Things to make and do in the fourth dimension
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 ).