Friday, July 22, 2016

One


Typical Monday morning staff meeting at The Drifter.
Staff researchers at the North Texas Drifter are a contrary bunch and have ignored their assignments again and gone off on a reading binge. Unfortunately, you, my poor NTD readers, subsequently pay for the truancy by having to read whatever my interns have been reading. Sorry about that. I wanted to post an article about my emergency contact person, but the interns said it was too boring. I'll post it anyway eventually but I got bounced today for an article about numbers. One number in particular.

One, or "1", is a separate and special entity called 'Unity' or 'Identity element'. 1 is actually the identity element under multiplication for the real numbers, since a x 1 = 1 x a = a. Mathematicians refers to 1 as the multiplicative identity (or better said, the reflexive identity of multiplication).

1 is NOT prime! Primes or prime numbers can be poetically described as the 'atoms' of mathematics - the building blocks of the world of numbers. But, mathematically speaking: "a prime number is a positive integer with exactly TWO positive divisors: 1 and itself". Modern textbooks consider 1 neither prime nor composite, whereas older texts generally asserted the contrary. In 1859, Henri Lebesgue stated explicitly that 1 is prime in "Exercices d'analyse numérique". It is also prime in "Primary Elements of Algebra for Common Schools and Academies" (1866) by Joseph Ray, and in "Standard Arithmetic" (1892) by William J. Milne. A list of primes to 10,006,721 published in 1914 by Derrick N. Lehmer includes 1 ("List of prime numbers from 1 to 10,006,721", Carnegie Institution of Washington).

1 is the solution of the equation: x3 - x = 0 (for x different from -1, or 0) [Note: x3 - x can be factorized as follows: x(x + 1)(x - 1)]

1 is the only real solution of the equation x3 + 3x - 4 = 0

Benford's law states that in a huge assortment of number sequences - in listings, tables of statistics, random samples from a day's stock quotations, a tournament's tennis scores, the populations of towns, electricity bills in the Solomon Islands, and much more, the digit 1 tends to occur with probability ∼30%, much greater than the expected 11.1% (i.e., one digit out of 9). Dr. Nigrini gained recognition by applying a system he devised based on Benford's Law to some fraud cases in Brooklyn. The idea underlying his system is that if the numbers in a set of data like a tax return more or less match the frequencies and ratios predicted by Benford's Law, the data are probably honest. But if a graph of such numbers is markedly different from the one predicted by Benford's Law, he said, "I think I'd call someone in for a detailed audit".

Mathematicians define a 'sphere' as the surface of a sphere, not a solid ball, so a sphere has 2 sides: the outside and the inside. However, there are also 1-sided surfaces! For instance, a Mobius strip.

f(x) = ex at the point x = 0 is exactly 1.

1 = 0!
Why 0! = 1? Because 4! = 4x3x2x1 and 3! = 3x2x1. Therefore 4! = 4x3! In the same way 3! = 3x2! and 2! = 2x1! So it follows that 1! = 1x0! Therefore 0! must be equal to 1 or 1! would be 0... And so 2! would be zero and then 3! and so on.

Curious multiplications using 1's:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
etc...

The numbers in the series 1, 11, 111, 1111, 11111, etc... are all triangular numbers in base-9.

During any police lineup the suspects wear nos. 2 through 9 because it is considered too suggestive to make anyone display the no. 1!

1 symbolizes the essence of all phenomena, which is a single unity, before being divided. It represents also the contrast between essence and existence; the enduring and the ephemeral; the unity in diversity (one/many). According to Hopper, the first advance towards counting is with the use of words for one and for many, the differentiation from the self from the group. We still say 'numero uno' to speak of ourselves.

"Taiji" (also termed as "Dayi" or "Taiyi"), in the Mystical Numbers of Taoism, represents the ONE, the Ultimate, the Order. The martial art known as "Taijiquan" based its movement's philosophies upon the notion of Taiji.

In the English language, there is a word with just ONE vowel which occurs 6 times: indivisibility.

'Strengths' is the longest word in the English language with just ONE vowel.

Impoverished counting system: 1 + 1 = ?

When it comes to counting, a remote Amazonian tribe have been found to be lost for words. In fact, researchers discovered that Pirahã tribe of Brazil, with a population of 200, have no words beyond ONE, two and many.

The word for "one" can also mean "a few", while "two" can also be used to refer to "not many"... (But is there any case where not having words for something doesn't allow you to think about it?)

The roots of the word one (un-, sim-, prin-, cen-) are hidden in the following words: inch (from Lat. uncia), onion, ounce, primal, primate, primitive, primrose, prince, recent, simple, simulate, sincere (from Lat. sincerus meaning "clean, pure, sound", derived from the Indo-European roots ‘sem’ and ‘ker’, the underlying meaning of which is: 'of one growth', hence 'pure, clean'), single, unanimous, unicorn, uniform, unify, union, unique, unit, universe; alone, any, lonely, only, none. In French: ensemble, oignon, premier, printemps, sanglier, semblable, sincère. In Spanish: centolla, centollo ('spider-crab', from Celtic *kintuollos, the largest one < *kĭntu-, first, and *ollos, big). Gaulish person names: Cintullus, Cintugnatos, 'first born' (< *kĭntu-, first one; cognates: Lat. re-cens 'new', Gr. kainos 'young, new').

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