The Golden Ratio

raceBannon writes "The book surprised and fascinated me. I thought it was going to be solely about the Golden Ratio. Mario Livio does cover the topic but along the way he throws in some mathematical history and even touches on the idea that math may not be a universal concept spread across the galaxy." Read on for the rest of raceBannon's review. The Golden Ratio author Mario Livio pages 320 publisher Broadway rating 7/10 reviewer raceBannon ISBN 0767908155 summary Through telling the tale of the Golden Ratio, Livio explains how this simple ratio pops up in all kinds of physical phenomenon and debunks the idea that the ratio is present in many famous man-made structures and art work. Along the way, he provides historical tidbits regarding some of the well-known and not so well-known mathematicians throughout the ages and he tells the story of some of the more famous and not so famous mathematical advances. Finally, he discusses the possibility that mathematics may represent some kind of global truth that exists throughout the cosmos.

I have to admit that it is a little spooky to me that this ratio, this irrational number (1.6180339887...), pops up in many varied natural phenomena from how sunflowers grow to the formation of spiral galaxies; not to mention that the Golden Ratio and the Fibonacci Series are related. It makes you want to think that there is a God with a plan.

The Golden Ratio is defined as follows: In a line segment ABC, if the ratio of the length AB to BC is the same as the ratio of AC to AB, then the line has been cut in extreme and mean ratio, or in a Golden Ratio called Phi.

On the flip side, Livio squarely debunks the idea that the Golden Ratio is present in many famous paintings and architecture that has been postulated in previous books. He rightly points out that you can find the Golden Ratio in anything depending on where you decide to place the measuring tape. The idea that the Golden Ratio is such a symbol of universal beauty that it appears by accident in our great man-made buildings and artwork does not carry any weight. I think Livio makes his point.

He also uses the Golden Ratio as a framework to illuminate other historical tidbits about key mathematical figures, guys like Pythagoras and Euclid, who continue to affect the mathematical world to this day. I love this kind of stuff; the historical context of how and why these legends did what they did is very interesting to me. For example, I did not know that Euclid himself did not discover geometry or even make any great new contributions to the field in terms of ways to apply it. What he is famous for is organizing the information into a coherent fashion. He was a teacher of the highest order; so much so that Abraham Lincoln himself used Euclid's texts, unchanged after all those years, to learn the subject back in Lincoln's log cabin days.

The book is not all a philosophical discussion. Livio does use some simple math examples to make his points but it was at a level that I could follow. According to my college professor, I escaped College Calculus by sheer luck. Livio does provide the rigorous math examples in appendices at the end of the book (I did not bother with these).

Finally, Livio takes a shot at the idea that mathematics is a universal concept across the entire universe. To be honest, I have always assumed that it was. After all, I am a Trekkie and this concept goes unstated throughout all four TV series. The idea that mathematics is a human construction and probably holds no water in another civilization that grew up on the other side of the universe makes a lot of sense to me. I have to admit; I need to ponder that one for a while.

I recommend this book. If you like the history of science, your high school algebra class is just a little more than a dark fog in your memory, and you get a charge out of scientific mysteries, you will not be disappointed.

You can purchase The Golden Ratio from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

Comments

The Galaxy??

[Gorimek]

The concept of math isn't even spread very far on this planet.

The Golden Ratio

[Anonymous Coward]

He who has the gold, makes the ratio.

Re:Movie

[ath0mic]

...which I think also holds the record for the "longest movie title in history."

:)

Re:Mathematics not universal?

[kfg]

I offer this argument to those who state "You create your own reality."

I kick them in the shin.

Then say, "Why did you do that?"

KFG

Phi

[Rupert]

I hate it when people use extreme amounts of decimal precision when talking about irrational numbers. Really, is 1.6180339887 (or 1.6180339887498948482045868343656) much more informative than 1.618? If you're going to do calculations with it, use the exact value:

1/2 * (sqrt(5) + 1)

and sort out the irrational bits at the end, rather than introduce rounding errors at the beginning.

That's just a rationalisation, of course. My real reason for complaining about decimals is that it feels wrong. 1.6180339887 does not look like a profound number. It's like the number is a beautiful woman, and the decimal representation is the pornographic pictures she posed for when she was young and needed the money. Yes, it looks like her, and it may even be useful. But the real thing is *so* much better.

Re:Numbers are numbers

[Lemmeoutada Collecti]

Borgolsmock is divisible using a thersian constant. To assume that just because your single dimensional mathematics cannot divide a borgolsmock does not similarly limit n-dimensional. Why the mere act of division is a limitation of linearly conecived time, a limitation we have never faced.

Aside from which, where you see a single item, I percieve an infinite semi recursive series. There are more than one apple in that one apple. There are an infinite (using your limited numbering) number of apples. That apple you call 'one' in fact contains the entirety of it's temporal measurement, which is a bounded infinite series. So now tell me about this concept you call singularity?

Re:math is not universal?

[Timmeh]

HEY! Don't push your modernist science bullshit on me, PATRIARCH. My goddess awakening mentor told me about you so-called intellectuals. Using 'symbols' and 'information' is just another form of OPPRESSION.

Now it all makes sense.

[Talinom]

The idea that mathematics is a human construction and probably holds no water in another civilization that grew up on the other side of the universe makes a lot of sense to me.

So that is why all of those UFOs are crashing all over the place.