If there's one thing the financial crisis has taught us, its' that we grossly misjudged the risk we were taking on. We offer five perspectives on rethinking risk -- on everything from finance to housing to social policy--in the hopes of stopping the next major meltdown before it starts.

How did it happen? How did the sub-prime mortgage crisis cascade into the Wall Street meltdown and then the worst recession since the 1930s? One answer crops up over and over: It was the math. According to Wired magazine, a single equation, the Gaussian Copula Function, brought down the financial system. Joseph Nocera of The New York Times attributes the Wall Street disaster to a mathematical system known as Value at Risk, which supposedly allowed a large financial company to calculate its exact chances of disaster. Financial writer Michael Lewis blames an older formula, the Black-Scholes model for pricing stock options. In other words, Wall Street came to believe that all risks could be priced and therefore known by math. If known, they could be managed.

That this was all a deadly illusion is now beyond argument. The financial and economic crises have their foundation in the most basic misjudgments about risk--not just about specific risks, although there were plenty of those--but about the nature of risk itself. In 1921, the economist Frank Knight distinguished between "risk" and "uncertainty." Risk was something that could be calculated, as in a game of roulette, whereas uncertainty (in John Maynard Keynes' more accessible summary) was something like "the prospect of a European war," about which "we simply do not know." In the frenzy of calculations, the concept of uncertainty--or what former Defense Secretary Donald Rumsfeld called "unknown unknowns"--was lost. And as the trader-turned-author Nassim Nicholas Taleb has argued, the delusion that risks can be managed often creates far greater volatility and danger.

The consequences of misunderstanding risk reached well beyond those who chose to take the risks--or their computers. Wall Street, supported by a political culture that was in awe of it, effectively socialized its risks onto the public (which is why we are paying AIG's bonuses today) while privatizing the rewards. At the same time, for households, risks that had once been socialized--through what remained of the American social contract--were privatized, borne by struggling workers and their families.

The social and political mood of the last 30 years was to embrace these trends rather than provide a countervailing force to reduce risk and increase security. Families shifted, usually involuntarily, from defined benefit pensions to vulnerable 401(k)s, from savings accounts to investments in individual stocks, and from secure health care to medical-savings accounts or no health insurance at all. Corporations, caught up in former General Electric CEO Jack Welch's doctrine that the corporation's primary obligation was to deliver ever-increasing returns to shareholders, steadily got deeper into debt while stripping away every cost that could not be directly related to short-term profit. In March, Welch renounced the business philosophy for which he is best known, calling it "insane." (The 30-year lifespan of the Welch doctrine coincides neatly with the years of conservative dominance of government, from Ronald Reagan to Barack Obama.)

A central mission of government is to manage risk and uncertainty, whether it is societal risk, such as war, or individual risks, such as unemployment or disability, which will befall only some of us and which can be accommodated only by spreading the costs broadly. Individuals not only can't manage to prepare for such risks but much research suggests that we are congenitally unable to think clearly about them. At its best, the U.S. government has helped Americans take risks that allow them to make the most of their talents (such as through student loans or the Federal Housing Administration) and avoid or insure against other risks. But during the Bush years in particular, government manipulated our perception of risk. It exaggerated some risks, as in Vice President Dick Cheney's "One Percent Doctrine," which held that if there were a minuscule chance of a terrorist attack--the ultimate uncertainty--we should act as if it were certain, at the expense of the Constitution and much else. And it dismissed other risks, promising an "ownership society" that would encourage households to take on even more of the risk of overpriced stocks and housing.

The resounding rejection in 2005 of a plan to convert part of Social Security to a system of private accounts was the beginning of a recognition that security and social insurance are not stale, outdated concepts but essential to providing the platform from which individuals are able to take the kinds of chances that lead to real opportunity and economic growth, not just asset bubbles. The collapse of the housing market, stock market, and much of the overgrown apparatus of Wall Street, together with the advent of a new political order that takes the middle class seriously, marks the end of that long era of irresponsibility.

But what comes next? We are starting from scratch. How can we rebuild a financial structure and a society in which we think more sensibly and constructively about risk and uncertainty, without the comfort of equations and markets? How do we rebuild government's role in protecting us from risk, a role it once served so well?

We need a new social contract, one not limited to regulation of financial markets, but one that reaches from Wall Street right down to the kitchen table, putting limits on systemic risks at the top, while providing a platform of security that allows individuals to take some chances--the kind of productive risks that will actually help them get ahead, like going back to school or starting a small business. At the top, managing risk requires more than markets; it requires institutions that can make choices and bear the consequences of the risk. The creation of endless markets for risk, fueled by the prices set by the equations, made revolutionary economic advancements possible. But it also made it possible to continually shift a dangerous risk around from one sucker to another.

We should know by now that social insurance remains a vitally important concept. No unregulated market and no basket of stocks can provide the kind of security against real uncertainty--the risks that we can never really know about--that a robust social contract, built on the idea of social solidarity, can. All aspects of the social contract are frayed and need updating, from unemployment insurance to Social Security, and new forms of security, such as paid family leave, are needed to give workers the ability to take their own chances and make the most of their talents in the economy.

And we should recognize that sometimes a little inefficiency is a good thing. Redundant systems provide a kind of security, and corporations stripped down to the bare bones in the quest for profitability carry untold risks. The financial crisis is a reminder that, in the name of efficiency, we can construct systems in which the institutions are so intertwined that the collapse of one brings down all of them. The Glass-Steagall law that separated commercial banks from investment banks, which was repealed in the 1990s, had the effect, although it wasn't its main purpose, of keeping banks smaller and putting some firewalls between different parts of their operations. A minuscule tax on financial transactions, sometimes called a Tobin Tax after the Yale economist who first proposed it, would have the beneficial effect of putting a little sand in the gears of transactions, deterring some of the colossal risks that banks were able to construct by piling one cheap transaction on another, and shifting them continuously through the market rather than making money the old-fashioned way, making loans and holding them.

Risk is not going away, but the genius of democratic capitalism is that we are able to build institutions that enable us to manage risk together, taking advantage of some risks while protecting both individuals and the system as a whole from the worst consequences. For at least 30 years, we have been transfixed by the idea that the market, with the help of some clever math, could practically do this alone. That idea has collapsed as quickly as the financial house of cards it supported.

Now we start with a blank slate. It's time to consider not just what happened during the era of risk and how we got into this mess but some alternative ways of thinking about risk. In the articles that follow, five academics, journalists, and financial practitioners (and some who have crossed those lines) point out the paths toward a new way of thinking about risk. For them, it's not just a matter of fixing the equations but of restoring government's role in protecting us from risk, of changing incentives at all levels to prevent the powerful from shifting the consequences of their risk-taking onto the rest of us, and of bringing risk down to earth by restoring a connection to local circumstances and community. Above all, though, they understand that risk, in the sense of taking chances, is essential to our continued prosperity but that only by managing risk well, both by regulation and by providing a platform of security for individuals and families, can we achieve its benefits for all without repeating the gut-wrenching economic disaster that we're living through today.