Tag: History

Jul 25 2013

Book review: The Subterranean Railway by Christian Wolmar

large-the-subterranean-railwayTo me the London underground is an almost magically teleportation system which brings order to the chaos of London. This is because I rarely visit London and know it only via Harry Beck’s circuit diagram map of the underground. To find out more about the teleporter, I have read The Subterranean Railway by Christian Wolmar.

London’s underground system was the first in the world, it predated any others by nearly 40 years. This had some drawbacks, for the first 30 years of its existence it ran exclusively using steam engines which are not good in an enclosed, underground environment. In fact travel in the early years of the Underground sounds really rather grim, despite its success.

The context for the foundation of the Underground was the burgeoning British rail network, it had started with one line between Manchester and Liverpool in 1830 by 1850 the country had a system spanning the country. The network did not penetrate to the heart of London, it had been stopped by a combination of landowner interests and expense. This exclusion was enshrined in the report of the 1846 Royal Commission on Metropolis Railway Termini. This left London with an ever-growing transport problem, now increased by the railway’s ability to get people to the perimeter of the city but no further.

The railways were the largest human endeavours since Roman times, as well as the engineering challenges there were significant financial challenges in raising capital and political challenges in getting approval. This despite the fact the the railway projectors were exempted from the restrictions on raising capital from groups of more than five people introduced after the South Seas Bubble.

The first underground line, the Metropolitan, opened in 1863 it ran from Paddington to Farringdon – it had been 20 years in the making, although construction only took 3 years. The tunnels were made by the cut-and-cover method, which works as described – a large trench is dug, the railway built in the bottom and then covered over. This meant the tunnels were relatively shallow, mainly followed the line of existing roads and involved immense disruption on the surface.

In 1868 the first section of the District line opened, this was always to be the Metropolitan’s poorer relative but would form part of the Circle line, finally completed in 1884 despite the animosity between James Staats Forbes and Edward Watkin – the heads of the respective companies at the time. It’s worth noting that it wasn’t until 1908 that the first London Underground maps were published; in its early days the underground “system” was the work of disparate private companies who were frequently at loggerheads and certainly not focussed on cooperating to the benefit of their passengers.

The underground railways rarely provided the returns their investors were looking for but they had an enormous social impact, for the first time poorer workers in the city could live out of town in relatively cheap areas and commute in, the railway companies positively encouraged this. The Metropolitan also invested in property in what are now the suburbs of London, areas such as Golders Green were open fields before the underground came. This also reflects the expansion of the underground into the surrounding country.

The first deep line, the City and South London was opened in 1890, it was also the first electric underground line. The deep lines were tunnelled beneath the city using the tunnelling shield developed by Marc Brunel, earlier in the 19th century. Following the first electrification the District and Metropolitan lines eventually electrified their lines, although it took some time (and a lot of money). The finance for the District line came via the American Charles Tyson Yerkes, who would generously be described as a colourful character, engaging in financial engineering which we likely imagine is a recent invention.

Following the First World War the underground was tending towards a private monopoly, government was looking to invest to make work and ultimately the underground was nationalised, at arms length, to form London Transport in 1933, led by the same men (Lord Ashfield and Frank Pick) who had run the private monopoly.

The London underground reached its zenith in the years leading up to the Second World War, gaining its identity (roundel, font and iconic map) and forming a coherent, widespread network. After the war it was starved of funds, declining – overtaken by the private car. Further lines were added such as the Victoria and Jubilee lines but activity was much reduced from the early years.

More recently it has seen something of a revival with the ill-fated Public-Private Partnership running into the ground, but not before huge amounts of money had been spent, substantially on improvements. As I write, the tunnelling machines are building Crossrail.

I felt the book could have done with a construction timeline, something like this on wikipedia (link), early on there seems to be a barrage of new line openings, sometimes not in strictly chronological order and to someone like me, unfamiliar with London it is all a bit puzzling. Despite this The Subterranean Railway is an enjoyable read.

May 25 2013

Book review: Empire of the Clouds by James Hamilton-Paterson

EmpireOfTheCloudsEmpire of the Clouds by James Hamilton-Paterson, subtitled When Britain’s Aircraft Ruled the World, is the story of the British aircraft industry in the 20 years or so following the Second World War. I read it following a TV series a while back, name now forgotten, and the recommendation of friend. I thought it might fit with the story of computing during a similar period which I had gleaned from A Computer called LEO. The obvious similarities are that at the end of the Second World War Britain held a strong position in aircraft and computer design, which spawned a large number of manufacturers who all but vanished by the end of the 1960s.

The book starts with the 1952 Farnborough Air Show crash in which 29 spectators and a pilot were killed when a prototype de Havilland 110 broke up in mid-air with one of its engines crashing into the crowd. Striking to modern eyes would be the attitude to this disaster – the show went on directly with the next pilot up advised to “…keep to the right side of the runway and avoid the wreckage”. All this whilst ambulances were still converging to collect the dead and wounded. This attitude applied equally to the lives of test pilots, many of whom were to die in the years after the war. Presumably this was related to war-time experiences where pilots might routinely expect to lose a large fraction of their colleagues in combat, and where city-dwellers had recent memories of nightly death-tolls in the hundreds from aerial bombing.

Some test pilots died as they pushed their aircraft towards the sound barrier, the aerodynamics of an aircraft change dramatically as it approaches the speed of sound, making it difficult to control and all at very high speed so if solutions to problems did exist they were rather difficult to find in the limited time available. Black box technology for recording what had happened was rudimentary so the approach was generally to try to creep up on the speeds at which others had come to grief with a hope of finding out what had gone wrong by direct experience.

At the end of the Second World War Britain had a good position technically in the design of aircraft, and a head start with the jet engine. There were numerous manufacturers across the country who had been churning out aircraft to support the war effort. This could not be sustainable in peace time but it was not for quite some time that the required rationalisation was to occur. Another consequence of war was that for resilience to aerial bombing manufacturers frequently had distributed facilities which in peacetime were highly inconvenient, these arrangements appeared to remain in place for some time after the war.

In some ways the sub-title “When Britain’s Aircraft Ruled the World” is overly optimistic, although there were many exciting and intriguing prototype airplanes produced but only a few of them made it to production, and even fewer were commercially, or militarily successful. Exceptions to this general rule were the English Electric Canberra jet-bomber, English Electric Lightning, Avro Vulcan and the Harrier jump jet.

The longevity of these aircraft in service was incredible: the Vulcan and Canberra were introduced in the early fifties with the Vulcan retiring in 1984 and the Canberra lasting until 2006. The Harrier jump jet entered service in 1969 and is still operational. The Lighting entered service 1959 and finished in 1988; viewers of the recent Wonders of the Solar System will have seen Brian Cox take a trip in a Lightning, based at Thunder City where thrill-seekers can play to fly in the privately-owned craft. They’re ridiculously powerful but only have 40 minutes or so of fuel, unless re-fuelled in-flight.

Hamilton-Paterson’s diagnosis is that after the war the government’s procurement policies, frequently finding multiple manufacturers designing prototypes for the same brief and frequently cancelling those orders, were partly to blame for the failure of the industry. These cancellations were brutal: not only were prototypes destroyed, the engineering tools used to make them were destroyed. This is somewhat reminiscent of the decommissioning of the Colossus computer at the end of the Second World War. In addition the strategic view at the end of the war was that there would be no further wars to fight for the next ten years and development of fighter aircraft was therefore slowed. Military procurement has hardly progressed to this day, as a youth I remember the long drawn out birth of the Nimrod reconnaissance aircraft, and more recently there have been mis-adventures with the commissioning of Chinook helicopters and new aircraft carriers.

A second strand to the industry’s failure was the management and engineering approaches common at the time in Britain. Management stopped for two hours for sumptuous lunches every day, it was often autocratic. Whilst American and French engineers were responsive to the demands of their potential customers, and their test pilots the British ones seemed to find such demands a frightful imposition which they ignored. Finally, with respect to civilian aircraft, the state owned British Overseas Airways Corporation was not particularly patriotic in its procurement strategy.

Hamilton-Paterson’s book is personal, he was an eager plane-spotter as a child and says quite frankly that the test pilot Bill Waterson – a central character in the book – was a hero to him. This view may or may not colour the conclusions he makes about the period but it certainly makes for a good read, the book could have been a barrage of detail about each and every aircraft but the more personal reflections, and memories make it something different and more readable. There are parallels with the computing industry after the war, but perhaps the most telling thing is that flashes of engineering brilliance are of little use if they are not matched by a consistent engineering approach and the management to go with it.

Mar 14 2013

Book review: The Eighth Day of Creation by Horace Freeland Judson

EighthDayMy reading moves seamlessly from the origins of cosmology (in Koestler’s Sleepwalkers) to the origins of molecular biology in “The Eighth Day of Creation” by Horace Freeland Judson. The book covers the revolution in biology starting with the elucidation of the structure of DNA through to how this leads to the synthesis, by organisms, of proteins – this covers a period from just before the Second World War to the early 1960s although in the Epilogue and Afterwords. Judson comments on the period up to the mid-nineties. Although the book does provide basic information on the core concepts (What is DNA? What is a protein?), I suspect it requires a degree of familiarity with these ideas to make much sense on a casual reading – the same applies to this blog post.

The first third or so of the book covers the elucidation of the structure of DNA. Three groups were working on this problem – that of Linus Pauling in the US, Franklin and Wilkins at Kings College in London and Crick and Watson in Cambridge. Key to the success of Crick and Watson was their collaboration: a willingness to talk to people who knew stuff they needed to know, and piecing the bits together. The structural features of their model were the helix form (this wasn’t news), specific and strong hydrogen bonding between bases, and the presence of two DNA chains (running in opposite directions). On the whole this wasn’t a new story to me, although I wasn’t familiar with the surrounding work which established DNA as the genetic material. Judson returns to the part Rosalind Franklin in the discovery in one of the Afterwords. It has been said that Franklin was greatly wronged over the discovery of DNA, but Judson does not hold this view and I tend to agree with him. The core of the problem is that the Nobel Prize is not awarded posthumously, and with her death at 37 from cancer, Franklin therefore missed out. Watson’s book The Double Helix was a rather personalised view of the characters involved most of whom were alive to carry out damage limitation, whilst Franklin was not – so here she was poorly treated but by Watson rather than a whole community of scientists. Perhaps the thing that said the most to me about the situation is that after she was diagnosed with cancer she stayed with Cricks at their home.

In parallel with the elucidation of the structure of the DNA work had been ongoing with understanding protein synthesis and genetics in viruses and bacteria. This included both how information was coded into DNA, with much effort expended in trying to establish overlapping codes. There are 20 amino acids and four bases in DNA, so three base pairs are required to specify an amino acid if the amino acid sequence is to be unconstrained but it was conceivable that two consecutive amino acids are coded by fewer than 6 base pairs but in this case there is a restriction on the possible amino acid sequences. This area was initiated by the physicist, George Gamow. I struggle a bit to see how it gained so much traction, this type of model was quickly ruled out by consideration of the amino acid sequences that we being established for proteins at the time. It turns out that amino acids are coded by three consecutive base pairs with redundancy (so several different base pair triplets code for the same amino acid). Also covered was the mechanism by which data passed from DNA to the ribosomes where protein synthesis takes place, important here are adaptor molecules which carry the appropriate amino acid to the site of synthesis.

Compared to the structure of DNA this work was a long difficult slog, involving intricate experiments with bacteria, bacteriophage viruses, bacterial sex, ultracentrifugation, chromatography and radiolabelling.

The final part of the book is on the elucidation of the structure of proteins, this was done using x-ray crystallography with the very first clear scattering patterns measured in the 1930s and the first full elucidation made in the late fifties. X-ray crystallography of proteins, containing many thousands of atoms is challenging. Fundamentally there is a issue, the “phase problem”, which means you don’t have quite enough information to determine the structure from the scattering pattern. This issue was resolved by heavy atom labelling, here you try to chemically attach a heavy atom such as mercury to your protein then compare the scattering pattern of this modified protein with that of the unmodified protein, which resolves the phase problem. Nowadays measuring the thousands of spots in an x-ray scattering pattern and carrying out the thousands and thousands of calculations required to resolve the structure is relatively straightforward but in the early days it was a massive manual labour.

As well as resolving structure a key discovery was made regarding the mode of action of proteins: essentially they work as adaptors between chemical distinct systems – when a molecule binds to one site on a protein it effects the ability of another type of molecule to bind to another site on the protein through changes in the protein structure induced by the first molecule’s binding. This feature opens up huge possibilities for cell biology – in the absence of this feature interactions between chemical systems can only occur if the participants in those systems interact with each other chemically.

It isn’t something I’d really appreciated properly but molecular biologists are quite organised in the organisms that they generally agree to work on. The truth is that there are uncountably many viruses and so to aid the progress of science one needs to select which ones to study: E. Coli, the T series bacteriophages, C. Elegans, D. Melanogaster and more recently the zebrafish, they almost play the part of an extra author.

Molecular biology was apparently dominated by physicists, I must admit I found this confusing in the past but Judson highlights the field as defined by its practioners: biochemistry is about energy and matter (and typically small molecules), molecular biology is about information (and typically macromolecules) – a more natural home for physicists.

I found the first and third parts an enjoyable read, my scientific background is in scattering so the technical material was at least familiar the central section on genetics I found fascinating but a bit of a slog. I’m somewhat in awe of the complexity of the experiments (and their apparent difficulty).

Looking back on my earlier book reviews, I read my comment on R.J. Evan’s book on historiography that history is a literary exercise as well as anything else, as a trained scientist this was something of an alien concept but in common with Koestler’s book the style of this book shines through.

 

Footnotes

My Evernotes

Nov 12 2012

Book review: The Sleepwalkers: A History of Man’s Changing Vision of the Universe by Arthur Koestler

Sleepwalkers_ArthurKoestler.Another result of my plea for reading suggestions on twitter; this is a review and summary of Arthur Koestler’s book “The Sleepwalkers: A History of Man’s Changing Vision of the Universe”. The book is a history of cosmology running from Pythagoras, in the 6th century BC, to Galileo who spanned the end of the 16th century, just touching lightly on Newton. It traces a revolution from a time when the cosmos, beyond the earth, was considered different, stable and perfect, to a time when it was shown to be subject to earthly physics, be changeable and not perfect by any reasonable definition.

Kuhn’s language of paradigm shifts seems rather overused to me but here is an example of a true paradigm shift. The sleepwalkers in the title refers to the idea that the protagonists didn’t really know where they were headed with their ideas and quite often were lucky with errors which cancelled each other out.

The book starts with a cursory look at Babylonian and early Greek astronomy; despite considerable observational acumen their models of the universe were outright mythical. The Pythagoranean Brotherhood although in many senses still mystical started to think about the physics of the universe. I have a tendency to think of the ancient Greeks as one blob but as the book makes clear there is a huge span of time, and outlook, between Pythagoras, Aristotle and Plato and Ptolemy. Koestler is quite clearly disappointed with the Greeks: they make a promising start with Pythagoras, Aristarchus developed a heliocentric model for the solar system and then with Plato, Aristotle and Ptolemy they regress back to a geocentric model.

Following on from the Greeks the Middle Ages are covered, James Hannam in his book “God’s Philosophers” has covered why this period wasn’t all that bad in terms of intellectual development. Koestler is less sympathetic, his key accusations are that they philosophers of the middle ages were in thrall to the later Greeks and furthermore there were elements of Christian theology that abjured the pleasure of knowledge for knowledge’s sake.

After these preliminaries, Koestler turns to the core of his work: the cosmological developments of Copernicus, Tycho Brahe, Johannes Kepler and Galileo Galilei.

The model of the universe handed down from the ancient Greeks was one of circles (often referred to in this context as epicycles), they believed that motion in a circle was perfect, that the heavens were a separate, perfect realm and that therefore all motion in the heavens must be based on circular motion. Further, the model dominating at the end of their period, held that the earth lay at the centre of these circular motions. The only problem with this model is that it doesn’t fit well the observed motions of the sun, moon, Mercury, Venus, Mars, Jupiter and Saturn – the observable solar system which lay against an unchanging starry background. Or rather you can get a rough fit at the expense of stacking together a great number of epicycles – something like 50.

Copernicus’ contribution, published on his death in 1543, was to put the sun back at the centre of the universe. Copernicus led a rather uneventful life, was no sort of astronomical observer and only published his thesis at the end of his life at the strong urging of Georg Joachim Rheticus. He’d discussed his model fairly freely during his life, and his reasons for not publishing were more to do with fear of ridicule from his contemporaries rather than theological pressure. After his death his work, with the exception of the astronomical tables, sank into obscurity partly because it was a difficult read and partly because he managed to ostracise his former cheerleader, Rheticus. Copernicus’ model still holds to the epicycles of the Greeks, and only marginally reduces the complexity of the model.

Next up comes Johannes Kepler, interspersed with Tycho Brahe. Brahe was an astronomical observer and nobleman, funded very well by the Danish king; given his own island Hveen where he built his observatory. As a keen astrologer he began his observation programme when he found a conjunction of Jupiter and Saturn was poorly predicted by current astronomical tables – how can you cast an accurate fortune under these circumstances?

Kepler was a theoretician rather than an observer but also a keen astrologer. I emphasise this because these days astrology is not held in high regard but it is the father of observational astronomy. He had started to develop a model of the solar system based on the Platonic solids – something of a mystical exercise but realised he needed better data to support his model. Brahe was the man with the data, Kepler was only just in time though – he travelled to work with Brahe when Brahe moved to Prague less than 2 years later Brahe was dead. Nowadays we know Kepler for his three laws of planetary motion – it’s worth noting that Kepler’s laws are labelled retrospectively.)

He left copious records of his progress which Koestler traces in great detail, Kepler’s struggle to recognise that planetary orbits were ellipses was heroic and has something of a pantomime air to it – “They’re right in front of you!”. His approach was unprecedented in the sense that he sought to accurately model the very best, most recent measurements. Kepler also made some attempts at a physical model to describe the motions but ultimately he is remembered for the detailed description of their motion. Since it is not central to his theme, Koestler makes only passing reference to Kepler’s work on optics.

The penultimate figure in the story is Galileo, despite Kepler’s best efforts Galileo pretty much ignored him. Galileo gets quite short shrift from Koestler who feels that he brought his troubles with the Catholic Church upon himself. Reading this account his position is not unreasonable. Galileo’s two big contributions to the story are his promotion and use of the telescope, and his work on the motion of terrestrial bodies, the generalisation of which and application to the solar system was Newton’s great triumph. Cosmologically he was only later in his life a supporter of the somewhat retro Copernican model which was a cul-de-sac in terms of theoretical developments. At the time the Catholic Church, particularly the Jesuits, were interested in astronomy and not particularly hardline about the interpretation of Scripture to fit observations. Galileo wound them up both by claiming all newly observed celestial phenomena as his own and by putting the words of the Pope in the mouth of an idiot in one of his Dialogues.

This highlights two of the wider themes that Koestler brings to his book. At one point he describes his cast of characters as “moral dwarves”, he states this is relative to their scientific achievements but returns to this theme in the epilogue where he feels that our scientific developments have not been matched by our spiritual development. The second is the schism between science and the Church that began in this period, Koestler seems to put much of the blame for this on Galileo’s head feeling that it is by no means inevitable. In the epilogue he also draws a comparison between biological evolution and scientific developments, highlighting specifically that there are long periods of not that much happening and many diversions from the “true” path.

The book finishes with a brief mention of Newton’s synthesis of Kepler’s laws and Galileo’s dynamics to produce a model of the solar system which is close to that which we hold today.

This really is a rollicking good read! This is a relatively old book, published in 1959 and one might anticipate that it has not fully caught up with modern historiography however a brief look around the internet suggests that he is not criticised in any great sense. Koestler does tend to focus on a limited number of “great” individuals and goes for “firsts” but this perhaps is what makes it a good read.

Footnotes

My Evernotes for the book are here, last page of the book at the top!

Oct 14 2012

Book Review: Alan Turing: The Enigma by Andrew Hodges

2012editionA brief panic over running out of things to read led me to poll my twitter followers for suggestions, Andrew Hodges’ biography of Alan Turing, Alan Turing: The Enigma  was one result of that poll. Turing is most famous for his cryptanalysis work at Bletchley Park during the Second World War. He was born 23rd June 1912, so this is his 100th anniversary year. He was the child of families in the Indian Civil Service, with a baronetcy in another branch of the family.

The attitude of his public school, Sherbourne, was very much classics first, this attitude seems to have been common and perhaps persists today. Turing was something of an erratic student, outstanding in the things that interested him (although not necessarily at all tidy) and very poor in those things that did not interest him.

After Sherbourne he went to King’s College, Cambridge University on a scholarship for which he had made several attempts (one for my old college, Pembroke). The value of the scholarship, £80 per annum, is quite striking: it is double the value of unemployment benefit and half that of a skilled worker. He started study in 1931, on the mathematics Tripos. His scholarship examination performance was not outstanding. Significant at this time is the death of his close school friend, Christopher Morcom in 1930.

King’s is a notorious hotbed of radicals, and at this time Communism was somewhat in vogue, a likely stimulus for this was the Great Depression: capitalism was seen to be failing and Communism offered, at the time, an attractive alternative. Turing does not appear to have been particularly politically active though.

During his undergraduate degree, in 1933, he provided a proof of the Central Limit Theorem – it turns out a proof had already been made but this was his first significant work. He then went on to answer Hilbert’s Entscheidungsproblem (German for “Decision Problem) in mathematics with his paper, “On computable numbers”1. This is the work in which he introduced the idea of a universal machine that could read symbols from a tape, adjust its internal state on the basis of those symbols and write symbols on the tape. The revelation for me in this work was that mathematicians of Turing’s era were considering numbers and the operations on numbers to have equivalent status. It opens the floodgates for a digital computer of the modern design: data and instructions that act on data are simply bits in memory there is nothing special about either of them. In the period towards the Second World War a variety of specialised electromechanical computing devices were built, analogue hardware which attacked just one problem. Turing’s universal machine, whilst proving that it could not solve every problem, highlighted the fact that an awful lot of problems could be solved with a general computing machine – to switch to a different problem, simply change the program.

Alonzo Church, at Princeton University, produced an answer for the Entscheidungsproblem  at the same time; Turing went to Princeton to study for his doctorate with Church as his supervisor.

Turing had been involved in a minor way in codebreaking before the outbreak of World War II and he was assigned to Bletchley Park immediately war started. His work on the “Turing machine” provides a clear background for attacking German codes based on the Enigma machine. This is not the place to relate in detail the work at Bletchley: Turing’s part in it was as something of a mathematical guru but also someone interested in producing practical solutions to problems. The triumph of Bletchley was not the breaking of individual messages but the systematic breaking of German systems of communication. Frequently, it was the breaking of a system which was critical in principle the Enigma machine (or variants of it) could offer practically unbreakable codes but in practice the way it was used offered a way in. Towards the end of the war Turing was no longer needed at Bletchley and he moved to a neighbouring establishment, Hanslope Park where he built a speech encrypting system, Delilah with Don Bayley – again a very practical activity.

Following the war Turing was seconded to the National Physical Laboratory where it was intended he would help build ACE (a general purpose computer), however this was not to be – in contrast to work during the war building ACE was a slow frustrating process and ultimately he left for Manchester University who were building their own computer. Again Turing shows a high degree of practicality: he worked out that an alcohol water mixture close to the composition of gin would be almost as good as mercury for delay line memory*. Philosophically Turing’s vision for ACE was different from the American vision for electronic computing led by Von Neumann: Turing sought the simplest possible computing machinery, relying on programming to carry out complex tasks – the American vision tended towards more complex hardware. Turing was thinking about software, a frustrating process in the absence of any but the most limited working hardware and also thinking more broadly about machine intelligence.

It was after the war that Turing also became interested in morphogenesis2 – how complex forms emerge from undifferentiated blobs in the natural world, based on the kinetics of chemical reactions. He used the early Manchester computer to carry out simulations in this area. This work harks back to some practical calculations on chemical kinetics which he did before going to university.

Turing’s suicide comes rather abruptly towards the end of the book. Turing had been convicted of indecency in 1952, and had undergone hormone therapy as an alternative to prison to “correct” his homosexuality. This treatment had ended a year before his suicide in 1954. By this time the UK government had tacitly moved to a position where no homosexual could work in sensitive government areas such as GCHQ. However, there is no direct evidence that this was putting pressure on Turing personally. Reading the book there is no sick feeling of inevitability as Turing approaches the end you know he has.

Currently there are calls for Turing to be formally pardoned for his 1952 indecency conviction, personally I’m ambivalent about this – a personal pardon for Turing is irrelevant: legal sanctions against homosexual men, in particular, were widespread at the time. An individual pardon for Turing seems to say, “all those other convictions were fine, but Turing did great things so should be pardoned”. Arnold Murray, the man with whom Turing was convicted was nineteen at the time, an age at which their activities were illegal in the UK until 2000.

What struck me most about Turing from this book was his willingness to engage with practical, engineering solutions to the results his mathematical studies produced.

Hodges’ book is excellent: it’s thorough, demonstrates deep knowledge of the areas in which Turing worked and draws on personal interviews with many of the people Turing worked with.

Footnotes

1. “On computable numbers, with an application to the Entscheidungsproblem”, A.M. Turing, Proceedings of the London Mathematical Society 42:230-265 (1936).

2. “The Chemical Basis of Morphogenesis”, A.M. Turing, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Vol. 237, No. 641. (Aug. 14, 1952), pp. 37-72.

3. My Evernotes for the book

4. Andrew Hodges’ website to accompany the book (link)