Ideas in the Night

Tag Archives: Fibonacci sequence

According to Galileo, the laws of the nature have been written in the language of the mathematics but can one say that there is mathematics in the nature? I mean, does mathematics exists in the nature?

The mathematics itself known by us is abstract, conceptual, in other words it “lives” in the world of ideas separately from physical world that can be touched. Some have interpreted, that the mathematical laws that describe the universe are irrespective of the human being and have always existed; the human being has discovered them by reason. And the discovering still continues.

But it is quite difficult to say that how mathematical laws could have always existed. How about the pure math itself, without any applications? Without its “invention” or “discovery” it would not have been possible to present the mathematical laws that describe the universe, the laws from which some people say, that those laws have always existed.

Fractals are again in fashion, but I’ll take as an example from mathematics the Fibonacci sequence. It conceals the golden ratio in it. In the nature this ratio can be detected by measuring everywhere where there are spirals (a geometric interpretation of the Fibonacci sequence), in the galaxies, in the flowers, in the human body itself… And also in music. Even in DNA.



Image courtesy of scottchan at 

In addition, this ratio appears to represent beauty in the nature. It’s no wonder, that this ratio has been used in art and architecture, and much more. Also, in the human body this ratio represents beauty. When the features of human face reflect this ratio, the face is generally considered to be beautiful. The teeth are considered to be very well constructed, when they retell the golden ratio. The 2010 dentist magazine (in Finland) says that the maxillary tooth crowns of clinical relations should follow the so-called “golden ratio”.

This ratio is irrational number, i.e., its decimal representation is infinite. The exact value is

½ (1 + √5)

which is a value of approximately 1.61803.

First 7 Fibonacci numbers are  0, 1, 1, 2, 3, 5, 8. The idea is that the next number is the sum of the two subsequent numbers in such a way that the sequence starts from zero, then follows to ones (sometimes the sequence is presented to start with two ones). Thus the next number in the sequence is 13. The golden ratio starts to form, when a sequence is continued far enough and two consecutive digits are divided by each other, the bigger by the lower. The limit in the infinity seems to be the golden ratio.

The Fibonacci sequence has been compared with the the universe so that like Fibonacci sequence has as a start but not an end, Fibonacci sequence is like the universe: It has a beginning, but not an end. Furthermore the Fibonacci sequence is interpreted to be very fundamental to the whole universe. But what the universe would now approach? Perfectness? Perfect beauty? One expression of beauty? Another view to the universe is, that it has an end, though.

How can such a simple formula can define beauty? How can something so simple be so fundamental to the entire universe? I must say that there’s still much to “discover”.

Does the great truth loom In the infinity, always one step ahead; just when we think, we have discovered something, there’s something else or new in the next step. But we already know what’s out there in the infinity: ½ (1 + √5)!

Previous chapter was my humor about comparing the Fibonacci sequence to the universe, because there is too much mystique attached to the sequence. It’s believed that big-money conspiracy is hiding the truth about the connection between Fibonacci sequence and the universe, so that people wouldn’t know the truth. It’s also believed that the Fibonacci sequence is some kind of sign of God’s mathematical designing of the universe (I don’t deny the existence of God, but I would criticize the idea that the Fibonacci sequence would be a sign of God)

So the golden ratio can be found in the nature by measuring, but does the quotient of two subsequent numbers of the Fibonacci sequence approach in the nature the golden ratio? I mean that in the nature there exist no numbers at all! Even in this blog post there exists no numbers, but logical representations of numbers as Ludwig Wittgenstein would put it. And he is right.

But in the nature there can be found patterns through interpretation, mathematical patterns. Also there’s no knowledge without interpretation, information must be interpreted. But this interpretation is only in the mind of interpreter. So what is there in the nature? A human being. According to the interpretation.

On Fibonacci on Amazon