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Fri, December 02, 2011
Fibonacci's Arithmetic Revolution - review
By David Bodanis
The story is extraordinary. Even as the world was mired in medieval darkness, with the crushing hand of religion blocking all scientific inquiry, a lone genius named Fibonacci appeared on the shores of the Mediterranean. Through magnificent creative struggles, he discovered a number with near magical properties.
The Man of Numbers: Fibonacci's Arithmetic Revolution by Keith Devlin
It is an infinite sequence that begins 1.61803… and is sometimes known as the Golden Ratio; sometimes as the Divine Proportion. Mathematicians symbolise it by the Greek letter phi, and it can be used to produce the most beautiful rectangle humans can recognise: one that already was understood when the Parthenon was designed and, in times to come, would be incorporated by Leonardo da Vinci in his greatest works of art. It appears today in the proportions even of the humble credit card.
Or so the internet, and many popular books, would have us believe. In fact, the man referred to in so many accounts, originally Leonardo of Pisa (Fibonacci came long after his death, from his family's name), was not much of a genius. Nor was he living in an age of ignorance. Nor does the shape that came to be associated with his name actually appear in Greek sculpture, or Renaissance art, or our Mastercards today.
The actual story – of how he got famous, and what he really did – is more interesting than the legend. Fibonacci was born in the 12th century, when a number of exceptionally efficient popes were organising Europe in a way that hadn't been managed for many generations. Armies were being sent – not always with great success – to conquer lands in the Middle East; universities were growing; trade, banking and technical innovation were at a peak.
But although a small amount of that innovation was generated internally, much of it arose because a handful of cities such as Pisa were managing to maintain small fleets that could link them with the far more advanced world that already existed across the Mediterranean. Centuries of Islamic civilisation had produced marvels most Europeans could only stare at in awe. The vessels that set out from Pisa were like primitive spaceships, reaching a distant planet where wonders could be glimpsed – and with good Italian acumen, quickly copied, or purchased, or sometimes just stolen, to be brought back to Europe's simple consumers for profit.
Fibonacci's father was a customs official who was living amid one of the Italian trading missions in Muslim north Africa, and when he sent for his son to join him, Fibonacci quickly noticed how backward the world he came from was. In particular, Europeans still used the same counting system that ancient Romans had. One was I, two was II, 10 was X, and 50 was L. To write the number 52, one had to write LII.
At first that doesn't seem too bad, but now try multiplying it by 10. Even the least numerate among us know that 52x10=520: it's so straightforward that it doesn't even seem like a calculation. In Roman numerals, though, one needs to multiply LII by X, and who can read off the answer from that?
North African Arabs and Berbers were already using the efficient system of twos and 10s and 50s; Fibonacci's father and the other Europeans were stuck with the unwieldy Roman numerals. The opportunity was ripe, and Fibonacci plucked it: he prepared manuscripts showing how the new counting system worked.
Keith Devlin doesn't leave the story there, though.
Please see THIS LINK to read the rest of the review...
And, about mathematics, The Urantia Book teaches:
12:9.3 Mathematics, material science, is indispensable to the intelligent discussion of the material aspects of the universe, but such knowledge is not necessarily a part of the higher realization of truth or of the personal appreciation of spiritual realities. Not only in the realms of life but even in the world of physical energy, the sum of two or more things is very often something more than, or something different from, the predictable additive consequences of such unions. The entire science of mathematics, the whole domain of philosophy, the highest physics or chemistry, could not predict or know that the union of two gaseous hydrogen atoms with one gaseous oxygen atom would result in a new and qualitatively superadditive substance—liquid water. The understanding knowledge of this one physiochemical phenomenon should have prevented the development of materialistic philosophy and mechanistic cosmology.
81:6.10 Science teaches man to speak the new language of mathematics and trains his thoughts along lines of exacting precision. And science also stabilizes philosophy through the elimination of error, while it purifies religion by the destruction of superstition.
104:3.2 Mortal man is passing through a great age of expanding horizons and enlarging concepts on Urantia, and his cosmic philosophy must accelerate in evolution to keep pace with the expansion of the intellectual arena of human thought. As the cosmic consciousness of mortal man expands, he perceives the interrelatedness of all that he finds in his material science, intellectual philosophy, and spiritual insight. Still, with all this belief in the unity of the cosmos, man perceives the diversity of all existence. In spite of all concepts concerning the immutability of Deity, man perceives that he lives in a universe of constant change and experiential growth. Regardless of the realization of the survival of spiritual values, man has ever to reckon with the mathematics and premathematics of force, energy, and power.
Link to External Source Article
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