Hi Bruno,
I was thinking about your primitive of arithmetic truth (numbers, 0, +, and
*, right?) and then your concept of 'the dreams of numbers', interviewing
Lobian Machines, etc and came up with this.
One single irreducible digit ॐ which represents a self-dividing continuum
of infinite perpendicular dialectics between eidetic dream states (in which
dream~numbers escape their numerical identities as immersive qualitative
experiences) and entopic non-dream states (in which number~dreams escape
their dream nature as literal algebra-geometries).
This continuum f(ॐ), runs from infinitely solipsistic/private first person
subjectivity (calling that Aleph *ℵ*)* *to infinitely discrete/public third
person mechanism (calling that Omega *Ω*), so that at *ℵ*,any given dream
is experienced as 99.99...9% dream and 0.00...1% number and at *Ω*, any
given machine or number is presented as 99.99...9% number and 0.00...1%
dream.
The halfway point between the *ℵ *and* **Ω* axis is the perpendicular axis
f(-ॐ) which is the high and low correspondence between the literal dream
and figurative number (or figurative dream and literal number depending on
whether you are using the dream-facing epistemology or the number-facing
epistemology). This axis runs from tight equivalence ("=") to broadly
elliptical potential set membership ("...")
So it looks something like this:
f(ॐ) ⊇ *{ℵ** "...**" ⊥** "=**" Ω**}*
To go further, it could be said that at *Ω*(Omega), ॐ (Om) expresses as *
10|O* (one, zero, line segment, circle referring to the quantitative
algebraic and geometric perpendicular primitives) while at *ℵ* (Aleph),
ॐ(Om) expresses as
יהוה (tetragrammaton or yod, hay, vov, hay, or in perhaps more familiar
metaphor, ♣**♠♥**♦(clubs, spades, hearts, diamonds)
where:
♣ clubs (wands) =Fire, spiritual, tactile
♠ spades (swords) = Air, mental, auditory
♥ hearts (cups) =Water, emotional, visual
♦ diamonds (pentacles/coins) = Earth, physical, olfactory-gustatory
Note that tactile and auditory modalities tune us into ourselves and each
others sensemaking (selves and minds), while the visual and
olfactory/gustatory sense modalities are about objectifying realism of the
world (egos or objectified selves/self-images and bodies). It should be
obvious that ♣ clubs (wands) and ♠ spades (swords) are stereotypically
masculine and abstracting forces, while ♥ hearts (cups) and ♦ diamonds
(pentacles/coins) are stereotypically feminine objectified fields.
Sorry for the mumbo jumbo, but it is the only way to be non-reductive when
approaching the qualitative side. We can't pretend to talk about the
eidetic, dream like perpendicular of number logic while using the purely
empirical terms of arithmetic reduction. We need symbols that can only
refer to named qualities rather than enumerated quantities.
Let the ignoring and insulting begin!
Craig
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