The Universe of Discourse

A message to the aliens, part 3/23 (exponentiation)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic)

This is page 3 of the Cosmic Call message. An explanation follows.

Reminder: page 1 explained the ten digits:

0

1

2

3

4

5

6

7

8

9

And the equal sign . Page 2 explained the four basic arithmetic operations and some associated notions:

addition

subtraction

multiplication

division

negation

ellipsis (…)

decimal point

indeterminate

This page, headed with the glyph for “mathematics” , explains notations for exponentiation and scientific notation. (This notation was first used on page 1 in the mersenne prime .)

Exponentiation could be represented by an operator, but instead the authors have chosen to represent it by a superscripted position on the page, as is done in conventional mathematical notation. This saves space.

The top section of the page has small examples of exponentiation, including for example !!5^3=125!!:

!!5^3=125!!

There is a section that follows with powers of 10: !!10^1=10, 10^2=100, 10^3=1000, !! and more interestingly !!10^{{}^-2} = 0.01!!:

!!10^{{}^-2} = 0.01!!

This is a lead-in to the next section, which expresses various quantities in scientific notation, which will recur frequently later on. For example, !!0.045!! can be written as !!45\times 10^{{}^-2}!!:

!!45\times10^{{}^-2} = 0.45!!

Finally, there is an offhand remark about the approximate value of the square root of 2:

!!2^{1\div 2} = 1.41421356…!!

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