Book Review — Things to make and do in the fourth dimension

Math is stranger than fiction and this book is filled with the many curiosities of the math world. It contains a glimpse into its intriguing lanes in an entertaining manner along with optional hands-on activities to enjoy.

Each chapter is not so much in depth that it is akin to a text book but just enough to get you started to play with the math, if the topic interests you. Dive in - you’ll be amazed at the sights (with a little math humor thrown in).

I won’t claim to have understood it all.

For e.g. The multidimensional world which was just too bizarre. (A helpful tip by Geoffrey Hinton -  ”To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say “fourteen” to yourself very loudly. Everyone does it.”)

But there is something in it for everybody.

Some delightful snippets -

  • Different-sized infinities
  • The strange cut outs from Mobius loops
  • Prime numbers ( considered pointless math till 1940 !! Now basis of digital communication )
  • A sphere that increases in size even when bounded by other packing spheres ( 26th dimension onwards ) !! Weird is an understatement !
  • Ramanujan summation where sum of all the positive whole numbers = -1/12 ! Used in string theory ( I am still trying to wrap my head around this ).
  • Knot theory - Trying to find one method to know if a tangled string is a knot and if so how to undo it with minimal effort. Why bother ? Biologists may be able to devise new wave of medical treatments based on this.
  • Uncomputable numbers !!! ( No amount of exclamations will do this justice ! )
  • Description of Gödel’s incompleteness theorem. Short, succinct and intuitive.
  • Riemann Hypothesis, e, π, Φ, infinite hotel do get a mention ( almost de rigueur I think ).

An engaging book about math; The language the universe speaks to us in. Fall into the fascination and there’s no going back.