What’s the Real Secret Magic in the Magic Square?

Text copyright © Aug 27, 2012 Dr. Elizabeth A. Garner, All Rights Reserved

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Dürer’s Melencolia I is the most debated image in all of art history, one of his most magical, and one of his most heavily encoded.

 

Durer's Melencolia and the secret code in the magic square
The 1514 Melencolia I

One of the fascinating symbols in Melencolia is what is known as the Magic Square, which is found in the upper right hand corner of the print on the wall, under the bell, above the winged woman.

The Magic Square

WHAT IS A MAGIC SQUARE?

 

Example of magic square
An example of a numeric magic square

Numeric Magic Squares consist of a series of numbers arranged in a square in such a manner that the sum of each row, each column and of both the corner diagonals adds up to the same amount, which is called the Magic Constant.

Numeric Magic Squares may be divided into two categories:

  1. “Odd” Magic Squares, which means that there is an odd number of cells on each side of the Magic Square.
  2. “Even” Magic Squares, which means that there is an even number of cells on each side of the Magic Square. “Even” Magic Squares may be further divided into two sub-categories:
    • “singly even” Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by two, but not by four (e.g. 6 x 6 and 10 x 10 Magic Squares)
    • “doubly even” Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by both two and 4 (e.g. 4 x 4 and 8 x 8 magic squares)
The Magic Square
The magic square

Dürer’s magic square is a doubly even 4 x 4 square whose magic constant is 34. Dürer’s magic square has the additional property that the sums in any of the four quadrants, as well as the sum of the middle four numbers, are all 34 (Hunter and Madachy 1975, p. 24). It is thus a gnomon magic square. In addition, any pair of numbers symmetrically placed about the center of the square sums to 17, a property making the square even more magical.

http://www.youtube.com/watch?v=11gwCkF80xY

Here’s a YouTube video link that explains it in more detail.  Unfortunately the math teacher did not know the difference between a painting and an engraving.

DAN BROWN’S LOST SYMBOL

Anyone who has ever commented on Dürer’s magic square seems to believe that it’s inclusion in this composition has something to do with alchemy or Freemasonry or some occult phenomenon.

Dan Brown’s inclusion of Dürer’s magic square as part of the symbol clues in his book the Lost Symbol was fiction. Nothing could be further from the truth.  The Lost Symbol was a great FICTION story but it has done nothing but confuse the real coding that is held in Dürer’s Magic Square.

MEDIEVAL SUDOKU

Do you like to play Sudoku or do you know someone who does?  Of course you do!  People in the Renaissance loved to play games as much as everyone does today.

 

Sudoku Puzzle
Example of a sudoku puzzle

Magic squares were common in medieval times and everyone loved them and many people owned them.  They were sold at market fairs all over Europe, and their availability was common.  They were considered amulets against disease, which was rampant in Europe. They were manufactured in tin for the masses and in silver or gold for the wealthy.

But the most important point is to understand that anyone who saw the magic square in this print in Dürer’s lifetime would not have connected the symbol with alchemy or something arcane.  They were games and amulets and fun.  Pilgrims often bought them, they were commonplace and would attract buyers.

Durer's Depiction of Medieval Pilgrim
One of Dürer’s famous depictions of a medieval pilgrim.

And anyone who saw the magic square in the print Melencolia was not going to suspect that Dürer was using steganography, the art and science of hiding messages in plain sight, to get a message across about what Melencolia is really about.

Dürer did do something unusual with the numbers in this magic square, which gives us a hint as to the message he was giving.  He rearranged the numbers from their usual order.  Agrippa (http://en.wikipedia.org/wiki/Marcus_Vipsanius_Agrippa) wrote much about magic squares in his Occulta Philosophia and claimed that the Tabula Jovis (http://www.scribd.com/doc/65262304/Adam-McLean-Dr-Rudds-Treatisse-on-Angel-Magick) had magic properties.  The Tabula Jovis configuration of the 4 x 4 square was as follows:

 

4  14  15 1

9    7   6  12

5  11  10  8

16    2    3  13

We can see that Durer changed his configuration dramatically from Agrippa’s.

WHAT CAN BE SEEN HAS BEEN IGNORED

The first thing that we must know about the Melencolia magic square is that Dürer originally created this composition with the “9” in the third row backwards.  We know this because there is one existing copy of the backwards “9” magic square in the British Museum.

Based upon how many copies of Melencolia are still existent, we can assume that Dürer changed his mind very quickly about how obvious the clue of the backwards “9” really was, and changed the copper plate to represent a forward “9.”

People don’t often understand that artists made mistakes and were very competent at fixing errors in woodblocks or copperplates in the Renaissance.  No one was perfect.  In woodblocks, the mistake would be cut out and a plug would be inserted and the correction made.  In engraved copperplates, the area would be buffed out and re-engraved.

So it wasn’t that big of a deal for Dürer to change the backwards “9” to a forwards “9.”

OOPS!

magic
Look closely at the “6” under the correction of the “5” in the first box at left, third row from bottom. The “6” is clearly visible under the “5.”

But no one pays attention to the correction of the “5” above the “9.”  Dürer had originally place the number “6” into that block and historians seem to think that OOPS, he made a mistake.  Not likely.  Dürer was also known as a famous scientist and mathematician during his lifetime, so the likelihood that this master of math and master of engraving just happened to OOPS! Put a “6” where a “5” should go is somewhat ludicrous.

What IF Dürer was actually leaving us a message with this “mistake?”  What if he meant to have the image of the “6” visible to all when he corrected it to a “5?”  What IF THAT WAS THE MESSAGE:  whatever the #6 represented was somehow hidden?  If this is true, we don’t truly have a magic square, because another number has been entered into the equation.

But it’s a great way to hide a message!  Something that most people in his lifetime would just ignore, being delighted with “magic” of the numbered square adding up to 34.

WHERE TO START?

And what no one has ever contemplated is this:  HOW is this magic square to be read?  Do we start at the upper left hand corner?  The lower left?  The upper right?  Or the lower right?  If Durer is passing a message steganographically, e.g. hidden in plain sight, the people who are supposed to get the message have to know how to read the code.

The reading of the magic square starts at the lower left hand corner.  What does that tell you?

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9 thoughts on “What’s the Real Secret Magic in the Magic Square?

  1. Durer’s magic square is upside down with respect to Agrippa’s.
    In the original backwards 9 square it appears to me that the backwards 9 would have originally been a 5 and likewise the 5 a correction of a frontwards 9.
    My question is if he did make not a mistake, then his engraving would have to have started with the 5 or 9 which, I presume begs another unanswerable question.

    Really enjoying your blog, I have only “discovered” it this evening.

  2. I surfed on dis topic only cuz i read Dan brown’s book however i dont understand how he deciphered d letters to d nos. can anybody pls. explain tat 2 me. Thanks .And great info. Keep it up.

    1. Thank you for your comment but you are totally wrong. The secrets to any of the what appears to be geometrical ssumbol in that print are purposeful deflections on the Duerer’s part and arrogance in showing hw completely adept they we at sung agh symbols in new ways t get OTHER messages across. in that print a noting to do with agh per se. But the mathmethetcians don’t like giving up their paradigms either. I would be in tereting i f you identified who this “great olver: is, for i was in deep discussion with someone who wha looking to publish stubbornly hs theory, and we just didn’t see yet to ey , biceasue i could prove he was wrong in the thesis, an he would have none f that.

      Please do identify this great solver.as I suspect I know who this person callus to be, I’m sure the rest of us would like to know what reigns as truh as published here with evidence and what and those of them are trying to remain with old paradigms dressed up with new sins

      Best,

      Elizabeth

    1. Thank you so much!
      we are for truth in this world when most has become lies and total manipulation. And don’t miss the marvelous videos on my Youtube channel created by the marvelous Joe Kiernan. We add even more into those videos. My Channel is Elizabeth Garner but it would be good to search for Elizabeth Garner Durer on Youtube because there are otter Elizabeth Garners there :)

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