in case the special characters don't come out...

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 (Om) 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(Om)), 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*(Omega), 
any given machine or number is presented as 99.99…9% number and 
0.00…1% dream.

The halfway point between the *ℵ *(Aleph) and* Ω* (Omega) axis is the 
perpendicular axis f (-ॐ(Om)) 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 (“=” equality) to broadly elliptical potential set membership 
(“…” ellipsis)

So it looks something like this:

f(ॐ) ⊇ *{ℵ** “…**” ⊥** “=**” Ω**}*

function (Om) is superset or equal to the continuum ranging from Aleph to 
ellipsis perpendicular/orthogonal to the inverse range from equality to 
Omega).

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!

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