Satan is thriving on human lust.

A few points, if I may be so bold:

Firstly, algebra cannot prove the existence of God. Theologians might have their own reasons for why this may be, but mine is probably more simple: that he doesn’t exist and that it’s awfully difficult to prove the existence of something that doesn’t exist – algebraically or otherwise. Secondly, unless I’m missing some big chunk of causality here, an alleged incident in a “Parisian” court chamber 200+ years ago doesn’t have any bearing on the fact that “Satan is alive and thriving on human lust”. Thirdly, I do still quite like the idea of an algebraic duel:

Sir, you have insulted me and I demand satisfaction. Meet me at 6 o’clock tomorrow morning and bring a blackboard. No calculators.

Fourthly, what does Fred want us to do? Not breed? Adam and Eve bred. Mary and Joseph bred (sort of). Hey, Mr and Mrs Schoeman (Snr) bred. Are these also examples of human lust upon which Satan is thriving? Fifthly, any line graph looks a bit like a snake on a wall. Any block graph resembles the Manhattan Skyline. Any pie chart has the appearance of… well… a pie. Deal with it. Sixthly, get your historical facts right if you wish to make a good impression on those reading, but remember that… Seventhly, just because you think something, doesn’t mean it’s a good idea to write it down and send it to the Cape Times. Lastly, just because you think something, doesn’t mean it’s a good idea to write 1300 words on it on your blog.