FULL CIRCLE

Dick Pountain /Idealog 360/ 07 Jul 2024 11:12

Astute readers <aside class=”smarm”> which of course to me means all of you </aside> will have noticed from various other features that this is the 30th Anniversary Issue of PC Pro, and since this is a monthly magazine, and since there are 12 months in a year, and since this is Idealog 360, the corollary is that I’ve been writing here since the beginning. I used the word ‘corollary’ there because it suggests a mathematical proof, and that is a ham-fisted way of introducing my theme for this month, which is mathematics. 

360 is a special number to me not simply because it represents 30 years, but because when expressed as an angle in degrees it represents a full circle, a return to the beginning. Another way to look at a full circle is in radians as an angle of 2π which I find more congenial because π is an irrational, even transcendental, number and I like to think of this column as being sometimes irrational and occasionally even transcendental (which you astute readers may have noticed). 

What I’m tiptoeing around here (in this nauseatingly arch manner) is a confession, namely  that I’m only posing as a computer nerd, that I’m actually a mathematician manqué, a math sheep in hacker/wolf’s clothing. At school, way back in the early 1960s, maths was my top subject in which I got a distinction at S level. I had to choose between reading chemistry or maths at uni but was seduced into the former by the lure of stinks and bangs over pencil and paper. My introduction to computing did come very early, in 1962, as part of a school team who built a prize-winning computer out of ex-RAF radar set parts, but that computer was analog, not digital, and all it could do was solve sixth-order differential equations and display the result as green squiggles on a cathode ray tube (which only real maths nerds could appreciate).

Math-nerdship never left me even once I discovered ‘real’ digital computers. At college I only ‘used’ London University’s Atlas to process the statistics for my biochemistry experiments. After Dennis Publishing (or H. Bunch Associates as we were called then) bought Personal Computer World in 1979, as the only maths nerd in the room I was delegated to take home a Commodore PET and learn how to program. I discovered that I loved it, but math-nerdship continued to steer my journey because after Basic I learned Pascal, Forth and Lisp, rather than C which would have been the obvious choice were I to want to make a living from coding (which I didn’t and don’t).   

Elsewhere in this issue you’ll find our nominations for the most important milestones in computing over the last 30 years, so rather than recap those here I’ll instead name a few of my favourite milestones in computer-related math-nerdship. Thanks to the internet everything is computer-related now, so I follow developments in maths through YouTube videos, Wikipedia articles, Royal Institution and TED talks, but most of all through the excellent, non-profit, Pulitzer-Prize-winning online magazine Quanta. 

Launched in 2012 to promote public understanding of mathematics, theoretical physics, theoretical computer science and the basic life sciences, Quanta is funded by, but editorially independent of, the Simons Foundation. James Simons is a mathematician, educated at MIT and Berkeley, who started out working on pattern recognition, string and quantum field theory, then went to Wall Street and used his maths as a  ‘quant’ investor to become the 51st richest person in the world.

My favourite recent Quanta pieces have been by Philip Ball on [The New Math of How Large-Scale Order Emerges | Quanta Magazine] and one on Dedekind [How the Square Root of 2 Became a Number | Quanta Magazine]. Number theory is the part of maths that still entrances me. Irrational and transcendental numbers like π have infinitely many, non-repeating digits after their decimal point which makes them a little awkward to handle. Dedekind found a stunningly elegant way to pin them down, by splitting the number line into everything below and everything above the one you want. 

I still write programs – in QPython on my Chromebook – though nowadays they’re almost always about maths, playing with palindromic numbers or fiddling hopelessly with the Collatz Conjecture, or just solving a puzzle from Quanta magazine. I watch tons of YouTube videos that use clever visualisation tricks to explain p-adic numbers and their relation to the Riemann Hypothesis. The great thing about maths is that it doesn’t require a lot of apparatus, just a brain plus some sand and a stick, chalk and a blackboard or pencil and paper (or Python and a Chromebook). And there’s always a chance of being that amateur who makes a significant discovery…   

[ Dick Pountain is quite satisfied with his slice of the π ]