In the year 1514, the great German artist Albrecht Dürer completed a famous engraving that he named Melancholia. In the upper right-hand corner he placed a “magic square” that contained an arrangement of the numbers 1 through 16, as pictured below:
Is there something really magic about this square? See for yourself: if you add the four numbers of any row or column, the total is always the magic number 34.
Or, if you add the four numbers of the two diagonals: 34 each time. And we’re just getting started!
Try adding the following:
The four numbers in the outside corners: 16, 13, 4, 1
The four numbers in the horizontal inside corners: 5, 8, 9, 12
The four numbers in the vertical inside corners: 3, 2, 15, 14
Zigzagging from bottom right to top left: 1, 2, 15, 16
Zigzagging from bottom left to top right: 4, 3, 14, 13
The four numbers in the upper left quadrant: 16, 3, 5, 10
The upper right quadrant: 2, 13, 11, 8
The lower left quadrant: 9, 6, 4, 15
The lower right quadrant: 7, 12, 14, 1
The middle quadrant: 10, 11, 6, 7
If you’ve been counting, this brings the total to twenty symmetrical combinations that add up to 34.
Since we’re past getting started, but still not there, let’s try some more.
Add these symmetrical combinations:
16, 3, 9, 6
5, 10, 4, 15
2, 13, 7, 12
11, 8, 14, 1
16, 5, 2, 11
9, 4, 7, 14
3, 10, 13, 8
6, 15, 12, 1
16, 2, 9, 7
3, 13, 6, 12
5, 11, 4, 14
10, 8, 15, 1
3, 2, 15, 14
5, 9, 8, 12
This brings the total to 34 combinations that add up to . . . 34!
And, if you look closely, you will see that Dürer included the date of his engraving in the bottom line of the magic square—with the two numbers, 15 and 14, side by side.
Also, if you connect the four numbers with a line, note the symmetry of the following four configurations: 1-2-3-4 . . . 5-6-7-8 . . . 9-10-11-12 . . . 13-14-15-16. That is, connect the numbers 1, 2, 3, 4 with a line, and so fourth, and note the recurring symmetrical recurring patterns.
In light of all this, Dürer’s Magic Square now qualifies for membership in what I call Meta-Fours, significant and sometimes a-musing ways in which the archetypal number four seems to turn up all over the place. Thirty-four has been my lucky number since high school days when it was the number on my football jersey. Since it combines two other mystic numbers, 3 and 4, and adds up to yet another, 7, I also find it richly symbolic.
