Complexity and Prediction Part V: The crisis of mathematical paradoxes, Gödel, Turing and the basis of computing

Before the referendum I started a series of blogs and notes exploring the themes of complexity and prediction. This was part of a project with two main aims: first, to sketch a new approach to education and training in general but particularly for those who go on to make important decisions in political institutions and, second, to suggest a new approach to political priorities in which progress with education and science becomes a central focus for the British state. The two are entangled: progress with each will hopefully encourage progress with the other.

I was working on this paper when I suddenly got sidetracked by the referendum and have just looked at it again for the first time in about two years.

The paper concerns a fascinating episode in the history of ideas that saw the most esoteric and unpractical field, mathematical logic, spawn a revolutionary technology, the modern computer. NB. a great lesson to science funders: it’s a great mistake to cut funding on theory and assume that you’ll get more bang for buck from ‘applications’.

Apart from its inherent fascination, knowing something of the history is helpful for anybody interested in the state-of-the-art in predicting complex systems which involves the intersection between different fields including: maths, computer science, economics, cognitive science, and artificial intelligence. The books on it are either technical, and therefore inaccessible to ~100% of the population, or non-chronological so it is impossible for someone like me to get a clear picture of how the story unfolded.

Further, there are few if any very deep ideas in maths or science that are so misunderstood and abused as Gödel’s results. As Alan Sokal, author of the brilliant hoax exposing post-modernist academics, said, ‘Gödel’s theorem is an inexhaustible source of intellectual abuses.’ I have tried to make clear some of these using the best book available by Franzen, which explains why almost everything you read about it is wrong. If even Stephen Hawking can cock it up, the rest of us should be particularly careful.

I sketched these notes as I tried to pull together the story from many different books. I hope they are useful particularly for some 15-25 year-olds who like chronological accounts about ideas. I tried to put the notes together in the way that I wish I had been able to read at that age. I tried hard to eliminate errors but they are inevitable given how far I am from being competent to write about such things. I wish someone who is competent would do it properly. It would take time I don’t now have to go through and finish it the way I originally intended to so I will just post it as it was 2 years ago when I got calls saying ‘about this referendum…’

The only change I think I have made since May 2015 is to shove in some notes from a great essay later that year by the man who wrote the textbook on quantum computers, Michael Nielsen, which would be useful to read as an introduction or instead, HERE.

As always on this blog there is not a single original thought and any value comes from the time I have spent condensing the work of others to save you the time. Please leave corrections in comments.

The PDF of the paper is HERE (amended since first publication to correct an error, see Comments).


‘Gödel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a land mark which will remain visible far in space and time.’  John von Neumann.

‘Einstein had often told me that in the late years of his life he has continually sought Gödel’s company in order to have discussions with him. Once he said to me that his own work no longer meant much, that he came to the Institute merely in order to have the privilege of walking home with Gödel.’ Oskar Morgenstern (co-author with von Neumann of the first major work on Game Theory).

‘The world is rational’, Kurt Gödel.

Unrecognised simplicities of effective action #2(b): the Apollo programme, the Tory train wreck, and advice to spads starting work today

A few months ago I put a paper on my blog: The unrecognised simplicities of effective action #2: ‘Systems engineering’ and ‘systems management’ — ideas from the Apollo programme for a ‘systems politics’.

It examined the history of the classified programme to build ICBMs and the way in which George Mueller turned the failing NASA bureaucracy into an organisation that could put man on the moon. The heart of the paper is about the principles behind effective management of complex projects. These principles are relevant to Government, politics, and campaigns.

The paper is long as I thought it worthwhile to tell some of the detailed story. At the suggestion of various spads, ministers, hacks and so on I have cut and pasted the conclusion below particularly for those starting new jobs today. This is in the form of a crude checklist that compares a) the principles of Mueller’s systems management and b) how Whitehall actually works.

You will see that Whitehall operates on exactly opposite principles to those organisations where high performance creates real value. You will also soon see that you are now in a culture in which almost nobody is aware of this and anybody who suggests it sinks their career. In your new department, failure is so normal it is not defined as ‘failure’. Officials lose millions and get a gong. There is little spirit of public service or culture of responsibility. The most political people are promoted and the most competent people, like Victoria Woodcock, leave. The very worst officials are often put in charge of training the next generation. For most powerful officials, the most important thing is preserving the system, closed and impregnable. Unlike for ministers, the TV blaring with DISASTER is of no concern – provided it is the Minister in the firing line not them – and the responsible officials will happily amble to the tube at 4pm while political careers hang in the balance and you draft statements taking ‘full responsibility’ for things you knew nothing about and would have been prohibited from fixing if you had.

For all those spads in particular who are moving into new jobs, it is worth reflecting on the deep principles that actually determine why things work and do not work. Nobody will explain these to you or talk to you about them. Sadly, few MPs these days understand the crucial role of management – they tend to think of it like science as a rather lowly skill beneath their Olympian status – so you will also probably have to cope with the fact that your minister is more interested in keeping one step ahead of Simon Walters (they won’t). The thing that officials will try hardest to do is convey to you that you have no role in personnel decisions and/or management.

If you accept that, you are accepting at the start that you will achieve very little. The reason why Gove’s team got much more done than ANY insider thought was possible – including Cameron and the Perm Sec – was because we bent or broke the rules and focused very hard on a) replacing rubbish officials and bringing in people from outside and b) project management.

You cannot reform the way the civil service works. Only a PM can do that and there is no chance of May doing it – she blew her chance and her reward is to be pushed around by Heywood and Sue Gray until her colleagues pull the plug and start the leadership campaign. You should assume that won’t be long so focus, manage a few priorities with daily and weekly timetables, and use embarrassing errors to negotiate secret deals with the Perm Sec to move rubbish officials out of your priority areas – trust me, Perm Secs understand this game and will do deals with alacrity to make their lives easier. Officials are less politically biased than you probably have been told – they are much more concerned with avoiding hard work and protecting the system than in resisting specific policies, and you can exploit this. Make alliances with the good officials who still have hope and have not been broken by the system, there are surprisingly many who will pop up if they think you actually care about the public rather than party interests.

You will also notice that fundamental issues of organisational culture described below explain the shambles of CCHQ over the past 8 weeks: the lack of information sharing, the lack of orientation, the culture of blaming juniors for the failures of overpaid senior people, bottlenecks preventing fast decisions, endless small errors compounding into a broken organisation because nobody knows who is responsible for what and so on. Every failing organisation has the same stories, people find it very hard to learn from the most successful organisations and people.

To the extent Vote Leave was successful, it was partly because I consciously tried to copy Mueller in various ways, though given my own severe limitations this was patchy. If you ever get the chance to exercise leadership, try to copy people like Mueller who tried to make the world better and build an organisation that people were proud to serve.

Finally, consider the basic condition that allows Westminster and Whitehall to be so rubbish and get away with it: they are not just monopolies, they set the rules of the game, and both the civil service and the parties make it almost impossible for outsiders to influence anything. But a) the combination of the 2008 crisis, Brexit, and extreme unhappiness about politics as usual provides a potentially powerful fuel for an insurgency, and b) technology provides opportunities for startups to catch public imagination and scale extremely fast. I’ve always been sceptical of the idea of a new UK party of any sort but I increasingly think there is a chance that a handful of entrepreneurs could start a sort of anti-party to exploit the broken system and create something which confounds the right/centre/left broken mental model that dominates SW1 and which combines Mueller’s principles with Silicon Valley technology.

If the Tory Party does not make some profound changes fast, then it faces being blamed for the disintegration of Brexit talks and the election of Corbyn after which it is possible that, rather than attempting a coup to take them over, entrepreneurs may decide it is more rational to build something that ploughs them into the earth next to Corbyn.

I said since last summer that if the Tory Party tried to carry on with Brexit and government using the same broken Downing Street operation, which spends its time on crap spin and has almost no capacity for serious management, and the same broken political operation, dominated by people who have failed to persuade the country convincingly for many years, then they would blow up. They failed to change Downing Street and they ran yet another fundamentally misconceived campaign that blew massive structural advantages. Kaboom.

[[Within minutes of publishing this blog I got the following email from someone I haven’t met but who I know was inside CCHQ with the para above highlighted and these words: ‘This is exactly my depressing experience – shit show run by people who don’t care about anything other than their jobs.’]]

MPs of all parties need to realise that the referendum makes it impossible to carry on with your usual bullshit – it forces changes upon you even though you want to carry on with the old games. The first set of MPs that realise this and change their operating principles will quickly overwhelm the others: there is a huge first-mover advantage especially in a field characterised by institutional incompetence that is susceptible to external shocks (terror, financial collapse) and which is opening up to technological disruption. And you will only get on top of Brexit if you realise that leaving the EU is a systems problem requiring a systems response and this means a radically different organisation of the UK negotiating team. The challenge is not far short of the political equivalent of the Apollo program and it needs similarly imaginative management.

For those who do want to do something better, the below will be useful. I encourage you to read the whole history HERE but for those rushing through a sandwich on Day 1 this summary will help you think of the big picture. If you want a detailed tutorial on how the civil service works then read The Hollow Men HERE

[Added later… It is also very instructive that despite the triumph of Mueller’s methods, NASA itself abandoned them after he left and has never recovered. Even spectacular success on a world-changing project is not enough to beat bureaucratic inertia. Also, the US Government passed so many laws that Mueller himself said in later life it would be impossible to repeat Apollo without making it a classified ‘black’ project to evade the regulations. JSOC, US classified special forces, has to run a lot of its standard procurement via ‘black’ procurement processes just to get anything done. The abysmal procurement rules imposed under the Single Market are just one of the good reasons for us to get out of the SM as well as the EU. I had to deal with them a lot in the DfE and had to find ways to cheat them a lot to get things done faster and cheaper. They add billions to costs every year and Whitehall refused for years even to assess this huge area to avoid undermining support for the EU.]


Excerpt from The unrecognised simplicities of effective action #2 (p.28ff) 

Core lessons [of Mueller’s systems management] for politics?

Finally, I will summarise some of the core lessons of systems management that could be applied to re-engineering political institutions such as Downing Street.  Mueller’s approach meant an extreme focus on some core principles:

  • Organisation-wide orientation. Everybody in a large organisation must understand as much about the goals and plans as possible. Whitehall now works on opposite principles: I doubt a single department has proper orientation across most of the organisation (few will have it even across the top 10 people), never mind a whole government. This is partly because most ministers fail at the first hurdle — developing coherent goals — so effective orientation is inherently impossible.
  • Integration. There must be an overall approach in which the most important elements fit together, including in policy, management, and communications. Failures in complex projects, from renovating your house to designing a new welfare system, often occur at interfaces between parts. Whitehall now works on opposite principles: for example, Cameron and Osborne approached important policy on immigration/welfare in the opposite way by 1) promising to reduce immigration to less than 100,000 while simultaneously 2) having no legal tools to do this (and even worse promising to change this then failing in the EU renegotiation) and 3) having welfare policies that incentivised more immigration then 4) announcing a new living wage thus increasing incentives further for immigration. They emphasised each element as part of short-term political games and got themselves into a long-term inescapable mess.
  • Extreme transparency and communication, horizontally as well as hierarchically. More, richer, deeper communication so that ‘all of us understand what was going on throughout the program… [C]ommunications on a level that is free and easy and not constrained by the fact that you’re the boss… [This was] the secret of the success of the program, because so many programs fail because everybody doesn’t know what it is they are supposed to do’ (Mueller). Break information and management silos — a denser network of information and commands is necessary and much of it must be decentralised and distributed between different teams, but with leadership having fast and clear information flow at the centre so problems are seen and tackled fast (a virtuous circle). There is very little that needs to be kept secret in government and different processes can easily be developed for that very small number of things. As McChrystal says of special forces operations generally the advantages of communication hugely outweigh the dangers of leaks. Whitehall now works on opposite principles: it keeps information secret that does not need to be secret in order to hide its own internal processes from scrutiny, thus adding to its own management failures and distrust (a vicious circle).
  • ‘Configuration management’. There must be a process whereby huge efforts go into the initial design of a complex system then there is a process whereby changes are made in a disciplined way such that a) interdependencies are tested where possible by relevant people before a change is agreed and b) then everybody relevant knows about the change. This ties together design, engineering, management, scheduling, cost, contracts, and allows the coordination of interdisciplinary teams. Test, learn, communicate results, change where needed, communicate… Whitehall now works on opposite principles: it does not put enough effort into the initial design then makes haphazard changes then fails to communicate changes effectively.
  • Physical and information structures should reinforce open communication. From Mueller’s NASA to JSOC, organisations that have coped well with complexity have built novel control centres to reinforce extreme communication. Spend money and time on new technologies and processes to help spread orientation and learning through the organisation. Whitehall now works on opposite principles: e.g. its antiquated committee structure and ‘red box’ system are ludicrously inefficient regarding management but are kept because they give officials huge control over ministers.
  • Long-term budgets. Long-term budgets save money. Whitehall now works on opposite principles: normal government budget processes do not value speed and savings from doing things fast. They are focused on what Parliament thinks this year. This makes it very hard to plan wisely and wastes money in the long-term (see below).
  • You need a complex mix of centralisation and decentralisation. While overall vision, goals, and strategy usually comes from the top, it is vital that extreme decentralisation dominates operationally so that decisions are fast and unbureaucratic. Information must be shared centrally and horizontally across the organisation — it is not either/or. Big complex projects must empower people throughout the network and cannot rely on issuing orders through a hierarchy. Whitehall now works on opposite principles: it is a centralising ratchet. E.g. Budgets and spending reviews are the exact opposite of Mueller’s approach. 1) They are short-term with almost no long-term elements. 2) They do not balance off priorities in any serious way. 3) They involve totally fake numbers — every department lies to the Treasury and provides fake numbers. Treasury officials dig into these. There are rounds of these games. Officials never stop lying. To maintain the charade the Chancellor never says to the SoS ‘stop your officials lying to us’ — candour would break the system. 4) The Treasury does not have the expertise to evaluate most of what they are looking at. The idea it is a department staffed by brilliant whiz kids is a joke. I saw DfE officials with very modest abilities routinely cheat the Treasury.
  • Extreme focus on errors. Schriever had ‘Black Saturdays’ and Mueller had similar meetings focused not on ‘reporting progress’ but making clear the problems. Simple as it sounds this is very unusual. Whitehall now works on opposite principles: routinely nobody is held responsible for errors and most management works on the basis of ‘give me good news not bad news’. Neither the culture nor incentives focus effort on eliminating errors. Most don’t care and you see those responsible for disaster ambling to the tube at 4pm or going on holiday amid meltdown.
  • Spending on redundancy to improve resilience. Whitehall now works on opposite principles: it tends to treat redundancy as ‘waste’ and its short-term budget processes reinforce decisions that mean out-of-control long-term budgets. By the time the long-term happens, the responsible people have all moved on to better paid jobs and nobody is accountable.
  • Important knowledge is discovered but then the innovation is standardised and codified so it can be easily learned and used by others. Whitehall now works on opposite principles: for example, in the Department for Education officials systematically destroyed its own library. The DfE operated with almost no institutional memory. By the time I left in 2014, after David Cameron banned me from entering any department officials would ask to meet me outside to find out why decisions had been taken in 2011 because three years later almost everybody had moved on to other things. The Foreign Office similarly destroyed its own library.
  • Systems management means lots of process and documentation but at its best it is fluid and purposeful — it is not process for ass-covering. The crucial ‘Gillette Procedures’ swept away red tape and Schriever battled the system to maintain freedom from normal government processes. When asked how he would do a similar programme to Apollo now (1990s) Mueller responded that the only way to do it would be as a classified ‘black’ project to escape the law on issues like procurement. Whitehall now works on opposite principles: its obsession is bullshit process for buck-passing and it fights with all its might against simplification and focus.
  • Saving time saves money. Schriever and Mueller focused on speed and saving time. Whitehall now works on opposite principles: its default mode is to go slower and those who advocate speed are denounced as reckless. Repeatedly in the DfE I was told it was ‘impossible’ to do things in the period I demanded — often less than half what senior officials wanted — yet we often achieved this and there was practically no example of failure that came because my time demands were inherently unreasonable. The system naturally pushes for the longest periods they can get away with to give themselves what they think of as a chance to beat ‘expectations’ but then they often fail on absurdly long timetables. In the DfE we often had a better record of hitting timetables that were ‘impossibly’ short than on those that were traditionally long. Also in many areas there is no downside to pushing fast — the worst that happens is minor and irrelevant embarrassment while the cumulative gains from trying to go fast are huge.
  • The ‘systems’ approach is inherently interdisciplinary ‘because its function is to integrate the specialized separate pieces of a complex of apparatus and people — the system — into a harmonious ensemble that optimally achieves the desired end’ (Ramo). Whitehall now works on opposite principles: it is hopeless at assembling interdisciplinary teams and elevates legal advice over everything in relation to practically any problem, causing huge delays and cost overruns.
  • The ‘matrix management’ system allowed coordination across different departments and different projects.  Whitehall now works on opposite principles. It is stuck with antiquated departments, an antiquated Cabinet Office system, and antiquated project management. Anything ‘cross-government’ is an immediate clue to the savvy that it is doomed and rarely worth wasting time on. A ‘matrix’ approach could and should be applied to break existing hierarchies and speed everything up.
  • People and ideas were more important than technology. Computers and other technologies can help but the main ideas came in the 1950s before personal computers. JSOC applied all sorts of technologies but Colonel Boyd’s dictum holds: people, ideas, technology — in that order. Whitehall now works on opposite principles: for example, the former Cabinet Secretary, Gus O’Donnell, recently blamed a ‘lack of investment’ in IT and a shortage of staff for a huge range of Whitehall blunders. This is really deluded. The central problem is known to all experts and is shown in almost every inquiry: IT projects fail repeatedly in the same ways because of failures of management, not ‘lack of investment’, and adding people to flawed projects is not a solution.

Ministers have little grip of departments and little power to change their direction. They can’t hire or fire and they can’t set incentives. They are almost never in a job long enough to acquire much useful knowledge and they almost never have the sort of management skills that provide alternative value to specific knowledge. They have little chance to change anything and officials ensure this little chance becomes almost no chance.

This story shows how to do things much better than normal. It shows that the principles underlying Mueller’s success are naturally in extreme competition with the principles of management that dominate all normal bureaucracies, public or private. People have been able to read about these principles for decades yet today in Whitehall almost everything runs on exactly the opposite principles: incentives operate to suppress learning. The institutional and policy changes inherent in leaving the EU are a systems problem requiring a systems response. Implementing Mueller’s principles would mean changes to most of the antiquated and failing foundations of Whitehall and bring big improvements and cost savings. Such changes are likely to be resisted by most MPs as well as Whitehall given few of them understand or have experience in high performance teams and would regard Mueller’s approach as a threat to their career prospects.

Because Whitehall is a system failure in which different failures are entangled, its inhabitants tend to potter around in an uncomprehending fog of confusion without understanding why things fail every day and therefore they do not support changes that could improve things even though these changes would be personally advantageous particularly for the first mover.

What is the minimum needed to break bureaucratic resistance and spark a virtuous circle?

How can people outside the system affect mission critical political institutions protected from market competition and resistant to major reforms?

How can we replace many traditional centralised bureaucracies with institutions that mimic successful biological systems such as the immune system that a) use distributed information processing to identify useful structure in the environment, b) find ‘good enough’ solutions in a vast search space of possibilities, and c) move at least ten times faster than existing systems?

[If you find this interesting and/or useful, then the PDF of the whole story is here. It involves some of the cleverest people of the 20th Century, such as John von Neumann.]

Unrecognised simplicities of effective action #2: ‘Systems’ thinking — ideas from the Apollo programme for a ‘systems politics’

This is the second in a series: click this link 201702-effective-action-2-systems-engineering-to-systems-politics. The first is HERE.

This paper concerns a very interesting story combining politics, management, institutions, science and technology. When high technology projects passed a threshold of complexity post-1945 amid the extreme pressure of the early Cold War, new management ideas emerged. These ideas were known as ‘systems engineering’ and ‘systems management’. These ideas were particularly connected to the classified program to build the first Intercontinental Ballistic Missiles (ICBMs) in the 1950s and successful ideas were transplanted into a failing NASA by George Mueller and others from 1963 leading to the successful moon landing in 1969.

These ideas were then applied in other mission critical teams and could be used to improve government performance. Urgently needed projects to lower the probability of catastrophes for humanity will benefit from considering why Mueller’s approach was 1) so successful and 2) so un-influential in politics. Could we develop a ‘systems politics’ that applies the unrecognised simplicities of effective action?

For those interested, it also looks briefly at an interesting element of the story – the role of John von Neumann, the brilliant mathematician who was deeply involved in the Manhattan Project, the project to build ICBMs, the first digital computers, and subjects like artificial intelligence, artificial life, possibilities for self-replicating machines made from unreliable components, and the basic problem that technological progress ‘gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we have known them, cannot continue.’

An obvious project with huge inherent advantages for humanity is the development of an international manned lunar base as part of developing space for commerce and science. It is the sort of thing that might change political dynamics on earth and could generate enormous support across international boundaries. After 23 June 2016, the UK has to reorient national policy on many dimensions. Developing basic science is one of the most important dimensions (for example, as I have long argued we urgently need a civilian version of DARPA similarly operating outside normal government bureaucratic systems including procurement and HR). Supporting such an international project would be a great focus for UK efforts and far more productive than our largely wasted decades of focus on the dysfunctional bureaucracy in Brussels that is dominated by institutions that fail the most important test – the capacity for error-correction the importance of which has been demonstrated over long periods and through many problems by the Anglo-American political system and its common law.

Please leave comments or email dmc2.cummings at


Specialist maths schools – some facts

The news reports that the Government will try to promote more ‘specialist maths schools’ similar to the King’s College and Exeter schools.

The idea for these schools came when I read about Perelman, the Russian mathematician who in 2003 suddenly posted on arXiv a solution to the Poincaré Conjecture, one of the most important open problems in mathematics. Perelman went to one of the famous Russian specialist maths schools that were set up by one of the most important mathematicians of the 20th Century, Kolmogorov.

I thought – a) given the fall in standards in maths and physics because of the corruption of the curriculum and exams started by the Tories and continued by Blair, b) the way in which proper teaching of advanced maths and physics is increasingly limited to a tiny number of schools many of which are private, and c) the huge gains for our civilisation from the proper education of the unusual small fraction of children who are very gifted in maths and physics, why not try to set up something similar.

Gove’s team therefore pushed the idea through the DfE. Dean Acheson, US Secretary of State, said, ‘I have long been the advocate of the heretical view that, whatever political scientists might say, policy in this country is made, as often as not, by the necessity of finding something to say for an important figure committed to speak without a prearranged subject.’ This is quite true (it also explains a lot about how Monnet created the ECSC and EEC). Many things that the Gove team did relied on this. We prepared the maths school idea and waited our chance. Sure enough, the word came through from Downing Street – ‘the Chancellor needs an announcement for the Budget, something on science’. We gave them this, he announced it, and bureaucratic resistance was largely broken.

If interested in some details, then look at pages 75ff of my 2013 essay for useful links. Other countries have successfully pursued similar ideas, including France for a couple of centuries and Singapore recently.

One of the interesting aspects of trying to get them going was the way in which a) the official ‘education world’ loathed not just the idea but also the idea about the idea – they hated thinking about ‘very high ability’ and specialist teaching; b) when I visited maths departments they all knew about these schools because university departments in the West employ a large number of people who were educated in these schools but they all said ‘we can’t help you with this even though it’s a good idea because we’d be killed politically for supporting “elitism” [fingers doing quote marks in the air], good luck I hope you succeed but we’ll probably attack you on the record.’ They mostly did.

The only reason why the King’s project happened is because Alison Wolf made it a personal crusade to defeat all the entropic forces that elsewhere killed the idea (with the exception of Exeter). Without her it would have had no chance. I found few equivalents elsewhere and where I did they were smashed by their VCs.

A few points…

1) Kolmogorov-type schools are a particular thing. They undoubtedly work. But they are aimed at a small fraction of the population. Given what the products of these schools go on to contribute to human civilisation they are extraordinarily cheap. They are also often a refuge for children who have a terrible time in normal schools. If they were as different to normal kids in a negative sense as they are in a positive sense then there would be no argument about whether they have ‘special needs’.

2) Don’t believe the rubbish in things like Gladwell’s book about maths and IQ. There is now very good data on this particularly in the form of the unprecedented SMPY multi-decade study. Even a short crude test at 11-13 gives very good predictions of who is likely to be very good at maths/physics. Further there is a strong correlation between performance at the top 1% / 1:1,000 / 1:10,000 level and many outcomes in later life such as getting a doctorate, a patent, writing a paper in Science and Nature, high income, health etc. The education world has been ~100% committed to rejecting the science of this subject though this resistance is cracking.

This chart shows the SMPY results (maths ability at 13) for the top 1% of maths ability broken down into quartiles 1-4: the top quartile of the top 1% clearly outperforms viz tenure, publication and patent rates.  


3) The arguments for Kolmogorov schools do not translate to arguments for selection in general – ie. they are specific to the subject. It is the structure of maths and the nature of the brain that allows very young people to make rapid progress. These features are not there for English, history and so on. I am not wading into the grammar school argument on either side – I am just pointing out a fact that the arguments for such maths schools are clear but should not be confused with the wider arguments over selection that involve complicated trade-offs. People on both sides of the grammar debate should, if rational, be able to support this policy.

4) These schools are not ‘maths hot houses’. Kolmogorov took the children to see  Shakespeare plays, music and so on. It is important to note that teaching English and other subjects is normal – other than you are obviously dealing with unusually bright children. If these children are not in specialist schools, then the solution is a) specialist maths teaching (including help from university-level mathematicians) and b) keeping other aspects of their education normal. Arguably the greatest mathematician in the world, Terry Tao, had wise parents and enjoyed this combination. So it is of course possible to educate such children without specialist schools but the risks are higher that either parents or teachers cock it up.

5) Extended wisely across Britain they could have big benefits not just for those children and elite universities but they could also play an important role in raising standards generally in their area by being a focus for high quality empirical training. One of the worst aspects of the education world is the combination of low quality training and resistance to experiments. This has improved since the Gove reforms but the world of education research continues to be dominated by what Feynman called ‘cargo cult science’.

6) We also worked with a physicist at Cambridge, Professor Mark Warner, to set up a project to improve the quality of 6th form physics. This project has been a great success thanks to his extraordinary efforts and the enthusiasm of young Cambridge physicists. Thousands of questions have been answered on their online platform from many schools. This project gives kids the chance to learn proper problem solving – that is the core skill that the corruption of the exam system has devalued and increasingly pushed into a ghetto of of private education. Needless to say the education world also was hostile to this project. Anything that suggests that we can do much much better is generally hated by all elements of the bureaucracy, including even elements such as the Institute of Physics that supposedly exist to support exactly this. A handful of officials helped us push through projects like this and of course most of them have since left Whitehall in disgust, thus does the system protect itself against improvement while promoting the worst people.

7) This idea connects to a broader idea. Kids anywhere in the state system should be able to apply some form of voucher to buy high quality advanced teaching from outside their school for a wide range of serious subjects from music to physics.

8) One of the few projects that the Gove team tried and failed to get going was to break the grip of GCSEs on state schools (Cameron sided with Clegg and although we cheated a huge amount through the system we hit a wall on this project). It is extremely wasteful for the system and boring for many children for them to be focused on existing exams that do not develop serious skills. Maths already has the STEP paper. There should be equivalents in other subjects at age 16. There is nothing that the bureaucracy will fight harder than this and it will probably only happen if excellent private schools decide to do it themselves and political pressure then forces the Government to allow state schools to do them.

Any journalists who want to speak to people about this should try to speak to Dan Abramson (the head of the King’s school), Alison Wolf, or Alexander Borovik (a mathematician at Manchester University who attended one of these schools in Russia).

It is hopeful that No10 is backing this idea but of course they will face determined resistance. It will only happen if at least one special adviser in the DfE makes it a priority and has the support of No10 so officials know they might as well fight about other things…

This is the most interesting comment probably ever left on this blog and it is much more interesting than the blog itself so I have copied it below. It is made by Borovik, mentioned above, who attended one of these schools in Russia and knows many who attended similar…

‘There is one more aspect of (high level) selective specialist mathematics education that is unknown outside the professional community of mathematicians.

I am not an expert on “gifted and talented” education. On the other hand, I spent my life surrounded by people who got exclusive academically selective education in mathematics and physics, whether it was in the Lavrentiev School in Siberia, or Lycée Louis-le-Grand in Paris, or Fazekas in Budapest, or Galatasaray Lisesi (aka Lycée de Galatasaray) in Istanbul — the list can be continued.

The schools have nothing in common, with the exception of being unique, each one in its own way.

I had research collaborators and co-authors from each of the schools that Ilisted above. Why was it so easy for us to find a common language?

Well, the explanation can be found in the words of Stanislas Dehaene, the leading researcher of neurophysiology of mathematical thinking:

“We have to do mathematics using the brain which evolved 30 000 years ago for survival in the African savanna.”

In humans, the speed of totally controlled mental operations is at most 16 bits per second. Standard school maths education trains children to work at that speed.

The visual processing module in the brain crunches 10,000,000,000 bits per second.

I offer a simple thought experiment to the readers who have some knowledge of school level geometry.

Imagine that you are given a triangle; mentally rotate it about the longest side. What is the resulting solid of revolution? Describe it. And then try to reflect: where the answer came from?

The best kept secret of mathematics: it is done by subconsciousness.

Mathematics is a language for communication with subconsciousness.

There are four conversants in a conversation between two mathematicians: two people and two their “inner”, “intuitive” brains.

When mathematicians talk about mathematics face-to-face, they
* frequently use language which is very fluid and informal;
* improvised on the spot;
* includes pauses (for a lay observer—very strange and awkwardly timed) for absorbtion of thought;
* has almost nothing in common with standardised mathematics “in print”.

Mathematician is trying to convey a message from his “intuitive brain” directly to his colleagues’ “intuitive brain”.

Alumni of high level specialist mathematics schools are “birds of feather” because they have been initiated into this mode of communication at the most susceptible age, as teenagers, at the peak of intensity of their socialisation / shaping group identity stream of self-actualisation.

In that aspect, mathematics is not much different from arts. Part of the skills that children get in music schools, acting schools, dancing school, and art schools is the ability to talk about music, acting, dancing, art with intuitive, subconscious parts of their minds — and with their peers, in a secret language which is not recognised (and perhaps not even registered) by uninitiated.

However, specialist mathematics schools form a continuous spectrum from just ordinary, with standard syllabus, but good schools with good maths teachers to the likes of Louis-le-Grand and Fazekas. My comments apply mostly to the top end of the spectrum. I have a feeling that the Green Paper is less ambitious and does not call for setting up mathematics boarding schools using Chetham’s School of Music as a model. However, middle tier maths school could also be very useful — if they are set up with realistic expectations, properly supported, and have strong connections with universities.’

A Borovik



Please help: how to make a big improvement in the alignment of political parties’ incentives with the public interest?

I am interested in these questions:

1) What incentives drive good/bad behaviour for UK political parties?

2) How could they be changed (legal and non-legal) to align interests of existing parties better with the public interest?

3) If one were setting up a new party from scratch what principles could be established in order to align the party’s interests with the public interest much more effectively than is now the case anywhere in the world, and how could one attract candidates very different to those who now dominate Parliament (cleverer, quantitative problem-solving skills, experience in managing complex organisations etc)?

4) Is there a good case for banning political parties (as sometimes was attempted in ancient Greece), how to do it, what would replace them, why would this be better etc (I assume this is a bad and/or impractical idea but it’s worth asking why)?

5) In what ways do existing or plausible technologies affect these old questions?

What are the best things written on these problems?

What are the best examples around the world of how people have made big improvements?

Assume that financial resources are effectively unlimited for the entity trying to make these changes, let me worry about things like ‘would the public buy it’ etc – focus on policy not communication/PR advice.

The more specific the better: an ideal bit of help would be detailed draft legislation. I don’t expect anybody to produce this, but just to show what I mean…

The overall problem is: how to make government performance dramatically, quantifiably, and sustainably better?

Please leave ideas in comments or email



Unrecognised simplicities of effective action #1: expertise and a quadrillion dollar business

‘The combination of physics and politics could render the surface of the earth uninhabitable.’ John von Neumann.


This series of blogs considers:

  • the difference between fields with genuine expertise, such as fighting and physics, and fields dominated by bogus expertise, such as politics and economic forecasting;
  • the big big problem we face – the world is ‘undersized and underorganised’ because of a collision between four forces: 1) our technological civilisation is inherently fragile and vulnerable to shocks, 2) the knowledge it generates is inherently dangerous, 3) our evolved instincts predispose us to aggression and misunderstanding, and 4) there is a profound mismatch between the scale and speed of destruction our knowledge can cause and the quality of individual and institutional decision-making in ‘mission critical’ institutions – our institutions are similar to those that failed so spectacularly in summer 1914 yet they face crises moving at least ~103 times faster and involving ~106 times more destructive power able to kill ~1010 people;
  • what classic texts and case studies suggest about the unrecognised simplicities of effective action to improve the selection, education, training, and management of vital decision-makers to improve dramatically, reliably, and quantifiably the quality of individual and institutional decisions (particularly 1) the ability to make accurate predictions and b) the quality of feedback);
  • how we can change incentives to aim a much bigger fraction of the most able people at the most important problems;
  • what tools and technologies can help decision-makers cope with complexity.

[I’ve tweaked a couple of things in response to this blog by physicist Steve Hsu.]


Summary of the big big problem

The investor Peter Thiel (founder of PayPal and Palantir, early investor in Facebook) asks people in job interviews: what billion (109) dollar business is nobody building? The most successful investor in world history, Warren Buffett, illustrated what a quadrillion (1015) dollar business might look like in his 50th anniversary letter to Berkshire Hathaway investors.

‘There is, however, one clear, present and enduring danger to Berkshire against which Charlie and I are powerless. That threat to Berkshire is also the major threat our citizenry faces: a “successful” … cyber, biological, nuclear or chemical attack on the United States… The probability of such mass destruction in any given year is likely very small… Nevertheless, what’s a small probability in a short period approaches certainty in the longer run. (If there is only one chance in thirty of an event occurring in a given year, the likelihood of it occurring at least once in a century is 96.6%.) The added bad news is that there will forever be people and organizations and perhaps even nations that would like to inflict maximum damage on our country. Their means of doing so have increased exponentially during my lifetime. “Innovation” has its dark side.

‘There is no way for American corporations or their investors to shed this risk. If an event occurs in the U.S. that leads to mass devastation, the value of all equity investments will almost certainly be decimated.

‘No one knows what “the day after” will look like. I think, however, that Einstein’s 1949 appraisal remains apt: “I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones.”’

Politics is profoundly nonlinear. (I have written a series of blogs about complexity and prediction HERE which are useful background for those interested.) Changing the course of European history via the referendum only involved about 10 crucial people controlling ~£107  while its effects over ten years could be on the scale of ~108 – 10people and ~£1012: like many episodes in history the resources put into it are extremely nonlinear in relation to the potential branching histories it creates. Errors dealing with Germany in 1914 and 1939 were costly on the scale of ~100,000,000 (108) lives. If we carry on with normal human history – that is, international relations defined as out-groups competing violently – and combine this with modern technology then it is extremely likely that we will have a disaster on the scale of billions (109) or even all humans (~1010). The ultimate disaster would kill about 100 times more people than our failure with Germany. Our destructive power is already much more than 100 times greater than it was then: nuclear weapons increased destructiveness by roughly a factor of a million.

Even if we dodge this particular bullet there are many others lurking. New genetic engineering techniques such as CRISPR allow radical possibilities for re-engineering organisms including humans in ways thought of as science fiction only a decade ago. We will soon be able to remake human nature itself. CRISPR-enabled ‘gene drives’ enable us to make changes to the germ-line of organisms permanent such that changes spread through the entire wild population, including making species extinct on demand. Unlike nuclear weapons such technologies are not complex, expensive, and able to be kept secret for a long time. The world’s leading experts predict that people will be making them cheaply at home soon – perhaps they already are. These developments have been driven by exponential progress much faster than Moore’s Law reducing the cost of DNA sequencing per genome from ~$108 to ~$10in roughly 15 years.


It is already practically possible to deploy a cheap, autonomous, and anonymous drone with facial-recognition software and a one gram shaped-charge to identify a relevant face and blow it up. Military logic is driving autonomy. For example, 1) the explosion in the volume of drone surveillance video (from 71 hours in 2004 to 300,000 hours in 2011 to millions of hours now) requires automated analysis, and 2) jamming and spoofing of drones strongly incentivise a push for autonomy. It is unlikely that promises to ‘keep humans in the loop’ will be kept. It is likely that state and non-state actors will deploy low-cost drone swarms using machine learning to automate the ‘find-fix-finish’ cycle now controlled by humans. (See HERE for a video just released for one such program and imagine the capability when they carry their own communication and logistics network with them.)

In the medium-term, many billions are being spent on finding the secrets of general intelligence. We know this secret is encoded somewhere in the roughly 125 million ‘bits’ of information that is the rough difference between the genome that produces the human brain and the genome that produces the chimp brain. This search space is remarkably small – the equivalent of just 25 million English words or 30 copies of the King James Bible. There is no fundamental barrier to decoding this information and it is possible that the ultimate secret could be described relatively simply (cf. this great essay by physicist Michael Nielsen). One of the world’s leading experts has told me they think a large proportion of this problem could be solved in about a decade with a few tens of billions and something like an Apollo programme level of determination.

Not only is our destructive and disruptive power still getting bigger quickly – it is also getting cheaper and faster every year. The change in speed adds another dimension to the problem. In the period between the Archduke’s murder and the outbreak of World War I a month later it is striking how general failures of individuals and institutions were compounded by the way in which events moved much faster than the ‘mission critical’ institutions could cope with such that soon everyone was behind the pace, telegrams were read in the wrong order and so on. The crisis leading to World War I was about 30 days from the assassination to the start of general war – about 700 hours. The timescale for deciding what to do between receiving a warning of nuclear missile launch and deciding to launch yourself is less than half an hour and the President’s decision time is less than this, maybe just minutes. This is a speedup factor of at least 103.

Economic crises already occur far faster than human brains can cope with. The financial system has made a transition from people shouting at each other to a a system dominated by high frequency ‘algorithmic trading’ (HFT), i.e. machine intelligence applied to robot trading with vast volumes traded on a global spatial scale and a microsecond (10-6) temporal scale far beyond the monitoring, understanding, or control of regulators and politicians. There is even competition for computer trading bases in specific locations based on calculations of Special Relativity as the speed of light becomes a factor in minimising trade delays (cf. Relativistic statistical arbitrage, Wissner-Gross). ‘The Flash Crash’ of 9 May 2010 saw the Dow lose hundreds of points in minutes. Mini ‘flash crashes’ now blow up and die out faster than humans can notice. Given our institutions cannot cope with economic decisions made at ‘human speed’, a fortiori they cannot cope with decisions made at ‘robot speed’. There is scope for worse disasters than 2008 which would further damage the moral credibility of decentralised markets and provide huge chances for extremist political entrepreneurs to exploit. (* See endnote.)

What about the individuals and institutions that are supposed to cope with all this?

Our brains have not evolved much in thousands of years and are subject to all sorts of constraints including evolved heuristics that lead to misunderstanding, delusion, and violence particularly under pressure. There is a terrible mismatch between the sort of people that routinely dominate mission critical political institutions and the sort of people we need: high-ish IQ (we need more people >145 (+3SD) while almost everybody important is between 115-130 (+1 or 2SD)), a robust toolkit for not fooling yourself including quantitative problem-solving (almost totally absent at the apex of relevant institutions), determination, management skills, relevant experience, and ethics. While our ancestor chiefs at least had some intuitive feel for important variables like agriculture and cavalry our contemporary chiefs (and those in the media responsible for scrutiny of decisions) generally do not understand their equivalents, and are often less experienced in managing complex organisations than their predecessors.

The national institutions we have to deal with such crises are pretty similar to those that failed so spectacularly in summer 1914 yet they face crises moving at least ~103 times faster and involving ~106 times more destructive power able to kill ~1010 people. The international institutions developed post-1945 (UN, EU etc) contribute little to solving the biggest problems and in many ways make them worse. These institutions fail constantly and do not  – cannot – learn much.

If we keep having crises like we have experienced over the past century then this combination of problems pushes the probability of catastrophe towards ‘overwhelmingly likely’.


What Is To be Done? There’s plenty of room at the top

‘In a knowledge-rich world, progress does not lie in the direction of reading information faster, writing it faster, and storing more of it. Progress lies in the direction of extracting and exploiting the patterns of the world… And that progress will depend on … our ability to devise better and more powerful thinking programs for man and machine.’ Herbert Simon, Designing Organizations for an Information-rich World, 1969.

‘Fascinating that the same problems recur time after time, in almost every program, and that the management of the program, whether it happened to be government or industry, continues to avoid reality.’ George Mueller, pioneer of ‘systems engineering’ and ‘systems management’ and the man most responsible for the success of the 1969 moon landing.

Somehow the world has to make a series of extremely traumatic and dangerous transitions over the next 20 years. The main transition needed is:

Embed reliably the unrecognised simplicities of high performance teams (HPTs), including personnel selection and training, in ‘mission critical’ institutions while simultaneously developing a focused project that radically improves the prospects for international cooperation and new forms of political organisation beyond competing nation states.

Big progress on this problem would automatically and for free bring big progress on other big problems. It could improve (even save) billions of lives and save a quadrillion dollars (~$1015). If we avoid disasters then the error-correcting institutions of markets and science will, patchily, spread peace, prosperity, and learning. We will make big improvements with public services and other aspects of ‘normal’ government. We will have a healthier political culture in which representative institutions, markets serving the public (not looters), and international cooperation are stronger.

Can a big jump in performance – ‘better and more powerful thinking programs for man and machine’ – somehow be systematised?

Feynman once gave a talk titled ‘There’s plenty of room at the bottom’ about the huge performance improvements possible if we could learn to do engineering at the atomic scale – what is now called nanotechnology. There is also ‘plenty of room at the top’ of political structures for huge improvements in performance. As I explained recently, the victory of the Leave campaign owed more to the fundamental dysfunction of the British Establishment than it did to any brilliance from Vote Leave. Despite having the support of practically every force with power and money in the world (including the main broadcasters) and controlling the timing and legal regulation of the referendum, they blew it. This was good if you support Leave but just how easily the whole system could be taken down should be frightening for everybody .

Creating high performance teams is obviously hard but in what ways is it really hard? It is not hard in the same sense that some things are hard like discovering profound new mathematical knowledge. HPTs do not require profound new knowledge. We have been able to read the basic lessons in classics for over two thousand years. We can see relevant examples all around us of individuals and teams showing huge gains in effectiveness.

The real obstacle is not financial. The financial resources needed are remarkably low and the return on small investments could be incalculably vast. We could significantly improve the decisions of the most powerful 100 people in the UK or the world for less than a million dollars (~£106) and a decade-long project on a scale of just ~£107 could have dramatic effects.

The real obstacle is not a huge task of public persuasion – quite the opposite. A government that tried in a disciplined way to do this would attract huge public support. (I’ve polled some ideas and am confident about this.) Political parties are locked in a game that in trying to win in conventional ways leads to the public despising them. Ironically if a party (established or new) forgets this game and makes the public the target of extreme intelligent focus then it would not only make the world better but would trounce their opponents.

The real obstacle is not a need for breakthrough technologies though technology could help. As Colonel Boyd used to shout, ‘People, ideas, machines – in that order!’

The real obstacle is that although we can all learn and study HPTs it is extremely hard to put this learning to practical use and sustain it against all the forces of entropy that constantly operate to degrade high performance once the original people have gone. HPTs are episodic. They seem to come out of nowhere, shock people, then vanish with the rare individuals. People write about them and many talk about learning from them but in fact almost nobody ever learns from them – apart, perhaps, from those very rare people who did not need to learn – and nobody has found a method to embed this learning reliably and systematically in institutions that can maintain it. The Prussian General Staff remained operationally brilliant but in other ways went badly wrong after the death of the elder Moltke. When George Mueller left NASA it reverted to what it had been before he arrived – management chaos. All the best companies quickly go downhill after the departure of people like Bill Gates – even when such very able people have tried very very hard to avoid exactly this problem.

Charlie Munger, half of the most successful investment team in world history, has a great phrase he uses to explain their success that gets to the heart of this problem:

‘There isn’t one novel thought in all of how Berkshire [Hathaway] is run. It’s all about … exploiting unrecognized simplicities… It’s a community of like-minded people, and that makes most decisions into no-brainers. Warren [Buffett] and I aren’t prodigies. We can’t play chess blindfolded or be concert pianists. But the results are prodigious, because we have a temperamental advantage that more than compensates for a lack of IQ points.’

The simplicities that bring high performance in general, not just in investing, are largely unrecognised because they conflict with many evolved instincts and are therefore psychologically very hard to implement. The principles of the Buffett-Munger success are clear – they have even gone to great pains to explain them and what the rest of us should do – and the results are clear yet still almost nobody really listens to them and above average intelligence people instead constantly put their money into active fund management that is proved to destroy wealth every year!

Most people think they are already implementing these lessons and usually strongly reject the idea that they are not. This means that just explaining things is very unlikely to work:

‘I’d say the history that Charlie [Munger] and I have had of persuading decent, intelligent people who we thought were doing unintelligent things to change their course of action has been poor.’ Buffett.

Even more worrying, it is extremely hard to take over organisations that are not run right and make them excellent.

‘We really don’t believe in buying into organisations to change them.’ Buffett.

If people won’t listen to the world’s most successful investor in history on his own subject, and even he finds it too hard to take over failing businesses and turn them around, how likely is it that politicians and officials incentivised to keep things as they are will listen to ideas about how to do things better? How likely is it that a team can take over broken government institutions and make them dramatically better in a way that outlasts the people who do it? Bureaucracies are extraordinarily resistant to learning. Even after the debacles of 9/11 and the Iraq War, costing many lives and trillions of dollars, and even after the 2008 Crash, the security and financial bureaucracies in America and Europe are essentially the same and operate on the same principles.

Buffett’s success is partly due to his discipline in sticking within what he and Munger call their ‘circle of competence’. Within this circle they have proved the wisdom of avoiding trying to persuade people to change their minds and avoiding trying to fix broken institutions.

This option is not available in politics. The Enlightenment and the scientific revolution give us no choice but to try to persuade people and try to fix or replace broken institutions. In general ‘it is better to undertake revolution than undergo it’. How might we go about it? What can people who do not have any significant power inside the system do? What international projects are most likely to spark the sort of big changes in attitude we urgently need?

This is the first of a series. I will keep it separate from the series on the EU referendum though it is connected in the sense that I spent a year on the referendum in the belief that winning it was a necessary though not sufficient condition for Britain to play a part in improving the quality of government dramatically and improving the probability of avoiding the disasters that will happen if politics follows a normal path. I intended to implement some of these ideas in Downing Street if the Boris-Gove team had not blown up. The more I study this issue the more confident I am that dramatic improvements are possible and the more pessimistic I am that they will happen soon enough.

Please leave comments and corrections…

* A new transatlantic cable recently opened for financial trading. Its cost? £300 million. Its advantage? It shaves 2.6 milliseconds off the latency of financial trades. Innovative groups are discussing the application of military laser technology, unmanned drones circling the earth acting as routers, and even the use of neutrino communication (because neutrinos can go straight through the earth just as zillions pass through your body every second without colliding with its atoms) – cf. this recent survey in Nature.