Wednesday, 13 June 2012

(Douglas Adams) - 42

The short explanation:

42 (forty-two) is the natural number immediately following 41 and directly preceding 43.

The long version:

For Mathematicians.

The 3 × 3 × 3 magic cube with rows adding up to 42.
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3×3×3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 cubes whose sum of values is 42.

Forty-two is a pronic number and an abundant number; its prime factorization 2 · 3 · 7 makes it the second sphenic number and also the second of the form { 2 · 3 · r }.

As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed by twin primes; 30 is also a pronic number and also rests between two primes.

42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30.

42 is the 10th member of the 3-aliquot tree.

42 is the product of the first three terms of Sylvester's sequence; like the first five such numbers it is also a primary pseudo-perfect number.

It is a Catalan number.

Consequently; 42 is the number of non-crossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged.

It is a partition number - the number of different ways 10 can be represented as the sum of natural numbers.

It is the reciprocal of the sixth Bernoulli number.

It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function".

42 is a Størmer number.

42 is a perfect score on the USA Math Olympiad.

In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).

42 is the only known value that is the number of sets of four distinct positive integers a,b,c,d, each less than the value itself, such that ab-cd, ac-bd, and ad-bc are each multiples of the value. Whether there are other values remains an open question.

For Scientists.

42 is the atomic number of molybdenum.

The angle in degrees for which a rainbow appears or the critical angle is 42.

In 1966, mathematician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the Earth, connecting a set of antipodes, evacuate it (remove the air), and then just fall through.

The first half of the journey consists of free-fall acceleration, while the second half consists of an exactly equal deceleration.

The time for such a journey works out to be 42 minutes.

Remarkably, even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity (also known as Gravity train) always works out to be 42 minutes, as long as the tube remains friction-free, as while gravity's force would be lessened, so would the distance traveled at an equal rate.

For The Religious

In Japanese culture, the number 42 is considered unlucky because the numerals when pronounced separately — "shi ni" (four two) — sound like the phrase, "unto death".

There are 42 principles of Ma'at, the Ancient Egyptian personification of physical and moral law, order, and truth. In the judgement scene described in the Egyptian and the Book of the Coming/Going Forth by Day (the Book of the Dead (which evolved from the Coffin Texts and the Pyramid Texts)).

There are 42 gods and goddesses of Egypt, personifying the principles of Ma'at, who ask questions of the departed, while Thoth records the answers, and the deceased's heart is weighed against the feather of Truth (Ma'at). These 42 correspond to the 42 Nomes of Egypt.

If the departed successfully answers all 42, s/he becomes an Osiris.

42 is the number with which God creates the Universe in Kabbalistic tradition.

In Kabbalah, the most significant name is that of the En Sof (also known as "Ein Sof", "Infinite" or "Endless"), who is above the Sefirot (sometimes spelled "Sephirot").

The Forty-Two-Lettered Name contains four combined names which are spelled in Hebrew letters (spelled in letters = 42 letters), which is the name of Azilut (or "Atziluth" "Emanation").

While there are obvious links between the Forty-Two Lettered Name of the Babylonian Talmud and the Kabbalah's Forty-Two Lettered Name, they are probably not identical because of the Kabbalah's emphasis on numbers.

The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.

The number 42 appears in various contexts in Christianity. There are 42 generations (names) in the Gospel of Matthew's version of the Genealogy of Jesus.

It is prophesied that for 42 months the Beast will hold dominion over the Earth (Revelation 13:5); 42 men of Beth-azmaveth were counted in the census of men of Israel upon return from exile (Ezra 2:24).

God sent bears to maul 42 of the teenage boys who mocked Elisha for his baldness (2 Kings 2:23).

In Judaism, the number (in the Babylonian Talmud, compiled 375 AD to 499 AD) of the "Forty-Two Lettered Name" ascribed to God. Rab (or Rabhs), a 3rd century source in the Talmud stated "The Forty-Two Lettered Name is entrusted only to him who is pious, meek, middle-aged, free from bad temper, sober, and not insistent on his rights".

Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names [Maimonides "Moreh"]. The apparently unpronounceable Tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Two Lettered Name of the Talmud.

The Gutenberg Bible is also known as the "42-line Bible", as the book contained 42 lines per page.

The Forty-Two Articles (1552), largely the work of Thomas Cranmer, were intended to summarise Anglican doctrine, as it now existed under the reign of Edward VI.

For ‘Hitchhikers Guide To The Galaxy’ Fans

The number 42 is, in The Hitchhikers Guide To The Galaxy, ‘The answer to the Ultimate Question of Life, the Universe, and Everything’, calculated by an enormous supercomputer over a period of 7.5 million years.

Unfortunately no one knows what the question is.

Thus, to calculate the Ultimate Question, a special computer the size of a small planet and using organic components was created and named "Earth". 

The fourth book in the series, the novel So Long, and Thanks for All the Fish, contains 42 chapters. According to the novel Mostly Harmless, 42 is the street address of Stavromula Beta.

Douglas Adams
‘It’s all very simple, really. 42 was a joke. It had to be a number, an ordinary, smallish number, and I chose that one.

Binary representations, base thirteen, Tibetan monks, are all complete nonsense.

‘I sat at my desk, stared into the garden and thought '42 will do', and I typed it out. End of story’.

(The Editors)

1 comment:

  1. Actually, it wouldn't surprise me if 42 came from Kabbalah Magical Evocation practices...Levum who is the 42nd genius of the Sun-sphere. He is the ORIGINAL Creator of ALL Magical Knowledge and the Kabbalah.

    SO many actors, directors, writers, novelists, casting directors, etc. etc. seem to be initiated in the Kabbalah and it's magical evocation practices.

    Just a thought...