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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.
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.
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I'd suggest The Da Vinci Code to people who are all sorts of interested in this sort of thing. Da Vinci played a small part in all this fun Phi stuff, and evidence of it can be found in his paintings. Besides, this is just a great book that everybody should read! They point out many places where one can find the "Golden Ratio" within this fine book.
I own the book, bought it a year ago myself. A good read.
If you're looking for something a bit along the same lines, but sprinkled with history, religion and conspiracy, I can recommend "the Da Vinci Code" by Dan Brown.
"After all, I am a Trekkie and this concept goes unstated throughout all four TV series." This is exactly how I feel about the Star Trek universe. All four TV series. You said it, my friend.
God, I think this is perhaps the worst book I've read in a few years. The Da Vinci Code is a "thriller" that cannot be followed at all and presents information as fact that is in fact complete bull. In terms of writing, the book is written similarly to a grade-school child who cannot use inventive vocabulary and sticks to the "He was shocked." and "It surprised him that X was that way." Please, read something else -- anything else.
This is my digital signature. 10011011001
That's what SCO's stock price would be in US$ were it not for unfounded litigation and rampant FUD.
Pseudoscience? While a biological basis for homosexuality is certainly not an established fact, there are several studies which strongly indicate that possibility. Read this summary, for instance. Please don't bother replying if all you have to offer is a proof by assertion. As for the Catholic church's position on homosexuals, I quote from the Catholic encyclopaedia:
"Homosexuality: Sexual activity between persons of the same sex. It is not a normal condition, the acts being against nature are objectively wrong." The Catholic Encyclopedia.
And this is the position of the APA
"The research on homosexuality is very clear. Homosexuality is neither mental illness nor moral depravity. It is simply the way a minority of our population expresses human love and sexuality. Study after study documents the mental health of gay men and lesbians. Studies of judgment, stability, reliability, and social and vocational adaptiveness all show that gay men and lesbians function every bit as well as heterosexuals." The American Psychological Association's Statement on Homosexuality, 1994-JUL.
Oh, and what do you have to say about the Bible's (often contradictory) position on women, which is largely the position of the Church today? I quote from Timothy:
12 I do not permit a woman to teach or to have authority over a man. She must be quiet.
"The slave who knows his master's will and does not get ready...will be be beaten with many blows."Luke 12:47-48
"If thou buy an Hebrew servant, six years he shall serve: and in the seventh he shall go out free for nothing. If he came in by himself, he shall go out by himself: if he were married, then his wife shall go out with him. If his master have given him a wife, and she have born him sons or daughters; the wife and her children shall be her master's, and he shall go out by himself. And if the servant shall plainly say, I love my master, my wife, and my children; I will not go out free: Then his master shall bring him unto the judges; he shall also bring him to the door, or unto the door post; and his master shall bore his ear through with an aul; and he shall serve him for ever" (Exodus 21:2-6).
How about this, which condones selling your daughter into slavery, and polygamy as well?
"And if a man sell his daughter to be a maidservant, she shall not go out as the menservants do. If she please not her master, who hath betrothed her to himself, then shall he let her be redeemed: to sell her unto a strange nation, he shall have no power, seeing he hath dealt deceitfully with her. And if he have betrothed her unto his son, he shall deal with her after the manner of daughters. If he take him another wife: her food, her raiment, and her duty of marriage, shall he not diminish"
I point these out, because they were used by southern Churches to justify slavery during the Civil war, and more recently, to justify apartheid.
"The slave who knows his master's will and does not get ready...will be be beaten with many blows."Luke 12:47-48