We do not know the past, present or the future

We don’t know the past, present or future, and we don’t even know the probabilities of the past present or future.

I was out rowing today I told my friend. "Oh on a lake?". No in the streets. "What?"

People are always basing their conditions on their experience and known world view, but the present is always changing, the underlying conditions are always uncertain. I love to row on the roads, especially in the snow, I love to bicycle on the ocean. I am not joking.

Paul Wilmott has some good points on his recent blog Magicians And Mathematicians, how wrong many bad-quant are when it comes to probabilities. Yes all probabilities are conditional; there is no such thing as unconditional probabilities. I tried to illustrate similar (but more exotic) concept in my “Coin Flip Blow Up Article” some years back in Wilmott Magazine (also in my book Models on Models). Paul's example is much more down to earth, much more practical, here the conditions are more normal, my example was based on some hidden conditions up in a zero gravity environment. My example was similar to watching a magician that you had no clue was a magician. But then that Paul’s example is more practical is again based on uncertain conditions. If some of my friends are astronauts then may be my 'coin flip blow up' example is more practical under my conditions. Paul tend to hang out with magicians and is also some sort of magician himself. I tend to hang out with people rowing in the streets.

Of course we never fully know the conditions or even the present, but most quants implicitly assume they do, at least in their models, and many of them even trust their models. We never know the present situation with full certainty. The present is changing continuously (or at least at every planck second depending on your probability assumptions/conditions around physics). And no object or living form can have all the information all the time. Information takes time to go from one place to another, and information is part of the present, information is energy, energy is mass, mass is energy , when information moves so also do the present. Even trying to collect information or observe something will affect the present and the future. If the magician gets the feeling some in the audience will recognize his trick, he will possibly change it into another trick in the last moment. If you want to observe properties of an electron you need to shoot something at it (other electrons, photons or whatever the physicist call these partly ‘unknown’ entities) and this will affect some properties of the electron you are observing. The more details you want to know about the present situation the more you will affect it and also the future. No this is not only at a quantum level but also in every day life, for real objects like humans. If you in the middle of a magic show suddenly run over to the magician to try to uncover his trick then you could certainly affect his trick (or his body guards). If you think a bank is quoting you a price you can arbitrage and you then get uncertain if this really is an arbitrage opportunity, then the more you dig into the situation the more likely the counterpart will figure out he/she is quoting a too good price. The more information you seek about the current situation then in general the more likely you are to affect the ‘current’ conditions. This happens in the market all the time, and then the counterpart could quickly pull their bid or offer. Well often I even tell people when they can be arbitraged, at least if they obviously simply miscalculated and gave me ridiculous wrong price in my favor. I also tell them when they try to rip me off. In general I want good long term business relationships (long term greed versus short term greed).

That all probabilities are conditional and that all conditions are uncertain, basically means there are no true probabilities. At best we can only talk about uncertain probabilities. Yes some probabilities are much more probable than others, the more information you collected the longer time series you have the better you will in general be to estimate probabilities. That is most of the time. But here also comes the danger. The more information you have, the more experience you have with standard probability calculus etc. the more likely you are to be confident or even over-confident. This is when you will do the biggest mistakes. When the conditions behind your probabilities have changed.

My friends next time I tell you I am going out to do some rowing, do not expect it to be in the streets or on water, it will be somewhere else.