The Golden Ration by Mario Livio - #Review

                           

         

Spread over nine chapters, this book proved to be an excellent 'thesis' on the 'ratio' φ. What more should one expect when Livio ventures into how and why 'phi' was introduced as he takes us through History, Art, Architecture, Mathematics, Physics and Biology and correlates the values reasonably.

Euclid was supposed to have discovered this relationship that Pythagoras also endorsed : 1.6180339887, also ad infinitum. Dubbed the "Golden Ratio" or the "Golden Number," he explains the harmonious geometrical characteristics in everything from pentagrams to the petals of a rose. The 'pi', altogether a different geometrical aspect is not to be confused with this number. Here the division of a line by Euclid into two parts such that the ratio of the larger part to the smaller gives a ratio of the whole line to the larger part.

Astronomer Johannes Kepler, who saw φ as the greatest treasure of geometry and Mathematician Leonardo Fibonacci of Pisa have been quoted in the beginning of the book with ample examples which cannot be mentioned in the review. However, here is a list of few things that have been discussed alongside (satisfying φ )

The Babylonians
Binet formula
Cubism
Egyptian Monuments
Euclid's definition
Flower petal arrangemnt
Galaxy
Great Pyramid of Khufu
Islamiah Mathematics (Al-khawrithm)
Kepler's laws
Lenonardo da Vinci (and his paintings, of course)
Music
Pacioli
Parthenon
Penrose Tiling
Pentagon
Phyllotaxs
Platonic solids
Poetry!
Quadratic equations
Quasi-crystals
Spirals (ubiquotous)
Stock market analysis
Violin Construction

There is mysticism at a few places. For instance it talks about the “mystical” properties of integer like 666, the number of the beast; there is this formula relating 666 and phi. I am not sure how sin 666? + cos(6 × 6 × 6)? gives a “good approximation” of the negative of phi. Added to this is a mention that President Ronald Regan changed his address from 666 in California to some 668!

Now, if you are a Physicist, you would find solace in 'Uncertainty Principle' along with hefty paradoxes supporting your claim. However, the author gives ample reference and at times the conclusion drawn is unconvincing.

There is a lot mention about the 'Golden Rectangle'. If you do a Fibonacci google under the image tab, you would get a lot of these and could find several examples. These are amazing given the fact that the author has found so much time and curiosity to come out with these conclusions. One can then create a spiral of smaller such rectangles that converge to a point which he calls “the Eye of God”.

The Bernoulli's brief histoy also caught my attention. The family is supposed to have contributed much to science in those days that also saw rivalry among themselves. A logarithmic spiral on the tomb of another Bernoulli is quite an interesting mention.

The final chapter of this book is also another book (Is God a Mathematician). In this chapter Livio looks at the idea, in a 'soon-to-be-published' scientific book (a review I have already done, because the order of my reading is not chronological with publications). Here he mentions that all of physics could be modeled by computer programs instead of mathematical equations. Quite incidentally there are a few themes common in both books, but in IGAM, the author talks more about Physics, Universe and Gravity. He considers man-made axioms at the most basic level; however, once those basic axioms were chosen they had consequences which affected the development of the entire mathematical system we know today. For example, we say that 1 + 1 = 2 because we live in a Universe of discrete objects. But suppose we were all blobs of liquid living in a liquid world. Then one blob and another blob would merge together to form one bigger blob. In such a world we might say that 1 + 1 = 1, and our entire mathematical system would be radically different. You would appreciate such ideas if you are passing through Quantum Tunneling.

Good read, finally.