Innumeracy

Book Review:

Innumeracy : Mathematical Illiteracy and Its Consequences ... John Allen Paulos

The book talks about our ignorance to the fact that in mathematics contrary to common perceptions problems or observations do not add up or scale always in the same way. For example:-

1. If there are 50% chances of raining on Saturday and 50% chances of raining on Sunday then we might conclude that there is 100% chance it is going to rain on the weekend.
2. In other cases we misread because of psychological impact of numbers e.g. 280 people died in such and such incidence would take away the focus from the fact that 280 in a population of 200M are insignificant. Also, when it comes to numbers don’t put personal face to them e.g. one of the 280 was just a kid such and such. People with innumeracy problems will always refute mathematical arguments with case like what if you were one of the 280, which if you were to compute probability, the chances of you being one of 280 would be minuscule.
3. Another such oddity is with small numbers, so if something impacts us by only 0.0001% then would tend to ignore it, but if we have a lot of such small things, they do compound to huge numbers, typical case being in computing each individual instruction is cheap to compute but if we put a lot of them together it could be the cause of big bottleneck or cost.

In summary:

Look at numbers, percentages and other statistics in perspective. You can make huge miscalculations if you take number without understanding the context and interplay of other factors.