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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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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.
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Comment removed based on user account deletion
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.
I have been pwned because my
Fictional is absolutely correct, sir. Entertaining, perhaps even compelling, but in the end purely a creation of someone else's imagination. Those who accuse "The Passion of the Christ" of being anti-Semitic should also be willing to point their guns at Dan Brown for being anti-Catholic.
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.
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.
for my english class. hope you enjoy it.
n quiry.asp?isbn=0767908155)
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/isbnI
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.
I'd be fascinated to hear more about this. I want to get the book but I'm impatient and want to discuss it now! :)
I would think that math in some was is universal, in the sense that every sentient creature has to figure out a method of counting. Some creatures count in base 10, others base six, maybe base 12. Other creates could figure out a counting base we haven't thought of yet. However, if they have a method of counting and measuring, I'm sure we'd have a method of translating their mathmatical models to our own, without too much trouble.
Perhaps the definition of math here is different than mine? Thoughts?
"All great wisdom is contained in .signature files"
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.
---- El diablo esta en mis pantalones! Mire, mire!
The Da Vinci Code is gripping fiction, but it's not in the same class as The Golden Ratio.
The Golden Ratio is carefully and deeply researched. The Da Vinci Codes is allegedly based on research, but the "research" behind it is recycling tired old conspiracy theories.
From his statements online and in his forward, methinks Dan Brown is trying to have it both ways: claim it's based on fact but use the plausible deniability of it being a fictional work. It is a gripping read, don't misunderstand me. But you have to remind yourself that it's totally fictional.
It's an interesting question: how far could a civilization get without math? IANA historian, but it seems to me the more sophisticated a (human) civilization, the better its mathematics. The Aztecs did develop a fair amount of math completely independently of Eurasian civilizations.
Could a race become spacefaring without math? Could they develop the radio communications we could use to detect them? I suppose they could if the circumstances of their environment or adaptation (Low-gravity, bio-radio communications) allowed it.
But how would you arrive at the necessary conclusions without an abstracted intellectual framework like math? Maybe progress would just be slower.
Hmmm... makes you wonder what we're still missing.
'In knowledge is power, in wisdom humility.'
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.
-Master Switch, one more element in the machine
should also be willing to point their guns at Dan Brown for being anti-Catholic
And why shouldn't he be? Why shouldn't anyone? They were responsible for lots of bad shit back in the day. Some of the things that happened back then even have far reaching global consequences today.
It may be shocking to some, but mathematics is an invented language. It is used to describe physical events around us. But invented it is. When we state that 1 + 1 = 2, we already make assumptions (such as the + and = operators are neutral) and we know that in the mathematics of quantum mechanics 1 + 1 is not two because "adding" injects its own effect and that "equal" depends on the situation (is it a wave or a particle - it depends on the experiment.) So is mathematics an invented language, yes. Is it a language that waited to be discovered, well, that is the question.
"A great democracy must be progressive or it will soon cease to be a great democracy." --Theodore Roosevelt
This book is absolutely excellent. Its aimed at everyone from a passing interest in math and up.
My favorite part of the book is where he essentially disproves the many claims to the appearance of the golden ratio in aniquity and before. He tries to nail down the moment of when the golden ratio was actually discovered.
And who is to say that God didn't design the system such that it balances itself in such a way?
People like you seem to take for granted that the universe just exists. That spacial dimensions and time all sort of slid together to happen to be this way. Matter just so happens to work in such a way that that puddle can exist (not just one puddle, but any infinite number of similar but totally different puddles) and sustain an entire eco system.
We can simulate the entire puddle and ecosystem in a computer with mathetmatical models, but it still is not the ecosystem. The whole is more than the sum of its parts.
no comment
"What else is natural science than a common set of rules for perception" is their answer and I can't answer it.
In a sense this is what science does. But my question is, who makes the rules? The postmodernist would argue that society does, that is, science is altered by our perceptions of it. The scientist (and, indeed, the philosophy of science) requires that the rules are cast by something external to humanity, that is, the rules are unalterable and are the same for each person. This is the basis of repeatable experimentation, and has proven itself far more successful than the alternative explanation.
I'm not totally unsympathetic to the postmodernists. You can look into the past and see where the "softer" sciences, especially psychology and medicine, have made errors based on prevailing social beliefs. But more fundamentally, I believe there are limits to scientific thought. For instance, perception is an important place to attack science, since science hasn't had much success in probing perception. This is probably because science deals in concrete concepts that can be described cleanly with language (e.g., the universe is expanding, the Earth goes around the sun every 365 1/4 days, every cell contains protein, etc.), but we can't describe perceptions in any way that is simple or concrete. For example, how would you explain the taste of an apple to someone who has only eaten meat?
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Their point is difficult to refute because it's true, obvious, and pointless, all at once.
All of the axioms of natural science are based on our observations. All observations depend on sensory input. Since our senses can be fooled, so can natural science. Ultimately, the only thing you can be sure of is "Cogito Ergo Sum," as old Rene once said. Everything else requires faith in the correctness of our perception.
However, it's a pointless observation. If we reject the input of our senses, we have nothing at all to go on which establishes even the existence of anything, yes. However, there is no way to demonstrate the total falsehood of observation because we have nothing else to go on.
Information wants to be anthropomorphized.
or they wouldn't have spent so much energy fighting over who invented it first.
Perhaps it was precisely to obscure the actual origin of the work that they spent so much energy fighting over who "invented" it first.
Bluster and a big show are a common technique used to take credit for someone else's work. Ever been to a meeting with your manager and your manager's manager?
spell it with me now...
the T-O-R-A-H
yes that's the book of greats
i stand alone on the word of g-d
the T-O-R-A-H
btw, i'm not jewish
When you look at the state of the world, how can you not become a radical, liberal anarchist?