Friday, August 25, 2017

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:

Golden ratio line.svg
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.


10 comments:

  1. There was a point in my youth when I would have loved a book like this. Somewhere along the way I had a math teacher that was so bad, they had to pass all the students in the class and provide us with free remediation to help us catch back up to our peers. It really affected my relationship with math for the rest of my life. Still, I went all the way to Cal 3 in college and studied allgorithms for Comp Sci, which I was terrible at. ;)

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    1. I wouldn't say I ever had a great math teacher, which is not to say they weren't competent. I just never had one who stoked the passion for me, and I was as primed to love math as any kid ever was. That just wasn't how the subject was taught in those days. Oh well, I can have fun with it now.

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  2. Ah, the Golden Ratio! Not to be confused with "Fee" the Tin Standard and what my bank surreptitiously attempts to remove from my accounts each month...

    This sounds like a fun one. I have some math-y pal in my grad school cohort who'd love this one. Thanks for recommending!!
    V:)

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    1. Definitely a worthwhile read for number geeks like me.

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  3. Equations, mathematics all boil down to calculations and numbers which cannot lie. Now I Know what your thinking, what has technology got to do with maths? Well plenty. So in the spirit of Dr McCoy, just don't expect me to turn into a darn computer. I'm a trekkie not mathematician. Great review.

    I'm half way to Red Mars! hehe but really I'll have my review up for Monday. I look forward to signing up for the rest of the voyage.

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    1. Numbers can't lie but the people who manipulate them most certainly can.

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  4. I am somewhat mathematically challenged but phi does sound interesting. I find all the math and the shapes that take place in nature fascinating. I don't recall ever hearing of phi before. Thanks for sharing. :)
    ~Jess

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    1. I had seen phi before but had no idea of its derivation. It figures in many geometric formulae.

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  5. This sounds interesting even though I'm not a huge fan of math (except for algebra :)

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    1. Algebra is awesome. The word derives from Arabic, as does the word algorithm.

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