Better than Newton

An article we wrote for the Big Issue, using material from our book Out of the Shadow of a Giant.


If you remember one thing from physics lessons in school, it ought to be Newton’s First Law of Motion, which says that any object that is not “at rest” moves in a straight line at a constant speed unless it feels an outside force. The truth of this law is familiar today from video of astronauts inside the International Space Station, or at a more local level in a game of air hockey. Clever old Newton. Snag is, he didn’t think of it. The first person to realise this fundamental law of Nature was Newton’s slightly older contemporary Robert Hooke. Hooke was also the first person to realise that gravity is a force of attraction in which everything in the Universe pulls on everything else – in particular, that the Sun pulls on the planets. Newton, until Hooke pointed this out to him, thought that the planets were carried around the Sun in eddies, like chips of wood in a whirlpool, by some mysterious cosmic fluid.

So how come we don’t talk about “Hooke’s First Law of Motion” and give him the credit he deserves as a pioneering physicist? Largely beacause Newton, who was a bit of a plagiarist and somewhat flexible with the truth, outlived Hooke, and wrote him out of history as far as he coiuld. When Newton became President of the Roylal Society, after Hooke died, the only known portrait of Robert Hooke mysteriously disappeared when the Society moved to new premises – the only picture to get lost in the move.

By minimising Hooke’s contribution to science, Newton also helped to encourage the impression that Hooke’s other activities were not particularly noteworthy. History tells us that Hooke played a part in the rebuilding of London after the Great Fire of 1666, with most accounts implying that he was some kind of assistant to Christopher Wren. In fact, Hooke was essentially an equal partner in Wren’s architectural practice, and was personally responsible for laying out the streets after the fire and much of the rebuilding. About half of the “Wren” churches in London are actually Hooke’s work. And it was Hooke who discovered the technique which Wren used to make it possible to build the spectacular dome of St Paul’s.

Along the way, Hooke was a pioneering microscopist, and made a careful study of fossils, convincing himself that the Earth was much older than the religious authorities claimed, and very nearly coming up with the idea of evolution. Our book is an attempt to set the record straight, and bring his genius out from under the shadow of Newton. But, as we discovered, he was not alone in that shadow.

Edmond Halley is at least remembered, for the comet that bears his name (although he did not, contrary to widespread belief, discover that comet). But what else did he do? He carried out the first astronomical survey of the stars of the southern hemisphere, and commanded a King’s ship on the furthest voyage south up to that time, to the edge of the Antarctic pack ice, to survey the Earth’s magnetic field. “Commanded” is a key word here – Halley is still the only civilian ever to be given command of a Royal Navy vessel and crew. He was so successful that he later carried out undercover missions, details of which have never been revealed, in the English Channel and the Adriatic, making him a combination of Jack Aubrey and James Bond. He also proposed the idea of an expedition to measure a phenomenon known as a transit of Venus from the Pacific Ocean; this would happen after he was dead. The expedition was duly carried out under the command of James Cook, and after completing their astronomical observations Cook went on to discover New Zealand and make a landfall in southeastern Australia. The French reached New Zealand a little later. Without Halley’s suggestion, New Zealand would probably have become a French colony, and there might have been some squabbling over Australia.

When we set out to bring these remarkable men out from the shadow of the giant Newton, the question we had the back of our minds was whether science would have made the great leap forward it achieved in the seventeenth century if Newton had never lived. Our conclusion is that it wouldn’t have made much difference. Newton’s singular contribution was to pull a lot of ideas together in his famous book the Principia. But the ideas were “out there”, and even then, Halley suggested the idea of the book, and he both edited it and paid for its publication out of his own pocket. Without Robert Hooke and Edmond Halley, we would probably never have heard of Isaac Newton. Without Isaac Newton, we would have heard a lot more about Robert Hooke, in particular, and Edmond Halley.



Probing the Universe

The announcement of the invention of a 3-D printer that can make 3-D printers that can make 3-D printers  .  .  .     prompts me to offer this extract from my book Computing With Quantum Cats:

Like Alan Turing, the computer pioneer “Johnny” von Neumann was fascinated by the idea of artificial intelligence, although he had a different perspective on the rise of the robots. But unlike Turing, he lived long enough (just) to begin to put flesh on the bones of those ideas.

There were two parts to von Neumann’s later work. He was interested in the way that a complex system like the brain can operate effectively even though it is made up of fallible individual components, neurons. With the early computers (and many even today), if one component, such as a vacuum tube, failed the whole thing would grind to a halt. Yet in the human brain, quite apart from everyday operation, it is possible for the “hardware” to suffer massive injuries and continue to function effectively, if not quite in the same way as before. Von Neumann was also interested in the problem of reproduction. Jumping off from Turing’s idea of a computer that could mimic the behaviour of any other computer, he suggested first, that there ought to be machines that could make copies of themselves and, secondly, that there could be a kind of universal replicating machine that could make copies of itself and also of any other machine.

Both kinds of mimic, or copying machine, come under the general heading “automata”. Von Neumann’s interest in working out how workable devices can be made from parts prone to malfunction, and his interest in how complex a system would have to be in order to reproduce itself, began to grow in 1947. This was partly because he was moving on from the development of computers like the one then being built at the IAS and other offspring of EDVAC, but also because he became involved in the pressing problem for the US Air Force in the early 1950s of developing missiles controlled by “automata” that would have to function perfectly, if only during the brief flight time of the rocket.

Von Neumann came up with two theoretical solutions to the problem of building near-infallible computing machines out of fallible, but reasonably accurate, components. The first is to set up each component in triplicate, with a means to compare automatically the output of each of the three subunits. If all three results, or any two results, agree, the computation proceeds to the next step, but if none of the subunits agree the computation stops. This “majority voting” system works pretty well if the chance of any individual subunit making a mistake is small enough. It is even better if the number of voters for each step in the calculation is increased to five, seven, or even more. But this has to be done for every step of the computation (not just every “neuron”), vastly (indeed, exponentially) increasing the amount of material required. The second technique involves replacing single lines for input and output by bundles containing large numbers of lines — so-called multiplexing. The data bit (say, 1) from the bundle would only be accepted if a certain proportion of the lines agreed that it was correct. This involves complications which I will not go into here; the important point is that although neither technique is practicable, von Neumann proved that it is possible to build reliable machines, even brains, from unreliable components.

As early as 1948, von Neumann was lecturing on the problem of reproduction to a small group at Princeton. The biological aspects of the puzzle were very much in the air at the time, with several groups looking for the mechanism by which genetic material is copied and passed from oner generation to the next; it would not be until 1952 that the structure of DNA was determined. And it is worth remembering that von Neumann trained as a chemical engineer, so he understood the subtleties of complex chemical interactions. So it is no surprise that von Neumann says that the copying mechanism performs “the fundamental act of reproduction, the duplication of the genetic material.” The surprise is that he says this in the context of self-reproducing automata. It was around this time that he also surmised that up to a certain level of complexity automata would only be able to produce less complicated offspring, but above this level they would not only be able to reproduce themselves but “syntheses of automata can proceed in such a manner that each automaton will produce other automata which are more complex and of higher potentialities than itself.” He makes the analogy with the evolution of living organisms, where “today’s organisms are phylogenetically descended from others which were vastly simpler”. How did the process begin? Strikingly, von Neumann points out that even if the odds are against the existence of beings like ourselves, self-reproduction only has to happen once to produce (given time and evolution) an ecosystem as complex as that on Earth. “The operations of probability somehow leave a loophole at this point, and it is by the process off self-reproduction that they are pierced.”

By the early 1950s, von Neumann was working on the practicalities of a cellular model of automata. The basic idea is that an individual component, or cell, is surrounded by other cells, and interacts with its immediate neighbours. Those interactions, following certain rules, determine whether cell reproduces, dies, or does nothing. At first, von Neumann thought three-dimensionally. Goldstine:
[He] bought the largest box of “Tinker Toys” to be had. I recall with glee his putting together these pieces to build up his cells. He discussed this work with [Julian] Bigelow and me, and we were able to indicate to him how the model could be achieved two-dimensionally. He thereupon gave his toys to Oskar Morgenstern’s little boy Karl.
The two-dimensional version of von Neumann’s model of cellular automata can be as simple as a sheet of graph paper on which squares are filled in with a pencil, or rubbed out, according to the rules of the model. But it is also now widely available in different form that run on computers, and is sometimes known as the “game of life.” With a few simple rules, groups of cells can be set up that perform various things familiar from living organisms. Some just grow, spreadIng as more cells grow around the periphery; others pulsate, growing to a certain size, dying back, and growing again; others move, as new cells are added on one side and other cells die on the opposite side; and some produce offspring, groups of cells that detach from the main body and set off on their own. In his discussion of such systems, von Neumann also mentioned the possibility of arbitrary changes in the functioning of a cell, equivalent to mutations in living organisms.

Von Neumann did not live long enough to develop these ideas fully. He died of cancer on 28 February 1957, at the age of 53. But he left us with the idea of a “universal constructor”, a development of Turing’s idea of a universal computer — a machine which could make copies of itself and of any other machine, a self-reproducing robot. Such devices are now known as von Neumann machines, and they are relevant to one of the greatest puzzles of our, or any other time — is there intelligent life elsewhere in the Universe? One form of a von Neumann machine would be a space-travelling robot that could move between the stars, stopping off whenever it found a planetary system to explore it and build copies of itself to speed up the exploration while sending other copies off to other stars. Starting with just one such machine, and travelling at speeds well within the speed of light limit, it would be possible to explore every planet in our home Milky Way Galaxy in a few million years, an eyeblink as astronomical timescales go. The question posed by Enrico Fermi (why, if there are alien civilizations out there, haven’t they visited us?) then strikes with full force.

There’s one other way to spread intelligence across the Universe, which von Neumann was also aware of. A universal constructor would operate by having blueprints, in the form of digitally coded instructions which we might as well call programs, telling it how to build different kinds of machines. An even more efficient means to spread this information across the Universe would be in the form of a radio signal travelling at the speed of light, rather than in a von Neumann machine pottering along more slowly between the stars. If a civilization like ours detected such a signal, it would be surely be copied and analysed on the most advanced computers available, ideal hosts for the program to come alive and take over the operation of the computer. In mentioning this possibility, George Dyson makes an analogy with the way a virus takes over a host cell; he seems not to be aware of the entertaining variation on this theme discussed back in 1961 by astrophysicist Fred Hoyle in his fictional work A for Andromeda, where the interstellar signal provides the instructions for making (or growing) a human body with the mind of the machine. Hoyle though, was well aware of the work of Turing and von Neumann.