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This convinced me hex ≫ dec.

Started by Geremia, September 05, 2016, 08:57:40 PM

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Decimal (base-10)
digits: 0-9
Hexadecimal (base-16)
digits: 0-9, A-F
Decimal (base-10)
 digits: 0-9
Hexadecimal (base-16)
digits: 0-9, A-F
1/2 = 0.51/2 = 0.811/16 = 0.6875B/10 = 0.B
1/4 = 0.251/4 = 0.413/16 = 0.8125D/10 = 0.D
1/8 = 0.1251/8 = 0.215/16 = 0.9375F/10 = 0.F
3/4 = 0.753/4 = 0.C1/32 = 0.031251/20 = 0.08
3/8 = 0.3753/8 = 0.67/24 = 0.29166...7/18 = 0.4AAA...
5/8 = 0.6255/8 = 0.A5/12 = 0.4166...5/C = 0.6AAA...
7/8 = 0.8757/8 = 0.E1/3 = 0.3333...1/3 = 0.5555...
1/16 = 0.06251/10 = 0.12/3 = 0.6666...2/3 = 0.AAAA...
3/16 = 0.18753/10 = 0.31/6 = 0.1666...1/6 = 0.2AAA...
5/16 = 0.31255/10 = 0.51/64 = 0.0156251/40 = 0.04
7/16 = 0.43755/10 = 0.725/64 = 0.38062519/40 = 0.64
9/16 = 0.56259/10 = 0.91/128 = 0.00781251/80 = 0.02
Look at how much simpler hex is for representing fractions! This is because 16, although it only has one more divisor than 10 does, has the property that its divisors are all powers of 2. Dividing something in two is much easier and more natural than dividing something in tenths or fifths.
This comes from Table 3 (p. 21) of Nystrom's 1862 Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to Be Called the Tonal System, With Sixteen to the Base, modified to use conventional hex digits (0-9,A-F). So as to distinguish numerals from letters, Nystrom invents his own symbols for hex's 9 & B-F and uses the symbol "9" for hex's A.
Down with the French Revolution's metric system!


My friend—who wrote some very fascinating, unpublished papers, e.g.:
—commented on the number-base that the ancient Hebrews used:
QuoteAbout the characteristics of the numerical systems correlated with the Hebraic alphabet, much would need to be explained, which many books on the history of numbers fail to adequately cover. When Moses arose from Egypt, he and the other savants of his time were keenly versed in both hieroglyphic writing and geometry. They used an alphabet comprising 25 cuneiform signs, the various combinations of which yielded syllables resembling ancient pictograms (of Mesopotamian and Phoenician origin). The art of naming numbers after the positional fashion of the ancient Sumerians was actually known to the Mosaic Hebrews. However their long stay in Egypt had accustomed them to hieroglyphic and hieratic non-positional systems.

The scribes trained during the early Mosaic era of Hebraic (oral and written) efflorescence endeavored to represent numbers using the same system of signs as that used to form words. They thereby conceived an alphabetical system of numeration. With the 27 letters of the complete Hebrew alphabet (22 + 5), they were able to design a decimal system wherein all ones, tens, and hundreds can be represented with a distinct sign. One can accordingly count and compute up to 999. Providing an additional sign (two little upper dots) to signal the passage into the thousands, one can count one's way up to 999,999. But the counting obsession ultimately is a modern constraint ancient religious civilizations did not impose upon themselves. They counted and practically used numbers to be certain. But they also thought about numbers and used them for sacred/religious purposes which, for the most part, escape us.

The inspired biblical text is not limited to a single numerical way of using the order and the number of letters comprising the Hebrew alphabet. It yields much meaning, besides merely describing and counting people or items, for example by including a "shifted" list of alphabetic numerals whose new values depend on their shifted order (while maintaining the significant total number of alphabetic numbers of 27 signs). The shifted order is "sacred" to the degree that it exactly relies on the idea of forbidding something (like the profane use of water once it has been blessed in order to be used for the holy purpose, for instance of signing oneself), namely the use of the first three numerical values (1, 2, 3) owing to the Thrice Holiness of YHWH (cf. Isaiah 6), by virtue of which 1 is now equal to 4. Arithmetically the numerical list wherein a number n is shifted by 1 = 4 can be expressed as:

4 + 5 + 6 +...+ (n + 3) = 1 + 2 + 3 +...+ n + 3n
= n(n + 1/2 + 3).
Furthermore, the Hebrew Bible incorporates other alphabetical and numerical influences from ancient Phoenicia, Mesopotamia (Sumer and Assyria through the lasting cultural influence of the Akkadian Empire), and Egypt (via Moses, based-10 hieroglyphic representation). Hence it is not surprising to also find heximal/hexagesimal references in sacred Scripture.