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: ‘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.

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