```Fibonacci Fibbing
2006

The Fibonacci Series of numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 .................
was formulated by the mediaeval mathematician, Leonardo of Pisa
(?1175-?1230), who was known as 'Fibonacci'. Starting from zero
and progressing to infinity, it is formed by the neat trick of
adding the two preceding numbers to form the next in the sequence.
It has long been maintained by some theorists that these numbers
are the aesthetic key to an ideal system of proportions. And
it can be related to another system of good proportions - the
Golden Section - a geometric ratio going back to ancient
Greece, which is expressed in a simplified and rounded arithmetical
form as 1:1.618. However, the practical application of either
system in art, architecture and design has been limited and -
where it is claimed to have been applied - difficult to discern.

Both the Fibonacci Series and the Golden Section (also know as
the Golden Mean or 'dynamic symmetry') are currently in peoples'
minds due to their having been featured in the The da Vinci
Code. Here they were given religious connotations and, reportedly,
sponsored interest in some school art classes - so it is appropriate
that we check out their veracity.

The Fibonacci Series is sometimes validated as a mathematical
metaphor of deep natural processes by reference to how a pair
of rabbits may quickly develop into a plague. (However, to accept
this, we have to ignore the first term in the series because,
of course, nothing can come from nothing!)

But, one can understand people being intrigued - even fascinated
- by the concept. Each of these integers seems to have a magical
or mythical vibrance, and the sequence seems to surpass mere
logic and exist in some rarefied spiritual space.
Zero - Nothingness, The Void - is followed by two expressions
of Unity, side by side, like twin planets revolving about a white-hot
Sun; but, also, they are the digits of computer technology.
Then comes Duality: the Eternal Couple, male and female, day
and night, left and right. The Eternal Opposites. The four-square
basis of all arithmetic. (Yet - 2+2=.NOT 3!)
But 3 is the Triad, the Holy Trinity, the trident, the tripod,
the stool of both the milk-maid and the Delphic Sibyl, the prophetic
and mystical pyramid (IM Pei's new entrance to the Louvre is
also in The da Vinci Code), the geometry of Euclid and
Pythagoras.
Next, the five fingers of the hand, the days of the (working)
week, the cosmic symmetry of the pentacle (also featured in The
da Vinci Code), the Stigmata, Dürer's Melencolia
I.
Eight seems stolid and dull in this company. But 13 is the
Devil's number!
And the series has a cosmic embrace: it runs from zero to infinity
in a kind of aesthetic perpetual motion.
Yes - intriguing, even mystical. It is no wonder that these arcane
quantities and relationships have often been seen as a metaphor
for the magic and mystery of proportion in art and design, let
alone a clue to the Holy Grail. Dimensions and relationships
having the properties of Fibonacci numbers must be automatically
ideal and 'beautiful' and - therefore - also 'true' and 'good'.
Obviously this is a most potent set of numbers.

But you don't need to be a mathematical genius to see that this
is nothing less than specious humbug. If we examine the numbers
themselves -
Zero is a totally useless dimension in the real world and any
ratio containing it will only be fantasy.
The proportion 1:1 can in no way be construed as 'dynamic symmetry'.
It is simple equal, bilateral division, which has rarely been
considered a felicitous proportional principle in art or design.
And 1:1 is arithmetically the same as 2:2, or 57:57, or 300:300,
or 1,730,569: 1,730,569 .................so of what significance
is it?
Similarly, 1:2 has never been considered 'dynamic symmetry'.
Thus, the aesthetic applicability of the first four terms of
the Series is easily demolished.

Next, the Series' utility is reduced markedly if - as some authorities
maintain - its use is confined to the ratios of adjacent numbers
(2:3, but not 2:8, for example). And we must eliminate all relationships
above the first half dozen in the series because they are too
recondite for most humans to intuit (34:55, for example). It
may be that they have a deep, unconscious effect, but this is
a mater of faith, not reason.

All this means that, for any practical application, the series
reduces itself to (possibly)
1 2 3 5 8 and 13. If it is allowed that all of these numbers
can relate universally to each other, a reasonably large, yet
comprehensible, range of possibilities results:
1:2 1:3 1:5 1:8 1:13
2:3 2:5 2:8 2:13 and so on
However, the system breaks down after 5 because the next number
(8) is divisible by 2, thus making 2:8 the ratio of 1:4. The
same calculation can be applied to 2:34 (=1:17), 2:144 (=1:72),
3:21 (=1:7), 3:144 (=1:48) and 5:55 (=1:11) - but the numbers
4, 7, 11, 17, 48 and 72 are not part of the Series! This
appears to be a major logical deficiency in the theory - if not
its total demolition!

So, in practical terms, the Series is actually limited to the
numbers and ratios 1 2 3 and 5 (all the numbers after 5 having
been eliminated by the invalidation of 8), or - if any of these
numbers may be related to any other,
1:2 1:3 1:5 2:3 2:5 and 3:5.
Any cursory examination of some of the great works of art and
design will reveal that some of these ratios are sometimes in
evidence, although this does little to explain their rich complexity.
In addition, because most paintings and sculptures contain few
straight lines, one has to choose the segment/s of the organic
shapes of a portrait or nude from which it is relevant to measure
the ratios, exercising a prior aesthetic judgment which will
probably be self-fulfilling. And, of course, mathematical approximations
are of no help to architects and other designers.

Thus, the theory of the use of Fibonacci numbers in art and
design is not only theoretically flawed, it is impossible to
apply.

The mathematical relationship between the Fibonacci Series to
the Golden Section is also a questionable one. Between the numbers
in the range of 5 to 34 in the Series, the ratio works out as
between 1:1.60 to 1:1.619 - never quite the Golden Section ratio
of 1:1.618, but approximating it. However - as The Oxford
Companion to Art points out - we can take any two
numbers and, adding them to form a series, will result in ratios
that approximate the Golden Section: for example, a series
2 2 4 6 10 16 26 42 68 .....................
yields, for most of the adjoining numbers, ratios approximating
the Golden Section, the best being the last three (1.615 and
1:1.619). So - what's special about the Fibonacci Series?

All this indicates that we must
be extremely cautious in accepting the Fibonacci Series as the
aesthetic 'philosopher's stone' - or, indeed, a clue to the Holy
grail!

```

BACK