|
Colour Factor actually used colour factorially,
the warm colours being for even numbers and the cold for
odd numbers. The rods took the form of sticks built on a
cubic module 1-12. The white, red, blue and yellow, being
primary colours were related in that order to the first
four prime numbers, 1, 2, 3 and 5. Black was related to
the prime 7 and all primes greater than 7. White was the
base upon which all colours could be displayed. White cannot
be made more white, just as 1 multiplied by itself any number
of times remains 1. Red has a potent effect on the eye,
and two is the most potent of the prime numbers. Its colour
red is readily distinguishable in at least three intensities.
Thus 2 x 1 is pink, 2 x 2 is scarlet, and 2 x2 x 2 is crimson.
These numbers 2, 4 and 8 grade from the white end of the
series towards the black end. Blue is associated with the
group of numbers based on 3 in the series from 1 to 12,
having only 2 members , namely 3 x 1 and 3 x 3. Thus 3 is
light blue and 9 is royal blue. Yellow is related to 5 and
orange to 10. Six is violet and seven is light grey and
eleven dark grey. Further explanations are given by the
teacher Seton Pollock in his book (see below).
There
are some problems involving colour that have puzzled mathematicians
for over a century. One of these is the famous map-colouring
question. How few colours do you need to colour-in a map
of fields so that no two fields of the same colour are contingent
? The most elegnat solutions are perhaps those of two Russian
professors of mathematical logic at Moscow State University
(see below).
Another
aspect of colour and mathematics is that of the mathematical
crystallographer, concerned with colour symmetries and classifying
all symmetrical subdivisions of the Euclidean plane. This
is likely to be of great interest in the field of design,
as well as visual and evironmental studies and architecture.
With reflection symmetry all seventeen diperiodic and seven
monoperiodic ribbon configurations need to be generated
by a logical process of mutual implications. An authority
on the subject is Arthur Loeb of Harvard Visual and Environmental
Studies. The history of colour-number ideas goes back to
Babylon and the sacred book of numbers, the Kabbala, said
to embody the inner and mystical aspect of Judaism. The
original Kabbala does make several abstruse remarks refering
to colour, using such terms as 'the yellow of all yellows
that includeth and concealeth all other yellows' or the
'backness of black' and the shining of 'white brilliance'.
The occultist, Sepharial, writing at the beginning of the
20th century, explained that :
The
number One - symbolised the fundamental unity of all things,
the Logos,. Its colour was the brilliance of the sun, &c.
The number Two - symbolised the duality of life, the law
of alternation, the binomial, subject and ofbject, plus
and minus, and creation, &c.
The number Three - symbolised all trilogies and trinities,
the three dimensions, and past present and future &c.,
&c.
Sepharial gave colours to the numbers or Sephiroth as these
powers are called, relating them to the colours of the planets.
His attributions, however, are not consistant (see below).
Another
occultist, a principal of the International Order of Kabbalists,
wrote at length on colours and the sephiroth, though he
explains that the relationship should be re-invented by
each person using the system :
Kether
(the first) had brilliance.
Chocma (the second) had blue.
Binah (the third) had black, and so on (see below).
This Kabbalist academic, James Sturzaker, also explained
that a popular outcrop from the Kabbala was the Tarot, in
which there is a suit for each World (the Merchants, the
Army, the Common People and the Church), composed of ten
cards plus page or jack, knight , queen and king to indicate
four sub-levels. The twenty-two cards relate to the paths
of the Kabbala tree.
DP
Bibliography
CUISENAIRE,
G. and GATTEGNO, C. (1954) Numbers in Colour. London: Heinemann.
Colour in school mathematics.
DYNKIN, E.B. and Uspenskii, V.A (1963) Multi-color Problems.
Chicago: Un. Chicago. Field-colouring problems.
LOEB, A.L. (1970) Color and Symmetry. N.Y.: Wiley. Relates
colour to the mathematics of crystallography.
PLEUGER, W.H. (1959) Discovering Arithmetic. London: Educational
Supply Association. The Stern system of coloured mathematical
sticks for schools.
POLLOCK, S. (1962) Colour-Factor Mathematics. London: Heinemann.
Colour in school mathematics.
SEPHARIAL (1911) The Kabala of Numbers. London: William
Rider. Inconsistencies can be seen in the colour attributions
p.60 vol.1, p.169 vol 2.
STURZAKER, D. and J. (1975) Colour and the Kabbalah. Wellingborough:
Thorsons. Occult colour in relation to the ancient book
of numbers. Has no bibliography. Sturzaker's colour scales
may have been taken from Aleister Crowley's four colour
scales, the Emperor's, Empress', King's and Queen's scales
from his book 777, London: Neptune, 1955. Crowley also quotes
the researches of Dr Jellinek on the colours of the Kabbala.
However it is difficult to take seriously a colour such
as 'white-red-whitish red-reddish-white'.
THOMPSON, H.A. (1962) Colour-Factor Mathematics. Reading
: Colour-Factor.
Colour in school mathematics.
|
Areas
of Knowledge
Options
