The Magic Square and Ladder in Melencolia l by Albrecht Durer

Albrecht Durer (1471-1528), in his 1514 engraving entitled Melencolia I, proves that indeed, ‘A picture is worth a thousand words’.   Filled with alchemical and mystical objects, a viewer could become lost in the forest of meanings.  Each item holds numerous layers of interpretation and I certainly won’t even begin to imply I understand all it conveys.  I am happy to wonder.

Thinking back to the sentence; “As a rough and unfinished block, man is taken from the quarry and by the secret culture of the Mysteries is gradually transformed into a trued and perfect pyramidal capstone,” which is written in the Secret Teachings of All Ages by Manly P. Hall, and shared in The Missing Capstone, I can’t help but wonder if this offers a connection to the prominently displayed stone in Durer’s image. This assumed truncated rhombohedron sits beside the grindstone and at the base of the ladder.

The ladder has often signified stages of intellectual growth and spiritual enlightenment.  It is a symbol of progress with the rungs marking the various levels.  It represents a climb, one step at a time, with each rung providing support to reach another, yet higher, understanding.  Could the stone, already beginning to be shaped, and positioned at the bottom rung, indicate wisdom starts with knowing one must make the effort to climb?  Upon moving up the rungs, man discovers, learns, and gains insight.  The rough stone (by progressing up the ladder), is transformed into a more perfect shape; like the capstone mentioned by Hall.

Interestingly, in between the third and fourth rungs of the ladder is depicted a cluster of buildings in Albrecht’s image.  Since there are seven liberal arts which are divided by the first three, the Trivium (grammar, logic, rhetoric), and then with the last four, the Quadrivium (arithmetic, geometry, music and astronomy/astrology), could this group of buildings portray a university?  Is a suggestion being made that higher learning begins at the joining of the 3rd and 4th rung which may represent the Trivium and Quadrivium?

This linking of 3 and 4 can relate to the order of 3 and 4 Magic Squares; of which one is displayed in the upright corner of Durer’s masterful work.  Magic squares are numerical grids in which the sum of any row, column, or diagonal equals the same number.  Grids with these properties are considered to have Divine powers and qualities ascribed to them.  In the case of Durer’s square, the magic constant is 34.  It is a fantastic example of a square portraying mystical meaning.  Not only does every row, column, and diagonal equal the magical sum of 34, so do the four corners (making it a gnomon square).  The center quadrant, the same cell from each quadrant, shape of the cross points, bottom half of a quadrant with the same above/below, and the diagonals of a quadrant with the opposite cells, all add to 34 as well.

Durer may have wanted a viewer to connect the structure found within the ladder’s 3 and 4 rungs to the magical summed 34 square.  Both can characterize learning.  But there is another, more significant way, the square connects.  Agrippa (1486-1535) assigned planets, and their attributes, to magic squares.  Durer’s order of 4 square (4×4) relates to Jupiter and its trait of concord.  Many researchers have suggested that Durer’s square offers a balanced solution to the engraving’s discord atmosphere.

Most notably illustrating the depressed atmosphere in Durer’s scene is the winged being sitting beneath the square.  In a frustrated posture, she is believed to be the personification of Melancholy. Assumed to be saddened by defeat for understanding, albeit momentary, she rests her head on her hand. This position was also used by Moretto da Brescia in Portrait of a Young Man and expresses the temporary feelings for both head in hand individuals.  Written under the man’s cap in the Portrait of a Young Man is, “Alas, I desire too much.”

In keeping with Agrippa’s attributes of the squares (believed to be Durer’s source), it is the order of 3 square (3×3) which can demonstrate disharmony and melancholy.  It is assigned to the planet Saturn and base element lead.  Although not shown, its traits are obvious in Durer’s scene and he clearly wanted to demonstrate it.

Amazingly, the cure for Melancholy’s disposition can be revealed to her, if she only changes her gaze in the opposite direction.  If she turns around, in front of her would be the visibly present order of 4 square.  Providing harmony to the characteristics of the order of 3 square, the order of 4 square offers the solution.  The importance of the joining of the 3rd with the 4th is again alluded to.  A balance or contentment can be found by uniting both.  Two opposite squares, balanced together, to convey a meaning which lifts one’s soul.

To go back to the ladder, it would seem a school of thought may be suggested where one of man’s goals is to continue to reach for higher learning; to go beyond the ordinary.  As the liberal arts, in older times, were considered essential studies in order to ‘free’ oneself or become a master, the precious value of both the trivium(3) and the quadrivium (4) can be recognized.  Could this be one of the meanings Durer so much wants to convey in the ladder and the square?  Both are limitless creations.

We do not see the top of the ladder in the image.  In Duncan Burden’s responses to Six Questions, he wrote, “ladders disappearing into the heavens”.  I love the image those words bring to my mind.  I love not knowing all and love the climb into the unknown.

So there are my 1000 words on the picture (a little less), but I would love to hear some of yours.  Feel free to comment on any object in the image or on the above.  It is a golden piece of work.


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24 Responses

  1. Madmonk says:

    There is alot going on in this pictures. You are right there are levels to mans development and with each reincarnation and depending on what part of adam ha rinson they belong too.

    we share first 3 levels with beast of this world, desire for food, shelter and sex.

    we have additional levels of desire that make us human : money, power,knowledge and spirituality.

    In the picture you can see all seven of these desires from the beast on the group to light shining from afar.
    This light is actual how we called upon its shines on us from afar and pulls us towards it, we are compled to climb.
    A person is only called upon once they fulfilled the 6 lower desires below the spiritual level.Its very special desire that can not be fulfilled by any material pleasures but by only moving towards the light can real pleasure be obtained.

    Hence the angel is sad , she looks up at the distance light and finds the material things she has played with empty and no longer pleasurable. Her pass lays all around here empty and worthless.(note when man relates to God as species are seen as female and God as male hence female in picture)

    I want to say some thing about ladders. A ladder is made up of rungs and 2 vertical posts. A person climbs up these rungs in bewteen the 2 vertical posts. This is how a person progresses towards the light.

    Duncan is correct in what says we don;t know what are next level on the rung of the ladder will be, this is out of our hands. All we can do is make the effort to climb and the rest is down to higher forces. With each new level of the ladder we are given additional material to build one side of the vertical post of the ladder. Once we built that additional post to next level the other vertical post is created automatical by higher realm and we move up to next level.

    Here lies a universal law. That we must always move forward with no apparent reward, stop and think about that. Doing something that gets harder and harder and harder the higher you climb. There is no reward for your effort. In fact it all you can see the one side of the vertical post and it seems to you things are getting worse.

    This is the path and system that prepares you for enter to the spiritual worlds. The work is done in complete darkness ( by darkness i mean we do not know why we are doing this work for no reward).

    People have already taken this journey and documented it for us. This knowledge is held in the Bible, Kabbalah sufism. etc.

    I could rabble on all day about this picture. Hope what i typed is useful 😀

  2. Hi MW

    Could I take you back to the truncated tetrahedron mystery? As a professional engineer and having seen how many attempts have been made in trying to solve the mystery behind this object I took what I suppose would be an unconventional step by imploding the entire shape. Notice how ‘all’ of its facets had been paired off together with one in reverse directly opposite the other. My suspicion is this was planned for a further revelation.

    In my experience hidden detail can often be an important factor during any planned construction.. So it occurred to me that if all the facets of the shape including the top and the bottom triangles in their geometric forms were joined together across the shape something spectacular would take place at the centre. You could say that a geometric collision would suddenly happen creating a fascinating star burst. To prove my point take just two of the opposing panels and join them together and notice how one six pointed star has been formed which I am sure you will instantly recognise. If you combine all of them in this way a stylised object not unlike the one shining in the sky above in the engraving is quite possible. But all this would be totally unseen by an outside untrained observer with out having insight..

    (An interesting quotation attributed to Albrecht Durer:: Whoever then proves his point and demonstrates the prime truth geometrically should be believed by the world, for there we are captured.)

    Do remember this is just a proposal and not in any way conclusive – the mystery continues

    Keep up the good work. Terence F. Dick.

  3. Mark says:

    A lot of of what you say does make sense. I especially like the idea of the “starburst.” Drurer had a similar painting (discussed on this website) regarding “Alchemy,” although I forgot the name of it. That painting also includes a light bursting in the background, which is reminiscent of a “starburst.” I also notice that that the TT is placed on it’s side, as if to make it appear as if it is unbalanced, and there is a “balancing of the scales” placed in the painting as if to draw attention to some fact, perhaps regarding the sides of the TT.

    Notice the Ladder in the painting. My own understanding is that the Angel in the picture with the compass in his hand is Jacob, and the theme of the painting has to do with Jacob’s struggle to understand the concept of “a ladder which leads to heaven.” “Melancolia” suggests a state of mind. The nails & saw & piece of torn wood on the floor suggests the tearing down and rebuilding of a house.

    It wouldn’t surprise me if the “balancing” theme has something to do with 2 of the sides of the TT. It’s possible that the Angel is using geometry in some attempt to figure which out which of the 2 sides of the TT help to bring it into balance to ignite it’s power.

    For example, let’s assume for a moment that the TT shape is some reference to a rock (or crystal). You might hold the TT in the palm of your hand on one side, and another side might be pressed against another part of the body. Then again, it’s difficult for me to tell whether or not each of the sides of the TT are equal. At least they don’t appear to look that way from the painting, but I could be wrong. Neither am I attempting to dismiss the “engineering” aspect of the whole mystery as it could relate to the understanding of things like the “Merkaba.” Then again, perhaps there’s different ways that apply to the understanding of a single mystery.

    • Just a thank you for your returned comment about the possibility of a geometric collision in Durer’s tetra. One other thought occurred to me did the number 34 in the magic square have some relationship between the square and the tetra? Taking one side/panel of its construction there presumes to be two parts to it – an equilateral triangle with a rectangle attached, the triangle 3 points and the rectangle 4 points, 34 perhaps? Why 34, added together = 7 another number I am told that had some special significance. I wonder if Durer has allowed us to use one of the keys attached to the angel’s belt to unlock a hidden secret maybe the other keys also need to be resolved. If only it had been possible to see what the angel using the dividers had drawn on the tablet. It is an ongoing puzzle but fascinating. Thanks again for the returned comment. Best wishes Terence F. Dick

  4. JC1117 says:

    Hello, Mark. Your comment about the angel being Jacob sitting next to the ladder…which leads to Heaven reminded me of a song by one of my favorite bands. I hope I’m not detracting by posting this. I am awed by the power of “The Heavens” sometimes. It’s inspiring to “look up” …especially in the midst of a storm.


  5. Mark says:

    To Terrence:

    I’m not certain of what the signicance is of all the numbers adding to 34 in the square is. The only thing that I can think of is it could be some reference to a number that appears in a verse from The Bible. Also interesting is the fact that a square & a triangle can be used to form the shape of a “house.” I can see your point regarding the detail in the Angels belt. True, the number 7 is regarded as a sacred number as is 8 because “on the 8th day (Sabboth) he rested. Notice how Drured included an hourglass next to the square as if to also make some point regarding the number 8, which is shaped like an hourglass. Also the number 8 in Hindu Astrology is designated to the planet Saturn which is associated with Chronos (God of time).

    I wish the number 7 was as clearly defined. It appears to be associated with the act of Creation in some way (perhaps the building of a house?). In Hindu Astrology, the number 7 is associated with the Moon’s South Lunar Node referred to as Ketu, which brings up another interesting point you mentioned. When you hear the word “Ketu,” it sounds like “Key to …” A rectangle forms the shape of a door which the key is used to open. Whereas the number 7 is regarded as a “lucky” number, Ketu is only regarded as lucky from a “spiritual” standpoint, but brings “material poverty” from a material standpoint.

    The number 3 (the triangle) is associated Jupiter, the planet of Fortune. Could this be a reference to the key? I’m really not sure because I’m mostly BS’ing my way through this whole thing. Ha Ha! But it is is true that 2 triangles form a square … A reverence to the dividers as some reference to the dividing line? Anyway, the number 4 (square or door) in Hindu Astology is associated with the Moon’s North Node Rahu, which is regarded as perhaps the most “unlucky” influence in Astrolgy. Interesting is the fact that when you hear & see the word “Rahu,” it reminds me of “Ray Who.” The starburst & the theme “melancholia ” remind me of Rahu in the sense that Rahu is associated with darkness, gloominess & mental disorders. So it’s almost as if you have this theme of 7 (the key), 4 (the door), & the 3 (the fortune which helps to unlock it).
    Either that, or I’m on a BS roll! lol.

    To JC

    “Stairway to Heaven” (Zepplin) & Jacobs Ladder (Rush). lol. The lyrics to Jacobs Ladder are pretty cool. Thank u for mentioning the song. Actually, I have never heard it, but I’m about to. I grew up listening to Rush, and like a lot of their songs too. Pretty “mind-bending” lyrics, kind of like the starburst. Dark side of the Moon, baby! lol

    Also sorry that it took so long for me to reply to both the posts. I almost forgot to check the posts to see if anyone “re-commented.” Also thanks, both of you, for responding to my post. What’s funny is that rarely happens to me & all of a sudden, twice in 1 day. Thanks again!

  6. Hi MW

    Interesting objects like the mysterious tetrahedron in Albrecht Durer’s ‘Melencolia I’ are always a fascination especially from an engineering perspective. Another study I made was of the labyrinth – Chemin de Jerusalem (Road of Jerusalem) at Chartres Cathedral France. I suspect you are quite familiar with the numerical sequences associated with the curved pathway sections that run from the beginning of the labyrinth into the centre covering all the areas of its 4 quadrants. By taking a much closer look at each of the curved pathway sections you can see how they are designed to run over either 1 quadrant or 2 quadrants only but never a 3. Taking the pathway out of the labyrinth and arranging it in a straight line the numbers can be seen to be quite compelling. To verify these numbers obtain yourself a plan copy of the labyrinth and take a finger walk along the pathway sections noting the numbers as you go. Notice how the numbers begin and then end the same. When you arrive at a central 2 position in the small group of 21(2)12 make a mark there and then carry on doing the same with the other two groups , you should locate three positions set in a very straight line facing east towards the altar from the centre. These locations were probably very important for each devotee while make their pilgrimage to the centre although my feeling now is that the centre may not have been the only main objective.
    1122112121211212121121212112211 = 31 curved pathway sections
    Much of the foregoing I am sure has already been discovered, but I had the idea of projecting and converting the numbers into solid vertical blocks according to their values of 1 or a 2. To my astonishment the block line changed into what looked very much like a long castellated wall – just by looking at the numbers you can see almost immediately how this might work. Thinking I suppose as engineers do I considered the possibility that the double numbers along the wall (11 & 22) might present something interesting so I carefully cut out the block line and bent all the double numbers at different right angles, after a simple manipulation a perfect 4 squared castellated walled enclosure with a very large spectacular towered type gate on the west wall was created just by bringing both ends of the line together – it eventually became what looked to be an outline of a well fortified structure.

    In my search to find some answers to back up this strange discovery a certain John of Wurztburg writing in 1160 -1170 quoted “When you descend to the main street, there is a great gate through which one may enter the great Courtyard of the Temple. On the right side toward the south, is a palace which they say Solomon built”. It sounded quite convincing but it pays to tread carefully.

    Many rumours concerning the labyrinth abound but an interesting question I am asking is while walking around the labyrinth are you symbolically walking around this mysterious courtyard presumed to be on the Temple Mount in Jerusalem – remember the labyrinth is known to be called the road to Jerusalem. But it is without doubt a truly astonishing design concept achieved by a medieval mathematical genius. I recommend that you build a small model of this courtyard from the labyrinth and then form your own opinion.

    Was it a small Templar memorial in memory of their once Jerusalem headquarters?

    Many best wishes – Terence F. Dick (Engineer)

  7. Nate Beck says:

    Interesting observations Terence! I just love labyrinths, especially the one at Chartres.

    As for the Solomonic/Jerusalem connection with these particular labyrinths, I would like to point out that the Biblical equivalent to a labyrinth as far as Jerusalem is concerned, is the Winding Staircase that was in Solomon’s Temple as described in 1 Kings 6:8 King James Version.

    This features significantly in the rituals and symbols of Freemasonry and may have featured in Templar lore or symbolism as well.

    It’s interesting that you point out that this involves a 1 quadrant and a 2 quadrant but never a 3, as the Winding Staircase led up from the 1st floor of the Temple at Jerusalem to the middle or 2nd chamber which led out to the third chamber, but the staircase terminated in the 2nd or middle chamber. Even in the Tracing or Trestle Board of the Second Masonic Degree of Fellow Craft the Winding Staircase only leads up to the 2nd chamber or floor!


  8. Nate Beck says:

    Also, the Winding Staircase plays no part in the 3rd Master Mason degree either!

    • Hi Nate Beck

      Thank you for your kind returned comment. I am afraid that any Freemasonry references to the Chartres Labyrinth are way out of my depth but I do accept your particular insight. By viewing these structures through many different eyes and seeing various applications will always add to the fountain of knowledge. All designs of this sort are undoubtedly magnets for seekers, as an engineer I have to say most of my time has been confined to plain sight structures but I do have a passion where design mysteries are concerned especially in ancient history. I am blighted with the nagging question was the designer perhaps looking beyond the plan in some visionary sense. Albrecht Durer was clearly a master of this art and viewers will always want to stare in wonderment at Melencolia I

      Many thanks again Terence F. Dick (Engineer)

      • Mark says:

        I just wanted to say to Terrence that I apologize for not having anything intelligible to say regarding the labyrinths. Actually, when Nate mentioned the spiral staircase as another type of concept for the understanding of the ladder, an idea occurred to me. I think that the ladder is a reference to a type of pyramidal shaped structure which occurs in steps referred to as a “Ziggernaut.” The idea is that the “highest step” on the ladder is found in the middle. That’s one of the reasons why I believe Drurer included “the balancing of the scales” in the painting. The idea is that the “Steps of the ladder” have to be perfectly balanced on each side with the highest step occurring in the middle, just like a “Ziggernaut.”

        Then again, the only reason why I figured that out was because I already understood something else. The middle finger, which is the highest finger is found in the middle (center) of the 5 fingers. Notice that there are 2 fingers (steps) on each side of the middle finger, with the middle finger representing the “highest step” and each of the 2 fingers descending in height in “balanced way,” much like the understanding for a “Ziggernaut.”

        The middle finger is associated with the element “ether” according to Paramahansa Yogananda, which is believed to be the “Heavenly” element. The Middle Finger is also associated with the planet Saturn (Chronos God of Time), and the number 8. The number 7 (3+4=34=7) is associated with Ketu (Key to), a reference to the key on the Angel (Jacob’s) belt. Notice that the hourglass (8 shaped/Time/Infinity) is located right next to “scales,” (Center/balance) which is located right next to the number square (for 34 = 7).

        The understanding is this: The “key to” (Ketu) the understanding the number 7 is the balance found through the understanding of the number 8, which is composed of 2 circles, representing the “2 circular steps” of the ladder (Ziggernaut) found on “each side of the ladder” (balancing of the scales or steps” of the ladder. Tell me ya’ boy ain’t good! lol

        • Mark says:

          Also, to add to that, the numbers 3 and 4 ( which add up to 34)

          3 = number of circular steps found on the ladder (Ziggernaut)
          4 = each of the 2 sides (steps) of the perfectly balanced Ladder (not including the top or middle step).

          “And on the 8th day, He (the number 7/God) rested.”

          Notice that the number 7 is shaped like a “step” on the Ladder. “Rested” is a reference to the center of the Number 8, which divides the 2 circles (composing the number 8) as a reference to the center (middle) as the “top step” of the ladder. The dividers in Jacobs hands could be a compass. Likewise, an “Arc” can be thought of as representing one-half of a circle. Notice how there are “2 arcs” (steps) in the number 3, which represents half of the number 8 (in shape). Thus 3 arc steps + 3 arc steps = number 8 (in shape). The number 4 is composed of 3 lines, possibly a reference to the 3 steps of the ladder (on each side).

          Surely, Mark, your not trying to tell us that the whole understanding of numbers might have had something to do with the understanding of a Ziggernaut? Hmmm … The more I think about it, the more I wonder.

        • Maria Rigel says:

          In the European esoteric tradition, Saturn is associated with 7. And the middle finger is associated with the heart, which is associated with Venus (in the soft, passive aspect) and Mars (in the hard, active aspect).

  9. Mark says:

    Thanks for getting that one for me, Nate. Good thing that you understand all of that stuff. I am completely lost right now!

  10. Nate Beck says:

    Thanks Terence 🙂

    Since you’re an engineer, please email me at I have something i think you might find veeeeery interesting. Thanks

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  12. Spallies says:

    Thought some of you might like this… Will be fun to watch and see what it goes for… 🙂

  13. Maria Rigel says:

    “The order of 3 square (3×3) can demonstrate disharmony and melancholy”

    This is probably because it’s the square of Saturn, and Saturn is associated with disharmony and melancholy. On the other hand, Saturn has other associations. I’m quite sure that it’s associated with the end of the journey, and the square of Saturn is used in the Royal Arch Mason ritual, though I’m still unclear about how.

  14. Maria Rigel says:

    The magic square of Durer can be reconstructed from only 8 numbers in the correct positions. If you read Dan Brown’s “The Lost Symbol” you may see why this is significant.

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