Answer:
From an email exchange with Professor Stewart:"It’s actually a fairly simple equation, mathematically speaking. What caused trouble was the complexity of the system the mathematics was intended to model.... You don’t really need to be a rocket scientist to understand that lending hundreds of billions of dollars to people who have no prospect of ever paying it back is not a great idea...."People took a theoretical equation too seriously, overreached its assumptions, used it to justify poor decisions, and built a trillion dollar house of cards on it. This made the crisis inevitable:"I think that the crisis became inevitable once the financial instruments being traded in gigantic quantities became so complex that no one could understand either their value or the risks they entailed. When markets trade real goods for real money, excesses can only grow to the limits of what is actually out there. When they trade virtual goods (derivatives) for virtual money (leverage), there’s no real-world limit, so the markets can gallop off into Cloud Cuckoo
Explanation:
Physicist: If you have plenty of chalkboard space and absolutely nothing better to do, you can write down numbers, letters (Greek if you’re δυσάρεστος), and mathematical operators and eventually you’ll have the longest equation ever written down. So if you really want to see the most complicated equation ever, call in sick for a few weeks. A better question might be “what is the most (but not needlessly) complicated equation?”.There are plenty of equations that are infinitely long, but often they’re simple enough that we can write them compactly. For example, This equation goes on forever, but it’s fairly straight forward: every term you flip the sign and increase the denominator from one odd number to the next. You can write it in mathspeak as . Like π itself, this sum goes on forever, but it isn’t complicated. You can describe it simply and in such a way that anyone (with sufficient time and chalk) can find as many digits of π as they like. This is the basic idea behind “Kolmogorov Complexity“; the length of the shortest possible set of written instructions that can produce a given result (never mind how long it takes to actually compute it).If you’re looking for an equation that needs to be complicated, a good place to look is physics (I mean, what else do you really need math for?). If you want to describe the behavior of a ball flying through the air it’s not enough to say “it goes up then down”; there’s a minimum amount of math that goes into accurately calculating the path of falling objects, and it’s more complicated than that.Arguably, the universe is pretty complicated. But like π, it is deceptively so (we hope). If you want to do something like, say, describe the gravitational interactions of every star in the galaxy, you’d do it by numbering the stars (take your time: star 1, star 2, …, star n), determine the position and mass of each, and , and then find the force on each star produced by all the others. In practice this is absurd (there are a few hundred billion stars in the Milky Way, but we can’t see most of them because there’s a galaxy in the way), but the equation you would use is pretty straight forward. The force on star k is: . This is just Newton’s law of gravitation, , repeated for every possible pair of stars and added up. So while the situation itself is complicated, the equation describing it isn’t. Evidently, if you want an equation that genuinely needs to be complicated, you don’t need a complicated situation, you need complicated dynamics.
If is confusing than I can use a different example:)