Let's Get Rid of Causation in Finance.

This chart comes from Zerohedge today.  It makes me laugh.  Is the world one?  That is, it is so interconnected in terms of web-based and email connections, that messages from the market manipulators instantaneously infects our own wet-ware so that we unconsciously push buttons that amplify particular messages in the noosphere?  "Correlation is not causation" so says Zerohedge repeating the mantra that distinguishes the knee-jerk Palovian-Skinnerian stimulus-response reductionism of our poor little brain from the rationality and decision-making processes of the game-theoretic monsters that can crunch big data until a particular solution fits the circumstances just inside the horizon of noncomputability (NP-Hard problems).  The best papers still in this area where SPIRITUALITY meets PHYSICS are by Emilie Nother -- Einstein's tutor in infinite-dimensional Hilbert space and lovely well-loved teacher who only wanted to teach but the idiotic German Universities could not even give her a proper teaching post.  In the long run of a future history, Germany in the late 19th and 20th centuries will be castigated not only for Nazism but also because its chauvinistic attitude against women--and Noether will be remembered far into the future, farther than when people forget about Hitler.  When Noether died, Einstein wrote something to the effect that she had discovered the first spiritual law of physics.  There are a couple Noether Theorems, but the one FINANCE THEORETICIANS SHOULD PAY ATTENTION TO but do not is the one that allows one to move from an energy conservation law to dimensional space.  How she moves from correlation-covariance is very similar to what the finance theorists from Bachelier to Miller tried with almost brute force.  Basically, Noether moves from correlation through covariance using symmetries. Symmetries as we know in the early to first half of the 20th century is the algebra of group theory, and allegedly, our standard model is based in the ideal on our methods developed in group theory.  Group theory to me looks like it depends on identity, associativity and invertibility (reversal).  I was studying this area for a while back in 2006-07, and then imagine my delight and surprise to find a theory that could encompass and ground group theory using only identity and associativity!  That is, why study Group Theory when Category Theory could do all of group theory and go even much farther?

So now we can come back to the two graphs above.  How do we compare them?  You might say, "Do a correlation analysis and determine the variance."  OK. Then you can do the "co-variance analysis" and come up with a number you can compare against other co-variances.  But this assumes a standard deviation metric underneath, in other words, a normal distribution.  As everyone knows in finance except the crazy financial regulators, there is no such animal in the de facto.  "Volatility" is not a good measure.  What would be a much measure would be a fractal dimension a la Mandelbrot.  If we got use to a Mandelbrotian measure, we'd have a much better feel for the "jitteriness" and "emotionality" of prices, and very importantly, we'd have much better metrics and therefore, a better language to gauge and communicate our intimations and observations of what's actually going on.

To realize these intuitions, I believe we have to build from the ground up, and link the above charts to particular geometries, and to talk about them properly, we would need a new vocabulary that would allow us to make comparisons between the charts and the contexts that surround them in an absolutely precise way.

While we would never say Chart 1 causes Chart 2 or vice versa, we could say without any problem that Chart 1 is isomorphic to Chart 2, and then we would be forced to make explicit exactly WHAT THE PROCESS that makes the isomorphism up.  If we could do that, we would not ever again bother with the concept of "causation" in finance.