I'm surprised I haven't yet seen a review/mention of Taleb's books on the
Agonist. "The Black Swan" should almost be prescribed reading for this
place.

http://fooledbyrandomness.com/

This book confirms the value of a broad global, long
term historical empirical rather than ideological view.

The Agonistas understand that the here and now rules our daily life,
but somewhere else,
- unpredicted and perhaps unpredictable
- and on a time scale much larger than a corporate accounting period,
are the events that will rule our future.

I'd love to take the author, Nassim Nicholas Taleb, of the book "The
Black Swan" to a lake a few kilometers from me. There are blacks swans
literally as far as the eye can see....and nary a white one!

Europeans, prior to bumbling down under (I resent the term
"discovered"), thought, on the basis of thousands of data samples,
that all swans were white...

If I were to reduce this somewhat large and rambling book to a
sentence, it would "Very Improbable events are more probable than we
believe, and have larger impact than we'd expect."

He amply justifies this statement from many angles....

He covers some of (very large) body of psychological experimental work
that enumerates just how appalling Bad we humans are at evaluating and
predicting low probability / high impact events. And how dysfunctional
our postfact rationalizations are.

This is a favourite hobby horse of Bruce Schneier, author of "Beyond
Fear : Thinking Sensibly about Security". Speaking of which, a basic
understanding of "Beyond Fear" should be a prerequisite to voting
rights.

Taleb uses perhaps too much page space on the historical, literary and
philosophical limitations of induction. Although his critique of
post-fact rationalizing bites hard. I feel ashamed and contrite.

The book would have been stronger if he had a chapter or two of solid
mathematics for those who grok it.

He expends too many lines, if I'm permitted to generalize Taleb
slightly, too much effort deriding our trust in finite moment
distributions as models for reality.

A bit more mathematics and more concrete examples would have done
a better job of convincing.

Although I concede his the point that even the best models in the
world will not save us from the unforeseen and unforeseeable. The
"unknown unknowns".

Anyway, he describes variables dominated by the mediocre as being from
"Mediocristan".

You (and, worse, the engineers who built the stands) would be utterly
shocked if the average weight of all the people in a football stadium
was dominated by the weight of just one man.

How ever, the average wealth most likely _will_ be dominated by that
of the richest man.

ie. Variables like wealth, web site hits, commodity prices, number of
posts on the Agonist etc. etc. are variables from Extremistan.

In deriding the use of Gaussian models, he perhaps overstates the
case. In estimating individual samples, a properly calibrated model
does just fine 90% of the time thank you.

In estimating aggregates like the effect of daily fluctuations on your
portfolio's value after a number of years. He is perfectly
correct. The extreme values and the "unknown unknowns" are the
dominant effect, Gauss normal models are hopeless.

Models where the probability of extreme values falls off
exponentially faster and faster are mathematically tractable. We can
do stuff with them, and they can be fitted very well to the common
ordinary everyday values we deal with.

Such models _don't_ fit the extreme values of many real world
quantities, and somewhere along the line, in a large aggregate, we are
going to have one or more extreme values.

And so our models will fail, since the extreme values will dominate the
aggregate.

Anyone being burnt by the current global subprime mortgage crisis and
wondering why, should be scrabbling to buy this book. NOW.

One of the reasons the lack of mathematics in the book hurts his case
is everybody on the planet, who has had a year or two of statistics,
knows the Central Limit Theorem.

This is what he really needs to dislodge. Not standard economics
models, but deeply ingrained yet half remembered factoids about the
central limit theorem.

I call it "The Brown Soup Theorem". (As in, mixed all the finest and
best ingredients on the planet in a pot and boil'em up, it will taste
and look like... brown soup.)

Almost everybody with a degree knows that averaging will, remarkably
rapidly, reduce anything to a nice tractable standard Gauss normal
bell curve distribution (or close relative).

Admittedly there's some fine print on that, but who remembers the fine
print after the exam has passed?

If pushed, most people will mutter something about independence
between the variables.

Well the fine print most have forgotten is, the central limit theorem
only works with variables that have finite variability (variance).

Extremistan Quantities like... ah, most financials, have infinite
variance, and yes, when you average them you produce things looking
remarkably like the appropriate member of the nice bell curve Gauss
normal family.

Except the average also has a long tail and the average _still_ has
infinite variance!

This point is in the book, but I wish it was much more prominent and
formally laid out since more than anything it shocks me awake. (I'm,
oh so guilty, of having plotted histograms of averaged quantities,
eyeballing them and saying that's sort of normally distributed and its
full width half maximum is....)

In summary: "The Black Swan" is broad scholarly and literary ramble
through the vital issue of why we consistently ignore, forget, fail to
foresee and then discount the improbable events that dominate and drive
history.

Read this book next, it's a Black Swan, a rare improbable book that
will substantially alter your interpretation of what you read there
after.