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

Mathematics not universal?

[s20451]

Didn't read the book.

If mathematics are not universal, then the mathematical reasoning that can be conducted to deduce the laws of nature is also not universal. Hence, if a different civilization has different mathematics, they have different physical laws as well.

This is basically a postmodern viewpoint, that reality is socially constructed. This viewpoint has been largely derided by the scientific community, and has failed to replace science because it hasn't really offered a compelling alternative. The only way I can see it being true is if other civilizations don't "exist" in the universe as humans do.

Do a google search for Alan Sokal for a scientist's viewpoint of postmodern scientific criticism.

Re:Mathematics not universal?

[Raindance]

Well, I wouldn't say that "if a different civilization has different mathematics, they have different physical laws as well."

Rather, I'd set mathematics and logic equal (there's a respected tradition that does, see Bertrand Russell, Principia Mathematica). Then, to say that mathematics isn't the same across the universe, one would say that logic isn't the same across the universe.

Now, "Logic isn't universal" is a damn meaningless statement. It'd translate into "Logic cannot describe [timespace-area/context] X." Which is, of course, a logical assertion about X.

I think either the reviewer's portrayal of the argument or the argument itself is bogus.

RD

Re:Mathematics not universal?

[Erich]

To those who would say "The sky is blue, and that's an absolute truth, whether I want it to be or not" ... How do you know what "Blue" is?

It's quotes like these that make me think postmodernism is based on pure stupidity, rather than any rational thinking system.

Blue, obviously, is radiation in the wavelength of around 475 nm. It is measureable. When you look up at the sky, if light is primarily coming in at wavelengths around 475nm, the sky is blue.

On the other hand, if it is sunrise or sunset, or the end of the world or something, and the wavelength is much longer -- around 650 nm -- the sky is red.

If you are colorblind, it doesn't change the fact that the sky is, indeed, blue. And, even with colorblindness, you can measure the color of the sky using scientific instruments.

So, wake up, and enjoy the reality that is the universe.

Re:Mathematics not universal?

[Listen Up]

Wow, the shear ignorance in this entire article and book write-up is amazing. Not to truly upset anyone, but everyone here on Slashdot also appears to have a high school alegbra or entry level college mathematics background.

To start with, Mathematics is not just as human as poetry. Where do you get that idea? Yes, pure mathematics (which is my passion in life) is essentially pure thought. BUT, nothing in mathematics is just 'made up'. All mathematics is based on fundamental, logical axioms (truths), and if anything were to violate those axioms, or the completely logical conclusions drawn therefrom, it would not be mathematics. You can think of mathematics as a grand puzzle, with each discovered piece and each mathematical truth found spelling out a larger picture. You can create bogus logic, bogus mathematical problems but it does not make it true mathematics.

You are also confusing human representation with mathematics in your other statements. On a fundamental level, a law is a law, mathematically/physically/logically/universally. The universe is not ruled by human imagination (i.e. completely imaginary human created friend(s) as in religions) and therefore the system to understand our universe has to follow the same sets of rules as the universe (even rules involving possible pure chaos, as in some areas of quantum theory). Without mathematics, our universe and all that lies within it could only be understood on a physical observation level. Mathematics is the language of the universe, it is the language of physics.

For a slightly deeper explanation, let me explain that Mathematics does not involve physical representations as you were taught in HS and earlier. For example, the number 1 as opposed to a capital S to complete addition (which is a logical law) means that 1+1=2 is the same as S+S=* because the system is beyond the physical characters used to represent the logic. The logic would not be different in an alien society. The laws of the universe do not change, therefore the same logic would be implemented. Using a 1 or an S would make no difference.

There is sooooo much more, but just reading this story and people's posts makes me sad on a certain level. One of the oldest "truths" in the world...The person who is always least understood is not an artist, it is a mathematician.

Why wouldn't math be known across the universe?

[ObviousGuy]

What reasons would there be for an alien to not understand or accept that one plus one equals two. Any being capable of human-equivalent level of thought would be able to count objects. Whether they did in this in base-2 or base-3 or base-10 or base-12, it doesn't matter because all these bases can be reconciled to each other.

Could there be some areas of mathematics that humans have discovered that has not been discovered by an alien race? Sure. Prior to Newton there was no calculus and so Kepler had to discover the period of planetary orbits using geometry and algebra. But this does not mean that Kepler would not have used calculus if it had been available to him, only that such a concept had not yet been thought of.

But counting and simple addition and subtraction are mathematical operations that are mastered even by animals. It is fairly condescending to assume that aliens could not even fathom those levels of mathematics.

Numbers are numbers

[Wind_Walker]

Regardless of what radix used (10-based, hex, octal, etc) "6" of something is still "6". Call it whatever you want, some alien name. There are still 6 items there.

By the same nature, prime numbers are always prime. There exist a certain number of things (5, 7, 11, etc) and cannot be evenly divided. Period. We call them prime numbers, and we use our base-10 radix. Aliens could call them Borgolsmocks in their base-182, but the fact still remains that a Borgolsmock cannot be divided evenly.

And I firmly believe that no intelligence would survive for long without a knowledge of mathematics. Counting the days for crop rotation, the ability to evenly divide food among the tribe, and communication of the number of animals in a herd... mathematics will be generated in the evolution of any intelligent species.

And it is truly universal.

Re:math is not universal?

[greatmazinger]

Math is just a way of describing objects, forces, and interactions..

Ummm, no. That's not math. That's physics. Math is more abstract and one can do math without associating any of the concepts with "reality". One you use math to model reality, it becomes science and engineering.

From your english class?

[iota]

for my english class. hope you enjoy it.

I presume you got an F. Since is a direct and obvious plagarism of the publisher's description of the book. (see: http://search.barnesandnoble.com/booksearch/isbnIn quiry.asp?isbn=0767908155)
It's obvious, because it doesn't really say anything other than what can be related to the title of the book (which is not unusual for back-of-the-book descriptions)
It's direct, because, well -- I can search google for any sentence in your text and find it.

Lame.

First-contact scenarios?

[bravehamster]

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. ... 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.

From what I understand, the vast majority of realistic first-contact scenarios postulated involve using mathematics as a common ground to bridge the language barrier. 1 + 1 equals 2 in every language on earth (except New Age holistic 1 + 1 = 3 crap). It makes sense and it works everywhere. It would be awfully damn hard to build a spaceship without mathetmatics, let alone trying to calculate launch trajectories or transfer orbits. Unless they had such an intuitive grasp of higher level mathematics that they don't even consider it worth talking about, I don't see how any species that had no concept of math could ever rise above the level of pointy sticks and sharpened rocks. And even then you'd probably want to keep track of how many rocks you had to make sure Lurg over there didn't *borrow* a few.

Don't confuse Syntax for Content

[Master Switch]

While the syntax we use for mathmatics is culturally defined, the content beneath them is not. We humans discover, not invent mathmatical constructs. As much as we would like to think we create, we do not. We iterate and find the best fit solutions.