When perusing this biography, the back-cover quote from an "Economist" review did reassure me that my lack of mathematical skills would not make this book inaccessible : "will give even the most innumerate reader an idea of the beautiful... world he is missing." Of course, on reflection, it is possible to read this quote in quite the opposite way, maybe the reviewer was warning the innumerate reader that this book WILL be impossible for him to grasp, and show him what he's missing?
If that is what the "Economist" meant to convey, I agree completely. I found the descriptions of the problems and solutions Alan Turing was involved with more of less incomprehensible. Obviously, this is completely my fault and some of the ideas that are being discussed here can only be simplified so much!
As to the description of Turing's life, this is an incredible story of a man contributing massively to the war effort, and to the shaping of the post War world, who was treated with almost unbelievable cruelty by the society which owed him so much. It ends, with the inevitability of a Greek tragedy with our hero's flamboyant, theatrical suicide.
Leavitt tells this story straight, but, for me, many interesting aspects,are dealt with with little or no detail, e.g. Turing's weirdly credulous belief in pseudo-science (p255) or the suggestion his suicide may have been faked (p278.) Perhaps most unforgivingly, while visiting the famous Bletchley Park code breaking centre, Leavitt actually meets a woman who knew his subject (p190) but seems to have made little or no effort to talk to her properly.
The strongest feeling reading this book is shock, shock that homosexuality was treated as a serious sex crime, and treated by chemical castration as recently as 1954. Really, "the past is a different country; They do things differently there."
on 20 July 2013
I knew someone who worked in Bletchley Park during World War II, though he steadfastly refused to talk about it. He got a first class degree in mathematics in Cambridge and there was no way that they were going to waste his brain in the forces.
There are other accounts of Turing's life, for example the 1983 biography after secret documents were released did they not give him his due. They ignore his sexuality or see it as a tragic blot on his career
Turing was a literalist - what we know label as Aspergers Syndrome. His ID card was left unsigned as he hadn't been told to write on it. He couldn't read between the lines.
The world owes much, probably its very survival, to him and to other `mad' men. Godel was convinced that someone was tying to poison him as in Snow White. Blackboard erasing took an extra ten minutes of silence waiting for it `to dry'.
Wittgenstein's inspiriting, off-the-cuff lectures demanded a regular attendance commitment and you weren't to treat common sense like an umbrella left outside.
Turing was absent-minded, naïve, oblivious to the forces that threatened him. Was his suicide like Snow White - or an experiment gone wrong? Homosexuality and belief in computer intelligence were both seen as threats to religion. He saw nothing wrong with his homosexuality. He was an outsider so he saw things that others didn't but also missed things e.g. a rival thesis published before his. As a child he invented words e.g. quockling = seagulls fighting over food, greasicle = candle guttering. He knew underlying principles, not just how to do sums. Watching school sport, he was thinking intellectually on the sidelines. His body and brain were like a machine according to a science book. At school, his form master complained about his scruffy work. A doctor had recommended the study of mathematics as a cure for homosexuality. He went up to Kings Cambridge, a liberal college. He believed that limits are contrary to the nature of maths. Bletchley's secrecy made a double life easy.
German laziness made un-encryption easier. He wore a gas mask on his bike, counted revolutions of wheels, his trousers tied with string with pyjamas underneath them. He gave the impression that he didn't notice women but was probably afraid of them.
Philosophical issues are mused upon: freewill and determinism, spirit and body, Is God to blame for how we learn, any more than a teacher? Turing suggests that if God were smarter he would have designed our brains better.
The homophobia of the period is well portrayed: security risk and blackmail, chemical castration and weight gain.
So it the politics: German maths reduced chaos to order, anti-war sentiment, he sympathised with Prince Edward against the archbishop - cf. homosexuality in public schools not talked about. Maths is not neutral - it was used by Germany to encrypt and by US to make atomic bomb.
The history is accurate - it gives Islam its due re- maths discoveries; biscuits were rationed to stop students `making a meal of them'.
All in all, a very worthwhile book. One dissenting voice in our group disliked the book because of pages and pages of mathematical formulae. He said that it `spoiled the flow of the book'; I advised him simply to skim through to the next bit of normal prose but he was unable to do that. He has to read a book straight through. Perhaps he, too, had Aspergers or was never taught how to skim read.
on 26 April 2012
This is popular science, but without the condescension normally associated with that term. Apart from summarising what we know of Alan Turing's life and death, a somehow pitiful report which reflects the short nature of his highly significant existence, it attempts to explain to educated people what he achieved, in the context of the mathematics of his time. This aim requires a diligent explanation of the intellectual appeal of pure mathematics and how this might be applied, and Leavitt largely succeeds in this aim. However, non-specialists will find this challenging, and although I affirm that success in the challenge will be thoroughly worthwhile, I suspect that they will not have the motivation to do it justice, modern education being so divided between 'arts' and 'sciences'. This book represents a way of partially rectifying this obtuse (and time-honoured) educational failure, and everyone who succeeds in grasping the wonderful principles of logical thought will be enriched by the experience. Turing was highly spiritual in a way which many will not be able to grasp, and seeing his mind in the context of his achievements highlights the man's humanity, and helps us understand his troubled life. I recommend this book to anyone who recognises that his education might be incomplete and who has the will to attempt correction of this.
on 23 March 2014
Here David Leavitt provides a fascinating insight into the mind of a genius – Alan Mathison Turin – the man who invented the computer – the machine that changed the world forever – but the work goes much deeper than simply examining how Turin’s thought processes led to his masterstroke to invent a ‘universal machine’ capable of being a spreadsheet one minute; a gaming machine in the next; or a word processor, audio-visual entertainment device, or a global networking and communication device - and all things in-between - in the next – all at the press of a button; a turn of a wheel; a click of a mouse; or a stroke of a screen.
Yes Turin’s early life is covered – illustrating how his genius approach to mathematics was on a level that was so superior to the masters that taught him, that in their inability to comprehend the work of this British genius, the best that the masters could do was demoralise him by saying that his work was ‘sloppy’; yes the record is set straight on how John von Neumann plagiarised Turin’s ideas and published them as his own – which led to IBM claiming to have invented the worlds first programmable computer – when in fact Turin had invented it 16 years previously and had several commissioned and built at Bletchley Park to serve its purpose to crack the most complex cipher ever invented (the ‘Enigma’), in Britain’s time of need in The Second World War; and yes the distasteful and ultimately tragic blot on an otherwise stellar career – eventually leading to a posthumous pardon given by David Cameron in 2012 – is addressed - along with much more besides; but on the way, the author offers a delightful discourse into how people such as Kurt Gödel and Alan Turin tore mathematics to shreds on three counts: incompleteness; inconsistency; and (the biggy) DECIDABILITY.
Gödel tackled consistency and reliability – to discover such things as to why when the square root of (say) nine yields a number (in this case 3) that when multiplied by itself correctly yields the original number (9 in my example), yet when the square root of TWO is calculated, it does NOT yield a number that when multiplied by itself yields TWO – which leads to errors in navigation – which is one of the reasons why your satnav is ALMOST correct – but not quite! Ask Christopher Columbus – the man who discovered America when he was aiming his ships for India.
Appreciating that mathematics as we know it cannot be used to prove itself consistent or complete – and hence cannot be TRUSTED as a means to test its own VALIDITY because of ominous disturbing flaws such as the simple example that I have just illustrated, Turin tackled DECIDABILITY – is there a way that mathematics could be pressed into service to make a DECISION about the ‘correctness’ of the result that a formula had yielded? (If this is ‘considered’ true then do that, otherwise do this instead).
The answer is a loud YES – Turin’s thinking changed mathematics irrevocably – and Turin’s wisdom gave the world the ‘thinking machines’ that we enjoy today in every aspect of our daily lives - be it a cardiogram monitor, or an intelligent and extremely ‘intuitive’ mobile phone – with many many more devices to improve mankind’s lot on the horizon in the foreseeable future.
The book itself is not an ‘easy’ read because the author gets himself bogged down with his valiant attempt to explain how a computer does what it does, whilst also getting bogged down with how the Enigma encryption system works, and how Turin went about cracking a polyalphabet encryption system whose cipher changed with every key press on a typewriter, as well as illustrating why maths as we know it is flawed; so one ends up entering a quagmire of fascinating but superfluous and somewhat complex concepts when: a) these could have been explained in a much simpler and more enlightening way (see my footnote below); and b) the digressions – as enthralling as they are - become distractions if one is attempting to read about Alan Turin and the fascinating and captivating ill-fated life he led in an eerie, sinister world that treated him with despicable, contemptuous disrespect – and why he was deemed to be ‘The man that knew too much’ – which begs the question ‘Was Turin’s suicide an accident?’
As an aside, should you wish to explore the potency of Turin’s ‘thought machine’ then obtain a copy of Arthur C Clark’s ‘2001 – a space odyssey’ (now available fully restored on BluRay).
Should you wish for a deeper insight into the mathematical side of things then purchase a copy of ‘An eternal golden braid’ by Douglas Hofstadter – which features the work of Gödel, Escher, and Bach.
I also recommend you visit Bletchley Park where you will see a fully operating replica of Turin's machine and enjoy much more besides.
Turin’s computer used two modes of operation: ‘fetch’ and ‘execute’.
The ‘fetch’ cycle ‘fetched’ the instruction from a ‘store’, which ‘told’ the central processor what to do.
The ‘execute’ cycle could fetch data to be processed from another ‘store’; manipulate the data; store the results elsewhere; and also made COMPARISONS. It was THIS leap in ‘decidability’ that gave Turin’s ‘Engine’ its mighty power.
If the comparisons MATCHED then a ‘match’ set of instructions was carried out.
If the comparison did NOT match then a ‘not match’ set of instructions was carried out.
Think of it as akin to looking for a person you know in a crowd – and they are wearing specific attire that you will recognise – and you spot someone wearing such attire. In the ‘match’ situation you would ‘execute’ an algorithm to ‘approach the person’ and then make a second comparison to see if the ‘matched’ person is the person you seek.
In the ‘not match’ situation you would ‘execute’ an algorithm to ‘continue to scan the crowd – always looking for the person that you will recognise wearing such attire’.
In the ‘comparison’ situation you would also carry out a ‘test’ to see if you have checked everyone, so as not to ‘lock up’ the computer in a fruitless ‘closed loop’ of never-ending tests.
Adopting the BINARY system, Turin used numbers in five unique ways:
1 As an incrementing ‘program pointer’ INTEGER (whole number) that ‘points’ to a location in a ‘read only’ ‘store’ (ROM) that contains a ‘sequential programme of ‘instructions’ – instructions which could be CHANGED to suit the requirement.
2 As a second ‘pointer’ called a ‘data pointer’ that ‘points’ to a location that contains the DATA in a ‘random access’ ‘store’ (RAM).
3 As a ‘machine code number’ that uniquely configures a ‘central processing unit’ (CPU) to perform a ‘one-step’ operation. Here, the ‘machine code’ is ‘fetched’ from the location ‘store’ that the ‘programme pointer’ is indexing, and then ‘copied’ into a REGISTER in the CPU (the ‘brain’) as a ‘one-step’ instruction to ‘tell’ the CPU what to do at THAT step of the process (for example add two numbers together).
4 As the DATA that requires manipulation – which is ‘fetched’ from the location ‘store’ that the ‘data pointer’ is indexing, and then ‘copied’ into a REGISTER inside of the CPU – in readiness for processing.
5 As a means of TESTING for VALIDITY using what we now refer to as ‘Boolean Logic’.
Using this approach, Turin and his team were able to swiftly look for points of vulnerability in the enciphered text and then ruthlessly take advantage of them by testing for ‘matches’ at great speed. His approach not only cracked the ciphertext generated by German Enigma machines, his ‘engines’ also determined the configuration of each encryption rotor and its relative position and setting in the Enigma machine – his ‘bombe’ (computer) had ‘intelligence’.
I now offer a simplified description of the fetch and execute sequences to obtain two numbers from a store, add them together, and then place the answer back into the store for your entertainment, so as to give you an insight into what you will encounter in the book as well as give insight into how the modern computer 'computes'.
The ‘program pointer’ points to store location ‘100’ and in store location 100 is the MACHINE CODE NUMBER ‘22’.
The ‘data pointer’ points to location ‘350’ and in location ‘350’ is the DATA VALUE ‘45’.
Let us assume that the CODE number ‘22’ instructs the CPU to put a data value indexed by the ‘data pointer’ into ‘Register A’.
On the ‘fetch’ cycle, the CODE number ‘22’ is clocked into the CPU. This instructs the CPU to put a data value from the data store (now called RAM) into ‘Register A’.
On the ‘execute’ cycle, the data value (45) that the ‘data pointer’ points to, is placed into ‘Register A’; the ‘program pointer’ is incremented by one, and now points to location 101; and the ‘data pointer’ is incremented by one - and now points to location 351 – which holds the data value ‘3’.
Let us assume that in location 101 is the machine code number ‘23’ and that the CODE number ‘23’ instructs the CPU to put a data value from the data store into ‘Register B’.
On the ‘fetch’ cycle, the CODE number ‘23’ is clocked into the CPU. This instructs the CPU to put a data value into ‘Register B’.
On the ‘execute’ cycle, the data value (3) that the ‘data pointer’ points to, is placed into ‘Register B’; the ‘program pointer’ increments by one and now points to location 102; and the ‘data pointer’ increments by one and now points to location 352.
Let us now assume that in location 102 is the machine code number ‘48’ and that the CODE number ‘48’ instructs the CPU to add the value in ‘Register B’ to the value in ‘Register A’.
On the ‘fetch’ cycle, the CODE number ‘48’ is clocked into the CPU. This instructs the CPU to add the value in ‘Register B’ to the value in ‘Register A’ - the RESULT will be in ‘Register A’.
On the ‘execute’ cycle, the data value ‘3’ copied from data store 351 into ‘Register B’ is added to the data value ‘45’ copied from data store 350 into ‘Register A’ – the result (48) now residing in ‘Register A’.
Let us now assume that in location 103 is the machine code number ‘56’ and that the CODE number ‘56’ instructs the CPU to put the data value in ‘Register A’ into the data store.
On the ‘fetch’ cycle, the CODE number ‘56’ is clocked into the CPU. This instructs the CPU put the data value in ‘Register A’ into the data store.
On the ‘execute’ cycle, the data value ‘48’ that resides in ‘Register A’ is transferred from ‘Register A’ into the location that ‘data pointer’ points to (352); the ‘program pointer’ increments by one and now points to location 104; and the ‘data pointer’ increments by one and now points to location 353.
As I trust this simplistic description illustrates, through a continuous series of ‘fetch’ and ‘execute’ sequences it is possible to programme the computer to perform ANY task – sequentially – one step at a time – just as you are experiencing right now!
on 31 January 2012
To get the best out of this book you need more mathematical nous than I have got, for Leavitt explains Turing's mathematical thinking in detail. So, I cannot claim to have got my head round it all. But the book also situates Turing admirably within his contemporary peer group and honours, without exagerating, his great contribution and his unique thoughts and concepts. The book is also revealing about Turing the man. He was open about being gay and paid a very high price for the sexuality which was an essential part of the genius he was.
on 26 November 2014
Great book about a tragic story. Alan Turing a man who was a key figure at Bletchley Park during WW2 who was pivotal in breaking the German Enigma and Lorenz codes (many others also helped let's not forget them). However he was a major performer. His life was tragic and David Leavitt explores his private / personal life very sensitively.
Fabulous book about an amazing man who was treated by the UK in an appalling way in the 1950's. It's a great read.
on 1 November 2013
If you are looking to mainly read about the WORK of Alan Turing, this book wouldn't be my first recommendation.
However, if you wish is to read about Turing's life, the time he lived in, the impact he had on society, both pre- and post WWII, then this book does a magnificent job.
I have read most of the more known works about Alan Turing, but this book moved me the most. A brilliant man he was!
on 8 May 2012
One of the greatest scientists working in this country in the mid Twentieth Century. A man who also contributed not a little to Britain winning WW2. He deserved the highest honours, not the shameful treatment meted out by the prejudiced establishment he saved. The book gives a good account of both science and biography. The mathematically challenged might do well to skip to the bio parts rather than give up.
on 1 April 2013
This is one of my favourite books!
It goes into some quite heavy detail on some of Turings work, but if you enjoy that sort of thing then you'll love this book.
Part of it are very sad as you might expect - even brought a tear to my eye towards the end.
If you are interested in computer science, this book really is a must read!
on 28 June 2015
David Leavitt does not shy away from what many see as complicated; thereby showing respect for the readers' abilities to comprehend topics in number theory that were central to the time of Alan Turing, but which still are critical to our understanding of computer architectures and artificial intelligence.
Though the topics are very advanced, the clear writing, consistent structure, and well chosen examples never left me unable to follow the text, albeit that some passages had to be read more than once. But, I prefer that above a writer who presumes this or that part of the text is beyond what the readers can take in, and as the subjects are never boring the occasional re-reading is easily accepted, particularly as it is probably due to my shortcomings in understanding rather than the author's in explaining.
Indirectly the book gives very interesting information on the personality and mind of Alan Turing: great brilliance comes along with perception that is - if not above - outside the average.