What is Chaos?
These are
systems which are non-deterministic. However, the interesting bit is that they
are often governed by deterministic equations. The sad part is that it is
difficult to reverse-engineer this process. So if you look at a random card
generator in a casino, you might think that it is completely random. However,
the machine uses certain rules (for the inquisitive minds – look up Rule 30 in
2-D cellular Automata) to generate this card. The trick lies in the difficulty
of deciphering this process as they are the closest realizations of true
randomness. Chaotic systems are also very sensitive to initial outcomes, a
small change in the input can lead to massive changes in the way the future
values turn out to be.
Why does Chaos matter for the oracles of today?
Now I hope
that most of us agree that many things in life are chaotic and this is what
makes them interesting. Say you are at some state and want to predict the
future – assuming the system is chaotic – the initial error can accumulate and
lead to massive difference in the prediction and the future reality. Added to
this there might be some Black Swan (See previous post!) awaiting you. I know
it is a bit fuzzy and abstract at this point – So let us take an example – Sorry
but the math cannot be delayed anymore!
Say we have
a function – x (n+1) = 4*x(n)*(1- x(n))
For Slightly
different starting values – let’s see how the future values turn out. I made a
small graph for some (read just 3) values. The errors in the initial input are
less than 1.5% and yet the future prediction can be way off. If we start at
0.75 (highly unlikely) it turns out to be a very stable outcome. Now think of
anything that diverges from this as your prediction error and look at your
ability to predict. This clearly highlights why prediction systems often fail!
Moreover, we seldom know the precise form of the equations and often calibrate
it based on past data. Imagine what a 5-10 % error (acceptable by many
standards) can do to your predictions! So we need to know whether the things
that we predict – markets, weather and book sales are such chaotic systems.
The
financial market analysts who “claim to” know the way the market will behave
rely on the equations (not developed by them) to do this. Given the present
state – the future should be deterministic they say. However, what they fail to
realize is that such equations are extremely sensitive to inputs and often
ignore (Alas!) the “highly (im) probable but highly consequential” Black swans.
You can't
see the future precisely because you don't really know what's causing it. This
is the huge problem with us. We almost always justify things and associate a
cause to things that were unexpected before they happened. As Taleb says – “We
attribute our success to our skills and our failures to all external factors
beyond control”.
How do we
deal with Chaos? We despise it. In-fact order is substituted with elegance. Remember
the time when you saw an elephant shaped cloud? This might be the pinnacle of
our ignorance – how we want to simplify things, put them in order for our
convenience. The only sad thing is – reality is a zillion miles away! As a
result we often see luck being mistaken as skill in many places (think if those
intelligent investors).
The problem does not end here –
Till this
point I have argued that we are terrible at predicting. It gets even worse when
we try to justify our forecasts and fail to learn from history. However the
problem bigger problem is – we are always too optimistic about stuff. We tend
to over-value a lot of things in the present and this is bound to make us
suffer in the future. One important idea made famous by Rob Shiller (Yale) is
that of “Irrational exuberance”. How we attach a irrational/sentimental value
to things we possess – making them seem more valuable in the present. At the
risk of making the discussion less general, lets venture into the field of
economics (surprise!).
