March 30, 2009

My Apologies

Lori, who is brilliant and keeps me grounded, read my earlier blog entitled "For Mormons Only" and had some choice words. She reminded me of a principal by which I try to abide, namely that I must never, under any set of circumstances, ever be the reason someone's faith is diminished. I would do nearly anything—anything but lose my integrity—to be completely assured that God lives, that Christ died for my sins, and that there are absolute truths that, like a line of mileposts, will direct me home. The fact that I can't achieve this shouldn't be taken as a sign that those who can have been deceived. Since I believe uncertainty to be a necessary human condition, I must accept the possibility that I've been deceived—or at the very least, that the truth is so complicated that all of us are right.

However, here is a point I seemed to have missed or didn't emphasize sufficiently: Even when I'm wrong (for example, let's assume I'm wrong about Prop 8) sometimes I'd rather be wrong and suffer the consequences than to embrace the alternative. I've mentioned in a previous blog that if I were given Abraham's choice between sparing my son or earning some greater gift from God, I would choose my son and not think twice about the decision. That seems fair, doesn't it?

Sorry again. I hope I didn't offend anyone.

Capital Markets Musing

I’m getting off topic here since I’m going to jot down a few thoughts that aren’t in keeping with the idea of a new Christian ethic, but I can’t help it. As someone who spent a lot of time structuring CDOs and Credit Default Swaps, I’m pulling my hair out listening to all the opinions and plans about a roadmap to economic normalcy and I have to say something.
Now, here’s my first observation: When it comes to a host of policy issues, there appears to me to be at least two courses of action. There are:
  • Politically expedient solutions that will satisfy the citizenry’s desire for blood, but in the end will do nothing to fix the problem, or
  • Market-based solutions that can help put our economy on the right track, but will likely cost a politician his or her career to defend and implement

Let me start out by saying our current economic malaise was destined to happen as soon as subprime lending became commonplace. Do you realize that mortgage loans were going to borrowers with FICO scores of 580 and lower, and who had no money for down payments? To understand how crazy this is, consider the following: The likelihood of a 580 borrower to default on some portion of his or her consumer credit within the next 90 days is 50%. Combine that with a lack of equity to mitigate potential loss and we have the perfect combination for a financial powder keg. Who let this happen? In a way, it was caused by some of the same people who are squawking loudest today—people who from their positions on the Senate Finance Committee (you know who they are) were demanding lenders, Fannie Mae and Freddie Mac included, to put more people in homes.

That was a bit of a digression, but the point I wanted to make is that our foreclosure woes were bound to happen as long as there was a lack of prudence in the lending process and regulators were complicit in the boundless stupidity. Accepting those circumstances as given, what was the first big mistake regulators made as the house of cards began to slip? Here’s my suggestion: We should have never let those pesky Bear Stearns hedge funds collapse.

I’ll tell you why in a minute, but imagine what people would have said if the government had stepped in to bailout a bunch of rich bastards who were investing a million dollars at a pop. Holy smoke, the outcry would have woken the dead and led to a slew of congressional committee hearings, where our nation’s leaders would have waxed sanctimonious in their outrage and never gotten around to asking a single enlightened question. Editorials would have been so full of vitriol, newspapers would have combusted in readers’ hands. Average Joes would have taken to kicking dogs just for spite. But saving those hedge funds would have saved us a lot of heartache—not to mention hundreds of billions of dollars in market liquidity. Here’s why.

(For a review of how we got to our financial meltdown, see my earlier blog entitled “Honesty: The First Step to Progress”)
To understand the role the Bear Stearns hedge funds had in driving market liquidity, it’s important to know something about the structure of Collateralized Debt Obligations, or CDOs. Virtually all subprime mortgages were once sold into CDOs, where a kind of financial alchemy was used to turn them into various securities that could be bought by institutional investors. The securities came in various risk classes or tranches. The highest classes—generally rated AAA and perceived to be low risk—were purchased by insurance companies, banks, mutual funds and similar institutions. By comparison, the other classes were more prone to losses and received lower (or no) credit ratings.

The reason why some tranches were more risky than others is that they were placed in a payment hierarchy referred to as subordination. In a typical deal, the lowest subordinated tranche (often called the “hurdle” or equity class) was the first to be hurt by defaults in the mortgage pool. It would take the first losses—reducing its pro forma yield—until it was completely wiped out. At that point, the next higher class would begin absorbing defaults and so on according to the increasing level of seniority. Obviously, the higher in the hierarchy a tranche appeared, the less likely that it would ever suffer a loss.

The role many hedge funds played, including those controlled by Bear Stearns, was as the investor in the hurdle class securities. Now, you won’t get an argument from me that the loan programs the investment bank sponsored were unsustainable. The programs were clearly unsustainable—no question about it—but the point to be made here is that the relatively small investments made by Bear Stearns made huge loan programs possible. When those hedge funds went away, a black hole was created that sucked away $250 billion worth of liquidity and the marketplace couldn’t handle it.

Nothing happened overnight, but that, my friends, was the beginning of the end. When those loan programs went away, the liquidity that had fueled the real estate engine diminished, leading to lower property valuations and higher foreclosure losses. Subsequently, a stampede of mortgage investors exited the marketplace, diminishing liquidity further and closing the first circle in a financial death spiral. What was once an easily surmountable credit problem became a more serious liquidity problem, which subsequently turned into today's seemingly intractable fear problem.

Why didn’t anybody do something? Here is the truly scary part of the historical record. We are far better at explaining quantum mechanics to lay people than we are at describing capital markets dynamics. In fact, universities don’t teach what occurs on Wall Street. The trading floor, rather than the ivory tower, is where financial theories are developed and put into practice. For that reason, regulators have little basis for understanding, much less regulating, the plethora of financial instruments and the technicalities of capital flows. Even if they did, they would make a lot more money on a trading desk, so why stick around?

Now here is the scariest point of all. I’ve worked with many of the Wall Street executives whose names appear regularly in the financial press. A small number are brilliant. John Meriwether, for example, who was the former president of Salomon Brothers, is the smartest man I know, not to mention the most knowledgeable financial guru this side of Pluto. He, however, is an exception to an abysmal rule. Wall Street has undergone unprecedented changes that have resulted in risk management complexities the old guard are unable to fix or fathom.

Prior to joining Lehman Brothers many years ago, I interviewed with all the people who filled, or would subsequently fill, the top jobs at the firm. They included Dick Fuld, the Chairman who would preside over the company’s demise. I remember sitting with a former COO of the firm one day to explain a transaction my team had successfully concluded. The trade was complex, but no more so than those undertaken by hedge funds today. I wish I could tell you differently, but the man clearly didn’t understand the transaction and never would to the day he left. You see, he had started out on Lehman’s commercial paper desk, a place he'd never left until he took management positions elsewhere within the firm. Take my word for it, the commercial paper desk is not the place to learn how to manage risk.

Unfortunately, I suspect many Wall Street firms are similarly led.

March 29, 2009

For Mormons Only

In a way, I started this blog as a substitute for church attendance, which I curtailed some months ago. While I love the people of my old congregation and would gladly take a bullet for many of them, I can’t imagine rejoining them any day soon. In that regard I know what people are thinking. I’m sure that when my name comes up in conversation, some sigh and say I’ve given up a heavenly reward to feed a petty objection. They have, no doubt, assumed that anger and pride are what’s keeping me from God’s good grace and that the church’s support of Proposition 8 was at the root of my small-mindedness.

While I certainly opposed Prop 8, I was never angry with the church’s position. Rather, from the mix of emotions I’d felt at the time—shock and embarrassment among them—the one feeling that emerged most dominant was an overwhelming sorrow. As someone who has suffered long episodes of depression, I had to put distance between myself and the church, if for no other reason than to protect my health. My reckoning was this: If God really wants gay men and woman to miss out on the most growth-promoting and love-inspiring of human relationships, I will accept the consequences of not worshipping Him.

That being said, nothing Christ ever taught gives me reason to fear.

I, like many young LDS men and women, fulfilled a proselytizing mission for the church. In my case, however, there was no burning conviction that I was doing God’s work. I could have easily declined the call, since my parents didn’t share my devotion and were alarmed, even upset, by my decision. But I went eagerly, hoping and believing that by my efforts the truth would be revealed to me—that everything I’d been taught would piece together like a finished puzzle and express itself as logical, beautiful and perfect. Yet by the end of my mission, that hadn’t happened. Neither has it happened since.

Instead, it became clear to me that the truth is far more complicated than I, or any mortal, can comprehend, which is why God said, “Let there be light,” instead of, “Let the universe be filled homogeneously and isotropically with a high energy density.” In this way, I liken the words of the prophets to first grade readers that point us in the right direction but leave for us a world of learning ahead. With respect to the teachings of the LDS church, no matter how hard I tried, I couldn’t accept two primary claims supporting it as God’s only “true” religion: namely that the church was led by a prophet and it possessed additional scriptures that revealed more of the mind of God. Nevertheless, the church seemed to offer a helpful—if not imperfect—rule of thumb as to how people should live and I supported it on that basis. Now, I no longer feel that way, but Prop 8 was only one of many reasons leading me there.

To me, Christianity should conform to Jesus’ teachings and not some lesser throwback to Judaism. In this failing, the LDS Church is not alone, but that doesn’t make it right. Its belief in blood atonement, for instance, harkens more to Old Testament justice and animal sacrifice than Christ’s admonition to forgive. The many Mormon scriptural references that describe God’s nature as vengeful and jealous smacks less of John than Leviticus. As a person of color, I’m offended that God cursed his wayward Book of Mormon children with a dark skin and called them loathsome, just like He’d done in Genesis. The numerous oaths Mormons take (and they know what I’m taking about) is consistent with Israelite practice, but is counter to Christ’s directive to “swear not at all.” The prohibition against gay marriage is an extension of the Mosaic Law’s demand to stone homosexuals—not to mention the LDS Church’s early restrictions against miscegenation—but it’s inconsistent with Christ’s ideal of love unfeigned. On this point I could go on and on, but to summarize: Jesus wants us to be better than the Ten Commandments, yet we remain more Judeo than Christian. And while the points I’ve raised may seem minor, they sum to an intolerant worldview that causes its followers to be motivated by fear and a loathing for the very human attributes God imbues in us.

If the church would grant me a wish, I would ask it to eliminate the phrase Mormons everywhere teach their children to repeat like a poor affirmation: I know the church is true. The sentiment not only leads to self-deception, but it runs counter to the intersection of two of the church’s most important beliefs, that: 1) we came to earth, in part, to develop faith and 2) faith is not a perfect knowledge. If we took these two beliefs to heart—embracing uncertainty as a necessary human condition that demands humility and eschews judgment—we would see our dogmatism for what it is: a silly kind of boastful swagger unbecoming of Christ’s disciples. If we were to do that, we might learn to love unconditionally and be the better angels inside of us.

And here’s a final note. If we did practice that kind of humble and non-judgmental faith, we would pray fervently that God, in His infinite wisdom, would make us instruments in His hands to help His gay sons and daughters find solace and a place of welcome somewhere. We would pray that they find joy, not to mention alternatives to what seems like an epidemic of suicide. Unfortunately, they won’t find that in the Mormon Church—not today—where prayers are never uttered in their behalf, but where that adage, “We love the sinner, but hate the sin,” rings as often as it is hollow and hackneyed.

March 19, 2009

The Necessity of Making People Owners

Bankers are being excoriated as examples of how greed corrupts. On this point I have a strong opinion: There are greedy people in every industry and walk of life, and you don’t have to be rich to be self-indulgent.

There’s no doubt, however, that self-interest runs amok at Wall Street firms, a condition that has led to behavior that’s harmful to the marketplace and Main Street America. You would think it’s a problem we should fix. Yet, from where I sit, I see none of the TARP money and threats about increased regulation aimed at correcting what will amount to an ongoing series of excesses and subsequent corrections. The problem, you see, isn’t the amount of compensation Wall Street pays its people, but how that compensation is determined.

To make my point, consider how an auto company executive (let’s say his name is John) eventually proves his worth to his employer. John is given an assignment to design a new body style for a line of cars. It’s an important responsibility and he works diligently to fulfill its requirements. After a period of time, he offers several style options, one of which is chosen based upon market research and lengthy internal discussion. Before the design can be put into production, however, some of the major components—the engine included—must be modified. In other words, a considerable length of time ensues before the first newly designed car rolls off the assembly line. Furthermore, it will take many more months—years perhaps—to determine whether the change leads to increased sales. In short, John and his managers won’t know how successful his design will be until years after the project is completed.

Now, let’s look at how Jim, a proprietary trader, seeks to make a name for himself. Jim is told to look for arbitrage opportunities and so he examines the marketplace for cheap securities and uncovers a five-year maturity bond that is paying 5%. He decides it offers extraordinary value, so he purchases $100 million of it, using cash that he borrows at 3% interest. Jim is suddenly making a spread of 2% (5%-3%) on the $100 million, or $2 million per year. Pretty neat, huh? But that’s not all. A salesperson comes to him and says he has a client who needs a guaranteed $2 million per year for the next five years and is willing to pay $8 million today for that annuity stream. The trader says, “You’re done,” and money changes hands. He has booked a nice profit.

This is a simplified example of a trade known as a swap. In reality, a swap is far more complicated and can involve an exchange of cash flows based upon multiple currencies, credit events, indices, and interest rate movements. However, the simplification doesn’t obfuscate key points to be made.

  • While the auto executive’s contribution to his company’s bottom line isn’t discernible until years have passed, the trader knows immediately and unambiguously how well he is doing on any given day.
  • While the trader has generated $8 million—which immediately flows through the company’s income statement—he also retains other positions, namely: a $100 million bond (an asset), a $100 million loan (a liability), and an obligation to pay $2 million each year for the next five years (another liability). These appear on the company’s balance sheet and their values are subject to change.
While all companies try to compensate employees on the basis of individual contribution, few are able to track performance in the way of a Wall Street manager by simply glancing at the tally in a trading ledger. From this perspective investment bankers are like ballplayers and actors: Trading gains have their corollary in home runs and ticket sales as an irrefutable and real time metric of success. High contributors, therefore, have considerable negotiating leverage. On the other hand, there is no tolerance for individuals who don’t perform. In fact, a Wall Street manager’s primary responsibility is to determine who among the workforce should receive walking papers prior to bonus season. Layoffs are expected each year and are meant to reduce the number of ways the bonus pool is split.

That being said, there’s a problem in how trading profits are calculated and you might have noticed it already—particularly if you consider what has happened at AIG. In the example above, the trader booked $8 million in profits today, but he still holds positions that can turn on him tomorrow. In particular, the $100 million liability is huge in comparison to the profit he booked. To demonstrate what can go wrong, let’s say the asset (the bond) defaults. The trader no longer receives the 5% payment from the bond, but he’s still required to pay: 1) the 3% on the borrowed money and 2) the $2 million a year on the swap. In addition, when the loan comes due in five years, the trader will have to repay $100 million and may not receive any money from the maturing bond. In short, while he made $8 million today, he exposed the company to a potential loss that could be in excess of a hundred million dollars.

So where am I going with this? The way Wall Street employees are compensated is based upon income in a given period and doesn’t fully reflect the residual risks of their positions. This encourages traders to book as much income as possible today and deal with future problems only as they arise. After all, getting a multimillion dollar payout this year will go a long way to easing the disappointment of getting canned the next. Do you think those AIG swap traders will shed tears if the company doesn’t survive? I’m sure they’ll cry all the way to their yachts.

And that’s the problem in a nutshell. The traders were compensated in such a way that they were encouraged to book income today that subjected the company (and the entire marketplace) to enormous risks for an extended future. One might say that they felt ownership for the periodic income, but not so much for the risks in the positions they retained. If we really want Wall Street to act with more integrity and prudence, bankers must be made liable for their mistakes. Forcing companies to reserve against leveraged positions and restricting bonus payments until trading positions mature or are unwound is the right direction. That would accomplish more than any other regulatory change to the industry.

Furthermore, on a broader scale the notion reemphasizes a point I’ve made in earlier blogs: When we make people owners of creative resources and value-generating processes they are more likely to act with a social conscience.

March 17, 2009

Wall Street: Is Greed the Problem?

Lori and I stick to a budget today and we worry about the next tuition installment with three boys at school. We, like most people, have seen our 401K—not to mention the equity in our house—drop like a rock in value. We’d like to sell our place and buy something smaller, but that might not be possible for years to come. I don’t know when I’ll be able to retire.

One day, while I was pondering these circumstances, I began to apologize to Lori about the twists and turns in our lives. We didn’t start out wondering how to make paychecks last. At one time we didn’t worry about money at all. Saving was something we could do without much thought or planning, but not anymore. Before I could finish my apology, Lori interrupted with what I thought were the kindest possible words: “I love that you turned your back on a good paying career to be a better person.”

I had to look away so she couldn’t see the feelings running through me—emotions as varied as they were powerful. On one hand, I felt grateful that she believed I’d left Wall Street to become a better me, but in truth, I wasn’t sure it was the best explanation for what I’d done. In the back of my mind, I’ve always wondered if I simply wasn’t tough enough to keep going.

It took me a long time before I could think of those years without hyperventilating or feeling a wave of nausea. Today my memories of Wall Street are accompanied by a feeling I can only describe as a murky cloud. It’s the same cloud that sought to engulf me every day I sat at a trading desk. Perhaps you will understand a portion of what I’m saying if I mention that I started my career structuring CDOs and went on to run a Structured Product desk that turned out, among other esoteric instruments, Credit Default Swaps. Both, as you probably know, have been significant contributors to our current financial debacle.

What you won’t know, however, is how much of my business was about avoiding regulations that were meant to protect shareholders and the integrity of financial markets. Nevertheless, I can say without equivocation that I never did anything illegal. In fact, I can point to a mountain of legal opinions to prove it. But therein lies the conundrum: If you need a legal or accounting opinion to prove you’re in compliance with regulations, chances are you’re trying to get away with something.

I learned early on that the most profitable Wall Street deals never appear on trading screens or League Tables, but are consummated quietly in order to hide embarrassing situations or past mistakes. Since confidentiality is always essential for these quiet deals, they're seldom subject to open bidding. Many are meant to fabricate income that isn’t really there, or avoid losses that really are. Some are tax-related and designed to assign losses to a party that needs them.

Even as I tell you this, I know what you’re thinking. I know because I've heard dozens of people say it, including the President: There's too much greed on Wall Street. Yet, if that’s the case, then I must suggest the problem is not limited to high finance. I’ve met executives from a range of industries who were just as greedy as people working on trading floors. If greed is the underlying problem with our economic malaise, it’s a general problem of which the majority of Americans are at fault. I will, in future blogs, describe the cause of Wall Street's risk taking and management problem and what can be done to fix it (Surprise! The solution is related to ownership!) but for now let me say this: Maybe I wasn’t tough enough to survive Wall Street, but I’m certainly a better person for having left it.

March 15, 2009

On the Prospect of Being a Grandpa

Shh…this is just between you and me, okay? I have a secret. You see, it appears that I’ll become a grandfather in June. Consider yourself informed. Now, mum’s the word.

At first, the news wasn’t easy for me to accept. It was another reminder that I was heading inexorably toward creaky-limbed old-fart status. What was to come next? Adult diapers and soft food didn’t seem too far behind it. Then something remarkable happened: I saw that little girl on TV. You know the one—the precocious child who demonstrates how to email a photo of her pet fish and ends the commercial by saying, “I’m a PC and I’m four and a half.” Suddenly, I wanted one exactly like her.

My change of heart is due, in part, because my daughter-in-law, Piper, is a beautiful young woman from China, whose childhood pictures remind me of that PC girl. But there’s more to it than that. During the twenty seconds, or so, while the commercial played, I was reminded again of the reasons we cherish children and how much we can learn from them.

Here are a few ways they are infinitely superior to us old coots.

Children are refreshingly honest. Even when they stray, they don’t make excuses. Listen to a child ask for sweets and what do you hear? They don’t say, “Nine out of ten dentists claim this is good for your teeth.” It takes them a while before they can justify, cajole and haggle like an adult. All they say is, “I want it.”

Children believe in magic. They jump from stumps and fence posts, run like the wind and act like masters of the universe. And because they are unburdened by adult fears, they are free to be motivated by love and the best of all intentions.

Children invest in dreams. I'm not speaking of our day-time musings or even our night-time fantasies, but rather the sense for who we can become. This sense is important, because the alternatives to proper dreams are horrific. In fact, it’s difficult to imagine anything as frightening as a human being with evil intent, unless it’s the mass of humanity with no intent at all. And while most adults have spent their dreams, children continue to invest in them. In the end, it’s what will save us all.

Children are insatiably curious. Despite their natural tendency to believe everything we say, children still ask “Why?” It’s the best of words. I’m sure a youngster invented it and it’s the driving force behind a child’s incredible growth.

Children are fair to a fault. Take the youngest child out for an ice cream cone and he or she will insist that you take more home for the siblings. They are our fairness monitors and they fulfill their roles to perfection.

On second thought, tell the world my secret. I’m starting to feel pretty darn good about the prospect of being a grandpa.

March 8, 2009

Why Noblesse Oblige IS Important

Do you remember that awful moment in American history, when the big news of the day was about a stain on an intern's dress? Do you recall the incredulity we felt as the Starr Report was published for the world to read and how we weren't sure what was worse: the arrogance of a man who'd deemed himself untouchable, or the incredible waste of time and energy the arrogance had caused?

At the time the facts were emerging, my family and I were living in Japan and my children were going to the American School on the outskirts of Tokyo. One morning my oldest boy got into trouble for making a reference to subject matter that had been covered in great detail in the media. When the school called to tell me of the punishment he would receive, I couldn't help but see a terrible irony in the situation. Both disappointed and embarrassed, I wrote the following letter, which was published in the Japan Times. Please, let's not ever say character doesn't count.

Dear Sirs:

Today my fourteen-year old son was told that, as punishment for something he said, he won’t be welcome on the school bus next week. This action raises an interesting question regarding what is–and is not–acceptable behavior.

The facts are not in dispute. There was a conversation at the back of the bus regarding the Starr Report. A boy asked a question that, though tasteless, was consistent with the juvenile curiosity of those involved. He speculated as to whether Ken Starr asked Monica if she, “spit, or swallowed.”

As a course of observation, my son replied, “There’d be no reason to ask that since the evidence was on her dress.” People within earshot agree: This was his only contribution to the discussion. However, a parent, who happened to be sitting nearby, complained to school officials. As a result, several students, including my son will have to arrange alternative transportation next week.

I won’t fight the punishment. I think it’s reasonable to maintain standards of taste and decorum. But what of Bill Clinton? In a world where a young boy can be punished for making a comment no more vulgar than the factual events detailed in the Starr Report, what lesson have we taught the most powerful man in the world about the acceptability of his behavior?

Yet more importantly, what underlying message have we passed on to our children? One thing is for sure; my son has learned a lesson and it’s not a pretty one. He might say: If you’re the president, it’s okay to engage in illicit sexual activity. Moreover, you can lie about what you’ve done and even get others to lie with you.

But if you’re a fourteen-year old boy, watch yourself. Don’t even talk about what the president does. That would be too vulgar.

The Great Debate

Let’s tone down the hyperbole. It just isn’t helpful. People on the pro-choice side of the debate are no more murderers than pro-lifers are Nazis trying to take away civil rights. Folks on both sides of the question are trying to do what they believe is proper—they simply have differing points of view. If we put aside the rhetoric, perhaps we can come to some common understanding.

To me, the issue reduces to this: When does human life begin?

One of the most interesting questions I heard during my years in school was: How do we define life? It’s not as easy to answer as one might assume. Is digestion or respiration life's defining component? If so, some chemical processes mimic the functions and would demand inclusion. Is sentience the requirement? That would exclude a whole host of what we consider life, including the beautiful oak tree I’m looking at beyond my back deck. Is the ability to propagate the standard by which we measure life? Here again, some inorganic processes involving protein strings might classify by such a definition. Life, therefore, is a lot like pornography: You might know it by looking at it, but defining it is a different matter.

But that’s exactly what we must do if we’re going to get anywhere in our often rancorous discussion about abortion. Between conception and birth, if there is a point beyond which life can be reasoned to begin, a woman should have a choice about her body prior to reaching it. On the other hand, once that point has been crossed, it becomes our Rubicon.

If we focus on the issue, rather than call each other names, we might find our way out of what seems an inextricable impasse. For a nice treatment of the subject, take a look at the following:

The author, Joe Huster, is an academic and lawyer, who makes a carefully reasoned appeal for understanding.

March 7, 2009

Musings on the Nature of Time

What is eternity? Is it simply a never ending series of days?

If Einstein taught us anything, it’s that time possesses extraordinarily complex physical properties. For example, one of the questions Brian Green raises in his book, Fabric of the Cosmos, is: Why does time appear to have an arrow? Why, in other words, does it seem to progress only into the future, when nothing in Einstein’s equations prevent it from slipping into the past?

Interest in the nature of time isn’t a recent phenomenon, as people have been musing on its properties for centuries. A central theme in Jewish mysticism, for example, is the unknowable quality of the infinite and eternal. The Greeks, too, considered time’s many complexities, asking whether it could be subdivided to some atomic equivalent, or if it was continuous in a way that defied division. They had two words for it: chronos and kreinos—the former being man’s time and the latter God’s time—which suggests it comes in two versions.

The study of mathematics has had far-reaching effects on our ideas of time. Einstein’s general theory of relatively, for instance, relies upon a complex number line to define what has been labeled the fourth dimension or time space. Complex numbers—sometimes referred to as imaginary numbers—appear often during the course of solving certain mathematical equations (the term x2 = -1 is an example) that results in the square root of a negative number. Such a solution shouldn’t exist—at least not in any world we understand. Mathematicians have invented a sleight-of-hand to deal with them, but for a long time people didn’t know what to do when complex numbers appeared. Then Einstein came along and showed how they were essential to a fully developed theory that would replace much of Newtonian physics.

Perhaps the most interesting discovery that furthered our understanding of time is Georg Cantor’s studies on infinity (which, if you think about it, is the mathematical corollary of eternity). His proofs are elegant and simple, but rather than show them here, let me summarize the implications of his work with a single sentence.

Infinity comes in various levels of value and complexity!

It seems incredible, I know, since every infinite set has no end to it, but they can differ with respect to dimension. One of the least complex varieties is, for example, the set of all integers, which relates to our common reckoning of eternity as a never ending number of days. It can be thought of as a number line—a single dimension. However, there are higher—much more complex—versions of infinity that are not bound by anything resembling a series of integers.

Cantor showed, for instance, that all the numbers between 0 and 1 (let’s call this set A) is greater than the set of all integers (this we’ll call B). Again, I won’t show the proof, but suffice it to say that A contains dimensions not included in B, including an infinite set of transcendental numbers. Transcendental numbers, as you probably know, include pi (π), which in their various decimal representations never end or repeat. (Pi is approximately 3.14159, but the digits continue on and on without pattern). If you’ve ever thought about transcendental numbers, you’ll have considered how they relate to a number line. We can show approximately where they are and do so with increasing degrees of precision, but they defy being placed in a precise location.

Is it possible that eternity is more than an endless number of days, but something that is unbound by time in the way of a complex number? Can a particular moment in eternity defy placement in the way of a transcendental number? At the very least, these are interesting ideas to ponder.