For over two thousand years the idea of a ‘Black Swan’ has been synonymous with something that does not exist or cannot exist, and comes down to us originally from Aristotle’s Prior Analytics where the concepts: white, black and swan are proposed as predicates in syllogisms using white + swan as a necessary relations and the black + swan as an improbable or impossible one – not an entirely unreasonable position when you consider that no one had ever seen anything but white swans and seven eights of the world was unknown to the Greeks.

The Black Swan form was further popularized from the 2^nd century on by Roman satirist Juvenal’s couplet:

rara avis in terris nigroque simillima cygno

[a rare bird in the lands, and very like a black swan]

Until quiet recently it probably seemed like a valid simile, since no one in the Western world had ever seen a swan with anything other than white plumage – right up until Dutch explorer Willem de Vlamingh discovered black plumed swans existing quite comfortably outside of the ken of science in 1697 at the Swan River in Western Australia.  Cygnus atratus was made official when it was described scientifically by English naturalist John Latham in 1790, and the metaphor continued to live on in modified form to connote a perceived impossibility that might later be disproved.

The notion of a Black Swan was picked up again by science from the 18^th century on from David Hume to, John Stuart Mill, Karl Popper [and beyond] in regard to the Problem of Induction in logic.  For today you will be spared any further reference to THAT particular problem.

Back to the Present

To give you some background on present argument Nassim Nicholas Taleb  is a Lebanese born statistician, financial trading expert, professor, essayist and author who has focused his work on problems involving randomness and probability particularly in the financial sector.  His best selling book The Black Swan encapsulates his theory about rare and hard to predict events that have great impact upon society which has been taken up and popularized as Black Swan Theory.

In a nutshell Black Swan Theory is a theory of the disproportionate impact of rare, unpredicted and undirected events in history and the subsequent rationalization that takes place in their aftermath to retroactively make the ‘Black Swan’ event explainable and ‘predictable’.  Examples that Taleb uses include:  World War I, the personal computer, the rise of the Internet and the September 11^th attacks.  The determining characteristics in each case being that the event was a surprise [at least to the observer] that the event had great and lasting impact and, unique to the theory, that the event was rationalized by hindsight.  Each one of these examples could be nit-picked, and I will, but for now we will accept them as being illustrative of the theory.

Black Swan Theory as presented by Taleb has three key characteristics:

1. The event is unpredicted, a surprise.
2. The event has extraordinary impact or consequences.
3. The event is rationalized retrospectively, as if it could or should have been predicted or expected.

Taleb describes it thus in the NY Times:

What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives.

Taleb’s Black Swan theory characterizes epistemological uncertainty, what we cannot know or predict, differently than earlier theorists in that, he posits a “fourth quadrant” where the usual statistical tools used by statisticians to gauge uncertainty and build models to simulate future events are no longer sufficient to predict the effects of rare, high impact events – both uncertainty and consequences become large – where as in the conventional three quadrants only uncertainty or consequences, or neither, are large.  Taleb calls this Fourth Quadrant dominated by large uncertainties and catastrophic impacts, “Extremistan”.

This “fourth quadrant” was not always recognized previously and people involved with using statistics often relied on a belief Taleb calls, the Ludic Fallacy, which is the assumption that the unstructured randomness found in life resembles the structured randomness found in games.  This, according to Taleb, is a dangerous assumption because the unexpected can be predicted from extrapolating [inferring] from statistics based on past observations only if they are assumed to represent a bell-shaped ‘normal’ curve or Gaussian distribution.  [remember economics class?]  As it turns out, Gaussian distributions aren’t normal in “Extremistan”.

While technical in nature, Taleb argues against Decision Theories that operate out of a fixed universe that ignore and minimize the effects of events that are outside the model, and are limited to considering only ‘known unknowns’ and that has no way to accommodate the ‘unknown unknowns‘ that populate a real universe with its fourth quadrant – some days its Normalville, some days it’s Extremistan and you will never be able to tell which it is going to be until you lookout your office window and see the nose of a 757 coming at you at 500 knots.

With Black Swan Theory Taleb has moved beyond on the classical problem of induction in logic, specifically, that of drawing general conclusions from specific observations that dogged earlier theories of improbable events and moves on to ‘high impact’ as the central and unique attribute to his theory, his claim being that “almost all consequential events in history come from the unexpected,” but a hindsight bias comes into operation after the fact.

While in I like Black Swan Theory and Mr. Taleb’s brand of thinking in general, particularly in regards to the safe and effective use of statistics [and strong sense of irritation at the French], the misuse of tutelary animals is where I draw the line.

The Tutelary Beast

Misuse of tutelary animals? Well that is a new one, and what pray tell is a tutelary animal exactly?

A tutelary animal [you could also have tutelary plants if you want] is an animal symbol that represents a set of key attributes of something in the human world.  For instance the horse might be considered to be the tutelary animal of the Age of Steam during the industrial revolution, that period in Western Europe and North America between roughly 1770 and 1914.  Think about it for a moment, “horse power” as the standard unit of mechanical power, and the “iron horse” as moniker for the steam locomotive, both point to the horse as the metaphor for the tractive effort of steam, tamed for the service of man.  Also, the early steam engine is articulated like the limbs of a horse, it consumes fuel and excretes waste, it ‘breathes’, and for thousands of years the horse had been a primary Western symbol for fieriness.  One could of course come up with different criteria and different animals to describe that period of Western history, but the point is that the animal symbol is supposed to teach you something about how to understand the concept under consideration, in our example the Age of Steam is supposed to be more understandable by recognition of the horse as being emblematic of the age.  It is in this way that the black swan is supposed to be a tutelary animal symbol for Nassim Taleb’s theory of rare, high impact events.

In the case of Black Swan Theory I think the tutelary animal used in metaphor was singularly badly chosen, for a number of reasons.  In particular if the black swan is supposed to be representative of rareness to the point of unpredictability, which I think it is not.  I think that for an intelligent and educated person that if you were making a broad survey of the category of swans, that a black swan is exactly the type of swan you might expect to discover if you were traveling to an exotic and distant land.  Consider that the ‘concept’ of ‘black swan’ predated the discovery by Western science of an actual black swan by almost two thousand years.  If you can hold open a category for the existence of an unexpected thing for thousands of years, exactly how unpredictable can you say it was when you finally run across one in nature?  It is also significant to observe the subcategory of ‘black’ is also a rather minor and superficial distinction in plumage color in comparison to ‘white’ especially in regards to the one’s knowledge of the entire class of Aves, – birds – black is a common attribute of birds, though not of swans.

Meet the Platypus

If one were a well trained naturalist visiting for the first time a distant and exotic land, what beast might you discover that would epitomize the notion of strangeness and unpredictability?  If you were visiting Australia in the 18^th century I might suggest that the discovery of the platypus is the one that would most astonish your set of categories about what is predictable or possible in the animal world.

The platypus, Ornithorhynchus anatinus,  is one of the strangest, most category defying creatures you are ever likely to come across, it has a bill and webbed feet like a duck [or a swan] a tail like a beaver, ankle spurs like a rooster which in the male deliver a powerful venom [very rare amongst mammals], the platypus and its four monotreme relatives are also the only known mammal to use electrolocation.  The platypus skeleton contains extra bones in the shoulder girdle not found in other mammals and has a reptilian gate.  To top it all off the female platypus, as with the other monotremes,  is also unique in that she lays eggs instead of giving birth live to her young like reptiles and birds, and her eggs are leathery and meroblastic like reptiles, yet she produces milk from mammary glands to nourish her young, but from pores in her skin. not from proper teats like other mammals.

The discovery and classification of the platypus was a thoroughly category defying event, it took science a century to fully come to terms with it, in fact when news of the platypus first reached the ears of the men of science [it really was the ‘men’ of science back then] the platypus was assumed by intelligent people to be a hoax.  From Wikipedia:

When the platypus was first encountered by Europeans in 1798, a pelt and sketch were sent back to Great Britain by Captain John Hunter, the second Governor of New South Wales.^[4] British scientists’ initial hunch was that the attributes were a hoax.^[5] George Shaw, who produced the first description of the animal in the Naturalist’s Miscellany in 1799, stated that it was impossible not to entertain doubts as to its genuine nature, and Robert Knox believed it might have been produced by some Asian taxidermist^.[5] It was thought that somebody had sewn a duck’s beak onto the body of a beaver-like animal. Shaw even took a pair of scissors to the dried skin to check for stitches.^[6]

The discovery, correct understanding and classification of the platypus was an unusually impactful event in science because it forced a general reexamination of the definition of what it was to be a mammal as well as taxonomical methods in making those types of categorical decisions.

For these reasons I propose a new tutelary animal to replace the black swan at the masthead of Taleb’s theory – The Platypus – as being vastly superior in teaching us what to know about what we do not know.  Not that I expect anyone to pay attention to my suggestion, Black Swan as a title has much more coolth to it than Platypus ever will – it sounds funny – it is funny, a platypus is an inherently absurd creature, never the less it is the correct tutelary animal for the theory at hand.

Unfortunately for my pet idea the term Black Swan has already become the accepted, and it is almost impossible to change such things once they start – too bad for me for being late on the scene.  Still, even though Black Swan is a much catchier title for a book, [who would pick up a book entitled, “The Platypus, the Impact of the Highly Improbable”?] Platypus is actually a much better teacher.  So, people will continue to buy and read Taleb’s book and rush out in into the world armed with this new theory and apply it with wild abandon to every next, big thing regardless of how truly unpredictable, impactful or retroactively reinterpreted it actually was.

People, I believe, would be much more circumspect about hanging the title of Platypus recklessly upon a event, which is exactly my point; it is this very strangeness and category defying aspect of the Platypus event which itself becomes a new key attribute to distinguish a truly unpredictable or rare event from the mundane.

Next up in the series I propose a Fourth Key to Black Swan Theory.

~ Visin