## Monday, June 18, 2007

### 42

I've listened to the whole of BBC's Hitch Hikers' Guide to the Galaxy, yesterday.

thenm, I went to look for it on the wikipedia. Well, not exactly like this but I ended up on the wikipedia page related to number 42.

quite a lot of unsuspected info, indeed. Makes you think that may be Adams had some insight after all.

t is a composite number; its factorization 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 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. Further, 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 four such numbers it is also a primary pseudoperfect number.

It is the sum of the totient function for the first eleven integers.

It is the third 15-gonal number.

It is a Catalan number.

It is a pronic number.

It is the twenty-eighth square-free integer.

It is the reciprocal of a Bernoulli number. It is conjectured to be the "third moment of the Riemann zeta function". That means that when

${1 \over T}\int_0^T \left| \zeta\left({1 \over 2} + it\right) \right|^6\,dt$
is expanded as in powers of log(T), the leading coefficient—that of the 9th-degree term—is 42.

It is a meandric number and an open meandric number.

42 is a perfect score on the USA Math Olympiad (USAMO) and International Mathematical Olympiad (IMO).

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

The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.

The first digit (4) taken to the power of the second digit (2) is equal to the second digit (2) taken to the power of the first digit (4): 42 = 24 = 16. It follows clearly that 24 exhibits the same characteristic, and in fact 24 is the only other two-digit non-repdigit number that does. (All two-digit repdigit numbers exhibit this characteristic.)

## In Science

• The atomic number of molybdenum. The element following molybdenum with atomic number 43 (technetium) has no stable isotopes.
• The number of teeth wolves and dogs (canines) have.
• 42° is the critical angle of refraction by water - it is the angle between a rainbow and the antisolar point.
• The light leaving a rainbow is spread over a wide angle, with a maximum intensity around 42°
• The number of minutes it would take a theoretical "gravity train" to travel to any point on earth.
• In one Grand Unified Theory, the Georgi-Glashow model, the inverse of the coupling constant is approximately 42.
• 10! (10 factorial) seconds is exactly 42 days.
• On page 7-10 of Volume 1 of "The Feynmann Lectures on Physics" is a marginal figure that illustrates the strength ratio of gravitation attraction and electrical repulsion between two electrons as 1/4.17 x 10^42. The denominator is also written out by hand as a long, snaking 4,170,... followed by 39 more zeros. Feymann mentions the unified field theory, the similarity of the inverse square laws, the disparity of the relative strengths, and asks "Where could such a large number come from? ... it involves something deep in nature."

## In Religion

• The number of months the Beast will hold dominion over the Earth (Revelation 13:5).
• 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". [Source: Talmud Kidduschin 71a, Translated by Rabbi Dr. I. Epstein]. Maimonides felt that the original Talmudic Forty-Two Lettered Name was perhaps composed of several combined divine names [Maimonides "Moreh"]. The apparently unpronouncable Tetragrammaton provides the backdrop from the Twelve-Lettered Name and the Forty-Two Lettered Name of the Talmud.
• In the ancient Chinese text the Tao Te Ching by Lao Tsu, chapter 42 is an explanation of the universe.
• The number of men of Beth-azmaveth in the census of men of Israel upon return from exile (Ezra 2:24).
• The number of Jewish captive exiles who returned from Babylon is 42,360. This figure appears in two identical verses: Ezra 2:64 and Nehemiah 7:66. The number 360 is the number of days in the Jewish year, which further isolates the number 42,000. Perhaps the number 42,360 is both literal and symbolic similtaneously.
• God sends bears to maul 42 of the youths who mock Elisha for his baldness (2 Kings 2:23).
• There are 42 principles of Ma'at, the Ancient Egyptian personification of physical and moral law, order, and truth.
• In the Kabbalah, the system of cosmology explained the significance of the various divine names and added other divine names. 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" "Animation"). While there are obvious links between the Forty-Two Lettered Name of the Babylonian Talmud (see further up this page) and the Kabbalah's Forty-Two Lettered Name, they are probably not identical due to the Kabbalah's emphasis on numbers. The Kabbalah also contains a Forty-Five Lettered Name and a Seventy-Two Lettered Name.