Sunday, 30 August 2009

The Sagrada Familia, Magic Squares, and the Hitch-Hiker's Guide to the Universe


I have known for a long time that there was a magic square, above [click to expand to full picture], on the Passion facade at Gaudi's famous Cathedral in Barcelona, the Sagrada Familia. But I recently got some additional information so here is the related part of the story from my MathWords web page:

Each row and column add up to 33, the supposed age of Christ at his death. In fact there are supposed to be exactly 33 different four number groupings that add up to 33; can you find them all?

In October of 2004 Ms. Sheila Knight sent me a note indicating that she and her Year 7 students at The Grays School Media Arts College had found a total of 42 four number groupings. She added, "Perhaps Gaudi was a fan of “The Hitch-hiker’s Guide to the Galaxy” where 42 is “the answer to life , the universe and everything” – this works when you consider it is on a church!". She was kind enough to send a PDF file of her results.

In Dec of 2006, Ahto Truu sent me an email in which he expanded her list to 54 different sums. He also reasoned that probably Gaudi had no knowledge of "Hitch-hiker’s Guide". Here is his post, clipped a bit:

"In fact, there are 48 of them if we don't allow the two 10's or the two 14's to be used at once, and 54 if we do.
In the list below, all the possible sums are listed in a systematic order, with the entries not on Ms. Knight's list marked:
1 3 14 15
1 4 13 15
1 5 13 14
1 6 11 15
1 7 10 15
1 7 11 14
1 8 9 15
*1 8 10 14
1 8 11 13
1 9 10 13
2 3 13 15
2 4 13 14
2 5 11 15
2 6 10 15
2 6 11 14
2 7 9 15
2 7 10 14
2 7 11 13
2 8 9 14
2 8 10 13
3 4 11 15
3 5 10 15
3 5 11 14
3 6 9 15
3 6 10 14
3 6 11 13
3 7 8 15
3 7 9 14
3 7 10 13
3 8 9 13
3 9 10 11
4 5 9 15
4 5 10 14
4 5 11 13
4 6 8 15
4 6 9 14
4 6 10 13
*4 7 8 14
*4 7 9 13
*4 8 10 11
5 6 7 15
5 6 8 14
5 6 9 13
5 7 8 13
*5 7 10 11
5 8 9 11
6 7 9 11
*6 8 9 10

*1 4 14 14
*2 3 14 14
*2 10 10 11
*4 9 10 10
*5 8 10 10
*6 7 10 10

Also, I find it quite unlikely that Antoni Gaudi could have been a fan of "The Hitch-Hikers Guide to the Galaxy", as he died in 1926, more than 50 years before the Guide appeared (the first episode of the radio show was aired in 1978, and the first book was published in 1979 :) "

A couple of years later, in 2009, I received a note from Christopher Mata that pointed out that the wall may have been influenced by the Hitch-Hikers Guide after all...

"I'd just like to note that the Passion façade was sculpted by Josep Maria Subirachs when he started work on the Sagrada Familia temple in 1987, not by Gaudí, and by then the hitchhiker's guide to the galaxy was in full circulation. Not that it is of any relevance to the matter, but for historical accuracy it isn't so much Gaudí's magic square as it is Subirach's, and was acquired bu rotating Dürer's Melancholia square and subtracting 1 from 15, 11, 10 and 16."

More information about the design and its transformation from the Durer Square can be found at this web page

I'm not sure if there is any symbolism intended in the location of the square, but it is located on the wall behind the sculpture depicting Judas betrayal of Christ with a kiss. You can see a photo of the setting here.

As a footnote about the number 42 and the "hitch-hiker's guide"; if you enter, "life , the universe and everything" in Wolfram-alpha, this is the response:
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