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3.56 AVERAGE
3.56 AVERAGE
so I stayed up past bedtime tonight to finish this book, not because I love this book, but because I would give anything to not be reading it anymore and now I'm not.
I'm not a platonist. I don't look at concepts made up by humans and say those describe things humans see so they must have a magical relationship to truth. I actually weirdly assume when people make things up those things should be related to what is true so it is a given they will relate to true things.
there were parts of this that felt like bible code. I suppose credit where it's due a lot of this is actually debunking the bible codesque shit, but why is it even the focus of a serious book... perhaps because this is not a serious book.
...
I mean really the fibonacci sequence describes the birth patterns of rabbits... no it doesn't it describes a word problem about rabbits. if you follow these 5 steps you get an amazing pattern that looks like a Fibonacci sequence by MAGIC. no you get it because you followed 5 steps. I mean I just don't buy any of this as meaningful.
I'm not a platonist. I don't look at concepts made up by humans and say those describe things humans see so they must have a magical relationship to truth. I actually weirdly assume when people make things up those things should be related to what is true so it is a given they will relate to true things.
there were parts of this that felt like bible code. I suppose credit where it's due a lot of this is actually debunking the bible codesque shit, but why is it even the focus of a serious book... perhaps because this is not a serious book.
...
I mean really the fibonacci sequence describes the birth patterns of rabbits... no it doesn't it describes a word problem about rabbits. if you follow these 5 steps you get an amazing pattern that looks like a Fibonacci sequence by MAGIC. no you get it because you followed 5 steps. I mean I just don't buy any of this as meaningful.
Here I go all math geeky again. I picked up this slim book (about 250 pages) a couple years ago and then I started thinking about it and felt compelled to read it. (Voices in my head. You know.) The golden ratio, or phi (pronounced "fee"), was first discovered by Euclid (remember him from geometry class?). Somewhere around 300 B.C. Euclid--
YOU: Whoa-whoa-whoa, wait a minute, Woodge... you actually read another book about math. For fun?! Are you for real?
WOODGE: Yeah, you TV Guide-reading eejit! Get yer head out of your ass! This stuff is interesting!
YOU: You are frikkin high.
WOODGE: Okay, yeah, fine, go back to your latest episode of THE APPRENTICE but I'm talking here so Shut It.
Anyway, Euclid put it thusly: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. The resulting ratio is phi, an irrational number equaling approximately 1.6180339887... it goes on forever without repeating a pattern. Phi is said to be the most irrational of irrational numbers. (The most famous irrational number is pi, the ratio of a circle's circumference to it's diameter.) Irrational numbers are called that because they can't be expressed as a ratio of any two rational numbers.
YOU: Dude, I'm falling asleep here.
WOODGE: Oh, don't be such a baby, the book is much more interesting than the nitty gritty of numbers 'n' stuff.
YOU: Huh? Did you say something? Donald Trump was saying something profound.
WOODGE: Mm-hm.
Anyway, this book was a breeze to read, even I was surprised. It delves into history, art, astronomy, philosophy, poetry, and is full of good quotes and fun historical facts. It also debunks a number of myths associated with the Golden Ratio. Much of this erroneous stuff can be found in other books treated as facts but Mario Livio, a theoretical astrophysicist by trade, gets behind the mumbo jumbo and gives you the straight dope. Maybe you've heard that the Golden Ratio is all over the Parthenon or was a big factor in building the pyramids or was the basis for many of Piet Mondrian's paintings? But that's just wrongedy-wrong-wrong! But some of the diverse places that the Golden Ratio actually does appear includes: the petal arrangements of roses, pentagrams, Platonic solids, the shape of distant galaxies, nautilus shells, and accounting fraud.
Much more than just blathering on about a freakin' number, this book gets into history and touches on Euclid, Pythagoras, Alexander the Great, Galileo, Johannes Kepler (and the fact that his mom was arrested for being a witch -- Burn her! Burn her! She's a witch!) and art history, and whether or not God was a mathematician.
And of course there's Fibonacci and his series of numbers which have a very close relationship to phi. The Fibonacci series begins 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... and each successive number is the sum of the preceding two numbers. If you take one of the numbers and divide it by it's previous number you get closer and closer to phi as you go further in the series. Fibonacci numbers are found everywhere; from the number of petals in a flower, to the number of spirals on a pineapple; to phyllotaxis (Greek for "leaf arrangement"); to the family tree structure of bees, et cetera.
I thought it all was pretty cool to tell you the truth.
WOODGE: So doesn't that sound pretty cool?
WOODGE: Hello? Anybody?
YOU: Whoa-whoa-whoa, wait a minute, Woodge... you actually read another book about math. For fun?! Are you for real?
WOODGE: Yeah, you TV Guide-reading eejit! Get yer head out of your ass! This stuff is interesting!
YOU: You are frikkin high.
WOODGE: Okay, yeah, fine, go back to your latest episode of THE APPRENTICE but I'm talking here so Shut It.
Anyway, Euclid put it thusly: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. The resulting ratio is phi, an irrational number equaling approximately 1.6180339887... it goes on forever without repeating a pattern. Phi is said to be the most irrational of irrational numbers. (The most famous irrational number is pi, the ratio of a circle's circumference to it's diameter.) Irrational numbers are called that because they can't be expressed as a ratio of any two rational numbers.
YOU: Dude, I'm falling asleep here.
WOODGE: Oh, don't be such a baby, the book is much more interesting than the nitty gritty of numbers 'n' stuff.
YOU: Huh? Did you say something? Donald Trump was saying something profound.
WOODGE: Mm-hm.
Anyway, this book was a breeze to read, even I was surprised. It delves into history, art, astronomy, philosophy, poetry, and is full of good quotes and fun historical facts. It also debunks a number of myths associated with the Golden Ratio. Much of this erroneous stuff can be found in other books treated as facts but Mario Livio, a theoretical astrophysicist by trade, gets behind the mumbo jumbo and gives you the straight dope. Maybe you've heard that the Golden Ratio is all over the Parthenon or was a big factor in building the pyramids or was the basis for many of Piet Mondrian's paintings? But that's just wrongedy-wrong-wrong! But some of the diverse places that the Golden Ratio actually does appear includes: the petal arrangements of roses, pentagrams, Platonic solids, the shape of distant galaxies, nautilus shells, and accounting fraud.
Much more than just blathering on about a freakin' number, this book gets into history and touches on Euclid, Pythagoras, Alexander the Great, Galileo, Johannes Kepler (and the fact that his mom was arrested for being a witch -- Burn her! Burn her! She's a witch!) and art history, and whether or not God was a mathematician.
And of course there's Fibonacci and his series of numbers which have a very close relationship to phi. The Fibonacci series begins 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... and each successive number is the sum of the preceding two numbers. If you take one of the numbers and divide it by it's previous number you get closer and closer to phi as you go further in the series. Fibonacci numbers are found everywhere; from the number of petals in a flower, to the number of spirals on a pineapple; to phyllotaxis (Greek for "leaf arrangement"); to the family tree structure of bees, et cetera.
I thought it all was pretty cool to tell you the truth.
WOODGE: So doesn't that sound pretty cool?
WOODGE: Hello? Anybody?
This book explains how the mathematical value of phi(fee) exists in the world and how it occurs naturally in many areas of the world, and the many people in the world who were fixated with the number, and how its amazing qualities gave it the title of the Golden Ratio. The good part is you do not need to be a math master to be able to rad this. All equations and use of math are simple enough that anyone who has taken high school math can read this book and comprehend the topic. This book is great for people who like to read books that supply amazing amounts of interesting facts.
I bought this book several years ago. I'll admit it, I bought it because of the Da Vinci Code. Dan Brown even has a quote on the cover! Which, after I read the book, I thought was kinda weird, because the author spends a lot of time debunking ideas about the appearance of the Golden Ratio in art and architecture. I liked the skeptical approach he took when looking at claims of it being used in the pyramids or the works of Da Vinci.
Really, anyone could read this book, ie non mathematicians, but for me it was slightly more technical than some of the other nonfiction I've been reading, which I appreciated. Some proofs are included in the text and others in appendices in the back.
And oh, the list of further reading/bibliography. I started reading it but had to stop because I was getting way too excited.
If you have any interest in math or the history of math, you'd probably like this book. However I think a lot of the information is probably quite basic/introductory so if you already have a strong background in it it might be a bit repetitive.
Really, anyone could read this book, ie non mathematicians, but for me it was slightly more technical than some of the other nonfiction I've been reading, which I appreciated. Some proofs are included in the text and others in appendices in the back.
And oh, the list of further reading/bibliography. I started reading it but had to stop because I was getting way too excited.
If you have any interest in math or the history of math, you'd probably like this book. However I think a lot of the information is probably quite basic/introductory so if you already have a strong background in it it might be a bit repetitive.
informative
medium-paced
This is one of the oldest (perhaps the oldest?) physical books I own and have yet to read. Goodreads suggests I’ve had it for nearly a decade. Oops. The truth is, I was never excited to read this. I love reading math books! But I am not particularly enamoured of books that explore one or two “special numbers,” and phi is perhaps my least favourite special number. The blurb from Dan Brown on the cover didn’t help. See, phi has been egregiously sexed up and romanticized by people, turned into a mystical number that recurs exactly throughout art and nature, and ascribed aesthetic properties it doesn’t deserve. I was nervous this book would repeat these claims. Well, I owe Mario Livio an apology. Not only does he critically challenge those claims and debunk a lot of the hogwash surrounding the golden ratio, but he also takes it upon himself to tell a broader and more complete story than focusing solely on this number. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number is a good story of the intersection of mathematics and society, and it provided one key insight that, as a math and English teacher, I find very valuable.
You would be forgiven for, having begun the book, thinking that Livio has entirely forgotten about phi for the first couple of chapters. Rather, he explores the history of numbers and counting in general, eventually ended up in ancient Babylon and Greece and making some connections with geometry. This creates a much richer backdrop for Livio’s later exposition of the golden ratio, and it also broadens the reader’s awareness for how various cultures developed and practised mathematics at different points in history. For example, Livio discusses the Rhind/Ahmes papyrus, which famously provides insight into Egyptian mathematics about 3500 years ago. He emphasizes the papyrus’ purpose as a teaching/reference tool—it specifically explains how to do practical calculations. Fast-forward a couple of millennia, and Fibonacci was doing the same thing—writing tutorials, essentially, for accountants.
See, I appreciate this, because most approaches to discussing the golden ratio focus on the idea that its use in architecture, art, etc., invokes certain ingrained aesthetic ideals in us. These approaches further seek to ground the golden ratio in the idea that its proponents and adherents throughout history have sought it out as a result of being fascinated with mathematical beauty. Livio, on the other hand, reminds us that a great deal of mathematics was (and remains) practical. It’s true that the Pythagoreans were a semi-mystical cult that believed their discoveries reflected the beauty of nature—but the problems they solved were motivated by questions of geometry and arithmetic that were relevant to life in Greece at the time. This has remained true throughout history: our development of mathematical approaches is driven by our needs as a society. The adoption of Hindu-Arabic numerals, for example, didn’t happen because they are “more beautiful” than Roman numerals—the accounts liked them better for arithmetic!
It might seem strange for a mathematician, especially one who loves pure math, to be arguing against the idea that beauty should be a foundational concept of mathematics. And I’m not, not really. But I agree with Livio that viewing mathematics in the past through a lens of beauty/aesthetics is ultimately an ahistorical reading that confuses more than it illuminates. Understanding the emphasis on practical applications for math helps us understand its place in our society.
And this is where The Golden Ratio really got me. Several chapters examine whether well-known artists used the golden ratio in their work. Livio discusses the works themselves, as well as numerous scholarly intrepretations both for and against the idea that the golden ratio played a part. I appreciate his extensive use of references and the way he engages with the topic as objectively as possible. Most importantly, Livio suggests that our desire to spot the golden ratio in this artwork undermines and devalues the artists’ general mathematical brilliance. If the aesthetic quality of a work of art were simply the matter of using the right shape of rectangle everywhere, what does that say about art and artists? Why wouldn’t we have made a computer program that can generate “the perfect work of art” by now? No, Livio concludes, the brilliance of these works of art is independent of their use, or lack of use, of the golden ratio. It comes from a far deeper grounding in mathematics than we care to credit—from the use of perspective to plane geometry, math is everywhere in art. He points out how some artists, like Durer, studied mathematics purposefully to improve and influence their artistic output.
I teach math. I also teach English. People treat me like a unicorn because of this, but I really don’t see them as all that different. Neither did Charles Dodgson, who wrote Alice in Wonderland. Livio cites numerous other poems and literary works that use math, as subject matter or metrical inspiration or both. He reminds us that this siloing of STEM is a recent and very artificial phenomenon, that throughout the majority of history, STEAM indeed was the rule of the day. The idea that if you have an artistic sensibility you must somehow be allergic to mathematics is ahistorical and untrue, for as Livio points out here, many of the most celebrated and famous artists studied, understood, and used math in their work.
In this way, The Golden Ratio provides a far more valuable story than simply “the world’s most astonishing number” (which phi is not). Livio’s tangents into philosophy, history, art, and music remind the layreader that mathematics is not this alien construct that only super-intelligent people can appreciate or do. It is fundamental to our lives, to our praxis, and to our pleasure—not for any innate beauty it possesses, but for the way its practice can help us create what we consider beautiful. The golden ratio does not play as big a role in this process as some want you to believe. Rather, as is usually the case, the truth is far more wonderful and broader in scope than the simple idea that one number can rule them all.
Originally posted at Kara.Reviews.
Originally posted at Kara.Reviews.
I think this is a necessary book. Whether you have read a lot about phi or not, this one is a "must read" if you like popular maths.
Mario Livio analyzes the presence of the irrational number phi (golden number, 1.61803...) in several subjects like art or nature.
And by contrast with so many books and articles published through centuries, Dr. Livio tries to refute this presence.
We usually read texts searching phi everywhere. And finding it. In most cases the presence of phi is pretty questionable, both in art and nature.
In "The Golden Ratio" Mario Livio refute this presence, from plants to the pyramids through astronomy. Sometimes true, sometime false and often doubtful.
I think Livio's view is successfull because he base his opinions about architecture above all in one fact: Was golden ratio known when they built it? If not, it seems obvius to me presence of phi must be random.
Furthermore, Livio says, and I agree, many times measures that show golden ratio are approximate, and "golden lovers" focus only on that which result golden ratio avoiding anything else.
Mario Livio analyzes the presence of the irrational number phi (golden number, 1.61803...) in several subjects like art or nature.
And by contrast with so many books and articles published through centuries, Dr. Livio tries to refute this presence.
We usually read texts searching phi everywhere. And finding it. In most cases the presence of phi is pretty questionable, both in art and nature.
In "The Golden Ratio" Mario Livio refute this presence, from plants to the pyramids through astronomy. Sometimes true, sometime false and often doubtful.
I think Livio's view is successfull because he base his opinions about architecture above all in one fact: Was golden ratio known when they built it? If not, it seems obvius to me presence of phi must be random.
Furthermore, Livio says, and I agree, many times measures that show golden ratio are approximate, and "golden lovers" focus only on that which result golden ratio avoiding anything else.
People who think that ridding humanity of religion and such will remove the weirdness and episodes of random oddball wackiness from the world will probably continue to be disappointed as long as there's math around. Case in point is an irrational number that goes by the name phi or the Greek letter Φ. Like its more famous cousin π, Φ comes from a geometric relationship. It's a way to divide a line in such a way that the ratio of the two unequal pieces added together to the longer piece is the same as the larger piece to the smaller one. And like the other one, it never repeats and never ends, starting out as 1.618033 and going on from there.
The ancient Greeks calculated the number which is called the Golden Ratio because of it's aesthetically pleasing quality. But things started to get weird when Φ started showing up in nature. Such as the spiral shell of a nautilus, which spiraled inward along the same ratio as the line. Botanists found it showing up in the distribution of leaves on a tree branch -- if not exactly, close enough often enough to be significant. Modern researchers have found it in different qualities on the molecular level.
Astrophysicist Mario Livio, in 2003's The Golden Ratio, reviews some of the places Φ is supposed to have shown up across history. He finds that in a lot of those cases, Φ's either not really there or the similarity to it is something of a coincidence. It probably didn't influence the construction of the pyramids or the way Da Vinci painted Mona Lisa, for example. But it does show up in enough different places to be weird enough.
The chapters get a little repetitive and it's possible that Livio could have dropped one or two suspected appearances of the Ratio that turned out to be incorrect. But he's a gifted science writer with a real knack for moving complicated concepts into the realm of lay understanding, and he leaves plenty of room for a readers to figure out for themselves what they think about the prevalence of Φ in the universe and why this particular mathematical expression shows up as often as it does in the real world.
Original available here.
The ancient Greeks calculated the number which is called the Golden Ratio because of it's aesthetically pleasing quality. But things started to get weird when Φ started showing up in nature. Such as the spiral shell of a nautilus, which spiraled inward along the same ratio as the line. Botanists found it showing up in the distribution of leaves on a tree branch -- if not exactly, close enough often enough to be significant. Modern researchers have found it in different qualities on the molecular level.
Astrophysicist Mario Livio, in 2003's The Golden Ratio, reviews some of the places Φ is supposed to have shown up across history. He finds that in a lot of those cases, Φ's either not really there or the similarity to it is something of a coincidence. It probably didn't influence the construction of the pyramids or the way Da Vinci painted Mona Lisa, for example. But it does show up in enough different places to be weird enough.
The chapters get a little repetitive and it's possible that Livio could have dropped one or two suspected appearances of the Ratio that turned out to be incorrect. But he's a gifted science writer with a real knack for moving complicated concepts into the realm of lay understanding, and he leaves plenty of room for a readers to figure out for themselves what they think about the prevalence of Φ in the universe and why this particular mathematical expression shows up as often as it does in the real world.
Original available here.
I have only a limited understanding of math, but I thoroughly enjoyed this book about the "golden ratio of antiquity" or 1.6180339887. This number is behind such beautiful things as the petals on roses, the seeds on sunflowers, the shape of galaxies, and the breeding patterns of rabbits. It's a good thing I have an eternity to perfect my mathematical comprehension!