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.

On the referendum #20: the campaign, physics and data science – Vote Leave’s ‘Voter Intention Collection System’ (VICS) now available for all

‘If you don’t get this elementary, but mildly unnatural, mathematics of elementary probability into your repertoire, then you go through a long life like a one-legged man in an ass-kicking contest. You’re giving a huge advantage to everybody else. One of the advantages of a fellow like Buffett … is that he automatically thinks in terms of decision trees and the elementary math of permutations and combinations… It’s not that hard to learn. What is hard is to get so you use it routinely almost everyday of your life. The Fermat/Pascal system is dramatically consonant with the way that the world works. And it’s fundamental truth. So you simply have to have the technique…

‘One of the things that influenced me greatly was studying physics… If I were running the world, people who are qualified to do physics would not be allowed to elect out of taking it. I think that even people who aren’t [expecting to] go near physics and engineering learn a thinking system in physics that is not learned so well anywhere else… The tradition of always looking for the answer in the most fundamental way available – that is a great tradition.’ Charlie Munger, Warren Buffet’s partner.

During the ten week official campaign the implied probability from Betfair odds of IN winning ranged between 60-83% (rarely below 66%) and the probability of OUT winning ranged between 17-40% (rarely above 33%). One of the reasons why so few in London saw the result coming was that the use by campaigns of data is hard to track even if you know what to look for and few in politics or the media know what to look for yet. Almost all of Vote Leave’s digital communication and data science was invisible even if you read every single news story or column ever produced in the campaign or any of the books so far published (written pre-Shipman’s book).

Today we have made a software product available for download – Vote Leave’s ‘Voter Intention Collection System’ (VICS) – click HERE. It was named after Victoria Woodcock, Operations Director, known as Vics, who was the most indispensable person in the campaign. If she’d gone under a bus, Remain would have won. When comparing many things in life the difference between average and best is say 30% but some people are 50 times more effective than others. She is one of them. She had ‘meetings in her head’ as people said of Steve Wozniak. If she had been Cameron’s chief of staff instead of Llewellyn and Paul Stephenson had been director of communications instead of Oliver and he’d listened to them, then other things being equal Cameron would still be on the No10 sofa with a glass of red and a James Bond flick. They were the operational/management and communications foundation of the campaign. Over and over again, those two – along with others, often very junior – saved us from the consequences of my mistakes and ignorance.

Among the many brilliant things Vics did was manage the creation of VICS. When we started the campaign I had many meetings on the subject of canvassing software. Amazingly there was essentially no web-based canvassing software system for the UK that allowed live use and live monitoring. There have been many attempts by political parties and others to build such systems. All failed, expensively and often disastrously.

Unfortunately, early on (summer 2015) Richard Murphy was hired to manage the ground campaign. He wanted to use an old rubbish system that assumed the internet did not exist. This was one of the factors behind his departure and he decided to throw in his lot with Farage et al. He then inflicted this rubbish system on Grassroots Out which is one of the reasons why it was an organisational/management disaster and let down its volunteers. After Vote Leave won the official designation, many GO activists defected, against official instructions from Farage, and plugged into VICS. Once Murphy was replaced by Stephen Parkinson (now in No10) and Nick Varley, the ground campaign took off.

We created new software. This was a gamble but the whole campaign was a huge gamble and we had to take many calculated risks. One of our central ideas was that the campaign had to do things in the field of data that have never been done before. This included a) integrating data from social media, online advertising, websites, apps, canvassing, direct mail, polls, online fundraising, activist feedback, and some new things we tried such as a new way to do polling (about which I will write another time) and b) having experts in physics and machine learning do proper data science in the way only they can – i.e. far beyond the normal skills applied in political campaigns. We were the first campaign in the UK to put almost all our money into digital communication then have it partly controlled by people whose normal work was subjects like quantum information (combined with political input from Paul Stephenson and Henry de Zoete, and digital specialists AIQ). We could only do this properly if we had proper canvassing software. We built it partly in-house and partly using an external engineer who we sat in our office for months.

Many bigshot traditional advertising characters told us we were making a huge error. They were wrong. It is one of the reasons we won. We outperformed the IN campaign on data despite them starting with vast mounts of data while we started with almost zero, they had support from political parties while we did not, they had early access to the electoral roll while we did not, and they had the Crosby/Messina data and models from the 2015 election while we had to build everything from scratch without even the money to buy standard commercial databases (we found ways to scrape equivalents off the web saving hundreds of thousands of pounds).

If you want to make big improvements in communication, my advice is – hire physicists, not communications people from normal companies and never believe what advertising companies tell you about ‘data’ unless you can independently verify it. Physics, mathematics, and computer science are domains in which there are real experts, unlike macro-economic forecasting which satisfies neither of the necessary conditions – 1) enough structure in the information to enable good predictions, 2) conditions for good fast feedback and learning. Physicists and mathematicians regularly invade other fields but other fields do not invade theirs so we can see which fields are hardest for very talented people. It is no surprise that they can successfully invade politics and devise things that rout those who wrongly think they know what they are doing. Vote Leave paid very close attention to real experts. (The theoretical physicist Steve Hsu has a great blog HERE which often has stuff on this theme, e.g. HERE.)

More important than technology is the mindset – the hard discipline of obeying Richard Feynman’s advice: ‘The most important thing is not to fool yourself and you are the easiest person to fool.’ They were a hard floor on ‘fooling yourself’ and I empowered them to challenge everybody including me. They saved me from many bad decisions even though they had zero experience in politics and they forced me to change how I made important decisions like what got what money. We either operated scientifically or knew we were not, which is itself very useful knowledge. (One of the things they did was review the entire literature to see what reliable studies have been done on ‘what works’ in politics and what numbers are reliable.) Charlie Munger is one half of the most successful investment partnership in world history. He advises people – hire physicists. It works and the real prize is not the technology but a culture of making decisions in a rational way and systematically avoiding normal ways of fooling yourself as much as possible. This is very far from normal politics.

(One of the many ways in which Whitehall and Downing Street should be revolutionised is to integrate physicist-dominated data science in decision-making. There are really vast improvements possible in Government that could save hundreds of billions and avoid many disasters. Leaving the EU also requires the destruction of the normal Whitehall/Downing Street system and the development of new methods. A dysfunctional broken system is hardly likely to achieve the most complex UK government project since beating Nazi Germany, and this realisation is spreading – a subject I will return to.)

In 2015 they said to me: ‘If the polls average 50-50 at the end you will win because of differential turnout and even if the average is slightly behind you could easily win because all the pollsters live in London and hang out with people who will vote IN and can’t imagine you winning so they might easily tweak their polls in a way they think is making them more accurate but is actually fooling themselves and everybody else.’ This is what happened. Almost all the pollsters tweaked their polls and according to Curtice all the tweaks made them less accurate. Good physicists are trained to look for such errors. (I do not mean to imply that on 23 June I was sure we would win. I was not. Nor was I as pessimistic as most on our side. I will write about this later.)

VICS allows data to be input centrally (the electoral roll, which in the UK is a nightmare to gather from all the LAs) and then managed at a local level, whether that be at street level, constituency or wider areas. Security levels can be set centrally to ensure that no-one can access the whole database. During the campaign we used VICS to upload data models which predicted where we thought Leave voters were likely to be so that we could focus our canvassing efforts, which was important given limited time and resources on the ground. The model produced star ratings so that local teams could target the streets more likely to contain Leave voters.

Data flowed in on the ground and was then analysed by the data science team and integrated with all the other data streaming in. Data models helped us target the ground campaign resources and in turn data from the ground campaign helped test and refine the models in a learning cycle – i.e. VICS was not only useful to the ground campaign but also helped improve the models used for other things. (This was the point of our £50 million prize for predicting the results of the European football championships, which gathered data from people who usually ignore politics – I’m still frustrated we couldn’t persuade someone to insure a £350 million prize which is what I wanted to do.) In the official 10 week campaign we served about one billion targeted digital adverts, mostly via Facebook and strongly weighted to the period around postal voting and the last 10 days of the campaign. We ran many different versions of ads, tested them, dropped the less effective and reinforced the most effective in a constant iterative process. We combined this feedback with polls (conventional and unconventional) and focus groups to get an overall sense of what was getting through. The models honed by VICS also were used to produce dozens of different versions of the referendum address (46 million leaflets) and we tweaked the language and look according to the most reliable experiments done in the world (e.g. hence our very plain unbranded ‘The Facts’ leaflet which the other side tested, found very effective, and tried to copy). I will blog more about this.

These canvassing events represented 80-90% of our ground effort in the last few months, hence some of the reports by political scientists derived from Events pages on the campaign websites, which did not include canvassing sessions, are completely misleading about what actually happened (this includes M Goodwin who is badly confused and confusing, and kept telling the media duff information after he was told it was duff). There was also a big disinformation campaign by Farage’s gang, including Bone and Pursglove, who told the media ‘Vote Leave has no interest in the ground campaign’. This was the opposite of the truth. By the last 10 weeks we had over 12,000 people doing things every week (we had many more volunteers than this but the 12,000 were regularly active). When Farage came to see me for the last time (as always fixated only on his role in the debates and not the actual campaign which he was sure was lost) he said that he had 7,000 activists who actually did anything. He was stunned when I said that we had over 12,000. I think Farage et al believe their own spin on this subject and were deluded not lying. (Obviously there was a lot of overlap between these two figures.) These volunteers delivered about 70 million leaflets out of a total ~125 million that were delivered one way or another.

While there were some fantastic MPs who made huge efforts on the ground – e.g. Anne Marie Trevelyan – it was interesting how many MPs, nominally very committed to Leave, did nothing useful in their areas nor had any interest in ground campaigning and data. Many were far more interested in trying to get on TV and yapping to hacks than in gathering useful data, including prominent MPs on our Board and Campaign Committee, some of whom contributed ZERO useful data in the entire campaign. Some spent much of the campaign having boozy lunches with Farage gossiping about what would happen after we lost. Because so many of them proved untrustworthy and leaked everything I kept the data science team far from prying eyes – when in the office, if asked what they did they replied ‘oh I’m just a junior web guy’. It would have been better if we could have shared more but this was impossible given some of the characters.

VICS is the first of its kind in the UK and provided new opportunities. It is, of course, far from ideal. It was developed very quickly, we had to cut many corners, and it could be improved on. But it worked. Many on the ground, victims of previous such attempts, assumed it would blow up under the pressure of GOTV. It did not. It worked smoothly right through peak demand. This was also because we solved the hardware problem by giving it to Rackspace which did a great job – they have a system that allows automatic scaling depending on the demand so you don’t have to worry about big surges overwhelming the system.

There were many things we could have done much better. Our biggest obstacle was not the IN campaign and its vast resources but the appalling infighting on our own side driven by all the normal human motivations described in Thucydides – fear, interest, the pursuit of glory and so on. Without this obstacle we would have done far more on digital/data. Having seen what is offered by London’s best communications companies, vast improvements in performance are clearly possible if you hire the right people. A basic problem for people in politics is that approximately none have the hard skills necessary to distinguish great people from charlatans. It was therefore great good fortune that I was friends with our team before the campaign started.

During the campaign many thousands of people donated to Vote Leave. They paid for VICS. Given we spent a lot of money developing it and there is nothing equivalent available on the market and Vote Leave is no more (barring a very improbable event), we thought that we would make VICS available for anybody to use and improve though strictly on the basis that nobody can claim any intellectual property rights over it. It is being made available in the spirit of the open source movement and use of it should be openly acknowledged. Thanks again to the thousands of people who made millions of sacrifices – because of you we won everywhere except London, Scotland and Northern Ireland against the whole Government machine supported by almost every organisation with power and money.

I will write more about the campaign once the first wave of books is published.

PS. Do not believe the rubbish peddled by Farage and the leave.EU team about social media. E.g. a) They boasted publicly that they paid hundreds of thousands of pounds for over half a million Facebook ‘Likes’ without realising that b) Facebook’s algorithms no longer optimised news feeds for Likes (it is optimised for paid advertising). Leave.EU wasted hundreds of thousands just as many big companies spent millions building armies of Likes that were rendered largely irrelevant by Facebook’s algorithmic changes. This is just one of their blunders. Vote Leave put our money into targeted paid adverts, not buying Likes to spin stories to gullible hacks, MPs, and donors. Media organisations should have someone on the political staff who is a specialist in data or have a route to talk to their organisation’s own data science teams to help spot snake oil merchants.

PPS. If you are young, smart, and interested in politics, think very hard before studying politics / ‘political science’ / PPE at university. You will be far better off if you study maths or physics. It will be easy to move into politics later if you want to and you will have more general skills with much wider application and greater market value. PPE does not give such useful skills – indeed, it actually causes huge problems as it encourages people like Cameron and Ed Balls to ‘fool themselves’ and spread bad ideas with lots of confidence and bluffing. You can always read history books later but you won’t always be able to learn maths. If you have these general skills, then you will be much more effective than the PPE-ers you will compete against. In a few years, this will be more obvious as data science will be much more visible. A new interdisciplinary degree is urgently needed to replace PPE for those who want to go into politics. It should include the basics of modelling and involve practical exposure to people who are brilliant at managing large complex organisations.

PPPS. One of the projects that the Gove team did in the DfE was funding the development of a ‘Maths for Presidents’ course, in the same spirit as the great Berkeley course ‘Physics for Presidents’, based on ideas of Fields Medallist Tim Gowers. The statistics of polling would be a good subject for this course. This course could have a big cultural effect over 20 years if it is supported wisely.