This is a beginning stab at addressing my earlier question about what we can learn from the current economic crisis. It will probably take several posts to lay out my hypotheses and opinions, so please indulge me, and feel free to chime in (*I mean it. Having a conversation with yourself is not what the web is made for and besides, I've got too many of those going on in my head already*).

To begin, I want to pick up on two of the items I mentioned in that last post:

- Mistaking wishful thinking for reality, and
- Ignorance of the assumptions and limitations that are built into the mathematical models upon which high-stakes financial bets were placed.

This is extremely common in all areas of life, but particularly so in the financial arena. Often, it evolved into a group delusion, akin to the psychiatric disorder,

folie á plusieurs(madness of many). Nobody bothered to pay heed the few who checked the facts and thought for themselves. That which did not fit with consensus reality went unheard and unseen, because with delusional systems, inconsistencies with one's world view literally 'don't compute.' It's odd how history repeats itself. This is something Daniel Defoe (1660 - 1731) wrote about theSouth Sea Bubbleof 1720:

Some in clandestine companies combine;

Erect new stocks to trade beyond the line;

With air and empty names beguile the town,

And raise new credits first, then cry 'em down;

Divide the empty nothing into shares,

And set the crowd together by the ears.

II. Ignorance of the assumptions and limitations that built into the mathematical models upon which high-stakes financial bets were placed.

Apparently, many of the problems that caused financial systems to implode were flaws in the financial models used to predict outcomes. These models include but are in no way limited to so-called 'neural networks' (Incidentally, 'neural networks' do not replicate the brain's computational actions in any known way. They are simply pared down, highly abstracted, regression equations).* The term "neural networks" smacks of marketeering: taking a form of statistical analysis that is in the public domain and can be done by anyone with the appropriate background, giving it a catchy new name, and making it sound far more special than it actually is.

Regression equations predict the likelihood of an outcome or outcomes, based on the input of a series of input variables (in other words, data about various characteristics that are hypothesized to be good predictors of that outcome. The highest possible adjusted R

^{2}(this is also called the 'regression coefficient), indicating a 100% likelihood that the array of independent or input variables will produce a particular outcome, simply does not occur in nature. The reason is common sense: any outcome has multiple predictors, some of which are known, some of which are knowable, and some of which are neither. Moreover, every predictive model by definition comes along with an error term (this is a statistic that shows the average amount of error that one can expect) and a confidence interval (this shows the band within which 68.2%, 95.4%, 99.6, 99.8%, 99.9%, and on and on, of the true scores are likely to fall. Note that one can never reach 100%. It is an asymptotic curve, that is a curvilinear line that approaches nearer to the 'destination' (in this case, 100% of the scores falling within the confidence interval) but, though infinitely extended, would never meet it.

In fact, one of the central tenets of mathematical prediction is that

no equation, no matter how perfect it is, can ever predict an individual outcomewith 100% certainty. Moreover, there are several critical assumptions that must be met for the equation to be valid (regardless of whether it is statistically significant or not). An unique feature of the current situation is that, due to advances in computer and communications technology, it is now possible to run equations on truly massive data sets. This enables the mathematician to achieve higher and higher levels of statistical significance and power (meaning that the likelihood of getting a result that is way off by chance alone is greatly reduced). However, as the data sets get bigger, so does the likelihood of the highly improbable occurring, as Nassim Nicholas Taleb notes in his book, The Black Swan: the Impact of the Highly Improbable. Well, guess what? They did. In a sense, the financial community, in the throes of itsfolie á plusieurs, failed to take into account that their seemingly brilliant decisions were made on a foundation ofinfauxmation, that is something masquerading as highly credibleinformation, but is distorted, inaccurate, presented without necessary caveats, or just plain wrong.

In Charles L.L.D. MacKay's 1820 book, Memoirs of Extraordinary Popular Delusions and the Madness of Crowds (worth reading based on the flamboyantly weird title alone, but also worth reading for its content), the author relays the following story:

An enthusiastic philosopher, of whose name we are not informed, had constructed a very satisfactory theory on some subject or other, and was not a little proud of it. "But the facts, my dear fellow," said his friend, "the facts do not agree with your theory."—"Don't they?" replied the philosopher, shrugging his shoulders, "then, tant pis pour les faits;"—so much the worse for the facts!

In short, financiers, government officials, and consumers in the throes of *folie á plusieurs * and 'armed' with infauxmation -- both amplified by speed, volume, and computing power -- constitute a marriage made in Hades.

Remember, this is just a beginning. There is much more to say and to discuss. For example, per George Santayana ("Those who forget the past are condemned to repeat it.”), there is the question of forgetting and of how we manage to get ourselves into these binds over and over again without, it seems, learning a thing. Another topic is the impact of elected (and selected) officials -- especially the creeping devastation that results when ideology dominates governance, crowding out the rule of law.

Oh yes, there is much more--so stay tuned!

* Statisticians, please forgive any simplifications I have made in the interest of increasing the comprehensibility of the concept's description.