This is Poggendorff’s illusion, said Zafar. Johann Poggendorff, he continued, was a nineteenth-century German physicist and the creator of a number of measuring devices. Your father will probably have heard of him. There are countless optical illusions of a similar type—you probably know the Müller-Lyer illusion: two parallel lines with arrows at the end, arrows inverted on one of the lines; which line is longer?
I know that one, I said.
But it’s Poggendorff’s illusion I like the most, because it reminds me of the distinction between a reason for doing something and an incidental benefit of doing it. But I’ll come to that. You say that once we know how the world actually is—once we see it correctly—we can fix things. Now that you know what the truth here is, let me ask you one more time: Which of these two diagonals on the right, the top one or the bottom, which of them looks—and I mean looks—like it’s the extension of the diagonal on the left?
The same. Nothing’s changed, I replied. It looks the same as before.
Knowing how things are doesn’t make you see them correctly, doesn’t stop you from seeing things incorrectly. Stare at the image as much as you like, it’s all in vain. It will never surrender the truth, not to your naked eyes; you have to go in armed with a straightedge.
Yes, yes, I said, somewhat defensively—this was a human cognitive failing, everyone’s shortcoming, but I couldn’t help feeling that somehow I’d been shown up.
Do you know Harvard’s motto? he asked.
Veritas.
And Yale’s?
No, I don’t.
Lux et veritas. Light and truth. Quite a distinction. Shining a light doesn’t always reveal the truth of things. Jan Evangelista Purkyně said: Illusions of the senses tell us the truth about perception.* So the question is, he asked me: Do you trust your senses, your perception of the world?
Trust is a slippery word, I said. When I tell you that I trust someone or something, a newspaper or politician, say, I mean that his behavior agrees with my expectations of how he’ll behave.
Do you trust your own perception of the world?
Optical illusions aside, I think the way the world behaves tends to agree with my expectations of what it will deliver.
Aren’t you putting the cart before the horse?
How so?
Your expectations are formed by your perceptions in the first place. Then you use later perceptions to determine if your expectations have been met. What if your initial perceptions make you form stupid expectations? What if your own perceptions are rigging the game before it’s started?
And we’re all living in a matrix of illusion, like the movie?
I looked for a response, but he just smiled.
Maybe, I continued, not trust then but believe. Don’t we have to believe in our perceptions? I asked. We have to have some faith. What’s the alternative?
Do you have to believe in evolution if you reject creationism?
Doesn’t it follow? What’s the alternative?
Why not hold off having a belief? Why do you have to have a belief one way or the other?
I read somewhere about a survey, I said, showing that most people who said they believed in Darwinian evolution actually got its basic ideas completely wrong when they were quizzed about it.
Exactly. Those people, said Zafar, have rejected creationism and placed their faith in ideas that they mistakenly regard as Darwinian evolution. Aren’t they better off suspending belief altogether rather than clinging to false gods? They don’t even meet your test.
What test?
Why do they need Darwinian evolution in their lives—their warped notion of evolution, that is? Didn’t you say you need to believe your perceptions—you need to believe something?
* * *
That day, I forgot to remind Zafar that he said he’d explain why he liked Poggendorff’s illusion more than others. When I recently researched the illusion, I discovered something quite extraordinary, which I suspect he had probably had in mind even as he looked out the windows of the café at the Union Jack above the British Museum.
According to one authority, the British national flag was designed in such a way as to overcome the pitfall of Poggendorff’s illusion, whose effect was known even before the German physicist formalized it. Here, some say it has to do with fimbriation and rules of heraldic design, and perhaps this is what Zafar was hinting at when he mentioned the distinction between a reason for doing something and an incidental benefit of doing it. In any event, the optical illusion is countered in the Union Jack by displacing the red saltire of St. Patrick slightly so that each spoke of the saltire can at least look aligned with its opposite spoke on the other side of the Cross of St. George. Along the length of each spoke of St. Patrick’s Cross, only one half of the width (not length) of the spoke is included in the Union Jack.
The flag is surprising for another, related reason. I expect many people think, as I did, that the flag is symmetrical about the central vertical and horizontal axes: that the top half is a mirror image of the bottom and the left half of the right. In fact, this is not true. The lack of reflective symmetry is visible in the corners of the flag. At the top right corner, the red saltire of St. Patrick meets the northern edge of the flag. If the flag had reflective symmetry about the axis that runs from left to right through the middle, then the upper left arm of the red saltire of St. Patrick would also meet the edge of the flag on its northern side. But it doesn’t; it meets the western edge. (The only symmetry the flag has is 180-degree rotational symmetry about its center.)
As I say, Zafar mentioned none of this business about the Union Jack. Instead, he proceeded, in his odd way, to where he was heading that day. I see that now.
* * *
Do you love her?
Meena?
Who else?
I’m not sure, I said.
Of course you don’t. But it doesn’t matter, right?
What do you mean I don’t love her? I didn’t say that; I said I’m not sure.
Does it matter?
Does what matter?
Does it matter whether you love her?
It might help.
So you don’t love her, said Zafar.
I didn’t say that.
I had always suspected him of a capacity for cruelty. I think I know why Zafar was attractive to women. I think I know how he drew them. He invaded their private spaces; he asked direct questions, questions just shy of inappropriate. For instance, he asked Eva—the young woman in Central Park—about her hair. That in itself should have scared women off. But Zafar was also manipulative. He invaded a woman’s space, but he let her know—he helped her believe—that she was safe when he did so. There was the smile, but there was also the mere fact of asking a question. It gives the illusion of control to the person who can choose her answer. When I thought of Zafar like this, when I understood how his manipulation worked, it brought him down a peg; he didn’t seem quite so charming. Maybe he didn’t know what he was doing. Maybe it was just ingrown habit. But the fact that it’s so well learned makes it no less manipulative. In fact, as I reflect on this, it seems to me that he and Emily had that in common; they were both highly manipulative. They had applied their skills in different directions, quite obviously, but whatever Zafar might ultimately have thought about the ways the two of them had been unsuited to each other, in this one regard—their respective capacities to manipulate—they had been perfectly matched.
You know what Erich Fromm said about love?
Who’s Erich Fromm?
Jewish German American philosopher and psychoanalyst. He said that we must give up the notion that since love is a condition of the mind, its presence can be proven by a form of words. We give up this idea when we see that far from being a condition of the mind, love is an activity, a form of conduct.
Interesting, but so what?
She’s away a lot, but you never call her.
Marriage isn’t a transaction.
So she calls yo
u, but you don’t call her, he said.
What’s going on?
I’m asking questions and you’re uncomfortable. Relax. I can stop, said Zafar.
Of course he could stop and I could have stopped him. I can hear it when I listen to the recording. I could have said Do stop, but I said nothing. It’s a difficult thing to admit, but Zafar’s potential for cruelty has always pulled me in, binding me to him. Here he was, staying at my home, eating my food, availing himself of my hospitality. I wanted to tell him that I was the successful one here. But the ungenerous thought couldn’t withstand the reality: My marriage was a disaster; my home, this retreat, was foreign soil, made bearable only by his arrival. And as I think about it now, even the huge house was a stucco-fronted lie made of bricks and mortar. I bought the house, as Zafar remarked, before I joined the firm, before my first paycheck. I’ve relied on my family in so many ways that can never be escaped. I used to think these were the bonds across generations.
I could have told Zafar I’d made something of my life, that I was still young and there was so much more I could do, but even then I knew the hollowness of it, the irrelevance of it. I had just been fired from the firm after a vote of the partnership, by people I had counted as friends, fired by an email asking me if I had a moment to spare for a chat, fired for taking risks whose payoffs funded their children’s schooling ten times over; risks that they encouraged me to take; risks that the regulators and central bankers encouraged us to take; risks that homeowners and governments the world over encouraged us to take; risks that no one knew would come back like this. Who would have thought in the first quarter of 2008 that Lehman Brothers would go belly-up before the year was out? Who actually thought that the markets were going to sink into the worst crisis since the Great Depression? None of the absentminded rocket scientists on Wall Street did. I’m not one of them, but I worked with them, hired them, and respected them. They’re smart people, very smart. Here was their golden opportunity to make a mint betting against the market—that’s what you can do, bet against the market, and if they’d thought the market would tank, then they’d have been the first to bet against it. Sure, there were mavericks here and there already betting against the housing market, where it all started. But they never gave you convincing reasons for their view. They might have said the housing market was heading south, but nothing they said, at the time, given what we knew, at the time, given what the market expressed, at the time, none of their reasons, at the time, nothing they said was ever more worthy of our belief, my belief, than what everyone else—the overwhelming majority—was saying. What do you do when everyone believes things are going well except the few who aren’t any more convincing?
And here was Zafar, opening the wounds, a friend coming at me from behind my back. Who did he think he was?
Do you remember what you said years ago in New York? Finance was a meritocracy, you said, and you liked that about it.
I remember, I said.
Well, was it?
By and large, I said. The was stung.
Why did that matter to you? Actually, hold that thought. I need the gents. Can’t put it off any longer.
It was a fair question. After all, back then I couldn’t very well have said that a meritocracy was likely to favor me. The evidence probably pointed the other way: I had gained only an upper second-class degree at Oxford and was able to stay on for a graduate program because I wasn’t relying on a scholarship or research council grant. I suspect that the extent of self-financing in higher education, at that time and, as far as I know, even now, is not common knowledge, but there it is; those in the know, the paying students and the receiving university, didn’t have much incentive to advertise the fact. And as for those who don’t go on because they can’t self-finance, they’re never heard from again. But that is how the world is and it seems to me little use to fight it, especially when no one else seems to be doing so.
As I waited for Zafar, the absurd notion formed in my mind that he might have vanished. That while I had been looking out the window, he had slipped out the door and simply disappeared.
I overheard two young women sitting at an adjoining table.
My friends think I’m mad, said one. They’re always saying, Cheryl, you’re mad, you are. But I think it’s all right, you know. It’s like you got to be a bit crazy, otherwise you’d go mad.
Mayonnaise is just posh salad cream, innit?
I suppose so, replied the one.
It’s American, right?
No, I think it’s French.
Yeah, but why do they say, “Easy on the mayo,” then?
On the telly?
Yeah.
Americans like French stuff.
You like it, don’t you?
It’s not as greasy.
You mean salad cream?
Greasier than mayo.
What’s pastrami?
At another table, a young American was talking about his yoga class. He complained to his friend: It was like someone in the room was draining my green energy.
So why, Zafar asked after he returned, did the meritocracy matter to you back then? It’s not as if you’d suffered because the world had failed to recognize your merits.
I expect you’re going to tell me.
I think it’s tougher for people like you. You guys make the right calls and things happen, whereas regular folks—like me, he said, shooting me a grin—regular people have grown up knowing full well the world is unfair. We don’t expect anything different, and we’re so battered by the unfairness that we don’t even hope for anything better. The world is—and I’m not trying to use your words against you; or were they my words?—anyway, for most of us, the world is what it is. You guys are the idealists.
Finance, I said, is by and large a meritocracy, and that’s a good thing. You can’t fault me for wanting to be a part of that. After all, you got something out of it, didn’t you?
But you weren’t really attracted to finance because of what it was but because of what it was not.
Here we go again, I said. I think I might have rolled my eyes.
Finance is not about connections, it’s not about who you know but what you know, it isn’t like your grandfather’s world, with secret deals on golf courses and in country clubs, kickbacks and Swiss bank accounts.
You don’t know him.
I don’t have anything to protect by lying to myself.
I think Zafar was wrong, but the irony is that I so wish he’d been right. The fact is that my own early success in finance did owe something to connections, connections that have now come home to roost.
What’s your point? I asked.
You could have tried for academe, but what if you’d failed? Or worse still, what if you’d ended up with a second-rate lectureship at a second-rate university somewhere? What would your father have thought? Ivy League or why bother? Now, finance, on the other hand, that was safer. At least you couldn’t be compared to your father or grandfather.
Or maybe I just knew what I wanted, I replied.
The conversation now taking place did not feel like two friends trying to figure something out. It had none of that affection and trust of conversations on our walks everywhere else all those years ago. There was instead an earnest, impatient drive to get to the root of things, dispensing with the markers of friendship. More than once, he’d asked me, Why does it matter to you?, a mischievous question that he loved. But this time there were no accompanying smiles, no unspoken gentleness. If anything, his comments and questions seemed presumptuous; I hadn’t seen him in years. One of those articles my father sent was about some studies that show that while every person thinks he himself has changed hugely over time, those close to him typically think he’s changed very little. Was that it? Did he think that he knew me because he believed people didn’t change?
Do you look down on Meena?
The question caught me by surprise, but that was Zafar’s way.
You think I do.
&
nbsp; You don’t want children with her, do you?
Come on, Zafar.
Class isn’t something you look at, it’s not stuff around you. It is you, it’s the eyes with which you see the world. And you have to look in the mirror to see your eyes. Do you know what Bertrand Russell said about mathematics?
I expect he said a lot about mathematics.
About why he liked mathematics?
No, but I bet you’re going to tell me, I said, slightly irritated by the all-too-familiar didactic tone.
A hundred pounds?
Tell me.
Russell said he liked mathematics because it was not human and had nothing in particular to do with this planet or with the whole accidental universe—because, like Spinoza’s God, it won’t love us in return.
That may be true, but how is it relevant?
You know that Russell was a philosopher and a mathematician, but he was also the grandson of a prime minister and in fact he was an earl himself. Mathematics is as far removed as you can get from that background.
But there have always been aristocrats in mathematics.
Yes, there have, in the one field where station and position and authority don’t matter a jot. Who you are counts for nothing. In 1900, at the second International Congress of Mathematicians in Paris, David Hilbert gave the keynote address and set out his famous ten problems, mathematical propositions that needed to be proven. Hilbert, as I’m sure you know, was the towering figure of mathematics in his day, a man of huge authority and unrivaled mathematical intuition. One of the problems was proving the consistency of arithmetic, and Hilbert believed the proof was close at hand.* But within thirty years of Hilbert’s challenge, a young man by the name of Kurt Gödel, at the very outset of his career, a man with no record of achievement, let alone anything to rival Hilbert’s, showed that the great master himself was wrong and that mathematics could not be proven to be consistent. And that was the end of that. Mathematics doesn’t care about authority, it doesn’t care about who you are, where you’re from, what your eye color is, or who you’re having supper with.
In the Light of What We Know: A Novel Page 22