...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Wednesday, September 17, 2014

Poundstone on People and Predictions

"Rock Breaks Scissors"  by William Poundstone

I keep seeing William Poundstone's latest book, "Rock Breaks Scissors" in the 'business' sections of bookstores… which I think is ashamed, because a lot of readers who would enjoy it may miss it there. More appropriately, and like most Poundstone books, it should be in a science/math area, or perhaps under psychology. Poundstone is one of my favorite authors; a good writer, dealing with subjects I find interesting, and at a level accommodating a lay readership.

Some of his volumes are deeper and richer, and others less so, but interesting and timely. This new book is in the latter category. It is yet another of the surprising array of recent volumes dealing with probability and numbers to hit the popular book market. Poundstone isn't dealing with math or probability in an academic context, as some popular volumes have attempted, but in a very reader-friendly, real-life practical sort of way.

The book is divided into two broad parts: Part 1 relates to "randomness" and part 2 relates to 'hot hand theory' -- the author tries to get across two opposing ideas that govern our actions: i.e., we often perceive things as random when in fact there is actually a pattern involved, and conversely, in other contexts of life we perceive patterns, where none exists and greater randomness is at work.

I'll briefly mention several chapters of the book:
The Prologue begins with some discussion of the work of information theorist Claude Shannon, but also includes mention of Bernie Madoff, as well as an entertaining, famous example from the retailer Target, a couple years back, when one of their purchasing algorithms deduced that a certain young lady was pregnant long before even her parents knew -- I mention all this simply to indicate the sort of diversity of subject that typifies this volume all the way through.

Chapter 1 is a little introduction to randomness, with some focus on examples from parapsychology, and also a well-known example from psychology of how poor, people are at creating "random" sequences when asked to do so (a knowledgeable individual or professor can pick out a human-created sequence from a truly random sequence).

Oddly, the title of the book stems from the quite short chapter 2 which is a treatment of the betting game, "Rock, paper, scissors," and various strategies to employ for greater success.

Chapter 3 covers some of the oft-used strategies (and patterns to look for) when taking multiple-choice exams, such as the SAT.

Chapter 4 offers strategies for playing lotteries -- I didn't find these very convincing (but then I don't play lotteries, so what do I know).

Some chapters follow delving into certain sports actions (tennis and soccer), and then card games, again always about how to better recognize, as a player, human predictability.

Chapter 9 is a practical one on creating passwords for the internet (especially after the author informs us that one "free hacking program, can test millions of passwords a second," and another "forensic" program "claims it can check 2.8 billion passwords a second." :-(

Chapters 11-13 are some of the most interesting ones, centered initially around Benford's Law (of integer distribution), and the ways it can be used to detect fraud, financial malfeasance, or just manipulated numbers.

Chapter 14 begins the second part of the book focused on "hot-hand theory." Hot-hand notions have been written about a lot in recent years (popularly in relation to basketball scoring runs), and it remains a controversial subject. Poundstone also notes that "hot-hand" notions are exactly opposite of another oft-cited prediction failure: "the gambler's fallacy" -- in the former, people overly believe a trend (sinking basketball shots) will continue to occur because it has in the recent past, but in the latter people erroneously believe a change will happen because of a non-probable trend that has just transpired (i.e., a roulette wheel will come up "red" because it just had 6 "blacks" in a row and is 'overdue.')
Anyway, chapter 15 moves on from specific hot-hand ideas to basketball betting pools (as in the NCAA March Madness tournament) -- oddly there is no mention of Tim Chartier's methods here, though they've received a lot of publicity the last couple of years.

Chapter 16 moves along to football pools, and I'll relate one quote I enjoyed from it:

"One problem with sports betting systems is that anyone who looks hard enough for a pattern tends to find one. It might be that the Denver Broncos always won on odd-numbered days in February when playing teams named after animals. Analytics is good at finding such patterns. It's not good at saying whether you should believe in them."

I think that more-or-less captures the message or sentiment of the whole second half of Poundstone's book.

Chapter 18, on 'Big Data' (everyone's favorite topic these days) is a fun, interesting intro to all the ways we can barely fathom that info is collected on us. Also, he gives a practical hint on how to get discount offers flowing your way, calling it the "abandoned shopping cart play." Again, I'll quote what to do when you're on a retail website:

"Put whatever you want to buy in a retail site's shopping cart. Click 'check out.' Begin filling out the form. Make sure you enter your e-mail address but don't enter any payment information. Leave the purchase in limbo and wait for the discounts to roll in."
(the point being that once you've expressed interest, but departed, the retailer is going to do whatever it takes to entice you back to complete an order)

The next couple chapters deal with pricing, followed by a chapter on predicting the future, where he notes that even professional experts are generally much better at forecasting far-off broad trends than predicting near-term happenings (which one might think would be easier to predict being so much closer in time) -- you might think in terms of predicting the percentage of heads in a thousand coin tosses versus predicting the percentage in say 10 tosses.

At close to 35 pages, Poundstone's final chapter, on the stock market, is by far the longest one of the book. If you're active in the market (especially if you trade for yourself) there will be MUCH of interest here, but if you have no connection to the stock market, and talk of things like PE ratios (which the chapter is VERY focused on) cause your eyes to glaze over, then this chapter will be a yawner.

Anyway, the volume is chockfull of examples and is a fairly fun romp (even if sometimes shallow and choppy) through many different, often timely, ideas. I do recommend it to folks, as I think most people will find various chapters of interest, and learn some practical or quirky tips along the way, though I can't predict ahead-of-time which chapters will be most rewarding to you, the individual reader... but then Poundstone probably could've predicted my limitation.

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