Monday, 28 November 2016

Newcomb's Problem

This appeared in the Guardian recently.
The problem: two closed boxes, A and B, are on a table in front of you. A contains £1,000. B contains either nothing or £1 million. You don’t know which. You have two options: Take both boxes, Take box B only. You keep the contents of the box/boxes you take, and your aim is to get the most money.

But here’s the thing. The test was set by a Super-Intelligent Being, who has already made a prediction about what you will do. If Her prediction was that you would take both boxes, She left B empty. If Her prediction was that you would take B only, She put a ₤1 million cheque in it.

Before making your decision, you do your due diligence, and discover that the Super-Intelligent Being has never made a bad prediction. She predicted Leicester would win the Premier League, the victories of Brexit and Trump, and that Ed Balls would be eliminated from Strictly Come Dancing. She has correctly predicted things you and others have done, including in situations just like this one, never once getting it wrong. It’s a remarkable track-record. So, what do you choose? Both boxes or just box B?
This is supposed to puzzle people. And puzzles that don’t seem to have a decent answer usually arise because they aren’t a decent question. Anyway, it originated with a physicist - a descendent of the brother of the famous Newcomb - and was popularised by Robert Nozick, and then Martin Gardener at the Scientific American. See where I’m going with this?

Suppose I say to a bookie: if I think Fancy Girl will win the 2:30, I will bet £100, and if I think Blue Boy will win, I will bet £50. His reply would be: all right which is it? I can’t place a bet that’s conditional on what I think will happen: the whole point of a bet is to pick one of the outcomes. The closest I can get to making a conditional bet is to put money on each outcome, and if the bookies are doing their job well, I will lose doing that.

What you want to do is this:
If I chose Box B alone, she will have predicted that and put the cheque in it. But if I chose both boxes, she will have predicted that and not put the cheque in. So I should choose Box B.
This assumes what the Special Theory of Relativity tells us cannot happen, that a future event can cause a past one. So let’s try this:
If she predicted that I would chose Box B alone, then she put the cheque there, and I should choose it. If she predicted I would choose both boxes, then she wouldn’t have put the cheque in Box B, so I should choose both boxes, because at least I’ll get £1,000.
The catch is that doesn’t tell you what to do, since you don’t know what she predicted and so can’t detach the consequents from the conditionals. The next one is silly...
If she predicted that I would chose Box B, then she put the cheque there and I should choose it. If she predicted I would choose both boxes, then she wouldn’t have put the cheque in Box B, so I should not choose both boxes, only Box B
That sounds good, but since there’s no cheque in Box B, you get nothing. But what you were going to do was this:
Suppose I choose Box B. Since her predictions are perfect, she predicted that and the cheque is there. But if I choose both boxes, again since her predictions are perfect, the acheque isn’t there. So I choose Box B.
This doesn’t require backwards-causality, but it does require someone to ensure the predictions are perfect. Russian hackers, presumably.(*) What we’re told is that she’s good, not that the game is rigged.(**) Now try this:
If she predicts Box B and I choose Both, I get the cheque. If she predicts Both and I choose B, I get nothing. If she predicts Both and I choose Both, I get £1,000. If she predicts B and I choose B, I get the cheque. So if she predicts B, I get the cheque no matter what I do, and if she predicts Both I lose if I choose B. So I take Both Boxes.
Those are the actual options assuming free will and imperfect predictions. The only way you get confused is to assume a) that her predictions are causal, or b) that your actions are temporally-backwards causal, or c) that someone is rigging the co-incidence between her predictions and your actions.

So how seriously you take her past performance on predictions? This starts to make it sound like we might want to use Bayesian Inference, and indeed the Wikipedia entry for this problem lists David Wolpert and Gregory Benford as having a Bayesian analysis that shows that the different arguments arise from different models of the assumptions, so that there isn’t a real paradox, just an old-fashioned ambiguity.

The real reason you choose both boxes In the Guardian’s example is this: it’s the only way you get anything. She’s a woman: the point was to get you to choose Box B, and now you have, by Briffault’s Second Corollary, she doesn’t have to give you the money, so she cancelled the cheque (***).

(*) Topical political joke.
(**) Another topical political joke.
(***) Robert Briffault

Thursday, 24 November 2016

Thursday, 17 November 2016

A Mathematical Joke

Why doesn't the Hamiltonian (operator) live in the suburbs?

Because it doesn't like to commute!


We're here all week folks!

(This was told me by a colleague at work, who says he made it up at university.)

Monday, 14 November 2016

The Sadness of Sixties Songs

I barely listen to the charts now, but the last time I did, most of the songs seemed to be about a) getting laid, b) getting high, c) how wonderful the singer thought his unstable, overweight girlfriend was. Or maybe I just heard too many songs written by Keisha and James Blunt.

Because we had real songs back when I was a lad at school. Oh yes. Like the Everly Brothers’ Wake Up Little Suzy, in which the singer tells his girlfriend that they've overslept and their reputations are shot. Or Gary Puckett singing, on family US TV, about nearly getting tricked by some jail-bait into a statutory story.

Like that would get past the legal department now.

But mostly the songs were about unrequited love, loneliness, heartbreak and death. Ode to Billy Joe was a chart song and Bobby Gentry is loved for it. It's about the suicide of the singer's boyfriend and the callous reactions of her family.

Real family entertainment. These weren't indie cult songs. These were concert-hall filling acts whose records sold in the hundreds of thousands. This was what played on the radio and the juke-box. Mainstream.

The Seekers, a hugely popular Australian band, and as apple-pie as you could wish. Island of Dreams is about someone trying to forget a love affair on “the island of dreams”, and life in the real world cannot compare to the life there.

And as for the boppy escapism of A World of Our Own?

Traffic’s first hit single was Paper Sun in May 1967.

It’s the story of a young girl who winds up abandoned on the beach after a summer affair with a young man who spends all her money. That’s almost as upbeat as John Boorman’s 1965 masterpiece Catch Us If You Can, written by Peter Nichols (who went on to write other upbeat movies such as Five Easy Pieces), and is nowhere near as much fun as the song. Except that song isn’t really about fun, since the second verse says
Now we gotta run, mmmm-mm-mm
No more time for fun, mmmm-mm-mm
When we're gettin' angry, mmmm-mm-mm
We will yell with all of our might
Despite that, it reached number 5 in the UK and number 4 in the US in 1965.

One of the brightest, shiniest songs there is, The Happening, sung by The Supremes, was actually about the moment you find out that life is not a fairy tale, but is a little bit of a disappointment. That’s “the happening”. Check the lyrics.

Exhibt Two: The Hollies’ Bus Stop for one. They balanced that with the breezy Carrie Anne, who only went out with the older boys, had no time for the pining singer and has the immortal lines: “you lost your charm as you were ageing / where is your magic? Disappearing”. As for Stop Stop Stop, it’s about a man over-reacting to a stripper and being thrown out of the club. And in case you think Look Through Any Window is an upbeat celebration of everyday life, remember that the singer is inviting us to look through the window, so that we are on the inside looking out, and the singer is asking "Where do they go? / Moving on their way / Walking down the highway / And the by-way". Real life is out there, and we're behind the window.

What they hey was going on?

Regret, loss, sadness, emotionally distant, compromised lives lived far from an island of dreams are adult experiences. Don’t Sleep In The Subway is about a reasonably stable grown-up telling a more volatile one that whatever the row was over isn’t worth sleeping in the subway or standing in the pouring rain.

These were songs for adults dressed up with bright tunes and some sparkling misleading imagery. Films, songs and novels were still aimed at adults, since they made up the largest market. I grew up then, and one thing we were clear on: being a grown-up was no fun.

One function of culture is to provide us with emotions and thoughts we would not ordinarily have in our daily lives. If we are caught in a dull routine under grey skies, a sad song about an Island of Dreams can be as much a support or a means of escape as a jolly tune. If not more. It says there is something out there that is more and better, even if it is out of reach, and the idea of it can provide hope. If it is dangerous to feel sad about our actual lives, we can more safely feel sad about the distance between our lives and something easier and more pleasant. Nobody wants to be a full-time beach-bum, but if it's only for one summer, how bad could it be, when reality is a long bus-ride to a job in the town's only department store? At the end of Catch Us If You Can, the advertising mogul says to the runaway model "I got here in the end", and the model's reply is "Yes, but you missed the journey". If dull adulthood awaits us all, can't we have some fun on the way there?

And then we have Goffin and King’s 1966 song Going Back. Sung by Dusty Springfield, it takes on an emotional depth far beyond the music and lyrics.

Dusty sings with sadness and vulnerability that says she is choosing to return to the simpler feelings and truths of childhood because the compromises and isolation of adulthood have exhausted her. That's not the song that Carole King wrote. Going Back says that adulthood is not worth it. It's the song of a young person who has taken a look, had a brief taste, and cannot see any benefits. We cannot avoid growing older, but we can stay young in heart and mind, and see the world in simpler terms. That way we "can play the game of life to win" and "live our days / instead of counting our years". That was how my generation felt, and we were barely teenagers.

It turns out that the dreary adulthood of the Golden Age depends on some very specific economic conditions: near-full employment, job security, some opportunity for promotion, seniority-based pay scales, and the promise of a decent pension. With those you can trap people. And when everyone is living like that, one song can speak to millions. Under the present exact conditions of really existing Capitalism, we are broken up into economic micro-segments, each with its own fears and resources, each generating its own emotional needs and lacks, each unable to identify and act or feel in solidarity with the other, and each with its own special music to add to the highs and fill in the lows. One song cannot now speak to millions. But once it could.

Thursday, 10 November 2016

God Bless America - Viva Los Despicables!

I can remember Thatcher-Reagan. This feels like that, but it's about different things.

Thatcher-Reagan was about ideology, and May-Trump is going to be about practicality. Theresa May wants to go down in history as the ultimate professional politician, the first of a new breed, acting on behalf and in the interests of the electorate, not selling them out in the name of abstract elite ideals. Trump? Same thing.

This is about ending the rule of the technocrats and the dominance of a virtue-obssessed febrile liberalism driven by a hatred of regular (white) people. The Austrians have a Presidential election and the Italians are voting on constitutional reform in December. The Dutch have elections in March 2017, and the French start campaigning in April 2017 for elections in June 2017. There are more German State elections in the first half of 2017 and then a German General Election in October 2017 at the latest. By this time next year the European political world will look totally different and the EC technocrats  - the guys who, when it gets serious, tell lies - will look like 1980's hairstyles.

And it's around then that it will occur to everyone that the Brexit negotiations are not about what Britain gets and gives, but about what the new EU is going to look like.

And no matter what happens, capitalism will make money from it.

Monday, 7 November 2016

That Brexit Court Judgement Is All Just Part of The Plan

Are Teresa May and I the only people who understand what’s going on with the British political system and Article 50? Everyone is banging on about what a disaster it is that three judges have ruled that Parliament must vote, whereas that’s all part of the plan.

Of course the eurocrats wanted to rush the Conservatives into invoking A50 by royal prerogative. Then they could refuse to accept it at any point in the negotiations because their tame Euro Court had ruled on request that because the referendum was non-binding, the British Parliament had to vote on it. On the other hand, politics being what they are, May could not say that she wasn’t starting until Parliament had voted for it, because the arguments and posturing would have gone on for months, to be decided by a General Election. So by the same mechanism that gets some Private Members Bills through while others vanish, a legal action brought by a hairdresser and a banker gets fast-tracked and accepted. Because your barber knows who to call to start an action like this. Right? So now Parliament will have to vote, not because the Prime Minister has asked nicely but because the Law has told them to. How the MPs will vote is entirely up to their consciences and what the Whip’s Office decides.

The British negotiators will go into the room with a constitutionally solid backing and a remit to report everything to Parliament, who will then discuss it in public. This is the best thing that could happen to them. On the other side of the table is a Belgian lawyer who is used to having his negotiations covered by confidentiality clauses and has never had the press go after him. Any time he tries anything remotely dodgy, the British team can say that while they, no they can’t have secret talks, because they have to report the day’s proceedings to Parliament, and no they can’t do sell open borders for lower trade tariffs because the British people were quite clear they wanted border controls. The EU negotiators will have no such political support. They will have twenty-seven countries which have conflicting goals and will be unable to promise or deliver anything. The British negotiators will look like masters of decisiveness by comparison.

If anyone thinks that Britain is going to stop plundering the world of cheap labour and smart, socialised young people, they have to be crazy. Of course tourists, students and businessmen will be free to come to the UK. Of course builders and economics graduates who have job offers will be free to come to the UK. And more controversially for the workers who voted Leave, of course seasonal unskilled labourers will be let in. There’s no alternative in the short term. Who can’t come in for more than a holiday or a business trip? Anyone who doesn’t have a job.

It’s then up to the British government and British employers if they want to stop dumping large numbers of British-born people on the scrap-heap because it’s too much trouble to socialise them as children in schools and at work. The competitive advantage of Spain, Poland and a bunch of other countries is that they have better parents and better schools which raise better-socialised and more work-ready young people. That, bluntly, is not going to change in a generation.

Here’s what’s going to change: first, the UK will become legally sovereign again, EU laws won’t automatically apply and their courts won’t have jurisdiction; second, the UK will be legally able to secure its borders against un-wanted economic migrants and whomsoever else it deems undesirable; third, the UK will be be legally able to remove people it doesn’t want. Of course, none of the organisations responsible for any of this will have the practical capability to enforce it, so that Brick Lane will still be full of illegal Pakistani cooks and waiters, Midlands factories will still be staffed by under-paid temporary workers from Szeged and Cluj-Napoca, and gangmasters will continue to supply Norfolk farmers with cheap labour from farms around Starachowice. (If you care about bankers, sure, about fifty-seventy thousand jobs will leave the financial services sector in London, but almost none of those will be presently done by British people. All those Japanese and Indian banks will transfer their offices and staff to Frankfurt or Amsterdam.)

What no-one will tell you until they come to write their memoirs is that “everyone” in British politics and banking knew that the UK had to get out of the EU before the Euro destroyed it. There was no way of doing so without actually saying as much, which doesn’t bode well for any negotiations. So a reason had to be manufactured. The British political establishment had to stumble clumsily into Brexit. Which is way Nigel Farage and UKIP were treated as if they mattered. UKIP did get almost 13% of the votes in the 2015 election, even if that translated into only one MP. There was no reason to hold that referendum, but they did. And Remainers conducted a campaign of spectacular stupidity, doing the one thing guaranteed to turn the ornery British voter against them: they talked down to Leavers, and pulled Project Fear. Really? They couldn’t do better than that? Because I could. So could you. Saatchi’s certainly could have.

The catch is that “everyone” isn’t actually everyone. So a lot of people have to be brought onside. I’m surprised by how much allegedly smart people are still on the wrong side of history on this. I voted Remain, and I’m not ashamed to say it, and it took me less than an hour to understand what had happened. I’m with the Brexit because it’s going to happen and we had better get the best deal we can. Teresa May is with the Brexit because she’s a professional politician and negotiating a good deal is her job. If she does it well, she goes in the history books along with Margaret Thatcher. She’s been at the Home Office for several years and knows what the issues are. Oddly, the journalists and other Good People who are still deploring the Leave vote, and show it by their spin on the news, have not worked at the Home Office.

I’m writing this three days before the Trump-Clinton election. I think I know what’s going to happen, but I don’t want to bring down the wrath of the whatever from high atop the thing.