Skip to main content

The Golden Ticket: P, NP, and the Search for the Impossible – Lance Fortnow ***

There is good and bad news early on in this book about the P versus NP problem that haunts computing. The good news is that on the description I expected this to be a dull, heavy going book, and it’s not at all. Lance Fortnow makes what could be a fairly impenetrable and technical maths/computing issue light and accessible.
The bad news is that frustratingly he doesn’t actually tell you what P and NP mean for a long time, just gives rather sideways definitions of the problem along the lines of ‘P refers to the problems we can solve quickly using computers. NP refers to the problems to which we would like to find the best solution’, and also that he makes a couple of major errors early on, which make it difficult to be one hundred percent confident about the rest of the book.
The errors come in a section where he imagines a future where P=NP has been proved. This would mean you could write an algorithm to very efficiently match things and select from data. Fortnow suggests that our lives would be transformed. This is slightly cringe-making as fictional future histories often are, but the real problem is that he tells us that the algorithm would make it possible to do two things that I think just aren’t true.
First he says that from DNA you would be able to identify what a person looks like and their personality. Unfortunately, these are both strongly influenced by epigenetic/environmental issues. Anyone who knows adult identical twins (with the same basic DNA) will know that they can look quite different and certainly have very different personalities. And they will usually have been brought up in the same environment. Fortnow is forgetting one of the oldest essentials of computing – it doesn’t matter how good your algorithm is, GIGO – garbage in; garbage out.
The other, arguably worse error is that he says that it will be possible to have accurate weather forecasts going forward X days. This is so horribly wrong. He should have read my book Dice World. The reason you can’t predict the weather at all beyond about 10 days is nothing to do with the quality of the model/algorithm, it is because the system is chaotic. Firstly we just don’t know, and never can know, the initial conditions to enough decimal places not to deviate from the real world. When Lorenz first discovered chaos it was because he entered the starting values in his model to 4 decimal places rather than the 6 to which the model actually worked. It soon deviated from the previous run. We can’t measure things accurately enough. The other problem is that the weather system is so complex – hence the slightly misleading title of Lorenz’s famous paper Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? – that we can’t possible take into account enough inputs to ever have so good a model as to go forwards that far. Sorry, Lance, it ain’t going to happen.
For the rest, the first half or so of the book goes along pretty well, gradually opening up the nature of P and NP, the problems that are of interest and the ‘hardest’ NP complete problems. I found the main example, used throughout, a hypothetical world called Frenemy where everyone is either a friend or enemy of everyone else confusing and not particularly useful, but Fortnow gets plenty of good stuff in. After that it’s as if he rather runs out of material and it gets a bit repetitious or has rather tangential chapters.
Overall, despite the flaws, a much better and more readable book than I thought it was going to be – but probably best for maths/computing buffs rather than the general popular science audience.

Hardback 

Kindle 
Review by Brian Clegg

Comments

Popular posts from this blog

The AI Delusion - Gary Smith *****

This is a very important little book ('little' isn't derogatory - it's just quite short and in a small format) - it gets to the heart of the problem with applying artificial intelligence techniques to large amounts of data and thinking that somehow this will result in wisdom.

Gary Smith as an economics professor who teaches statistics, understands numbers and, despite being a self-confessed computer addict, is well aware of the limitations of computer algorithms and big data. What he makes clear here is that we forget at our peril that computers do not understand the data that they process, and as a result are very susceptible to GIGO - garbage in, garbage out. Yet we are increasingly dependent on computer-made decisions coming out of black box algorithms which mine vast quantities of data to find correlations and use these to make predictions. What's wrong with this? We don't know how the algorithms are making their predictions - and the algorithms don't kn…

Infinity in the Palm of your Hand - Marcus Chown *****

A new Marcus Chown book is always a treat - and this is like a box of chocolates: a collection of bite-sized delights as Chown presents us with 50 science facts that are strange and wonderful.

The title is a quote from William Blake's Auguries of Innocence: 'To see a World in a Grain of Sand, / And a Heaven in a Wild Flower, / Hold Infinity in the palm of your hand, / And Eternity in an hour.' It would seem particularly appropriate if this book were read on a mobile phone (so it would be literally in the palm), which could well be true for ebook users, as the short essays make excellent reading for a commute, or at bedtime. I found them distinctly moreish - making it difficult to put the book down as I read just one more. And perhaps another. Oh, and that next one looks really interesting...

Each of the 50 pieces has a title and a short introductory heading, which mostly give a feel for the topic. The very first of these, however, briefly baffled me: 'You are a third mus…

How to Invent Everything - Ryan North ****

Occasionally you read a book and think 'I wish I'd thought of that.' This was my immediate reaction to Ryan North's How to Invent Everything. The central conceit manages to be both funny and inspiring as a framework for writing an 'everything you ever wanted to know about everything (and particularly science)' book.

What How to Invent Everything claims to be is a manual for users of a time machine (from some point in the future). Specifically it's a manual for dealing with the situation of the time machine going wrong and stranding the user in the past. At first it appears that it's going to tell you how to fix the broken time machine - but then admits this is impossible. Since you're stuck in the past, you might as well make the best of your surroundings, so the aim of the rest of the book is to give you the knowledge you need to build your own civilisation from scratch.

We start with a fun flow chart for working out just how far back in time you are…