On Versions and Presentation

The paragraph below the box con­tains the full, u­su­al­ly long­er, ver­sion of the same note. It is pre­sent­ed with­out at­tempt­ing to a­chieve a com­plete right-a­line­ment* for any screen, win­dow or frame wide e­nough to ac­com­mo­date any two successive words or or­tho­graph­i­cal syllables in the text on one line. (Such a text jus­ti­fi­ca­tion can on­ly be ac­com­plished correctly by means of soft or 'shy' hy­phens which may make pos­si­ble search terms im­pos­si­ble to find.)

• where there are spelling variants priority will be giv­en to the pho­ne­mat­ic and mor­phe­mat­ic prin­ci­ples over the et­y­mo­log­i­cal principle

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When Sawing Is Not Progressive

Do you know what the verbal ing form (also called "the continuous" or "progressive") expresses in English grammar? That the action is in progress and of limited duration. Therefore, it is not We saw the magnificent age-old tree but We are sawing the magnificent age-old tree!

Is 80 Really Interesting?

So long as 80 deserves no more attention than 79, 81 or any other number, integer or natural number, 80 is simply a number which equals 79+1 and 81-1 on the zero-level of iteration, which is the level of addition and subtraction (where nothing is re­peat­ed). Also on the first level of iteration, the one of multiplication and division, 80 is just 1*80, 2*40, 4*20, 5*16 or 8*10 and vice versa, while 80 (unlike 4, 8 and 16) does not play a role on any higher level of iteration. When 80 arouses an at­ten­tion for which there is no in­de­pend­ent substantive reason, it is because 80 is in a sense thought or felt to be 'numerically significant'. What counts in the decimal-denary double sys­tem (with radixes ⅒ and 10) is that 80 = 8*10, a multiple of 10, albeit an or­di­nar­y one. (That's also why ten-fingered fetishists will always write it that way, with a 0 at the end.) Nev­er­the­less, the fact that 80 = 5*16 as well gives the number 80 the same type of numerical significance in the 'micro-macrobinary' system, a numeral supersystem based on the ½-2 couple of radixes and on the squares (of squares (of squares ...)) of them, among which ¹⁄₁₆ and 16. (Denary myopes call the for­mer number "a custom fraction"!) From the point of view of numerical significance 80 attracts more attention than 71 to 79 and than 81 to 89 in the radix-10 system, but not more than 70 and 90. In the radix-16 sys­tem, how­ev­er, 80 attracts more at­ten­tion than 65 to 79 and than 81 to 95, but not more than 64 and 96. (As a matter of fact, 64 may be 4*16, but more interesting is that it equals 4^3 and 2^6. Yet, this is still not as interesting as the squares of squares 16, which equals 4^2, and 256, which equals 16^2.) Wheth­er the number 80 also deserves the extra at­ten­tion it arouses de­pends ultimately on the qual­i­ty of the rea­son­ing by which the radix(es) of the numeral (super)system were or —more im­por­tant­ly— will be selected.