Sunday, 10 October 2010

The Real Truth about 42

Today is Sunday, 10/10/10, an appropriate day to reflect on the number 42. I’d better explain for the sake of the sanity of non-mathematicians that binary 101010 is in fact the number 42 in disguise.

An obvious feature of 42 is its prime factorization: 2x3x7. Obvious can be boring so I'll add the more obscure fact that the sum 2x3 + 2x7 + 3x7 = 41, just one less than 42. I don’t know if anyone has named the class of numbers whose pair-wise sum of its prime factors plus 1 equals the number itself. That sum emerged en route on a visit to Hove so if anyone really needs a name how about a ‘Hove number’? Not an exceptional inspiration, but possibly a brand new observation to add to a large literature on the topic of 42.

More ‘fascinating’ facts about 42 can be found at Wikipedia - 42 (number) where I learned Charles Dodgson, writing as Lewis Carroll, was also fond of 42. Perhaps it’s in the Oxford tap water. Computer programmers may be amused by the fact that the wildcard character ‘*’ has character code 42 in ASCII and Unicode.

Truth is, the number 42 has been regarded as special for (probably) over 5000 years.

Traditionally, Ancient Egypt was divided into administrative districts, usually called ‘nomes’ nowadays (from the Greek word for ‘district’, Νομός; also Egyptian spꜣt/𓈈/etc.). Curiously when I placed ideograms for the 20 nomes of Lower Egypt and 22 nomes of Upper Egypt into the first draft for the (as then) proposed Unicode standard for Egyptian Hieroglyphs, it was only afterwards that 42 clicked ‘not that number AGAIN’. I expect the fame of 42 goes back to the dawn of writing and mathematics itself.

Thoth, a (male) Egyptian deity (Egyptian Ḏḥwty; 𓅝, 𓁟 etc.), was associated with wisdom, magic, writing, mathematics, astronomy and medicine. Maat, a (female) deity (Egyptian Mꜣꜥt; 𓁦, 𓁧 etc.) was associated with truth, equilibrium, justice and order. She represents a fundamental concept in Ancient Egyptian philosophy. In some later traditions which featured male-female pairing between deities, Thoth and Maat were linked together (although rarely in a romantic sense). Both deities are prominent in the judging of the deceased as featured in the ‘Book of the Dead’.

The Papyrus of Ani gives a list of 42 ‘negative confessions’ for the deceased – “I have not committed sin”, “I have not murdered” etc. The ‘Ten Commandments’ of the Old Testament can be thought of as a condensed version. Sometimes referred to as ‘the doctrine of Maat’. 42 associated deities, supervised by Thoth, were assigned to the judgment of the deceased during his or her passage through the underworld.

I can’t resist mentioning that the modern name “Book of the Dead” was invented by Karl Richard Lepsius (the Egyptian rw nw prt m hrw has been more literally translated as the ‘Spells of Coming Forth by Day’ or similar). It can be no more than coincidence that the publication in question, “Das Todtenbuch der Ägypter nach dem hieroglyphischen Papyrus in Turin mit einem Vorworte zum ersten Male Herausgegeben” was published in 1842. Lepsius was a major and influential figure during the emergence of the modern discipline of Egyptology as well as being responsible for the creation of the first hieroglyphic typeface as implemented by typographer Ferdinand Theinhardt, the “Thienhardt font”.

The ’42 Books of Thoth’ aka ’42 Books of Instructions’ were composed from around 3rd century BC supposedly based on earlier traditions. Only fragments remain from this Hermetic text which apparently contained books on philosophy, mathematics, magic, medicine, astronomy etc. A legendary source, highly influential in later traditions of mysticism, alchemy, occultism and magic. The 42 Books have been believed by some to contain the hidden key to the mysteries of immortality and the secrets of the Universe. A fruitful topic I guess for Dan Brown and other writers of fiction.

Trivia. Visiting the South Coast last December, I was amused to discover the return rail-fare from Oxford was £42. Got me thinking how often 42 has cropped up in my life. Coincidence can be good fun. I decided to keep an eye open for incidents involving near neighbours of 42: 40, 41, 43, and 44. A prospect so intriguing and exciting I’m surprised I woke up on the approach to a snow and ice encrusted Hove before the train rattled on its way to Worthing. I can now report the scientifically meaningless result after 10 months ‘research’. Those worthy siblings 40, 41, 43, 44 just don’t cut the mustard compared with their famous colleague. Perhaps it’s just me. Although when my son started at secondary school this September, there was a certain inevitability about his reply when asked in what number classroom his form was based. For a moment I thought he was kidding.

I can't really leave the topic without mentioning the obvious.

The writer most credited for the prominence of 42 in modern times is the late Douglas Adams. In his radio series “Hitchhikers Guide to the Galaxy” (BBC Radio 4, 1978), the “Answer to the Ultimate Question of Life, the Universe, and Everything” is calculated to be 42. The meme exploded. Adams later claimed to have picked 42 pretty much at random.

We will never know whether Adams knew of the antiquity of 42 as a profound and famous number, indeed as the answer to his very own ultimate question. Its easy to speculate that he must have held some knowledge, at least at some subconscious forgotten level. A remarkable coincidence otherwise, unless 42 is in fact the answer.

Yet not impossible. After all there is something rather cute and appealing about 42. She still looks good for her age. Don’t you think so too?

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