Wednesday, June 25, 2014

Book Skimpression

The Math Book

The Math Book is written by Clifford A. Pickover and it is an excellent book which puts the different major discoveries in mathematics in chronological order.  The book was an awesome and easy skim through book because half the pages contain short summaries of mathematical discoveries and half the pages contain pictures related to those discoveries.  There were 250 million different discoveries mentioned in The Math Book and they range from 150 Million BC to 2007.  

I did not read each and every discovery that this book discussed but while skimming through I did stop for a few that caught my attention. Enjoy!

Ant Odometer (150 Million BC)
> A type of ant called the cataglyphis fortis would travel immense distances and were able to return to the nest using a direct route.  It was believed there was a built in "computer" that functioned as a pedometer.  Researchers then studied the effects of either giving the ant stilts or amputating their legs to study the results.  Results showed that ants with stilts traveled passed the nest, while ants with amputated legs didn't reach the nest.  Another interesting result was that if the ant started with modified legs, the journey back to the nest could be completed.  

Wheat on a Chessboard (1256)
> This was used for centuries to demonstrate the nature of geometric growth/progression
> It is the earliest mention of chess in puzzles
> Basically each square multiplies by the number of grain in the prior square and therefore each square has 2^n number of grains
> If the the number of grains on a chessboard were put onto trains, that train would be able to reach 1000 times around the Earth

Prisoner's Dilemma (1950)
> The following scenario is given:
You have two suspects that are to be tried.  If both suspects confess, the punishment is five years of wandering in a desert.  If only one suspect confesses, the confessor is free to go and the other is doomed to crawling/eating the dust for 30 years.  If neither suspects confess the punishment is just six months wandering in the desert.  The most forward solution to this problem is that neither suspect should confess and you would get the least lengthy term.  However, research done to analyze the non-zero-sum-squares shows that the suspects are more likely to both confess in the hopes the other doesn't so they can achieve freedom.  This study in mathematics helped in a number of other fields including psychology, sociology, biology, political science, and economics.

Again, those are just a few major milestones which struck my interest in my skim through.  I think this book would be great for any audience.  It is a very easy read and it is quite interesting to see how some of our everyday things came from these mathematical concepts.  I think the most interesting thing about this book is that there are concepts addressed in here that seem so miniscule but when you think about if that concept wasn't discovered, it could change the way you think about life!

1 comment:

  1. Ant experiment - clever but disturbing.

    Skimpression - check.