Category Archives: Critical Thinking

How Not To Be Wrong by Jordan Ellenberg

Review: How Not To Be Wrong by Jordan Ellenberg (Penguin, 2014)

How Not To Be Wrong by Jordan Ellenberg‘Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.’

Yep, Jordan Ellenberg sure is keen about his chosen field of study. The imagery described above, guaranteed to make any nerd tremble at the knees, is a perfect precis of his current release, How Not To Be Wrong: The Power Of Mathematical Thinking. The objective of the book is twofold. Firstly he’s addressing the age-worn question, posed in best whiny-student voice, “But what will I ever use algebra for after school?” Secondly it’s asking us to change our outsider view of mathematics, to see it not as a field entirely concerned with black and white, truth and falsity but as one which specialises in probabilities, the grey areas between right and wrong where politicians fear to tread.

How Not To Be Wrong takes a fairly comprehensive journey through modern maths, organised as a series of stops in fairly wide-ranging sub-fields which, despite our protestations to the contrary, impact our daily lives in ways we rarely imagine. For example, the topic which opens the book is a mixture of probability and expectation. Ellenberg piques our interest with a real-life puzzle posed to a team of boffins during WW2. Aircraft returning from missions were examined on landing and the bullet-holes in various parts of their bodies logged. The top brass were anxious to lose as few planes as possible and this meant providing armour but heavy metal plating on a lightweight aircraft means a trade-off in terms of speed and maneuverability. So, where to put the armour for maximum effect?

The data provided showed marked differences in which areas appeared to be bullet magnets. Typically the fuselage would contain several holes, the wings and cockpit slightly fewer and the engine block one or two if any. If you’re anything like the average thinker (and even most above-average thinkers) then you’d say it’s a no-brainer, you slap that armour on the fuselage to soak up some of the excess damage. And you’d be wrong. I’ll leave the reasoning behind the solution as a brain-teaser for you until you buy the book (unless you ask in the comments) but to understand it you might want to think about what we are not seeing in the bullet-hole data…

This is the key to How Not To Be Wrong’s success as a layman’s guide to what seems to be becoming an increasingly murky and ill-understood world. Ellenberg is simply one of the most gifted writers I’ve encountered when it comes to taking an easily-comprehended real world problem or situation and slowly peeling away the layers until we come to the revelatory maths underneath. Think Freakonomics but with fewer shoddy inferences and a lot more hard thinking behind the scenes, the kind of book that lets you coast by on a superficial read but will increase its rewards exponentially with every extra ounce of effort you impart.

That said, it’s not all rosy. I was jolted out of my mathematical revery once or twice by utterly inexplicable and entirely unnecessary attacks on atheism, characterising atheism’s recent rise in popularity as ‘two billion billion fighty books on the topic of “you should totally be a cool atheist like me”’, as if completely blind to the fact that pro-religious books in any store outnumber the freethinking ones by a factor of ten easily. Not to mention the proliferation of churches, temples, etc around the world, the lack on non-religious leaders, the fact that atheists are labeled as terrorists or even threatened with death sentences in some countries. Better stick to maths Mr Ellenberg, methinks you’re ill-prepared for other arenas as your unashamed admiration of Pascal’s Wager betrays.

However such minor blemishes certainly won’t affect the experience for the majority of readers. They’ll delight in attacks on our legal systems (‘The purpose of a court is not truth, but justice.’), sly asides on late-night pot sessions and the conspiracy theories they engender (‘It’s a very interesting mental state to be in. But it’s not conducive to making good inferences.’) and examinations of the truly insane status of wealth in our modern world (‘if you’re down a million bucks, it’s your problem; but if you’re down five billion bucks it’s the government’s problem’). How Not To Be Wrong is a true eye-opener of a book, one with a very real power to help you view the world from a different perspective. From the lofty peaks of mathematical awareness, and with a little practice and discipline on your part, you may well find your day-to-day errors in judgement, expectation and calculation diminishing noticeably if not entirely. And even if not you’ll certainly be hugely entertained along the way by a mostly amenable and charming host. That’s got to be worth a few hours of your reading time.

Find a copy of How Not To Be Wrong via Indiebound


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Intuition Pumps by Daniel Dennett

Intuition Pumps by Daniel DennettReview: Intuition Pumps by Daniel Dennett (W. W. Norton and Co., 2013)

Or, to give the book its full title, Intuition Pumps and Other Tools for Thinking. Daniel Dennett has broached many topics in his illustrious writing career but he remains by far best known for his forays into the murky depths of consciousness and free will. Within the realms of psychology, neuroscience and philosophy it’s hard to imagine two more highly charged and contentious issues as these. Battle lines are drawn in the journals and intellectual blood is shed with every publication but often the conflict boils down to, “If you could only see things from my perspective! You’d change your mind immediately!”

Intuition Pumps is Dennett’s attempt to solve this very problem. In an extensive series of very short chapters, often only a few pages long, his aim is to equip the reader with an armoury of thinking tools. These tools or pumps, mostly taking the form of simple and well-known thought experiments, guide us slowly, inexorably towards Dennett’s conclusions; namely that free will is an illusion (albeit a useful one we need not discard, the Compatibilist stance) and that consciousness is nothing but a by-product of mechanical processes in our brains. Not the most romantic of opinions admittedly, but certainly the one bearing the closest resemblance to the ever-expanding mountain of evidence provided by neuroscientists and psychologists alike. It also happens to be the view I’ve shared ever since my degree in Mental Philosophy. So, how does he fare in guiding novices and old hands alike towards his desired goal?

Well first, to be clear, this book is indeed accessible to the lay reader despite its daunting mix of content from computer programming to gestalt psychology and all stops in between. In fact the book’s structure makes it all the easier for non-experts to get up to speed with the less familiar concepts, while Dennett provides handy guidelines as to which sections can be skipped by the pro’s. The books initial sections are more or less Critical Thinking 101, training the reader to analyse the arguments they encounter and specifically to be on the lookout for certain classes of error. He provides bite-sized guides to basic notions familiar to all philosophy students such as the Reductio Ad Absurdum as well as his own extensive list of polemical errors (‘rathering’, ‘Goulding’ and so on). Key among these is his command to all readers to tweak the controls of any thought experiments or analogies cast before them – play with the variables, break out of the boundaries imposed by your interlocutor and see if it still holds water. Much fun to be had!

Soon the topic moves to computing, and here you actually have to get your hands dirty by imagining the most basic of machines and considering how to program it using a limited vocabulary. This leads slowly into evolution, a topic with which any Dennett reader will be familiar. Evolutionary theory underpins every aspect of his thinking and he is rightly evangelical about it given that it is possibly the most successful thinking tool we have ever encountered. Doubting Thomases be wary. It’s only in the closing chapters of the book that we get to the really meaty topics, free will and conscious experience as viewed from an arch-materialist’s perspective. By this point it’s somewhat harder going and readers should be reminded that there’s no shame in backtracking to wrap your head around any number of points. Hell, I do it all the time and I studied this for four years!

For my money the book is a resounding success. I will admit that I may be biased in that I already agreed with his conclusions (more or less) before beginning the book. However, the path down which he leads his audience is straight and true. It was carved out by classes of Philosophy graduates in Dennett’s own classes where he tested the material, all the wrinkles ironed out before publication. While some similar tomes can feel like a mental struggle this was more like being pulled towards your by a welcome and increasingly strong current.

That’s not to say the book won’t have its critics. Dennett pulls no punches when confronting the likes of John Searle and Stephen Jay Gould on their stances regarding artificial intelligence and evolution respectively. Supporters of these camps will no doubt attempt to pick holes but try as I would to be Devil’s Advocate I could find precious few chinks in the armour, and no significant ones. Honestly the only fault I could find was the familiarity of much of the material, large swathes of it being pulled from his previous books and other publications. For the Dennett newbie this will not be a problem though, so I can let it slide.

Will Intuition Pumps succeed in changing the minds of staunch dualists, anti-evolutionists, AI doubters or free will advocates? I’m not sure. The arguments contained within are sound but it’s well known that rational argument tends to have little effect on the already entrenched. On the other hand, as an introduction to the fundamental interconnectedness of the range of topics it covers – philosophy, critical thinking, computation, AI, evolution, free will and consciousness – it’s difficult to think of a better volume. Easily digestible but substantial enough to give you plenty to meditate on for months, as well as exponentially increasing your reading list. Another victory for advocates of rationalism, skepticism and the scientific method.

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Thinking, Fast And Slow

Thinking, Fast And Slow by Daniel KahnemanReview: Thinking, Fast And Slow by Daniel Kahneman (Farrar, Straus and Giroux, 2011)

Before we start, try a little experiment. You’re going to need some walking space, nothing more. Start walking, get a nice steady pace going. Now, try to find the answer to this sum: “2+2=?” Did you manage it? Unless you’re the kind of mouth-breather who has trouble manoeuvring a knife and fork at the same time then it should have posed no problem. Now, get your stroll on again. Try this one on for size: “23×42=?” Those of you with exceptional gifts for mental arithmetic may have managed it, for the rest of us mere mortals it caused us to at least break our stride and probably stop altogether. In fact, unbeknownst to us our heartrates increased and our pupils noticeably dilated.

In Thinking, Fast And Slow Nobel laureate Daniel Kahneman gives us a guided tour of two distinct mental systems we constantly and unconsciously use for processing different kinds of data. System 1 gives us an up-to-date picture of our surroundings, dealing with easy problems and reacting at lightning speed – you might be tempted to call it ‘instinct’. System 2 on the other hand is concerned with the trickier situations and requires a great deal more energy, hence the discomfort caused when attempting the second calculation. It’s more aligned with what we’d call our logical and rational selves, as opposed to the more emotional character of System 1. Though we are aware of neither in our daily lives, nor of the switching between them, they guide our every action and, as Kahneman takes great relish in demonstrating, lead us into all manner of cognitive biases.

Kahneman orders his book into a series of discussions on the various heuristics, or mental shortcuts, which System 1 will take in order to keep us comfortable. It turns out that we always prefer to be lazy, no matter how diligent we profess to be. System 1 will always take whatever shortcuts it can to minimise effort, response times and anxiety. (And don’t worry if it sounds like we have two autonomous homunculi controlling our lives, it’s just easy shorthand to help us understand our mental operations.)

One of the easiest to demonstrate is the availability heuristic. A wonderful yet grisly  example of this heuristic at work is the United States immediately following the 9/11 attacks (taken from Dan Gardner’s wonderful Risk: The Science And Politics Of Fear). The media during that period was pushing one transport-related story only – planes are bad. The images of the burning towers were everywhere you looked. Everyone knows the death toll, the 3,000 who lost their lives that day. Few are aware that in the following year over half that number again died on America’s roads as a direct result of choosing to drive instead of fly.

In the terminology of Thinking, Fast and Slow, this was an error of System 1. It was asked the question, “Should I fly or drive to this meeting?” but instead of passing the work on to meticulous but labour-intensive System 2, it substituted another question instead. It asked “What information about flying is close to hand?” The answer was obvious, yet the information to hand failed to mention that flying remained a far safer option than driving. The results of 1,600 such errors speak for themselves.

Throughout the rest of the book Kahneman details several other such heuristics which lead us down alleyways of faulty logic. The framing heuristic determines how a slight and logically insignificant change in the wording of a statement or question can have massive differences in our reactions to it. Would you prefer a medical treatment which would give you a 90% chance of living or one which gives you a 10% chance of dying? Depends which system is at work. There is also loss aversion, a remarkably powerful heuristic whose operation results in the stunning and repeatedly demonstrated fact that optimists are healthier, happier and live longer that pessimists. (Unfortunately reading this made me even more of a pessimist. Thanks Daniel.). By combining studies of loss aversion, overconfidence and our tendency to simplify the world around us, Thinking, Fast And Slow manages to unite all manner of previously inexplicable human behaviour under one relatively simple explanation.

Don’t worry, though, it’s not all bad news. Kahneman is at pains to point out that for the vast majority of our lives Systems 1 and 2 perform their assigned tasks immaculately. Our continued existence is testament to their efficacy. The main point he wishes to drive home is that with some effort we can become more aware of their failings. With this in mind we can hope to reduce our own susceptibility to cognitive biases, although as a disclaimer he does note that it is far, far easier to notice these shortcomings in others and hence this book is aimed more at ‘gossips and critics’. Despite this warning, anyone interested in skepticism, critical thinking and psychology should devour this book and start spreading the word.

Then start annoying their friends with calls of “Ha, your System 1 is a jerk!”.

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Filed under Critical Thinking, Psychology, Skepticism