The main point of Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics by Robert B. Banks, is that mathematics is a language that can describe, measure, and help inform us about everyday points of human activity. The book uses mathematics such as differential equations, integro differential equations, the calculus of variations, and some physics (mainly the laws of motion and free body diagrams) and statistics (least squares regressions). Using these methods Banks explains many events such as; the impact of objects falling from the sky, the shape of a sagging flexi-cable, the shape of a jumping rope, how to throw a curve ball, how strong waves are, oscillations in the records of football teams, how fast one can run and how high and efficiently one can jump, how strong bridges and buildings are, how fast epidemics spread, how far it is possible to tow an iceberg… and how fast dominoes fall.

Like all good books, this one can be read on many levels and many times over. I read it because I want to see how math could better prepare me to understand the physical and market factors that move. I found it very interesting in this context, and particularly liked the many uses of the Logistic equation to explain such as the spread of rumors. I also enjoyed seeing the various estimates of pi that simple geometric diagrams like inscribed circles in a square can generate.

Unfortunately the author is woefully uninformed about statistics. Indeed it does not look like he knows how to compute a standard deviation from individual observations, as he classes observations into groups and intervals and then computes the standard deviation based on the numbers in each group rather than the individual observations. Nor does the author know about the common limitations of regressions, when such factors as multi-co-linearity appear, and why one should hesitate to use squares and cubes in some regressions. The chapters where he applies mathematical methods to deficits and debts contains numerous omissions and errors of analysis. His discussion of predicting the future height of a child based on the child’s percentile height at an early age, which is the kind of thing that market people think about all the time, is terribly naive and misleading. Indeed on all the subjects that I have even a rudimentary knowledge of, such as those that touch on economics, I find the discussions and models painfully inadequate. But they are suggestive.

The author is a professor of fluid mechanics and he is not sheepish about believing that the lay reader has some expertise in that field. Within the first eight pages he develops a mathematical model of a baseball that assumes the reader knows about functional relations between viscosity, roughness, velocity, the Reynolds number, the velocity of sound in a gas, and such things as the Fronde and Weber numbers. Admittedly , my physics knowledge is deficient, having had only a college level course in the field and dabbling in electronics as a hobby, but it would have seemed that the author could have chosen a subject for his introductory chapter that the educated layman who he is writing for, might have had more familiarity. Indeed, most of the chapters suffer from either being much too technical for a reader not familiar with physics and accustomed to using such things as free body diagrams, or, when the author deals with economics, being much too naive and out of date to have much import.

Despite this, the topics covered raise many interesting ideas and tests for the market speculator. Some that sprang to mind after reading the book the second time were: What is the area of a chart that is covered by points, and lines, relative to randomness? How long can one market tow another along for? What is the time to travel a certain distance in a market that is showing parabolic growth? What is the price limit of how much a soybean oil can sell for when it is limited by the size and price of the soybean crop itself — perhaps according to a logistic relation? What is the easiest and most effective path for a price to take from one level to another a’la a pitcher throwing a curve ball to the plate? How high can a stock go, based on its initial ascent during a year or a day?

The author is apparently an old timer who likes to use puns and jokes, and I believe that his persona and style is captured by the following quote:

I decided to be a bit light hearted in the analysis of some of the problems. It just seemed like a good idea to not always be entirely serious about everything.

I recommend this book to all market people who have a reasonable interest and background in physics, and to all others who like to gain insights from other fields and other methods of analysis that might help them to improve their feel for the markets.

Rick Foust adds:

For anyone seeking a practical compilation of engineering formulas and methods, the books engineers use to prepare for Professional Engineer exams are hard to beat. These are available at most university book stores.

Or If you prefer a high tech approach Mathcad is the tool of choice. And then there are various widely accepted topical references, such as Crane Technical Paper 410, Flow of Fluids.

But as in statistics, it is essential to understand the assumptions implicit to the formula.

A standard engineering calculation follows the format: Problem Statement, Data, Assumptions, Formulation, Calculation and Conclusion. Of these sections, “Assumptions” is the most important. Assumptions are the cornerstones for calculations ranging from bridge to nuclear reactor design.

The worst calculations I have seen were generated by engineers having excellent memories yet poor understanding. As an example, such a fellow engineer once asked me to verify his perfectly logical three page calculation that proved a long bolt can take more torque than a short bolt (it can’t, of course). Fortunately, important calculations are typically verified by a second engineer, and engineers like to find things wrong with the works of other engineers.





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