Objects in the Mirror…

It goes far beyond the familiar warning about objects in our rearview mirrors, by now. I hate to tell you this, but all sorts of objects, everywhere, might not be anything like they appear.

I’ve been reading a book that my friend Ron recommended, called The Drunkard’s Walk: How Randomness Rules Our Lives, by Leonard Mlodinow. By a few pages in, I loved it so much, I wanted to weep. Give me a book about geeky-fascinating, blow-your-mind science stuff, and I’m a goner.

The book is about (and do NOT run away here – I’m getting ready to tell you some funky-cool things) probability theory, chance, and how psychological illusions cause us to misjudge the world around us – not because we are stupid or gullible, but because these illusions are so powerful.

I think of it this way: our complex psychological and emotional makeup constantly interferes with our ability to analyze data and use pure reasoning. But also, we exist in both a microscopic world and a macro universe, the scopes of which are virtually impossible for most of us to grasp.

Our elegant brains are simply hard-wired to misinterpret data. Here are a few examples.

Our perceptions of probability and cause & effect are skewed.

We tend to think, in our own lives and in the world at large, that an event is either more or less likely to occur because it has (or has not) happened recently. (We think: “Her luck has run out…” “He is due…”) This is the same reasoning behind the hiring and firing of CEO’s or studio heads, when they’ve had a run of several good or bad years/movies.

We – and executive boards, and recruiting agents, and on and on – reason that results are based on performance…isn’t this what we’ve been taught, all our lives? But, as has been mathematically proven (and the book goes into great detail on this), much of what happens in the world is the result of randomness – the result of what is called “Bernoulli’s theorem” (after a 17th-century mathematician) or “the law of large numbers.”

Of course, Kobe Bryant’s talent allows him to perform much better in the NBA than, say, my neighbor Sandra would. But Kobe’s individual performance from game to game, or season to season, or throughout his career, is due almost exclusively to chance, and not to fluctuations in his abilities. This might sound like hooey, but it’s a scientific fact.

Success, as it turns out, really is most often a matter of repetition. Bad news for the exceptionally talented of this world. Fantastic news for the exceptionally dogged.

Our perceptions of relevance, and our interpretation of statistics, are skewed.

During the O.J. Simpson murder trial, it was an accepted fact that Nicole Brown had been previously battered by O.J. So one of the arguments that the defense team pulled out was this: Of the 4 million women who are domestically battered each year, only about 1 in 2,500 are killed by their partners.

This was a true fact. It was a very convincing argument, to the jury. And on an intuitive level, it appeared to be completely and totally relevant to the O.J. case.

But it wasn’t.

Why not? Well, the previous statistic dealt with women who are NOT killed – and Nicole most definitely had been killed. The relevant statistic (and one the prosecution failed to bring up) was this: of all the battered women in the U.S. who are killed (and Nicole was part of this category), 90 percent of them are killed by their abuser.

The first (irrelevant) statistic created such a powerful illusion, it helped convince the jury to acquit a double-murder defendant.

Our perception of logic is skewed.

Here’s a fun example of the way our brains resist reality, from The Drunkard’s Walk.

Let’s say you know that someone has twins, and you wish to determine the likelihood that both children are girls. If you don’t know the gender of either child, then the chance that they are both girls is 1 in 4. Sounds logical, right?

Moving along, let’s say you find out that at least one of the children is a girl. Now the chance of them both being girls increases to 1 in 3. (Still sounds right.)

However, if you are told that one of the children is a girl named Florida (!), then the chances of them both being girls increases to 1 in 2.

Whoa, whoa, whoa, back that train up.

How can this be? How can one girl’s strange-sounding name affect the odds on the gender of the other child?

And yet, as Mlodinow painstakingly proves over a few pages, this outlandish statement is an absolute fact. In this example (and in so many others, throughout the book), my own instincts for mathematical reasoning completely failed me.

Moving away from The Drunkard’s Walk

Our perceptions of space and time are skewed.

As we’ve all heard, we (and everything else in the universe) are not moving in a linear way through space and time, from point A to point B; instead we are moving through four dimensional space-time, a concept that even Stephen Hawking calls “impossible to visualize.”

When we look at the sun, we are seeing it in the past, as it existed eight minutes ago – but since everything we perceive comes to us via signals (which require time to travel), even as you read these words, you are looking at your computer screen as it existed in the past (infinitesimally so, of course.)

We’re not just “lost in space,” peeps – we’re lost in time.

Our perception of reality might even be skewed!

The more you start thinking about all these problems with perception, the more widespread you realize they are. Indeed, this recent article from Discover Magazine suggests that our entire universe might be – are you ready for this? – a giant hologram.

This theory will never be proved in our lifetime, of course, but it certainly dovetails nicely with the Christian belief that this world is but a pale twin of another dimension, the “real” reality that is our eternal destination.

(And may I humbly submit: if you are someone who rejects the concept of God and/or Christian beliefs because they seem too far-fetched, too “hocus-pocus” for practical people, then you haven’t been paying attention to the world of science in the last decade. From space exploration to theoretical physics and everything in between, the physical laws of this universe are far wackier than anyone ever imagined. You can still have personal objections to Faith, if you like – but you really can no longer reject it on intellectual grounds.)


I’ve barely scratched the surface here – but it sure would be nice if this information made us think twice, the next time we want to dig in our heels about our points of view on something. Because chances are very good that our perception is flawed – that there are factors we haven’t considered, or aren’t even aware of.

If mankind understood this concept, it would deliver a death sentence to arrogance of every sort – intellectual, spiritual, societal.

And that would be a very, very good thing.


Writing that rocks – Fermat’s Enigma

Classification: Science, non-fiction

You cannot imagine how excited I am right now. I get to tell you about one of my very favorite non-fiction books of all time, Fermat’s Enigma by Simon Singh.

I often find myself recommending this book to anyone who will listen. I try to shoehorn it into conversations whenever I can – which sometimes requires great topical leaps. You visited Guatemala last month and went cliff-diving and ate snake kabobs and met a long-lost cousin? That sounds exciting! You know what else is exciting? Fermat’s Enigma!

And so on.

I first heard of the book when I read a glowing review about it in the New York Times, some eight years ago. The next day I went out and bought a copy. It didn’t take much longer than one sitting to read; it’s that mesmerizing. The book follows the quest to solve a centuries-old mystery, and is full of suspense, and wonderfully eccentric and whip-smart characters, and prize money; there are dead-ends and setbacks and close calls.

Oh, I might as well tell you right now. Please remain in your seat and keep the aisles clear.

Fermat’s Enigma is about advanced mathematics.

I’m sorry, are you looking for your mouse so you can click yourself elsewhere? Well, I hid it, and I’m not giving it back until you’ve finished reading this. Trust me – the story is a thriller, and you don’t have to be a great mathematician to love it (I’m certainly not one.) This is no textbook; it’s one of the most exciting adventure stories I’ve ever read.

Here’s a summary:

In the early part of the 17th century, a delightful and mischievous Frenchman named Pierre de Fermat started fiddling around with mathematics as a hobby. He had no formal training, but he quickly proved to have a natural genius for the subject and made some interesting discoveries. For example: he figured out that 26 is the only number in existence that comes between a square (25) and a cube (27.)

In 1637, Fermat came up with the following theorem: “It is impossible for any number which is a power greater than the second power to be written as a sum of two like powers.” In other words, the equation “X(n power) + Y(n power) = Z(n power)” has no solution when n>2.

Pretty straightforward – but mathematics is all about proof. Fermat wrote his theorem in the margins of his math textbook, and then he scribbled something that would haunt generations of scientists:

I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.

He was claiming that he’d found the proof to his theory. And that was his last, enigmatic word on the subject.

For the next 360 years, Fermat’s theorem was the most famous unsolved math puzzle in the world. The theorem was believed to be true, but when nearly every top-tier scientist in the field tried to find the proof that Fermat had dangled in front of them, they all failed.

Three hundred and sixty years, people. And then, in the 1990’s, along came Andrew Wiles.

Wiles looks exactly how you expect a brilliant mathematician to appear (if you don’t mind employing wild stereotypes): enormous glasses, crooked teeth, distracted smile, far-away look in the eyes, hair flying up in every direction. And man oh man, what a beautiful mind.

As a ten-year-old child, Wiles had been captivated by the world’s most famous math riddle, and dreamed of solving it. While he was growing up and starting his career, momentum had been building toward a proof of Fermat’s theorem – indeed, at various times, people had announced they had a solution, only to have other researchers discover flaws in their work. Wiles was determined to succeed where everyone else had failed.

After seven years of mostly solitary effort, he finally believed he had found his proof, and in June of 1993 he gave a lecture to a packed house at Cambridge University, detailing his solution. When he finished, he laid down his chalk and said simply, “I think I’ll stop here.” Two hundred of the world’s finest mathematicians erupted in applause. Publications the world over celebrated his accomplishment

Of course, as in all good thrillers, there was one final set-back before ultimate triumph. When research “referees” pored over Wiles’s 200-page proof, they found an error. Although crushed, Wiles doggedly went back to the drawing board, and after another year of labor, he found a way to fix the hole in his work. This time, the proof was flawless, and it was accepted as one of the most significant achievements in modern-day science.

In Simon Singh’s hands, throughout the book, the most complicated math equations and theory all make beautiful sense. You cannot stop turning the pages. Imagine, for a moment, just how much talent a writer has to have, to pull off that trick. Singh (himself a physicist) turns the story into a cross between Number Theory for Dummies and The Bourne Identity – he makes the hunt for a mathematical proof read like the hunt for Carlos the Jackal. (Who is still alive, by the way, which I did not know. You learn something new every day.)

Singh’s little book, like the event it details, is stunning. In fact, writing about it has made me want to read it all over again. Just for kicks.

(If you remain unconvinced, take heart. My next book post will cover a fun work of fiction. I’m trying to decide between several, right now.)