How big is infinity according to Tony Crilly?

I am not a maths fan. I always found it difficult because numbers, figures, statistics and Greek letters are so impersonal and detached (unless we’re talking about pi…that just made me hungry).

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There is a right answer and, in this regard, I have always found it to be a black and white sort of subject and I much prefer shades of grey (although I have yet to read Fifty Shades of Grey, so I’ll have to get back to you on that one).

 

Yet, reading Tony Crilly’s book, How Big is Infinity?, has made me reconsider and I have enjoyed it much more than I thought possible. 

 

 

Crilly’s work addresses, in his words, “the 20 big maths questions” which ranges from wondering if a butterfly’s wings can cause a hurricane to asking if mathematics can guarantee riches (I was most intrigued by this one!). 

 

Through taking a range of perspectives means that we look at maths and core concepts from a variety of different angles with the theories and ideas of different philosophers mentioned and a run down of the history involved in maths.

 

The very history of numbers are explored and we are taken through how counting began as tally sticks to evolve into the system we require today which keeps this book interesting and very unlike a maths textbook (which is what I warily expected).

 

As well as steering clear of a textbook style, concepts and ideas are well explained in language that is easily understandable, which is no easy feat when it comes to putting into words ideas like the Klein bottle (which requires four dimensions, rather than three) and game theory.

 

Diagrams throughout are incredibly helpful and the real life examples used, like the Cuban Missile Crisis, means it’s much you become engrossed in the maths of everyday life without knowing it. 

 

 

Please do imagine the sub-heading in Buzz Lightyear’s voice (from Toy Story) for the desired effect. 

 

It’s the chapter titled “How big is infinity?” that grabbed my attention because infinity is such an elusive concept and I feel like I’m owed an answer given the title of the book. We get a concise and understandable explanation of how people define infinity (without bounds) and consider thought experiments, like Hilbert’s Hotel and set theory. 

 

It is slightly mind-boggling as we learn about a host of infinities and that infinity, whilst mostly though of as large, can also be thought of as a number which we can endlessly make smaller and smaller as a fraction of one. Then, once you manage to wrap you mind around that idea, it’s concluded that rather than one notion of infinity, there is the possibility of an infinite notion of infinity.

 

See? Mind boggling. 

 

 

So, where does this leave you? What came of the chapter on the wings of a swallow-tail butterfly and if it can cause a hurricane? And more importantly, does mathematics guarantee riches? Well, as each chapter is clear and not overly long it’s easy to jump straight to what interests you most, whether it be infinity or whether imaginary numbers are actually imaginary.

 

Giving away the answers wouldn’t be much fun at all, particularly as I cannot even attempt to give you the logic, reasoning and history behind the conclusions reached.

 

So, I’ll leave you with the mind-boggling idea of infinity above and hopefully the wish to read How Big is Infinity? because you most definitely will not be disappointed.