The Nothing that is: A Nature History of Zero

Titile: The Nothing that is: A Nature History of Zero

Author: Robert Kaplan

Publisher: Oxford University Press

When I was a senior undergraduate, in class the professor once told us his classmate in John Hopkins spent one hour explaining why one and one is two. 

“Is it possible to prove 1+1=2?”

Year by year this question pops out in my mind occasionally. Since I’m not bothered by this question, I didn’t try to find the answer until now I read this book that gives me the hints for answering my question.

The author is a mathematician but very knowledgeable in related but different subjects. He quoted from lots of historical, psychological, artistic literature which make this book very inaccessible. I often cannot ascertain a sentence he quoted is a joke or a key point. More often I cannot see any relationship between quotes and the subjects. 

The most impressive I learn from this book is that it explained how to generate 1 (a whole thing) from 0 (nothingness) by an empty set. Given 0 and 1, we can generate all numbers, including rational, fractions, etc. by Farey sequences. In other words, it reveals an amazing result: everything is from nothingness. It corresponds to the famous theorem explaining how the universe was born: after a big bang, the universe that incorporates everything was formed. Before the big bang, nothing exists. 

Return to my old question. According to this book, only 0 and 1 are defined by nature, why bother to consider other symbols representing any number generated by 0 and 1? 2 is just a symbol; it means one whole thing and one whole thing are together.The other method to show 1+1=2 should not be a question is by contraction. In the language of computer science there are only 0 and 1. 1+1=10 is natural and convenient for their works in programming.  It is Ancient Roman said I and I is II; Modern People recognize 1+1=2 for convenience. 

The question that had haunted me for eight years is proved to be nothing.