Innumeracy , a book that was referred by Zhao, the fictional teacher in " The art of profitability ". It deals with the lack of a specific set of skills among a lot of people, the lack of a sense of numerical proportion and an appreciation for the irreducible probabilistic nature of the world.
In a sense, the book makes readers aware of a lot of common fallacies that pervade our world view and consequently, our thinking . Innumeracy , in authors words, is the inability to deal comfortable with the fundamental notion of number and chance.
John Allen Paulos urges the readers to develop the skills of estimation by posing few interesting questions like :
- How many trucks would be needed to displace Mount Fiju / Himalayas completely, considering that there is a truck available to remove the rubble every 15 minutes ?
- How large should be a container be , in order to fill the blood of the entire humanity ?
- In any random selection of people of more than 23 people in a room , what is the probability of 2 people having the same birthday? answer to this is pretty surprising
- Human hair grows at what speed ? in miles/hours
- How many cigarattes are smoked in a day in US/India ?
In all these questions, it is not important to know the answers to the precise decimal point. However the answers to any of these questions involves getting some basic estimates about various things right ? Now one might be wondering the reason for thinking about these questions.The reason is that it gives one a healthy sense of handling big numbers. Now why should one get a healthy sense of big numbers ? Because , getting a sense of large numbers is a must to get a sense of context and its chance of occurring.
Be it while conducting a business transaction, or reading a newspaper clipping, having a healthy sense of big numbers helps one to take better decisions and be in a better position to analyze opinions and random facts which are publicized in the media.
Apart of focusing on a number of simple mathematical concepts, here are a few learnings from the book :
- Law of large numbers states that in the long run, the difference between probability of some event and the relative frequency with which it occurrs approaches zero.Implies difference between 1/2 and freq of heads approaches zero
- Gambler’s Fallacy : Mistaken belief that because a coin has showed head several times, it is going to show tails in the next event.Hence, it is important to distinguish between Law of large numbers and gambler’s fallacy.
- Central Limit Theorem : Averages and Sums of non normally distributed quantities will neverthless have a normal distribution
- Type I and Type II errors : Type I is when true null hypo is rejected, Type II is when true alternate hypo is rejected. Here are a few good examples to understand the above errors : When money is distributed , the stereotypicl liberal tries hard to avoid Type I errors (deserving not receiving their share )and conservative is more concerned avoiding type II error(undeserving receiving more than share). When punishment is meted out, conservative is concerned with avoiding Type I error(deserving not receiving their due) and liberal worries about avoiding Type II (undeserving receiving undue punishment)
- Broad base fallacy : Strategy of quoting the absolute number rather than the probability of some rare phenomenon whose underlying base population is large – for example : Holiday Carnage kills 500 over 4 day weekend !!! -(This is no of people killed in any four day period)
Overall , a brilliant account of examples and principles which help us view the word in a numerical sense . I was so excited and kicked about the way the principles were presented, that I just rushed to the book store to gulp the sequel to this book , a review on the same will be posted soon…Right now, I am off to dive deep in to the sequel " Beyond Numeracy"
Links : Innumeracy