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More or Less
The maths of spies and terrorists
00:24:07
After the killing of a British soldier on the streets of Woolwich in London, it that...
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- [00:00]
Tim Harford
Thank you for downloading More or Less from the BBC. This is the version of the programme first broadcast on BBC Radio 4. Here's Tim Halford.
- [00:09]
Hello and welcome to More Or Less the programme which refreshes the numbers other programmes cannot reach. This week, this man is planning to make an unusual gift and he wants to know how much it's worth.
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Jason
I think we were actually by the pool in Italy and I said, I think I want to give away my kidney.
- [00:27]
Tim Harford
But first, following the killing of drummer Lee Rigby in Woolwich, the security services have been criticised because it transpires the suspects were known to them. Surely they could have been followed around. Shouldn't the security services be paying more attention to people who are known to be dangerous? Parliament's Intelligence and Security Committee is to investigate the case. Well, I've been speaking to the former head of MI5, Dame Stella Rimmington. Is this sort of criticism, I asked, reasonable?
- [00:55]
Dame Stella Rimmington
Well, if the implication of that criticism is that the security service should know everything that everybody who is known to them is doing every hour of every day, then it clearly isn't reasonable. I mean, I don't know how many suspects there are, but let's say, and one has read this in the newspaper, that there are about 2,000. And if you want to follow an individual around 24 hours a day, you would probably need a team of, let's say, six people, and that's probably under egging it with cars, so that they would be ready either to follow this person away if he went out the car or to leap out the car and follow him if he was on foot. But that team of people would work for, let's say, six hours a day. So you need to do it 21st day, you need three shifts that for one person and then you might need other people, static surveillance people sitting in a house, for example, to alert these people when the person was coming out. Because you can't just sit outside the house, you've obviously got to sit somewhere else. Then you've got to have a control centre who is obviously receiving the information coming in from these people and directing them. Then all that information has to go to a desk officer who is in charge of the case. So you're building up a large group of people and we're only talking about one of these manifold suspects we hear about and doing that 24 hours a day, seven days a week. While you're the mathematician, you do the sums. It's an awful lot of people.
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Economist (possibly Tim Harford or another economist guest)
I'm an economist and that sounds expensive. So we're talking about tens of thousands of people. Clearly.
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Dame Stella Rimmington
Clearly.
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Economist (possibly Tim Harford or another economist guest)
One question that occurred to me is we sometimes talk about this list of suspects as though the bad guys are definitely on the list and there's nobody on the list by mistake.
- [02:48]
Dame Stella Rimmington
The people who will be on the list, if there is a list, will be people who have, for one reason or another, come to the attention of the security services either because they've done something else or some source of information has reported these people, or they've been associating with other people who are already known to be bad guys. But there are degrees of potential involvement. And the whole art of the intelligence operations is to try and identify the people who are most likely to do something and focus their attention on those people. And of course that means that you might sometimes get it wrong. And everybody who knows anything about intelligence says there's no such thing as 100% certainty.
- [03:34]
Tim Harford
With intelligence as a matter of simple economics, then it's not possible to follow every suspicious character around the clock. But even if we could, that would present mathematical problems of a different kind. Imagine that we had unlimited resources to spy on bad guys. Or more plausibly imagine that the intelligence services could use computers to monitor everyone's email and phone lines and spot trouble.
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Professor Elemental
So professor, we turn to you. Designed for us a machine that can detect the character of a rogue even when he's concealed by a huge crowd of decent law abiding countrymen. Yours, etc, etc sincerely, and so forth. The home office. Of course it can be done. I'll simply recalibrate my needle in a haystack machine. I'll change it so it searches for ne' er do wells in the data
- [04:21]
Tim Harford
array rather than Professor Elemental there, musician and comic genius from the intertubes. Since we weren't sure where to reach him by telegram, we called another Professor Howard Wehner, a professor of statistics at the Wharton School of the University of Pennsylvania. He's imagined something much like Professor Elemental's great machine for catching villains. Unlimited wiretapping tied to ADV voice analysis software on everyone's telephone line that could detect would be terrorists within the utterance of the first three words on the phone, it's 99% accurate. And there's just one tiny problem.
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Professor Howard Wehner
We said. Suppose there are 3,000 terrorists in the United States. If the software is 99% accurate, you would be able to pick up almost all of them, 99% of them. However, if you're listening to everybody, if they're listening to all 300 million of us, 1% of those are going to be picked up by mistake. 1% of 300 million is 3 million. And so, mixed in with the 3,000 true terrorists that you've identified are going to be 3 million completely innocent people who are now being sent off to Guantanamo Bay. And so for every terrorist you have on Guantanamo, you've got 999 innocent but really pissed off people.
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Tim Harford
The problem arises because terrorists are rare. The bad news is that in reality, your terrorist detector will be nowhere near 99% effective. The good news, on the other hand, is that security services are much more selective in who they monitor. If you narrowed your target population to the point that the prevalence is up to, say, one actual terrorist per hundred people wiretapped and assume a 90% effective test, even then, the chance of a false positive is still high. When someone does trigger an arrest, Howard Waner says, The odds are 11 to 1 that they're not a terrorist, as Professor Elemental may be about to discover.
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Professor Elemental
Dear Professor, I enclose a photographic plate showing three members of the Bournemouth Amateur Dramatic Society following their arrest and public flogging. It transpired they were only engaged in a performance of the Pirates of Penzance. It seems the machine mistook their stage attire for that of undesirables or scallywags.
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Tim Harford
Professor Elemental, who has since abandoned such exploits and lent his support to the open rights group which is campaigning against the draft communications bill. If passed, that bill would require Internet and phone companies to keep records of UK citizens phone and Internet use, although that now looks less likely after Nick Clegg, the Deputy Prime Minister, withdrew his support for the measure. Still, there's no getting away from the use of algorithms to find patterns. They're used everywhere from Tesco club cards to credit scores.
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Professor Louisa Moore
Of course, the problem of a false positive in a Tesco club card data is very different from the problem of a false positive in a national security question.
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Tim Harford
That's Professor Louisa Moore from the University of Durham in the uk. She's been studying how algorithms can be used to spot suspicious patterns in the data. For instance, in information on air passengers, these patterns might be used to identify terrorists.
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Professor Louisa Moore
So one example of that might be to travel to Pakistan and to spend three months there before returning. And actually, you may already begin to think about how the algorithms used to detect possible risky connections might be adapting. For example, post Boston, there may now be more attention in the US to travel to particular parts of the world, perhaps including Chechnya and Dagestan. We could imagine post Woolwich that there might be greater attention in the refining of algorithms to think about patterns of travel and links to deportation. But of course, the question remains, though, this is an automated system, it's using data from past events. So our research is suggesting that the tuning of the algorithm reflects almost always past events.
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Economist (possibly Tim Harford or another economist guest)
So the algorithms are always fighting the
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Professor Louisa Moore
last war, in a sense. Yes. Yes, they are.
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Tim Harford
Professor Louisa Moore. It's certainly not an easy task, as Dame Stella Rimmington explains.
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Dame Stella Rimmington
Now, it seems to me, looking at this entirely from the outside, that what they're dealing with is largely a group of individuals with certain views, not necessarily directed from any headquarters. And this is a much, much more difficult target, I think, than the targets of the old days.
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Economist (possibly Tim Harford or another economist guest)
Just looking forward, people have got very excited about big data and we can track people's phones, we can read their emails. In principle, we can do all of these things and it doesn't take manpower to do it, you just ask a computer to do it for you. Do you see this as a very useful tool or as a terrible threat to individual liberty? Or actually as neither. It's just a lot of hype about something that's going to be a side issue.
- [09:16]
Dame Stella Rimmington
Well, I think the communications data bill that was designed to allow the intelligence services to know more about our emails and our use of modern communications. As I see it, that was merely a way of bringing up to date the powers which the intelligence services already have to intercept our old fashioned communications. I mean, they can now intercept our telephone communications if they can get a warrant from the Home Secretary to do it. They can plant microphones to overhear what we're saying in rooms, etc. And they need, obviously, you know, to be able to do the same thing with modern forms of communication. If you have too much information, of course, you suffer from what the Stasi in eastern Germany suffered from, which is an overdose of information. And intelligence services can strangle themselves if they have too much information because they can't sort out what they need to know and what they don't need to know, etc. So in all this search for information, you've got to be pretty focused and targeted.
- [10:19]
Tim Harford
Dame Stella Rimmington, formerly the head of MI5 and a loyal more or less listener, worrying news on the front page of the Daily Telegraph on Wednesday. If you take 15 people having elective surgery in any English hospital, including relatively common procedures such as hip replacements, tonsillectomies and hernia operations, one of those 15 will be dead within the month. It's an astonishing mortality rate of 6.7%. That means that in the three years. Between 2008 and 2011, over a quarter of a million people have died in England shortly after surgery. It's quite astonishing. Or alternatively, the Telegraph put the decimal point in the wrong place. The 30 day mortality rate after elective surgery in English hospitals isn't 6.7%, it's 0.67%. One person in every 150. Something of a relief and something of a trend for the Telegraph, which made a similar front page error almost exactly three years ago, telling us that the cost of funding public sector pensions was almost £4,000 per household per year. The Telegraph thought The figure was £3,620 and rounded up, but the true figure was 1/10 that, £362, which funnily enough, is actually smaller than the amount by which the Telegraph had decided to round up. The Telegraph's web version of the article was updated without noting the original mistake, and I'm not surprised they were embarrassed. To misplace one decimal point might be considered a misfortune. To misplace two looks like carelessness. You're listening to More or Less with me, Tim Harford. Now let's return to the subject of NHS surgery, but dapple it with a little Italian sunshine. Why not?
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Jason
I think we were actually by the pool in Italy and I'd been thinking about it and I said, I think I want to give away my kidney.
- [12:21]
Tim Harford
This is loyal listener Jason, a nurse in the nhs. Jason is joining a small and special group of people in the uk. He's becoming an altruistic, non directed kidney donor. That means that out of the goodness of his heart, he's volunteering for an operation to donate one of his kidneys to a stranger whom he will probably Never meet. Around 175 people have done this since new rules were introduced to allow it back in 2007. Now, Jason contacted us via more or lessbc.co.uk because he had a question.
- [12:55]
Jason
I want to know how much for the NHS my kidney is worth?
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Tim Harford
How much does it cost to transplant a kidney and keep it working compared to the alternative, which is kidney dialysis? Here's Keith Rigg, a consultant transplant surgeon at Nottingham University Hospital Trust, who's working on a committee drawing up a national tariff for adult kidney transplants. I asked him how much they cost.
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Keith Rigg
A kidney transplant costs around 18,000 pounds for the first year, which includes the cost of the transplant operation, all the investigations, the follow up and the drugs. Once a patient gets to a year after a transplant, then it will then cost £5,000 every year subsequently, and then again, that will include the follow up and the drugs. What that price doesn't include is the workup cost, and that varies from patient to patient. But it's estimated that it probably costs around £5,000 to have something worked up and to be maintained on the national waiting list.
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Tim Harford
So that's how much it costs to get the recipient up and running with a second hand kidney. But what about the donor who must get a thorough check up, testing for compatibility and of course, a separate operation and aftercare? Mr. Rigg estimates that that cost is an additional £5,000. Totting it all up, we reckon that a kidney transplant costs 28,000 pounds in the first year, plus 5,000 pounds a year after that. Around 73,000 pounds in total if the kidney lasts 10 years. Kidney dialysis, on the other hand, costs 30,500 pounds a year for each patient. It's more expensive than a transplant, even in the year that the transplant takes place. Now, there are complications to this story. Only 3 in 10 would be donors make it through screening, for instance. So there are other costs for each person who's screened out. And of course, nobody knows in advance how long a kidney will last. One kidney in 10 fails or is rejected by the recipient's body in less than a year. But six out of 10 kidneys last for at least a decade. And those figures include kidneys from dead donors, which don't tend to last as long. Jason's kidney will probably last at least 10 years and perhaps much longer. So the NHS could easily save a quarter of a million pounds from Jason's donation. Possibly less, but quite likely more. As an economist, I'm not just interested in the costs and benefits to the nhs. What about the costs and benefits to the two people at the heart of the transplant, the donor and the recipient? Well, here's someone who understands that better than most. Jason himself. He works on a surgical ward and he often comes into contact with patients who have kidney failure.
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Jason
People on dialysis have to come in three times a week for treatment. If they go anywhere on holiday, they have to arrange dialysis when they're away, they have frequent admissions to hospital, they have frequent infections, they're very prone to other illnesses, and it's generally quite a limited lifestyle that they're allowed to lead.
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Tim Harford
Receiving a kidney therefore eliminates these problems, leading to a much improved quality of life and longer life expectancy. But what about Jason? What's the cost to him?
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Jason
I've been told that for 24 hours I'll be on a morphine pump that I can control. I'd expect to be in three to four days and then up to six weeks recovery for myself. The main thing is sort of about the discomfort and pain and I think that I'll be able to cope with it. And in terms of risk for the future, health for me, I've had through the process, sort of fairly clean bit of health at the moment, so I know that I've not got anything immediately underlying and it's a risk that I'm willing to take.
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Tim Harford
The National Health Service suggests that the risk of death for a kidney donor is around 1 in 3,000, which is low, unless, of course, the Daily Telegraph gets involved, in which case it could increase tenfold at the stroke of a journalist's calculator. So we've looked at the economic benefits for the NHS and the health benefits for the recipient of the kidney. Well, now here's a who should enjoy those benefits? Kidney donors are allowed to donate to a specific person, usually a family member or close friend. But people like Jason, who are donating to strangers, aren't allowed to attach strings to that gift. The choice is made by the nhs. But how? There are some simple considerations. Children tend to get a high priority, for example. But the NHS also has to think about compatibility. Not every patient is compatible with every kidney and some people get stranded on the waiting list for far longer than average. When the right kidney comes up, then such people will tend to be prioritized. One way around the compatibility problem is to set up kidney exchanges. Imagine you had a close friend with kidney failure and you were willing to give them your kidney, but you weren't compatible. One possibility is to find another pair in a similar situation and swap the donated kidneys. You donate to the other kidney patient while the other donor gives a kidney to your friend. The UK runs a kidney exchange system like this, where up to three pairs of people can exchange kidneys. The tricky thing is that everyone has to have their operation on the same day to make sure nobody backs out. Jason decided not to donate into that pool. He's giving a kidney. The least he wants is to be able to arrange the date of the surgery. Now, in the United States, this process of kidney exchanges has gone still further. So an altruistic donor such as Jason could could donate to a recipient. A friend of that recipient would then donate to a second recipient. A friend of that second recipient would then donate to a third recipient, and so on and so on over a period of months. A never ending chain of donations. In the uk, the NHS only allows short chains of two donations. So should donors like Jason be donating to these kidney pools, possibly triggering many donations, rather than simply helping the highest priority compatible patient on the waiting list? I asked Lisa Burnap, lead nurse for the NHS's living donation scheme, why not have longer chains?
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Lisa Burnap
We know the things that matter to patients and the things that make a difference to people wanting to be part of the scheme, and it's having confidence that it works. So we've run this scheme for just about a year and we will be looking at when we can then go on to the next stage of the longer chains.
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Tim Harford
And the key thing with the chains
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Economist (possibly Tim Harford or another economist guest)
is that the operations don't have to be simultaneous once you move to a chain, or is that just.
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Lisa Burnap
In the States, that's a different system. So they do run non simultaneous chains and you will.
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Tim Harford
And they can be really long.
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Economist (possibly Tim Harford or another economist guest)
They can be 30, 40, 50 people
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Lisa Burnap
and they're staggered over a period of months. And it's one of the things, obviously, that we need to consider here. Very best.
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Tim Harford
This sounds really cool.
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Economist (possibly Tim Harford or another economist guest)
One altruistic donor triggers 50 donations.
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Tim Harford
That's amazing.
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Lisa Burnap
It does. What we're not clear about, if you actually delve into the detail of that, is to whether or not overall, you achieve more transplants. I think that the jury's still out on that.
- [19:33]
Tim Harford
Lisa Burnap of NHS Blood and Transplant. And I'm pleased to say that since we recorded our interview with Jason, he's had his operation and he tells us that both he and the recipient are recovering. Well, you're listening to More or Less. I know we heard from the Chancellor of the Exchequer last week, but I just can't wait a moment longer to hear more about his plans to save taxpayers money.
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Chancellor of the Exchequer
These plans don't involve the privatisation of the criminal justice system. They do propose things like making sure that we use much less paper. The Crown Prosecutions Service Print 1,000,000 pieces of paper every day. Now, in an age of the Internet and emails, that surely isn't necessary.
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Tim Harford
A million pages a day is a lovely round number, which is always nice, but is it a big number? The Crown Prosecution Service deals with about 1.5 million cases a year, including both court cases and pretrial decisions. We're Talking about roughly 250 pages printed out per case, which doesn't seem an impossibly wasteful amount. How much would it cost? We used retail price quotes to estimate that those 365 million pages would cost around £2 million for paper and another £5 million for printer ink, for a total of £7 million. Now, that's less than five pence per case, and it's probably an overestimate, since we had hoped that the purchasing department at the Crown Prosecution Service would be able to secure a bulk discount. And surely nobody expects the CPS to print nothing at all in future. And surely, too, Nobody expects a PayPal assistant to be free. The currently available ones cost a pretty penny. But even accepting the idea of saving the full 7 million pounds on printouts, that is, alas, just 1% of the total 680 million pound budget reduction the Department of Justice is supposed to produce. The first principle of more or less always ask if it's a big. Over the centuries, many top mathematicians have tried and failed to solve some of the great mathematical challenges. It took 100 years to prove the Poincare conjecture. That was quick when compared to the 358 years it took to solve Fermat's last theorem. However, recently on BBC one's the Apprentice program, we discovered a new maths conundrum for the 21st century. Doing the sums, company director Alex.
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Alex
I'm just working out 17 pounds and we've got to divide that by two, which is going to be. Oh, so it's so simple, I'm just forgetting it now, which is, yeah, get a calculator out. But I work it, it's going to be £25 50, so that's going to then be £21, 25. And that is for 50 liters just in two. But you know what, then working out now divide by two. What? Total of 40? £24.75. But I'll shake your hand if you want to do 40 quid.
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Tim Harford
Dividing 17 by 2. It seems impossible, a challenge to defeat the finest brains in mathematics. But there's just one chance. I know a man who might be up to solving the riddle. The man who instilled in me my childhood love of mathematics, TV's Johnny Ball. It's a long shot, but if there's anybody out there who can figure out how to divide 17 by 2, maybe it's him.
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Johnny Ball
Right, dividing 17 by 2. Well, in essence, all even numbers divide evenly by 2 very easily. So let's go one less and call it 16. Half of 16 is 8. And now you've taken one off, so you. Half of 1 is a half. So the half of 17 is 8 and a half. Half of 17 pounds is 8 pounds, 50.
- [23:28]
Tim Harford
Johnny Wall Hero. And that's all we have time for this week. But you can download more editions of the programme via our website BBC.co.uk More or less the website is also the place to read more or to send us your comments and your questions until we return next week or for Daily Telegraph journalists in 10 weeks time.
- [23:51]
Goodbye more or less was presented by Tim Harford. The producer was Ruth Alexander. The program is made in association with the Open University. You can Download many more BBC Radio 4 programs for free. Find these at BBC Co UK Radio 4.