Why interactivity¶

Sources & anchors

Stack component: Meta
Canonical artifact: idea note §Conceptual frame 7-paradigm table
Workshop session: Day-1 AM kickoff (10 min)
Outline: _outline.md §B

Frame¶

7-paradigm taxonomy (from idea note) translated to research workflow; the manipulable workflow as the gap.

The borrowed taxonomy¶

The argument that interactivity is a medium, not just a feature, has been made most carefully for mathematics. The Deep Research synthesis Interactive Mathematics Beyond the Static Page identifies seven interaction paradigms that recur across the modern mathematical-software ecosystem, each closing a specific representational gap that static prose cannot. The table below reproduces the taxonomy from the idea note §Conceptual frame with the mathematics paradigm on the left and the research-workflow analog on the right.

Math paradigm	Research-workflow analog	What it makes visible
Domain coloring	Pipeline state heatmap	Where in the DAG; what's stale
Reactive notebook	Marimo / Observable for analyses	Param → cascade
Executable notebook	Jupyter / Marimo narratives	Code + prose + figure together
Diagrammatic	Snakemake DAG, projio dependency graph	Composition of computations
Proof-aware doc	Provenance-aware doc (claim ↔ data ↔ commit)	Reproducibility as navigable object
Expository animation	Manim explainer	Why a workflow is shaped a certain way
Geometry viewer	Project topology viewer (multi-repo, cross-link)	What touches what

The translation is not metaphorical. In each row the representational problem is structurally the same: a high-dimensional or path-dependent object that resists being read off a page. The mathematics ecosystem solved its version of that problem by inventing interaction paradigms. Research workflows can borrow most of them directly: a Snakemake DAG is already diagrammatic, a Marimo notebook is already reactive, and a worklog goal graph is already a proof-aware document in everything but name.

The gap¶

The Deep Research synthesis singles out operator theory as the under-served subfield of mathematics — the area where individual computations (matrix pseudospectra, finite-dimensional solvers) are well-instrumented but the ambient structure (resolvents, continuous spectrum, semigroup growth, Banach-space geometry) has no mature interactive layer. The analog for research practice is direct: tools exist for individual computations — Jupyter for analysis, Snakemake for pipelines, DataLad for data — but nothing makes the whole research workflow a manipulable object the way complex-analysis.com makes a complex function manipulable. The workflow is the operator theory of research. projio, worklog, and this handbook exist explicitly to close that gap.

The relevant move is not to add yet another notebook. It is to extend the set of paradigms up one level: from interactive computations to an interactive composition of computations. A pipeline state heatmap that shows which rule fired on which subject; a permission scope diagram that shows what a sandboxed agent can touch; a goal critical-path render that shows which task unblocks which milestone — these are the workflow-level analogs of phase portraits and string diagrams.

Reusable media forms¶

The Deep Research synthesis makes one further observation that this handbook takes seriously: the most influential interactive resources did not just produce content, they invented forms that other people then reused. Sanderson's Manim style, Wegert's phase portraits, IMAGINARY's exhibition format, and JuliaDynamics' interactive bifurcation diagrams have become genres in their own right. The handbook commits to three candidate forms — small enough to be sustainable, opinionated enough to be recognizable — and uses each one repeatedly so readers learn the vocabulary by example.

Workflow trace. A visual representation of a research session as it actually unfolds: a note becomes a captured idea, the capture is promoted to a task, the task dispatches a run, the run produces an output, the output is recorded back as a note. This is what an audit trail looks like when the audit trail is the primary deliverable. The notio chapter introduces the underlying log; the orchestration chapters show how traces span projects.
Permission scope diagram. A picture of a project's sandbox: which MCP servers are wired up, which Bash patterns are pre-approved, which paths the agent can read or write. The diagram makes the agent's blast radius legible at a glance. It first appears in permissions and bounded context and recurs whenever a chapter introduces a new MCP surface.
Goal critical path. A render of a worklog goal as a milestone graph with the critical path highlighted, click-through to each milestone's captures and dispatched tasks. This is the orchestration layer's flagship form — a planning artifact that is also an inspection artifact. It is the worked example in goals and critical path.

These three forms are not exhaustive and not final. They are the minimum working set of media that the handbook commits to making recognizable. If a reader can leave the handbook able to read and produce a workflow trace, a permission scope diagram, and a goal critical-path render, the vocabulary has done its job.

A worked example (placeholder)¶

The chapter's running example is a workflow trace rendered as a live explorable: the reader manipulates a small task graph and watches the worklog scheduler resolve dependencies and dispatch in order. The explorable is built as a Marimo notebook exported to WASM and embedded inline; the surrounding stack is taught in handbook explorables. The prototype is tracked separately (docs/log/task/task-arash-20260507-222051-589638.md). Until the prototype lands, the slot below is intentionally empty rather than mocked.

Explorable E1 — Workflow trace: notes → tasks → dispatched runs → outputs. Prototype pending.

The caution¶

The same Deep Research synthesis that motivates this chapter also issues a warning: interactive systems mislead when rendering artifacts, hidden defaults, or discretization choices get confused with the underlying mathematics. The research-workflow analog is the agent's confident output when the underlying provenance is broken. A polished workflow trace that omits a failed run, a permission scope diagram that does not reflect the real settings file, a goal graph rendered from stale capture data — all of these can produce plausible-looking artifacts that are wrong in ways the reader cannot see. The handbook's standing answer is the same as mathematics': keep the symbolic and numerical layers close together, expose the source, and link every rendered claim back to the data and commit that produced it. The provenance-aware document is not a luxury; it is what makes the rest of the medium honest.