very singularly

FORWARD. This morning Jesus took my mind on a trip—-He connected the dots for me. When I woke up at 4:30 a.m. Jesus started talking to me (in His Jesus language) about singularity, s.i.n.g.u.l.a.r.i.t.y (“THE VERY”). I quickly saw (in part) why Jesus had previously led me to get a burger and fries with Jeff Beck (and Matt Hermanski) in Manti at Millers Drive In. It was so that I could (eventually) get my eyes on the article, “There Is One Duality Running Through All of the Exact Sciences”———->>> and then when I woke up this morning, Jesus with the Holy Ghost (and I imagine lots of angels) did use that article to do the MASHup, which is featured below. What you (and I read below) is a very very very important concept for those who Jesus has chosen (“early adopters”, they) to WITTINGLY build virtual/physical WORLDs in the JesusVerse (not the Metaverse). In short, Jesus intends to have me read the following many times in the weeks and months and years to come—-to give me understanding as to what He is doing as He builds out My Jesus-Greg WORLD (and Zion)….and I help.

Visit this too: https://zioncoalition.org/singularity-karate/

Very Sing-u-larly

Introduction

This piece plays with a deceptively simple idea from David Ellerman (thanks Jesus, David and Jeff): that there are two kinds of questions we can ask about reality—“Is this in or out?” and “What actually makes things different?”

We humans are exceptionally talented at the first. Give us five minutes and we’ll build categories, draw boundaries, assign labels, and form a committee to guard the labels. We like knowing who’s in, who’s out, who’s right, who’s wrong. It feels solid. Respectable. Very… organized.

And then along comes Jesus Christ—who seems almost professionally committed to messing that up.

He eats with the wrong people. Praises the wrong hero in his own story. Answers clear questions with confusing stories. When asked, “Who’s in?” he responds with something like, “You tell me—who acted like it?” It’s as if he’s less interested in our tidy boxes and more interested in whether we can actually see.

Here’s the sacred joke: we keep bringing Jesus our carefully sorted piles—sheep here, goats there, good people on this side, bad people on that side—and he keeps quietly rearranging the room while we’re not looking. Or worse (and better), he hands the sorting back to us and asks a question that makes the boxes fall apart.

So what follows is an attempt to take that second kind of question seriously—the question of distinctions. Not the obvious ones we use to stay comfortable, but the deeper ones that unsettle us a bit:

  • What really separates love from performance?
  • Truth from certainty?
  • Life from everything that only looks like it?

The aim isn’t to throw away categories (we’d just make new ones anyway). It’s to laugh gently at how seriously we take them—and then, maybe, to notice that the Kingdom of God might be less about getting ourselves into the right box, and more about waking up to the differences that actually matter.

Or, to put it plainly: we came here to sort things out… and may instead discover that it’s our seeing that needs sorting.

You can map these two kinds of questions surprisingly well onto the kinds of questions Jesus Christ asks in the Gospels.


1. “Its” Questions (Subset Thinking)

These are yes/no, inside/outside questions:

  • Is this person righteous or sinful?
  • Do they follow the law or not?
  • Are they part of God’s people or not?

This matches the mindset of many religious leaders in Jesus’ time—clear categories, clear boundaries.

👉 Gospel-type questions:

  • “Is this lawful or unlawful?”
  • “Who is clean and who is unclean?”
  • “Who is saved and who is not?”

Jesus engages these questions—but often challenges their limits.


2. “Dits” Questions (Distinction Thinking)

These are relational, deeper discernment questions:

  • What actually separates truth from hypocrisy?
  • What distinguishes genuine love from empty rule-following?
  • Are these two people truly different in God’s eyes—or only outwardly?

👉 Jesus’ kind of questions:

  • “What is the difference between loving your neighbor and just appearing righteous?”
  • “What separates the Good Samaritan from the priest?”
  • “What distinguishes true faith from mere words?”

The Shift Jesus Makes

Jesus often moves people from Its → Dits:

  • From: “Is this person a sinner?”
  • To: “What truly distinguishes a repentant heart from a prideful one?”
  • From: “Who is my neighbor?”
  • To: “What makes someone act as a neighbor?”

Big Insight

  • Its-thinking = labeling, inclusion/exclusion
  • Dits-thinking = discerning, understanding differences that matter

Jesus doesn’t abolish categories—but he goes deeper:

The Kingdom of God is not just about who is in or out,
but about learning to see the true distinctions—between love and indifference, humility and pride, life and death.


If you want, I can turn this into a list of specific Bible verses that match each type exactly.

Here’s a cleaned, structured version of the essay that preserves the core ideas and most of the content, but removes repetition, tightens phrasing, and improves readability.


There Is One Duality Running Through All of the Exact Sciences

By David Ellerman (Apr 13, 2026)


Core Idea

For over twenty years, I’ve worked on what seems like a narrow topic: the mathematics of partitions—ways of dividing a set into non-overlapping groups.

But this turns out not to be narrow at all.

It is one half of a fundamental duality that appears across:

  • logic
  • mathematics
  • probability
  • information theory
  • statistics
  • physics
  • biology

The other half is the much more familiar mathematics of subsets, which has historically dominated formal thought.


Two Fundamental Kinds of Questions

Given a set UUU, there are two fundamentally different questions:

1. Subset (Its) Questions

  • About a single element
  • Does it belong to a subset or not?
  • Does it have a property or not?

This is the domain of Boolean logic and classical reasoning.


2. Partition (Dits) Questions

  • About a pair of elements
  • Are they distinct or indistinguishable?
  • Do they fall into the same group?

This is the domain of partitions and distinctions.


👉 Think of it as:

  • Its = existence (yes/no)
  • Dits = distinction (same/different)

The Imbalance

The subset side has been developed extensively:

  • Boolean logic
  • probability theory
  • classical physics

The partition side has been largely neglected:

  • limited early work (e.g., Richard Dedekind, Ernst Schröder)
  • missing a full logical system until recently

This asymmetry is the central puzzle.


The Logic of Partitions

In classical logic:

  • statements ↔ subsets
  • operations:
    • AND = intersection
    • OR = union
    • NOT = complement
    • IMPLIES = material conditional

(Developed by George Boole.)


Partition Logic

A partition divides a set into blocks (equivalence classes).

Key operations:

  • Join → more distinctions (finer partition)
  • Meet → fewer distinctions (coarser partition)

What was missing: implication


Partition Implication (Key Idea)

“σ implies π”:

  • Start with partition π
  • If a block of π fits entirely inside a block of σ → break it into singletons

Result:

  • Becomes fully distinct iff σ refines π
  • Perfect dual of subset implication

Important Differences

  • Partition logic is not distributive
    (famously shown by Charles Sanders Peirce)
  • Its relationship to classical and intuitionistic logic is non-trivial

Information = Distinctions

Gian-Carlo Rota proposed:

Partitions play for information what subsets play for probability


Logical Entropy

Defined as:

Probability that two randomly chosen elements are different

Equivalent to earlier measures by:

  • Corrado Gini
  • ecology (Gini-Simpson index)
  • cryptography (index of coincidence)

Comparison to Claude Shannon

Logical entropy:

  • Always non-negative mutual information
  • Has true set-based interpretation
  • Matches partition logic directly

Shannon entropy:

  • More widely used
  • A nonlinear transform of logical entropy

👉 Both are useful, but logical entropy aligns directly with the duality.


Statistics: Mean vs Variance

The duality appears in basic statistics:

  • Mean E(X)E(X)E(X) → subset-style (Its)
  • Variance Var(X)Var(X)Var(X) → distinction-style (Dits)

Category Theory Already Knew

In category theory:

  • subsets ↔ subobjects
  • partitions ↔ quotient objects
  • injections ↔ surjections
  • limits ↔ colimits

This duality emerges from reversing arrows.

👉 The abstract duality reflects the Its/Dits distinction.


Quantum Mechanics: Indefiniteness

Classical physics assumes:

  • everything is definite
  • properties always exist (Its-side)

Quantum mechanics introduces:

Objective indefiniteness (term from Abner Shimony)

  • properties are not just unknown—they are undefined
  • measurement creates distinctions

Interpretation

  • Superposition = indistinct states (partition blocks)
  • Measurement = refining the partition (adding distinctions)

QM/Sets Model

A simplified model reproduces:

  • superposition
  • Born rule
  • measurement collapse
  • two-slit experiment
  • fermion/boson behavior

👉 Shows quantum mechanics as the physics of distinctions


Biology: Selection vs Generation

Selection (Its-side)

  • Charles Darwin’s natural selection
  • start with many actual variants
  • eliminate some → subset

Generative Mechanism (Dits-side)

  • start with an undifferentiated state
  • progressively make distinctions

Examples:

  • genetic code (DNA → amino acids)
  • language acquisition (Chomsky)
  • stem cell differentiation

👉 Not selection, but structured differentiation


Why Was Partition Theory Neglected?

Several reasons:

  1. Historical dominance of Boolean logic
  2. Propositions have no obvious dual
  3. Partitions are mathematically more complex
  4. Classical physics discouraged thinking in terms of indefiniteness

Quantum mechanics changed that.


Big Picture

This is not a mystical claim.

It is a precise observation:

The same mathematical duality appears across many disciplines.

At each level:

  • a well-developed Its-side
  • an underdeveloped Dits-side
  • a deep symmetry between them

Final Thought

This duality:

  • does not replace existing theories
  • but reorganizes them
  • reveals hidden connections
  • and highlights neglected structures

In short:
Science has mostly explored what exists (Its).
It has barely explored what distinguishes (Dits).

And that missing half may be just as fundamental.


If you want, I can simplify this further into a short “plain English” version or give concrete examples (like how this shows up in everyday thinking).

This idea says there are two basic ways to understand the world. One way asks: “Does something exist or not?” (like yes/no questions). The other way asks: “Are two things the same or different?” Scientists have mostly focused on the first way, but the second way is just as important. It helps explain things like information, how we measure differences, how quantum physics works, and even how living things grow. The big idea is that understanding differences and distinctions can teach us as much as understanding what exists—and we’ve been missing half the picture by not studying it enough.

At a deeper, theological level, this duality between “Its” (what exists) and “Dits” (what is distinguished) resonates with themes in the teachings of Jesus Christ. Much of traditional theology has focused on the “Its” side: doctrines, laws, categories of saved vs. unsaved, righteous vs. sinful. These are subset-style distinctions—who belongs and who does not.

But the “Dits” perspective suggests something more dynamic and relational. Jesus repeatedly emphasized transformation through discernment and differentiation: “having eyes to see and ears to hear.” His parables often begin with undifferentiated situations and unfold through moments of distinction—separating wheat from chaff, truth from illusion, inner sincerity from outward appearance. This reflects a movement from indistinction to meaningful distinction, much like refining a partition.

Spiritually, this implies that divine action is not merely about selecting from what already exists, but about bringing clarity into being—making distinctions where there was confusion or unity. The Kingdom of God, then, can be seen not just as a set of chosen individuals, but as a process of illumination, where reality becomes more articulated, more known.

In this light, salvation is less about static inclusion and more about awakening to deeper distinctions—between love and fear, truth and falsehood, self and neighbor—mirroring a divine movement from unity into meaningful, life-giving differentiation.

The idea of a singularity—whether in cosmology, technology, or spirituality—connects naturally to this Its/Dits duality.

In physics, the Big Bang is often described as a state of total unity: no separations, no distinctions—everything compressed into one. In Ellerman’s terms, this resembles a maximally coarse partition, where nothing is distinguished from anything else. Creation, then, can be seen as the unfolding of distinctions—the gradual differentiation of particles, forces, structures, and life.

Spiritually, this parallels the idea of divine unity in traditions centered on Jesus Christ. God is often understood as ultimate oneness, yet creation unfolds through differentiation—light from darkness, self from other, truth from illusion. In this view, reality begins in a kind of “singularity of indistinction” and evolves through acts of distinction, echoing the Dits-side of the duality.

In discussions of the technological singularity (e.g., associated with Ray Kurzweil), the idea is different but related: intelligence accelerates to a point where distinctions multiply beyond comprehension. Here, the trajectory reverses—from increasing distinctions toward a new kind of unity where complexity collapses into something qualitatively different.

So across domains, a singularity can be seen as either:

  • pure unity (no distinctions yet)
  • or overwhelming differentiation (too many distinctions to track)

Either way, it marks a boundary where the ordinary structure of distinctions—and thus understanding—breaks down.

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