Unity In Diversity: Magic Squares

DURER: Magic Square of 4×4: A Palette of 36 Combinations Summing to 34: Unity In Diversity  

Albrecht Durer, the Renaissance artist is best known for his depiction of “Melancholia”, completed in 1514. At the top right corner of this engraving is the Magic Square of 4×4. Of interest in this Durer Square, as it is now famously known, is the information seen in the bottom row, whose 4 numbers are:
4 – 15 – 14 – 1 

Let us inspect the two central numbers of this line,
which are “15” and “14” and joined together it reads as “1514” which is the precise year that Durer designed this. This famous number 1514 has thus become Durer’s most clever, chronological signature.

It is one of 880 possible permutations of the Magic Square of 4×4.
By definition, it must have its 4 columns and 4 rows and 2 diagonals all summing to 34 which is known as The Constant or Magic Sum or Harmonic Sum.
This square though has other surprising features, like the 4 centre numbers also sum to 34, the 4 quadrants and the 4 corner numbers, opposing pairs… very special.
These exciting group of patterns summing to 34 constitute 2 cosmic statements:
1- Order Amidst Apparent Chaos.
2- Unity In Diversity.

I believe that Magic Squares, apart from their mathematical beauty, are integral keys to the future sciences, that they are templates for atomic structures and crystalline lattices.

Did you know that there are 36 possible ways of making the sums of particular 4 numbers, in symmetrical configurations like crosses and stars, to equal 34. This includes the obvious 4 vertical columns, 4 horizontal rows and 2 diagonals constituting 10 permutations, and the chart above indicates there are another 26 unique ways, even though you are only seeing 12 squares. One of the squares, has the 4 quadrants and this therefore counts as 4 permutations. All the other squares show 2 complementary ways that achieve sums of 34. In fact, there may be other configurations of 34-ness not yet discovered.

Jain 108