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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:
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 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. The next article, to appear 2015-08-14, will discuss page 3, shown at right. (Click to enlarge.) Try to figure it out before then.[Other articles in category /aliens/dd] permanent link |