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    • AMMDI is an open-notebook hypertext writing experiment, authored by Mike Travers aka mtraven. It's a work in progress and some parts are more polished than others. Comments welcome! More.
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The Algebra of Being

11 Sep 2026 - 07 Nov 2026
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    • I'm sorry, pretentious much?
    • But I mean something like the way self, other, god are all images of each other, all variants in a way. Reflections, that's an algebraic concept.
    • "Algebraic" to me means something like, "with a complex but rigorus conceptual structure"
    • Can't define this but some examples:
      • Meaningness structure of stances, stages, and qualities. Very complex, thorough, worked-out.
      • The Four Agreements simpleminded slogans that nevertheless combine at some existential-semantic layer to fix you (or such is the claim)
      • Meditations on the Tarot
      • William Blake his "genius at crystallization". Fearful symmetry
        • Get exact quote
          • Ask Claude
            • The search results don't surface a "genius at crystallization" quote about Blake. Let me search more specifically — this is likely something written about Blake, not by him.
            • The phrase isn't surfacing. Let me try a more targeted search — it may be from a specific critic like Yeats, Swinburne, or Northrop Frye writing about Blake.
            • Found it. The phrase is from Northrop Frye, and the full context is now clear from two sources.
            • The quote is from Northrop Frye's Fearful Symmetry: A Study of William Blake.
            • Northrop Frye called Blake the "finest gnomic artist in English literature" and hailed his "genius for crystallization."
            • The fuller critical context, from Patrick J. Keane's essay, gives the exact phrasing in context:
            • Yeats emulates "not only his mentor's attack on Locke (and Newton), but also his genius for epigram and crystallization, Blake being 'perhaps the finest gnomic artist in English literature.'"
            • And from a review of Fearful Symmetry itself:
            • Frye illuminates Blake's undertaking as a triumph of vision and "an instance of the poet's inexhaustible 'genius for crystallization.'"
            • So the exact phrase is "genius for crystallization" (not "at crystallization"), attributed to Northrop Frye in Fearful Symmetry (1947), paired with the description of Blake as "perhaps the finest gnomic artist in English literature." Those two phrases go together as a single critical judgment.
             (hah I should relabel these as rabbitholes)
      • Marvin Minsky
        • hm aside from Hofstadter I think he'd disdain this company
      • Many other spiritual or psychological systems.

    • Related pages

      • self-reference except that is almost orthogonal. It's not so much self-reference as the way central concepts are related to each other through reflection and negation.

    • Alright wise one

      • Does this concept make sense, does it already have a name, what is it I am trying to get to?
        • Ask Claude
          • Yes, the concept makes sense. It's real and coherent, and it has several partial names — none of them quite capture what you're after. Let me try to map this out.

          • What you're pointing at

          • The core intuition seems to be: **certain conceptual systems have a rigorous internal architecture — operators, transformations, symmetries, relations — such that the structure itself does the philosophical work, not just the content.** And more specifically, you're noticing that many of the most penetrating systems (spiritual, psychological, literary) seem to encode the same underlying structure in different notation.
          • That's not exactly "self-reference" — self-reference is a property within a system. What you're pointing at is more like: the deep structure of being-as-experienced has an algebraic shape, and that shape recurs across wildly different discourses.

          • Names that partially fit

          • 1. Formal Ontology — closest in the philosophical tradition.
          • The term was first used by Husserl to signify the study of those formal structures and relations — above all relations of part and whole — which are exemplified in the subject-matters of the different material sciences.
          • But this is usually done in an analytic/academic register, not the existential-spiritual register you're in. It doesn't capture the psychoactive quality of your examples.
            • Damn Claude you sure get it.
          • 2. Strange Loop — Hofstadter's term is the most famous near-hit.
          • Hofstadter coined "strange loop" to refer to the paradoxical, self-referential apparently upward movement through a hierarchy of levels of abstraction or structure which astonishingly returns to its source — "a paradoxical level-crossing feedback loop."
          • This captures GEB and I Am a Strange Loop perfectly, and touches on the self/other/God mirroring you mention. But it's one specific mechanism, not the general phenomenon.
          • 3. Laws of Form / Primary Algebra — Spencer-Brown is doing something very close to what you mean.
          • Those who agree point to Laws of Form as embodying an enigmatic "mathematics of consciousness", its algebraic symbolism capturing the implicit root of cognition: the ability to "distinguish."
          • And critically: Spencer-Brown is explicit about the identification of action and naming in the conception of the mark, and by the end of the book reminds the reader that "the mark and the observer are, in the form, identical."
          • That's your self/other/god collapse right there, in algebraic form. Notably, Spencer Brown also studied with psychologist R.D. Laing— your Knots connection isn't accidental.
          • 4. Ontological Grammar — a newer but apt phrase.
          • Grammar doesn't merely report an independently segmented world — it encourages certain forms of segmentation. Nouns suggest things. Subjects suggest authors. Predicates suggest owned properties. Temporal grammar encourages persistent bearers moving through a sequence of presents. These structures are useful, but their fluency repeatedly outruns their ontological warrant.
          • This gets at the structural/grammatical nature of your thing, but it's still more linguistic than existential.
          • 5. Structural Homology — from Lévi-Strauss / structuralism.
          • The idea of "formal structural homology" describes the reproducibility of structures on different levels such that a series of transformations can produce a group of models of the same general type.
          • This is what you're noticing when self, other, and God look like variants of each other — they occupy isomorphic positions in different systems. But "structural homology" sounds like a biology term and has no existential charge.
          • 6. Relational Ontology / Dialogical structure — Buber's whole project.
          • There is no I taken in itself, but only the I of the primary word *I–Thou and the I of the primary word I–It*.
          • And crucially for your self/other/God point:
          • in Buber's view, all of our relationships bring us ultimately into relationship with God, who is the Eternal Thou — every time someone says Thou, they are indirectly addressing God.
          • Buber's system has real algebraic structure: two operators (I-Thou, I-It), transformation rules between them, and a fixed point (God as the limit of Thou). But it's not usually called algebra.
          • 7. Perennial Philosophy — adjacent but wrong. The perennial philosophy claims that reality has a certain structure, and that this structure has been recognised — partially, variably, but recognisably — across cultures and centuries.
          • But perennialism is about shared content (God/Self/Ground are the same thing), whereas you're more interested in shared structure (these systems have the same operators and symmetries, whatever their content). That's a real distinction.

          • The best available term, and what might be missing

          • The closest existing concept to what you mean might be "structural isomorphism across experiential ontologies" — but that's a mouthful nobody uses.
          • What you're really reaching for seems to be something like: existential algebra — systems where a small number of primitive terms (self, other, world, void, God, form, ground) are related by a small number of operations (reflection, negation, re-entry, distinction, encounter), and the structure of those operations is what does the therapeutic, spiritual, or illuminating work. The Four Agreements works because its four operators happen to cover the generative space of neurotic misinterpretation. Laws of Form works because a single operator (distinction) generates the whole of logic and, Spencer-Brown claims, consciousness. Buber's system works because two operators and their transformations exhaust the space of possible relating.
          • What unifies your list is precisely that: **not what the systems say, but their operative structure — that they are, in some sense, complete, that their primitives generate their whole domain, and that the domain turns out to be experience itself.**
          • The most honest answer is: this concept doesn't have a single established name. The closest traditions are formal ontology (Husserl), structural anthropology (Lévi-Strauss), and strange loop theory (Hofstadter), with Spencer-Brown's Laws of Form being the most rigorous attempt to actually do the thing rather than describe it. Your instinct to call it "algebra of being" is not pretentious — it's actually quite precise.