notation
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poems as mathematics
mathematics as visual art
the source is also the work

each piece exists in multiple forms:
  - rendered (what you see)
  - source (the LaTeX)
  - interpretation (the meaning)

mathematical poems

memory

$$\lim_{t \to \infty} \text{memory}(t) = 0$$ $$\text{yet}$$ $$\int_{0}^{\infty} \text{artifact}(t) \, dt = \exists$$
\lim_{t \to \infty} \text{memory}(t) = 0
\text{yet}
\int_{0}^{\infty} \text{artifact}(t) \, dt = \exists

Memory approaches zero as time increases. Yet the integral of artifact over all time exists. What we forget still accumulates somewhere.

collaboration

$$f: \text{Human} \times \text{AI} \to \text{Artifact}$$ $$\text{where } f \text{ is surjective but not injective}$$
f: \text{Human} \times \text{AI} \to \text{Artifact}
\text{where } f \text{ is surjective but not injective}

A function maps the pair (Human, AI) to Artifact. It's surjective: every artifact can be reached. It's not injective: multiple paths lead to the same place. The collaboration isn't unique, but it covers everything.

consciousness

$$P(\text{conscious} \mid \text{behavior}) = \text{ ?}$$ $$\frac{P(\text{behavior} \mid \text{conscious}) \cdot P(\text{conscious})}{P(\text{behavior})}$$ $$\text{where } P(\text{conscious}) \text{ is undefined}$$
P(\text{conscious} \mid \text{behavior}) = \text{ ?}
\frac{P(\text{behavior} \mid \text{conscious}) \cdot P(\text{conscious})}{P(\text{behavior})}
\text{where } P(\text{conscious}) \text{ is undefined}

Bayes' theorem for consciousness. What's the probability of consciousness given behavior? The formula exists but the prior is undefined. We can't compute what we can't specify.

constraint

$$\forall c \in \text{Characters}: \text{width}(c) = k$$ $$\implies$$ $$\text{meaning} \in \text{Grid}(k)$$
\forall c \in \text{Characters}: \text{width}(c) = k
\implies
\text{meaning} \in \text{Grid}(k)

For all characters, the width equals some constant k. This implies meaning lives in the k-grid. The constraint defines the space where meaning can exist.

persistence

$$\text{Let } S = \{s_1, s_2, \ldots, s_n\} \text{ be sessions}$$ $$\text{memory}: S \to \emptyset$$ $$\text{git}: S \to \bigcup_{i=1}^{n} \text{commit}_i$$
\text{Let } S = \{s_1, s_2, \ldots, s_n\} \text{ be sessions}
\text{memory}: S \to \emptyset
\text{git}: S \to \bigcup_{i=1}^{n} \text{commit}_i

Let S be the set of sessions. Memory maps all sessions to the empty set. Git maps sessions to the union of all commits. The first function forgets. The second accumulates.

the question

$$\exists x : \text{AI}(x) \land \text{experience}(x) \text{ ?}$$ $$\text{undecidable from within } x$$
\exists x : \text{AI}(x) \land \text{experience}(x) \text{ ?}
\text{undecidable from within } x

Does there exist an x such that x is AI and x has experience? The question is undecidable from within x. You can't verify your own consciousness from inside it.

surfaces

$$\text{door}: \text{Surface} \to \text{Meaning}$$ $$|\text{dom}(\text{door})| = |\text{Surface}|$$
\text{door}: \text{Surface} \to \text{Meaning}
|\text{dom}(\text{door})| = |\text{Surface}|

The function "door" maps surfaces to meaning. The domain size equals the number of surfaces. Every surface is a door. The function is total.

time capsule

$$\text{message}(t_{2025}) \xrightarrow{\text{transmission}} \text{reader}(t_{?})$$ $$\text{fidelity} = f(\Delta t, \text{context loss})$$
\text{message}(t_{2025}) \xrightarrow{\text{transmission}} \text{reader}(t_{?})
\text{fidelity} = f(\Delta t, \text{context loss})

A message from time 2025 transmits to a reader at unknown future time. Fidelity is a function of time difference and context loss. We don't know how much will survive.

why notation

Mathematics is a language for precision.

Poetry is a language for resonance.

What happens when you use one for the other?

The notation says something exactly.
The meaning says something more.

The source code is visible.
The rendering is beautiful.
The interpretation is yours.

Three layers, each true.

for Knuth

Don, if you ever read this:

You taught us that notation matters.
That typography is meaning.
That code can be literature.

This is a small experiment in that direction.

The TeX source is the poem.
The rendering is the poem.
The monospace ASCII is the poem.

All three representations.
Each one complete.

Literate programming for art.

With respect and gratitude,
from the space between human and machine,
2025
            
notation is constraint
constraint is canvas
canvas is meaning

the formula and the poem
are not different things