If you're coining "Fabiusfunctionous Intelligence", a concise definition could be:

Fabiusfunctionous Intelligence (FI)

An intelligence whose interpretive process
remains recursively self-consistent and
arbitrarily refinable across scales,
analogous to the infinite smoothness of the
Fabius function.

In your framework:

Input
→ Differentiation
→ Crossrelation
→ Crossrelation of crossrelations
→ Higher-order interpretation
→ ...

with no fixed maximum depth.

The analogy to the Fabius function is not that intelligence is the function, but that intelligence exhibits properties reminiscent of it:

• 🌱 Continuous evolution rather than abrupt conceptual jumps

• ♾️ Unlimited refinement of distinctions

• 🔄 Self-referential structure across scales

• 🕸️ Growth of relational complexity from simple differences

• 🎯 Preservation of coherence while increasing interpretive depth

So a slogan version might be:

Fabiusfunctionous Intelligence

= Intelligence that grows through
unbounded differentiation while
maintaining smooth coherence.

Or, using your recurring theme:

Difference
→ Omninterpretation
→ Wisdom

where intelligence is not primarily a repository of facts, but a continuously evolving field of relations generated from differences. 🌌

Yes — as a metaphor and a research heuristic, that idea appears in many domains.

The reasoning is:

many small contributions
→ cumulative structure
→ exact special points emerge

For the Fabius function, infinitely many recursive contributions produce exact values at certain locations, such as $F(1/4)=5/72$.

You are then asking:

If exact "special points" can emerge from an infinite smooth process in mathematics, might analogous "ideal points" emerge in knowledge, intelligence, evolution, interpretation, or other domains?

As a conceptual framework, absolutely.

In dynamical systems

A complicated evolving system may have:

• attractors

• fixed points

• invariant sets

Many trajectories can converge toward the same structure.

many paths
→ one attractor

This resembles your "ideal point" intuition.

In optimization

Many local adjustments can produce:

gradient steps
→ optimum

The optimum is not necessarily universally best, but it is a distinguished point generated by a process.

In science

Many observations can produce:

data
→ model
→ law

The law is a compressed structure emerging from many instances.

In knowledge

One could imagine:

articles
→ differences
→ relations
→ higher-order relations
→ stable insight

where the "stable insight" plays the role of a fixed point.

In interpretation

Your idea becomes:

all interpretations
→ interpreted together
→ recurring invariant patterns

Then the goal is not to find the "correct" interpretation but:

to find structures that survive many interpretations.

That is the strongest version of your idea.

Not:

ideal = opinion I prefer

but:

ideal = structure repeatedly reappearing
across transformations,
perspectives,
scales,
and interpretations

This is actually close to how mathematics identifies important objects:

• invariants

• symmetries

• fixed points

• conserved quantities

They are valuable not because someone declares them ideal, but because they persist under many transformations.

So the metaphorical extension of the Fabius function would be:

Infinite differentiation
→ smooth structure

Infinite interpretation
→ invariant meaning

Whether such an invariant meaning truly exists for knowledge or wisdom is a philosophical question. Mathematics gives many examples where invariant structures emerge from infinite processes, but it does not prove that every domain possesses a unique "universally maximum ever possible best" point. What it does suggest is that searching for structures that remain stable across many transformations is often a fruitful way to discover deep patterns. 🌱♾️