Book Review: Innumeracy, by John Allen Paulos

In Innumeracy – Mathematical Illiteracy And Its Consequences  John Allen Paulos launches himself against the tide of mathematical illiteracy both as a polemicist and as a teacher.

 His stated purpose is to appeal to innumerates with enjoyable and illuminating examples of everyday, as well as fanciful, uses of mathematics.  I enjoyed the book, and some Bankers Anonymous readers would as well.

 The problem: only the numerate will read the book.  All innumerates – the intended audience – will put the book down by the 3rd paragraph of the first chapter.

 Probability and Coincidences

Paulos provides a valuable example of the stock market promoter who sends out a newsletter to 32,000 potential customers, predicting a specific upward or downward movement in a stock.  At the end of 6 such random predictions, this promoter will have been right 6 times in a row to approximately 500 astonished people.  At this point, the promoter can offer a $500 subscription to those remaining 500 people.  If they pay up, he pockets $250,000. 

A variation of this classic example is explained well in Nassim Taleb’s Fooled by Randomness as well, and should be kept in the forefront of the minds of everyone who interacts with the Financial Infotainment Industrial Complex.

Just as coin tosses of a completely fair coin frequently run in hot streaks in seemingly improbable ways, many of the patterns we think we see in financial markets are more noise than signal.


Pseudoscience will fool people who don’t have numbers fluency.  Seemingly improbable ‘coincidences’ turn out to be less miraculous with a little bit of math.  Highly unlikely events become highly likely – given enough chances. 

I appreciate that Paulos repeats a great piece of wisdom my college advisor once told me: Any system of orthodox thought ,like Freudian psychology or Marxism, which cannot be criticized – without exposing oneself to counterclaims of ‘neuroses’ or ‘class-blindness – is a pseudoscience. 

Real systems of thought, however powerful, are open to criticism from the outside.  It’s a simultaneously humbling but empowering idea.  No system of thought, however powerful, is without its weaknesses.

A useful book – but who will read it?

 Paulos fills his book with examples of how we can be easily misled about numerical scale.

 I find this is true in personal finance – not understanding the incredible scalable power of compound interest, for example, or in public finance – not grasping the power of large numbers when it comes to the national debt.

 Innumeracy is probably most fun for people who already understand 95% of the math Paulos uses.  The book then becomes for readers a confirmatory exercise in ‘Look at me and the math I already understand,’ rather than fulfilling his stated purpose of ‘More people should be relatively numerate and I’m going to make that case, at the same time helping innumerates get started on a better math path.’  I don’t see his supposed intended audience – innumerates – making it through from start to finish.

 I’m not making this critical argument about a book that came out 25 years ago in order to point out a flaw in something few people have read.  What I’m doing in reviewing Innumeracy is thinking out loud (ok, in print) about the problem I face with personal-finance writing.  Namely, how do you convince an audience of smart-but-non-finance folks that:

A. They should want to understand finance better for their own good, and

B. They should read my stuff to help them get started down the learning-finance path.

 I fear that my personal finance writing attracts people already comfortable and fluent with financial topics, seeking confirmation of their relative sophistication.  “Look at me, I understand finance and I read stuff by a former Wall Streeter still in recovery from his finance profession,” readers may say, rather than, “I’m an educated but non-finance person eager to get started in better understanding my world through a financial lens.” 

Obviously I want both kinds, or rather all kinds, of readers.  But my highest value-added proposition, in terms of a personal finance book, is for the non-expert reader.

Reviewing Innumeracy, which, in my opinion, fails in its stated goal, reminds me of the challenge ahead.

 Suggestions on this present conundrum, from all kinds of readers, are welcome!


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