Special Numbers: 0 and 1

Genesis 1:3-1:4

Among the integers, I believe 0 and 1 are the most interesting. Adding 0 to any number does not change that number. More precisely, a + 0 = a and 0 + a = a for all integers a. In group theory terminology, 0 is the identity element under addition or the additive identity. You may ask, is there also such a thing as multiplicative identity? Yes, there is! In fact, by the title of this post you probably know what it is. One is the multiplicative identity. That is, a x 1 = a and 1 x a = a for all integers a. Does 0 play an important role in multiplication? Yep! Multiplying by 0 always yields 0. More precisely, a x 0 = 0 and 0 x a = 0 for all integers a. We may also say that 0 the absorbing element under multiplication.

A field has at least 2 elements

A field is a set together with two operations satisfying certain conditions. An example of a field is the set of real numbers under addition and multiplication. By definition, the additive identity and multiplicative identity of a field must be different. That is, 0 is not equal to 1. The binary field consisting of two elements is the smallest field. The underlying set is

$\mathbb{Z}_2 = \{0, 1\}$

with addition and multiplication described as follows:

Lightness and darkness

Now what do all these have to do with the quote I posted at the beginning? Well, it is a well-known fact in physics that a black object absorbs all wavelengths of light while a white object reflects all wavelengths of light. So we may make an analogy that 0 is "dark" while 1 is "light". And "God divided (separated) the light from the darkness" would be an analogue to the fact that 1 is different from 0 in a field. Yeah, I know. It's probably a stretch. But I like analogies like these. It connects theology, mathematics, and physics in one common theme: lightness and darkness. It's like hitting three birds in one stone.

'Til next time!

- JGC

Comments

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