Wed, 12 Aug 2015
A message to the aliens, part 2/23 (arithmetic)
Earlier articles: Introduction Common features Page 1 (numerals)
This is page 2 of the Cosmic Call message. An explanation follows.
Reminder: the previous page explained the ten digits:
 0 |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 |
This page, headed with the glyph for “mathematics” 
, explains the arithmetic operations on numbers.
The page is in five sections, three on top and two below.
The first four sections explain
addition 
,
subtraction 
,
multiplication 
, and
division 
. Each is explained with a series of five typical arithmetic equalities. For example, !!4\times 3= 12!!:
The subtraction sign actually appeared back on page 1
in the Mersenne prime !!2^{3021377}-1!! 
.
The negative sign 
is introduced in
connection with subtraction, since !!1-2={}^-1!!:
Note that the negative-number sign is not the same as the subtraction sign.
The decimal point 
is
introduced in connection with division. For example, !!3\div 2 =
1.5!!:
There is also an attempt to divide by zero:
It's not clear what the authors mean by this; the mysterious glyph
does
not appear anywhere else in the document. What did they think it
meant? Infinity? Indeterminate? Well, I found out later they
published a cheat sheet, which assigns the meaning “undetermined” to
this glyph. Not a great choice, in my opinion, because !!1÷0!! is not
numerically equal to anything.
For some reason, perhaps because of space limitations, the authors have stuck the equation !!0-1 = {}^-1!! at the bottom of the division section.
The fifth section, at lower right, displays some nonterminating decimal fractions and introduces
the ellipsis or ‘…’ symbol. For example, !!1\div 9 = 0.1111\ldots!!:
I would have put !!2÷27 = 0.0740…!! here instead of !!2\div 3!!, which I think is too similar to the other examples.
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