The
old custom to colour Easter eggs and to exchange them is still living in
Bulgaria.
Here you are such an egg painted with my own hand. |
Explanation for non-logicians:
Why did I called this egg BOOLEAN? Because it is a picturesque representation of the Boolean algebra of 8 basic colours (in fact, paints): white W (no colour), 3 prime colours (red R, yellow Y, and blue B) together with their dyadic mixtures (R plus Y give orange O, Y plus B give green G, B plus R give purple P), and all three primers together giving black K. I have applied here the traditional palette used by artists instead of the modern system CMYK (cyan, magenta, yellow, and the superfluous black). The system RYB was firstly mentioned in different context by Leon Battista Alberti (1435) and later on by Leonardo da Vinci (c. 1510) in their treatises on painting. The thesis that red, blue, and yellow form a necessary and sufficient set of paints was explicitly lanced by J. W. von Goethe in 1810 and is still being in use by painters and scholars as a more intuitive colouristic foundation. Regarding as a Boolean algebra, the set of all 8 paints is ordered by the relation containing: K contains all paints, each paint contains W ("lack of paint"), G contains both Y and B, etc. B is 0 and W is 1 of the algebra. Mixing paints plays the rτle of disjunction. The common component of two paints is their conjunction. The well-known to the artists complementary colours serve the negation (e. g., R vs. G, P vs. Y, W vs. K, etc.).
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The Boolean algebra of colours is a floury illustration of Leibniz's ideas (above right). A prime number is attached to each primary colour. Composite paints obtain the product of the numbers of their components. Notice that now 1 is not the symbol of algebra's maximal element but is the number of white. In the other end, the number of black is no more 1 but 2·3·5. A few elementary questions together with their calculated answers follow. Does orange contain red? Yes, because 2·3 is divisible by 3. Does green contain red? No, because 2·5 is not divisible by 3. Are orange and purple contained in any colour? Yes, but only in black, because 2·3 and 3·5 together contain all factors. Do orange and purple contain a common colour? Yes, because 2·3 and 3·5 have a common divisor 3 and this colour is red. Which is the "negative" (complementary) colour of blue? 2·3·5 divided by 5 gives 2·3 and the answer is orange.
In order to be colouring better visible I replaced the "cube" with the stellated octahedron inscribed in it and sharing its vertexes. The result was J. Kepler's stella octangula (left). Furthermore, a discrete approximation of the egg was obtained by cutting out the pyramids. Of course, a normal convex octahedron was constructed in this way (right). |
One may recognize in the octahedron a triangular antiprism. Indeed, the white and the black sides are the two bases (twisted relative to each other) and 6 triangular faces go alternatively up and down. My illustration is a coloured modification of an excellent animated octahedron from the Wikipedia. It is an own work by the user Cyp. Enjoy!
Finally, the Easter egg was designed as a continuous "interpolation" of the 8-element Boolean algebra. As we see, many phenomena were joined in this topic. I tried to present it ab ovo usque ad mala. And my modest contribution was to link in a golden braid Alberti and Leonardo, Goethe, Leibniz, Boole, and... Jesus Christ.
A Calendar Note:
In general, there is a difference between the dates of Easter according to the Catholic and the Orthodox Churches. In some years the days coincide but in other they can differ by more than a month! The Easter days are shown bellow for the years of this decade.
Year | Catholic | Orthodox |
---|---|---|
2010 | 4 April | |
2011 | 24 April | |
2012 | 8 April | 15 April |
2013 | 31 March | 5 May |
2014 | 20 April | |
2015 | 5 April | 12 April |
2016 | 27 March | 1 May |
2017 | 16 April | |
2018 | 1 April | 8 April |
2019 | 21 April | 28 April |
2020 | 12 April | 19 April |