UNDER THE OLD WHIFFLETREE

Dick Pountain/PC Pro/Idealog 214 11/05/2012

It all started when I was asked to write a preface for a new book on the history of Dennis Publishing, which required reminiscing about our start in the early 1970s. That triggered memories of the way we put magazines together back then:  type the copy on an IBM Selectric "golfball" composer, cut it up into strips with scalpels and stick it down on the page with hot wax. The smell of that hot wax and the machine-gun rattle of the IBM came flooding back.

That prompted me to look up IBM Selectric on this new fangled Web thingy, where I soon stumbled across a neat little video clip by engineer Bill Hammack (http://www.up-video.com/v/57042,ibm-selectric-typewriter-.html) which shows how that unforgettable sound arose, but more importantly explains that the IBM golfball mechanism contained a fiendishly cunning example of a mechanical digital-to-analog converter. The problem that needed solving was to rotate an almost spherical print-head around two different axes, to position the correct character over the paper - unlike older typewriters, this print-head moved while the paper stood still (as in all modern computer printers which it foreshadowed). Rotation control involved adding together two digital "signals", using four bits to specify the tilt and 22 bits to specify rotation around the vertical axis, which originated as depressions of keys on the keyboard and were then transmitted via cables like those used to change gears on a bicycle. The mechanism that performed this addition went by the glorious name of a "whiffletree" (or whippletree). Now I was hooked.

Googling for whiffletree produced a total surprise. This mechanism has been known since at least the Middle Ages, perhaps even in the ancient world, as a method for harnessing horses to a plough! It solves the problem of various horses pulling with different strengths, by adding together and averaging their pulls onto the plough. It's a "tree" in exactly the same way a directory tree is: each *pair* of horses is harnessed to a horizontal wooden bar, then all these bars get connected to a larger bar and so on (a big team might require three levels). The pivot links between bars can be put into one of several of holes to "program" the whiffletree's addition sum: if the lead horse is pulling twice as hard as the others, put its pivot at the two-thirds mark. Without a diagram it's hard to convey just how damned elegant this mechanism is.

As an aside, at this point I ought to tell you that my first ever brush with computing happened in the sixth-form at school in 1961, as part of a team that built an electronic analog computer from RAF surplus radar components to enter a county prize competition. It could solve sixth-order differential equations in real-time (for instance to emulate the swing of pendulum that travels partially through oil) and we programmed it by plugging cables into a patch-panel, like an old-fashioned  synthesiser or telephone switchboard.

In thrall to the whiffletree, I wondered where else such ingenious devices have been used, and that lead me straight to Naval gunnery controllers. Throughout WWII and right up into the 1970s, American warships were fitted with electro-mechanical fire control systems that worked on a principle not unlike the IBM Golfball. An enemy plane is approaching, your radar/sonar system is telling you from which direction, keep the anti-aircraft gun pointed in such directions that its stream of shells intercepts the moving plane's path. This problem was solved continuously in real-time, by gears, levers, cables and a few valves.

Ever since Alan Turing's 1936 seminal paper we've known that digital computers can imitate anything such mechanical or electrical analog devices can do, but sometimes there's little advantage in doing so. We used to be surrounded by simple analog computers, especially in our cars, and still are to a lesser extent. One that's long gone was the carburettor, which slid needles of varying taper through nozzles to compute a ferociously complex function relating petrol/air ratio to engine load. One that remains is the camshaft, whose varying cam profiles compute a similar function to control valve timing. A less obvious one is the humble wind-screen wiper, whose blade is actually attached via a whiffletree to spread the torque from the motor evenly along its length.

Just as my analog nostalgia was starting to wane, I turned on BBC 4 last night and watched a documentary about the Antikythera mechanism, an enigmatic bronze device of ancient Greek origin that was found on the sea-bed by pearl divers in 1900. Over fifty years of scientific investigation have revealed that this was a mechanical analog computer, almost certainly designed by Archimedes himself, whose rear face accurately calculated the dates of future solar and lunar eclipses, and front face was an animated display of the then-known-planets' orbits around the sun. It worked using around 70 hand-cut bronze gears with up to 253 teeth each. We're constantly tempted toward hubris concerning our extraordinary recent advances in digital technology, but once you've allowed for some four hundred years of cumulative advances in chemistry and solid-state physics, it ought to be quite clear that those ancient Greeks possessed every bit as much sheer human ingenuity as we do. And look what happened to them...