Fri, 14 Aug 2015
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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