A colleague of mine who was a part-time professor once told me that he always emphasized with his students the importance of being quantitative in their thinking. He said it gave them a tool for assessing the credibility of various claims that people might make.
The example he gave was as follows: “Suppose someone tells you they’ve read a million books during their lives.”
How credible is that claim? Well, it depends on the age of the person making the claim, but we can put an upper bound on it with a few simplifying assumptions, and see if we get an estimate that is in any way realistic.
First, we can assume that the person is 100 years old. Second, we can assume that they have been reading essentially since birth, i.e. that they have been reading for all of their 100 years.
This means that average number of books they have read in a year is:
(1,000,000 books) / (100 years) = 10,000 books per year
This means that the average number of books they have read in a week is:
(10,000 books per year) / (52 weeks per year) = 192 books per week
This means that the average number of books they have read in a day is:
(192 books per week) / (7 days per week) = 27 books per day
This means that they would have had to read a little more than 1 book per hour, non-stop, 24 HOURS A DAY, 7 DAYS A WEEK, 52 WEEKS PER YEAR, FOR 100 YEARS. SINCE BIRTH.
Speaking for myself, this seems like quite a stretch even for the most extreme bookworms and speedreaders I know.
We can come up with a more realistic estimate by doing the calculation in reverse using some more realistic assumptions. Let’s start by assuming that even the most dedicated bookworm and speedreader might polish off 3 books per week.
In a year, they will read:
(3 books per week) x (52 weeks per year) = 156 books per year
If they are fortunate enough to live to be centenarians, then in a lifetime they will read:
(156 books per year) x (100 years) = 15,600 books in a lifetime
Remember that we are estimating here. The exact number is much less important than getting a “ball park” value to determine the credibility of a claim.
If a retired person claims to have read several thousand books, and you know that they have been an avid reader for most of their lives, then their claim is believable.
If a teenager, who only has about 10 years of reading under their belts, tells you that they have read 1,000,000 books or even 10,000 books, then it is pretty safe to conclude that they are blowing smoke at you. A more realistic claim for such a person would be on the order of a few hundred books.
Remember that this is just one example. Math, and the power of quantitative thinking, gives you a very effective tool for assessing the credibility of any such claims when people start throwing numbers around.