Talk:Melencolia I

Hebrew version

The Hebrew version contains an illustration of the famous Magic Square which appears in the engraving. The illustration was done by me (he.User:Noon is my User Page), and is released to the Public Domain. --85.250.24.90 11:30, 25 Mar 2005 (UTC)

Who asked for a fricking Hebrew version?

2x2 subsuares

notes: The following can be verified with exhaustive tests, proofed:

For all 880 magic squares of order four [1] beside the raws, columns and diagonals the following will sum to the magic constant

1. the sum of the four corners will equal
2. the sum of the inner four cells will equal to the
3. the two cells left of the four inner cells together with the two cells right of the four inner cells
4. the two cells above of the four inner cells together with the two cells below of the four inner cells

This means that if we count the 2x2 subsquares obtaind with wrap around of raws and colums all will have at least 4 such subsquares which sum to the magic constant. The distribution is like this:

120 squares have only 4 such 2x2 subsquares

520 squares have 8 such 2x2 subsquares

192 squares have 12 such 2x2 subsquares

48 squares have 16 such 2x2 subsquares

Last are called most-perfect magic squares.

unique pattern for associative magic squares of order 4

→ Associative Magic Square
→ How many magic squares are there?

Dürers square is an associative magic square. The binary representation of this square is as follows:

binary color code a div 8 = 1 →   a div 8 = 0 →   (a mod 8) div 4 = 1 →   (a mod 8) div 4 = 0 →   (a mod 4) div 2 = 1 →   (a mod 4) div 2 = 0 →   a mod 2 = 1 →   a mod 2 = 0 →

values 0 to 15 15 02 01 12 04 09 10 07 08 05 06 11 03 14 13 00 Melancholia I

same square  with binary color code

You can see that each of the colors occur only two times in each row, each column and in each of the diagonals. If we look at the definition of an associative magic square we can see that for every cell a all colors differ in the symmetrical cell of cell a:

a) changing "a div 8 = 1 with "a mod 2 = 1" and vice versa would give the square:

15	 2	 8	 5
 4	 9	 3	14
 1	12	 6	11
10	 7	13	 0

If we "change" only the weights for the binary representation we will have 4! permutations and the values "0" and "15" will be always fixed.

b) changing "a mod 2 = 1 with "a mod 2 = 0" and vice versa would give the square:

14	 3	 0	13
 5	 8	11	 6
 9	 4	 7	10
 2	15	12	 1

We can see that doing this there are 16 times more possibilities. Together we would have 4!*16 squares. The number considering the Frénicle standard form is 48. (It can be seen easily that all 8 transitions - rotations and transpositions are represented in the "pattern"). Gangleri | Th | T 21:33, 18 August 2005 (UTC)

Written anew

Albrecht Dürer's engraving Melancholia I (originally known by Dürer as Melencolia I) is an allegorical depiction of the symptoms of melancholy, now better known as depression.

what does it mean : "known by Durer as melencolia"? Researchers apparently agree that Durer was aware that such a spelling is neither german nor latin. Also "allegorical depiction of symptoms": perhaps it would be better to leave that to the care of the medical profession and to say something about symbols.

My redaction: Albrecht Durer's engraving known as Melancholia I is an allegorical composition which supports various interpretations. The title comes from the deviantly spelled word 'melencolia' appearing within the engarving itself. The most obvious interpretation takes the image to be about the depressive or melancholy state and accordingly explains various elements of the picture. Among them most conspicuous are:...

Added a link to D. Finkelstein's impressive exegesis. www.physics.gatech.edu/people/faculty/finkelstein/DurerCode050524.pdf al 09:39, 14 July 2006 (UTC)

- I agree with most of your points here, but Melancholy is originally Greek (melan=black, choly=bile I think), although it has an "a" in Greek too. The OED lists by my count 16 English spellings for "melancholy" and "deviant" is I think an inappropriate description for any spelling in any European language in 1514 - no dictionaries, no spellcheck. I have changed it to "unusual" Johnbod 03:09, 13 November 2006 (UTC)

Why the modernized spelling?

Shouldn't we use the name Dürer gave his own work? Aleta 04:12, 2 January 2007 (UTC)

I tend to think so (see just above), but it might be arguable the other is now the commonest spelling in EnglishJohnbod

An incorrect spelling even if it is a common spelling, is still an incorrect spelling —The preceding unsigned comment was added by 86.198.240.254 (talk) 09:23, 6 February 2007 (UTC).