New Articles as of October, 2023

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:::::::::: by RKJoyce ::::::::::
I will begin posting new material as of October, 2023.
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[*231201]

‘0.|0 This post is here to provide a slightly technical description of this blog’s ‘riffs’ and ‘posts’ labeling method for finding posts and ‘riffs’ that remind readers of concepts and terms that relate to matters while they are being discussed. You can simply ignore these labels when they are not of help, and simply omit them in comments

‘1.|0 Various passages in the posts will be marked by ‘riffs’. These riffs are short labels that refer to passages that may provide requisite definitions and expositions. This labeling scheme is optimized to expedite the find function of word processors, and also reference to passages in printed documents.

‘2.|0 In each riff ”X.|Y’, ”X’ will be in base_10 notation and ‘.|Y’ will be in base_8 (i.e. octal) notation. This is because base-8 numbers are much easier to divide by 2. Note that 1/4 is expressed as ‘0.25’ in base 10, but 1/4 is expressed as ‘0.2’ in base 8, since base_10 1/4 = base_10 2.5/10 = ‘0.25’, but base_10 1/4 = base_8 2/8 = base_8 ‘0.2’.

Note that the digits ‘8’ and ‘9’ never appear in octal numbers. This riff marking scheme will serve us well. An example of a reference to a riff is (‘vide’ or ‘see’) ‘376.|4 [^200715] (see below).

‘3.|0 Nominally ‘dated’ designators such as ‘[^YYMMDD]’ will reference designatums (‘targets’) such as ‘[*YYMMDD]’, which will be placed in posts in order to simplify reader access. Blogging system-assigned (‘platform’ or infrasystem assigned) publication dates may differ from these author-assigned reference dates.

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Extra clues for those who would rather not have to recall 6th grade ‘number theory’

The so-called ‘numbers’ written on paper are actually just symbols for designating actual ‘designatums’ that are concepts in the abstract mathematics world, not the physical one. The symbol ‘479.25’ is a physical designator of an actual abstract mathematics world (real) number. So we can use differing ‘symbol systems’ to designate the various numbers of the mathematics world.

Base ten positive real numbers can be represented as:
(…C⛌10³ + B⛌10² + A⛌10 + Ω⛌1 + a⛌(1/10) + b⛌(1/10)² + c⛌(1/10)³…)

Base eight positive real numbers can be represented as:
(…C⛌8³ + B⛌8² + A⛌8 + Ω⛌1 + a⛌(1/8) + b⛌(1/8)² + c⛌(1/8)³…)

So (base 10) ‘479.25’ can be represented in base ten as:
4⛌10² + 7⛌10 + 9⛌1 + 2⛌(1/10) + 5⛌(1/10)² + 0⛌(1/10)³ = base-10_479.25

And (base 10) ‘479.25’ can be represented in base eight as:
7⛌8² + 3⛌8 + 7⛌1 + 2⛌(1/8) + 0⛌(1/8)² + 0⛌(1/8)³ = base-8_737.2

That was great fun, wasn’t it!