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It's Complicated


Ross M. Miller
Miller Risk Advisors
June 13, 2011

This commentary was going to be about teaching finance, but that's complicated and so will have to wait until later in the summer at a minimum.

My hard drive now a directory with 388MB of PDFs that are the manuals for the various things I own that require a manual and for which the manual is readily available in PDF form. This collection does not include several important manuals, such as the one for my car, nor for most of the software that I use because those manuals live elsewhere on my main hard drive. I do not remember anything coming with a manual in my youth (except for the Cub Scout Manual). My first notable manual was that for the Harman Kardon 230A stereo receiver that I purchased in 1973. The manual for that receiver is in my PDF collection even though I destroyed the receiver itself in 1981 by inadvertently covering its top air vent, something the manual did not adequately warn me not to do. (The physical manual itself could be somewhere in my attic if it did not succumb to one of my periodic toss-everything-out sprees; I know that I keep it for quite a while for the sentimental value.) The receiver was reincarnated two years ago in my house as the Harmon Kardon 3490, which is probably the cheapest receiver available with any chance of driving Magneplanar speakers adequately. (Mini review: Lots of power, horrible tuner section, pathetic Chinese build quality, does the job, has not broken yet.)

I may have all of these manuals, but I clearly don't know most of what is in them. I have been driving the same car for four-and-a-half years, but I only recently discovered that I could switch quickly between the FM and XM radio using two dashboard buttons and without leaving with the navigation system display. Supposedly I can talk to my car and get it to do all sorts of things, but then I'd have to learn exact what to say to it to get it to do things. I have a variety of Bluetooth headsets, but I have no idea how to initiate a phone call with any of them. Even simple things like the iPod Touch and iPad have all sorts of quirky specific ways in which one must interact with them to use them.

Fortunately for me, my brain is still here and working, possibly not as well as it was in my twenties, but it is going strong nonetheless. I just have better things to do than read manuals and memorize what a certain pattern of flashing lights means. If I ever need to know anything, I know where to find the manuals and how to use Google.

Nonetheless, there is something out there that it much more difficult to deal with than all my electronic stuff combined and that is Mathematica. I have been with Mathematica from Day One-I have an article in the premier issue of the Mathematica Journal about doing the Black-Scholes model in Mathematica (this was before unfortunate revisionist thinking added Merton to the mix, more on him when I start going senile). All of my market mechanisms and robots are coded in Mathematica and this summer I am turning my attention back to Mathematica in the hopes of coding some more.

Mathematica has grown considerably in the over twenty years that it has been around. It used to have a 1500-page book that served as its manual, but now its total documentation, which is not available in book form, exceeds 10,000 pages. Moreover, that documentation is massively incomplete. Much of Mathematica can only be figured out by trail-and-error combined with attempt to think like a physicist who was a child prodigy. Unlike LISP and APL, languages close to my heart from which it evolved, Mathematica lacks a solid logical foundation. While LISP is based on a mathematically elegant concept of recursive evaluation, Mathematica is about "simplifying" expression rather than evaluating them. One can write LISP-like code in Mathematica, I certainly have, but that misses the point. This summer I am trying to get more in the swing of Mathematica to create things that leverage its capabilities much more than I have in the past by channeling my inner physics prodigy. Right.

I began the summer ambitiously thinking that I could convert my entire existence to Mathematica, including how I teach finance. I was going to create nifty Mathematica notebooks with all the big concepts of finance there, including direct access to its financial databases, a new feature in Version 8. The problem is that while Mathematica has "player" software that does not require the user to know Mathematica, that software is highly limited in how it can retrieve financial data. Really useful notebooks require the use of Mathematica itself and not some extremely limited subset of the language.

Of course, any software with over 10,000 pages of documentation has a learning curve as steep as Everest. Things that are simple in Excel, like printing a WYSIWYG copy of what is on your screen, are mind-bogglingly difficult in Mathematica. (By default, Mathematica printouts look nothing like what is on the screen and use microscopic fonts to save paper.) There is also no way to get around the fact that working with Mathematica involves doing real computer programming in a language that has nearly as many square brackets as LISP has parentheses. Without a crack team of teaching assistants to field student questions, using Mathematica in an introductory finance course is an invitation to an endless stream of anxious student e-mails. (With teaching assistants, it may just be an invitation to endless teaching assistant e-mails.) Also, some of the cutesy stuff in Mathematica that use sliders can be done in Excel with only a minimum of programming.

Ironically, even with its massive complexity, Mathematica is trivial compared with finance. My collection of finance-related PDFs now exceeds 1GB and that excludes virtually everything that I have in book form. Furthermore, Mathematica is a well, if somewhat poorly, defined man-made system. Finance, on the other hand, is a hybrid system that defies definition. Introductory finance courses (other than mine) act like it all works nicely and is easily understood, when nothing could be further from the truth. This summer my research will grapple with the importance of all this complexity; my commentaries will stay more down to earth. Next time, I finally get to a topic that I mean to write about earlier this year and explore Tucson and Kashmir.

Copyright 2011 by Miller Risk Advisors. Permission granted to forward by electronic means and to excerpt or broadcast 250 words or less provided a citation is made to