# Illiteracy and Innumeracy – Why Quantitative Reasoning? 精选

The problem of ILLITERACY is obvious to everyone. It is one of the most important, if not the most important problem, any developing nation tries to solve. The problem of INNUMERACY, however, is far less obvious. But in an increasingly digitalized and globalized world, more and more people need to be able to deal with things and events that are associated with numbers. The current call by the US President Obama to emphasize mathematics and sciences in American schools so as to enable US to compete with Asia more effectively is but one reflection of the increasing need to eliminate innumeracy in a civilization. All entering Freshman at Harvard regardless of their major are required to successfully pass a test on quantitative reasoning before they are allowed to graduate (the other two requirements are the ability to swim and to take a course on English composition).

Thus what is innumeracy and its opposite –quantitative reasoning? Let me give an example (due to Professor Brian W. Kernighan of Princeton University). At the height of the last oil crisis in 2008 when oil reached the price of $110/barrel (see http://bbs.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=23518 ), and gasoline at$4.25/gallon,  a New York Times article suggest that the US used its strategic oil reserve of some 600 billion barrels stored inside a huge cave  to increase supply and lower oil prices. Thus the questions arise as to whether this is a good idea and if used how long will the reserve last? And if you were the President of the US or the Secretary of Energy how would you answer such questions?

Let us attempt some “quantitative reasoning”. First we need to know how much gasoline the US uses per year which in term lead to the question

How many cars are there in the US?

We know there are approximately 300 million person in the US (a fact most people know and taught in every elementary school). Let us assume there is one car for each person. At first glance this may seemed high since babies obviously do not own cars. But then we realize that there are many public cars, such a police vehicles, taxis, buses, etc . Thus one car/person may not be excessive.

Now most drivers in the US know that on the average each car gets about 20 miles/gallon and a car averages about 10,000 miles per year. Simple calculation then yields the fact that each car consumes an average of 500 gallons per year or an approximate total of 150,000 million gallons per year for the whole nation.

Next we must answer the question

How many gallons are there or can we produce from one barrel of oil?

Most of us have seen an oil drum and a gallon can. We can make an educated guess. 10 gallons/barrel seems too low. And one hundred gallon/barrel appears too high. Thus 50 gallons per barrel is more plausible. (If we want to have an independent check on such an estimate, then we can do the following. At $110/barrel of oil and$4 per gallon of gasoline, we have a factor of approximately 25. However, typically cost of material is half of the selling price. Thus another factor of 2 should be added to 25 producing the same number of 50 gallons/barrel).

Now combining these two facts we deduced, we see that the US consumes approximately 150,000 million gallons of gasoline per year and have 50x600 billion gallons = 30,000,000 million gallons of gasoline in reserve. Or the astounding “fact” that our reserve can supply us with gasoline for 200 years. THERE IS OBVIOUSLY SOMETHING WRONG HERE! It turns out that the usually reliable NYT make a numerical mistake. Our reserve is 600 million, and not billion, barrels. Most people lose a sense of proportion when numbers get beyond a million, billion, and trillion. This is surely the case with the writer or copy editor of this article whom we are sure are well educated in literacy but possible not in quantitative reasoning or numeracy.

Professor Kernighan ( as well as if you Google  “innumeracy”) has many examples of such grossly wrong facts being propagated in Wall Street Journal, the New York Times, and Wikipedia. In fact he teach a course on quantitative reasoning at Princeton on (In)numeracy to non-science students. See also http://www.princeton.edu/as/LNL/presentations/spring2010/LnL020310KernighanInnumeracy2.pdf

The point he want to drive home is that we should develop the numeracy of our population just as literacy. All we need is nothing beyond elementary arithmetic (add, subtract, multiply and divide) and common sense. (see note 1 added).

Sometime, persons or groups with an agenda will utilize innumeracy of a population to advocate and exaggerate their particular point of view or to scare people. The well known phrase made popular by Mark Twain – “Lies, Damn Lies, and Statistics” as well as the book by the same name by Joel Best . and even better known the book “How to Lie with Statistics?” by D. Huff in 1954 are examples of such manipulation relying on innumeracy of the public.

In conclusion, question numbers or statistics you read in popular press. Arm yourself with some well established facts (such as the size of the population of the US, and the average mileage of a car as in the above example), use common sense and elementary arithmetic to guide yourself and not be misguided intentionally or un-intentionally by others.

(Note 1. It is a matter of parental pride that when I mentioned the oil example to my adult daughter who is a non-science major in college her immediate response were the two pointed questions I analyzed above. In fact from these questions she deduced the one car/person and 50 gallons/barrel figures herself exactly as Professor Kernighan suggested.)

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