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Monday, 30 May 2016

Numbers (2) - Fibonacci

Today's blog is the result of several blog ideas that all pointed to Fibonacci numbers: island gigantism (1), symmetry (2), a possible new 5th force in nature, and obviously my 29 May 2015 blog on the Fibonacci number 7 or network science or six degrees of separation. I never wrote about Fibonacci numbers despite briefly mentioning him in my 5 February 2016 blog on the origin of numbers.

Leonardo Fibonacci (c. 1170 – c. 1250) was an Italian mathematician. Fibonacci popularized the Hindu–Arabic numeral system to the Western World primarily through his composition in 1202 of Liber Abaci (Book of Calculation). In this book he introduced the sequence of Fibonacci numbers to Europe although this sequence had already been noted by Indian mathematicians as early as the sixth century (Wiki). Remarkably, Fibonacci numbers seem to rule the Universe.

Galileo Galilei, Italian astronomer & physicist (1564 - 1642), once stated that "Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth".

For years, there has been a "particular theory that relates dark energy to a fifth, hypothetical fundamental force, in addition to the four we know – gravity, electromagnetism, and the two nuclear forces". This 5th force could (help) explain why gravity calculations "have produced a multitude of different values. This is assumed to be due to various experimental errors and the official value of G is routinely updated to reflect this, with the assumption that the values will eventually converge". (New Scientist, 2013)

Since several days, news reports claim that a team at the Hungarian Academy of Science's Institute for Nuclear Research, led by Attila Krasznahorkay, may have detected this 5th force in nature. They "examined the possible existence of dark photons - the analog of conventional photons but that work with dark matter" (eg, Nature, Phys, Science Alert, Wiki).

MIT Professor Avery A. Morton (1892-1987) has written about the relationship between the periodic table of elements (Wiki) and its Fibonacci sequence and concluded that "the pattern for a Fibonacci series is evident" (publication). Others did similar efforts (eg, link 1, link 2).

Personally, I am always intrigued by Fibonacci number 2 and its related symmetry in animals and humans (eg, eyes, ears, arms, legs and even nose holes). I think, feel and believe that our perception of beauty is largely based on (the lack of) symmetry. Although insects do show symmetry by having three pairs of jointed legs, this feature may be another reason for my 27 March 2015 blog: Why do we hate insects?

Galileo Galilei's earlier statement is often abbreviated to the following quote: "Mathematics is the language in which God has written the universe".

John Mayer - Gravity (2007) - artist, lyrics, video, Wiki-1, Wiki-2

Gravity is working against me
And gravity wants to bring me down

Oh I'll never know what makes this man
With all the love that his heart can stand
Dream of ways to throw it all away


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