Innumeracy

Innumeracy is the name of a best-selling book by John Allen Paulos.

The key message of the book is that having a good understanding of mathematics is an essential part of our existence in this knowledge-based, digital & technological world. It can improve our everyday lives by empowering us to understand the happenings around us and how they may affect us.

He argues that if we can’t critically interpret numbers and statistics, we lose one of our most basic and reliable guides to reality.

It can provide a better perspective over the news that we hear or enable us to detect a pseudoscience or a fake discount.

Innumeracy is widespread in our society affecting all sections of the society, including the intelligentsia and the media.

The root cause of innumeracy is the ineffective teaching of math in our schools. Our schools teach math much in the same way it was taught centuries ago.

They focus on numerical computations and sidestep the conceptual understandings in math.

The last 200 years have seen an exponential growth in the various branches of mathematics including coding, machine learning & AI.

Obviously, our schools are overwhelmed by all this knowledge explosion.

We will provide a few examples of innumeracy in our life.

The biggest issues are our understandings of data presentation as graphs, charts & tables. With digitization the amount of data available in an economy has become vast. Most news articles & policy documents present data in all forms and draw conclusions. Without an understanding of this data we would be hard pressed to make the right decisions in social, economic, political and professional lives.

Conclusions based on statistics & probability (chance) are many times counterintuitive and can lead us to wrong decisions. There is also a lot of confusion between causation and coincidence.

People do not realise that often probabilities are multiplied (hence reducing their value enormously) and not added.

Statistics proves that in a room of just 23 persons, the chances are very high that any two of them would share the birthday. We cannot believe this as we confuse this with the possibility of any two persons sharing a particular birthday!

A partial understanding of these issues leads us to believe in pseudo sciences like astrology & palmistry and numerology.

Today with the spread of social media, spreading such “fake” news has become extremely easy.

Numbers represent quantities and they can be written with different digits (numerals), depending on the number base that we adopt. This reveals the illogical basis of numerology.

Astrology uses calculations and hence even computers can draw up horoscopes. There is a wrong belief that anything which involves math calculations” has to be correct!

Fractions & percentages are another area of confusion. Both are based the relation between wholes & parts. In many instances, the “wholes” in question change during an event.

A common mistake is to think that if I get a 10% discount on top of the initial discount, I get a total discount of 20%. What is missed is that the original discount is on the “full price”, whereas the second discount in on the net price (which would be 9/10ths of the full price.

Many math-related jokes are based on such misunderstandings. Here are some.

“A politician asked a statistics professor about the chances of a bomb being there on a plane he would be travelling. When the statistician gave him a figure, the politician said that it was too high and asked for an alternative. The statistician suggested that the politician carry a bomb in his hand bag as “the chances of his travelling in a plane with 2 bombs would be halved!”

“A math professor was about to drown in the deeper part of the swimming pool. He was 5ft 6in in height and he had been told that the “average depth” of the pool was only 5 ft!”

Another area of math which throws us off track is not understanding the power of exponentiation. Though we study formulas for exponentiation and its application in calculating compound interest, we miss a feel for the enormity of the compounded increases.

Our number system itself is based on exponentiation of powers of ten. We lose any understanding of the enormity of numbers like million & trillion, though we can use them casually in our daily speech.

The logarithmic scale used for expressing intensity of earthquakes and sometimes used in graphs are instances of using exponentiation. There is a clear danger of not understanding the data.

Politicians, the press, and advertisers use numbers in entirely inappropriate ways (intentionally and not), but their advantage. Largely innumerate population readily allows itself to be duped, to its own detriment.

On Feb. 6, 1897, Indiana's (in the US) state representatives voted to declare 3.2 the legal value of pi!

The media is not interested in remedying innumeracy. They look for sensational news which will attract many readers and innumeracy provides them with enough fodder.

The frequent posts in social media, of confusions in evaluation of simple expressions using BODMAS/ PEMDAS rules are examples which confuse most adults.

Innumeracy -- like illiteracy -- is unacceptable, and the cost to society (in bad decisions made on the basis of bad and misunderstood maths) far too great. Individual decisions and broader policy decisions are far too often made on the basis of badly understood statistics, data, and mathematical principles.

The only way out of this situation is effective teaching of math in our schools, focussing on a clear understanding of the foundations of numeracy. With this foundation, people would have enough knowledge, later in life, to understand more complex aspects.