Cephalopod Coffeehouse: August 2017

Welcome one and all to the Cephalopod Coffeehouse, a cozy gathering of book lovers, meeting to discuss their thoughts regarding the works they enjoyed most over the previous month.  Pull up a chair, order your cappuccino and join in the fun.  If you wish to add your own review to the conversation, please sign on to the link list at the end of my post.

Title: The Golden Ratio: The Story of Phi, The World's Most Astonishing Number
Author: Mario Livio

via Amazon

The number ϕ, approximately 1.6180339887, is the Golden Ratio, studied by mathematicians since Pythagoras and Euclid.  Imagine a line segment, AB.  There is a point on AB, let's call it C.  The ratio of the length of AB to that of AC is the same as the ratio of the length of AC to that of CB.  That ratio is ϕ (phi, pronounced "fee").  Here's a diagram:

By Traced by User:Stannered - en:Image:Golden ratio line.png, Public Domain, Link

Over the centuries since, this number has proven to be deeply embedded in the fabric of universe.  No, I'm not exaggerating.  ϕ plays a role in the placement of petals on a rose and branches on a tree, in the shapes of nautilus shells and even the spiral arms of galaxies.

Mario Livio explains it all in his marvelous book, covering a great deal of mathematical history as he goes along.  I think it's actually more the sort of book I had in mind when I read The Magic of Numbers by Eric Temple Bell (see here) earlier this year.  ϕ is even related to the Platonic solids, my most exciting discovery in Bell's book.  Livio discusses "recreational mathematics," a fancy term for number games I'd never even heard of before though I've been practicing it for most of my life.

While Livio is enthusiastic about ϕ, he is also skeptical of many of the assertions that have been made about its use in the Parthenon, the Great Pyramid, numerous paintings, etc.  Much of the book is devoted to debunking these myths.  Some artists and architects, though, have been explicit in experimenting with the Golden Ratio: Frank Lloyd Wright and Salvador Dali, among them. 

The book's final chapter considers ϕ in light of one of the oldest questions in philosophy: is mathematics a human invention or a human discovery?  The numerous natural phenomena related through ϕ suggest an existing order to the universe that predates us all.  Could those relationships, though, be just as clearly defined by another civilization through a means of understanding completely different from our math?

If you love numbers, this is a great book.  I don't know how much it offers to one who is not mathematically inclined but I think Livio does a fair job of explaining the technical concepts in simple terms.  The telling question for me is always would I give it to my wife to read?  In this case, I believe the answer is yes.

Please join us and share your own review of your best read from the past month.  This month's link list is below.  I'll keep it open until the end of the day.  I'll post September's tomorrow.  Meetings are the last Friday of each month.  Next gathering is September 29th.