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Interactive labs

Interactive teaching labs for probability, chaos, forecasting limits, and other concepts that are easier to understand by experimenting.

Hands-on simulators and teaching surfaces that turn abstract concepts into things users can adjust, rerun, and explain.

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Interactive lab

Probability Signal Simulator

A hands-on lab for seeing why new information can make switching the stronger choice.

This Monty Hall-style lab teaches the probability shift without assuming the concept is already familiar. Make an initial choice, remove a known miss, then run repeated trials in real time to watch the keep-versus-switch results settle into their long-run pattern. Deeper simulation modes expand the same rule to larger starting sets and partial reveals.

What this shows

The simulator starts with a first choice, reveals information that is known to be wrong, and then compares keeping the first choice against switching after the new information arrives.

How to read it

One round can feel noisy. Repeated trials show the pattern: the original choice keeps its starting probability, while the remaining unrevealed alternative can carry more of the probability from the options you did not choose.

Why it matters

The lab is a small model for decision quality. A person can make a reasonable first choice, receive new information, and still need to update the decision instead of defending the original pick.

Limits

This is an educational probability lab. It is not a market model, investment recommendation, or proof that switching is always the right action in every real system.

Related

Compare it with Chaos Divergence Explorer and Market Intelligence Field Notes.

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Interactive lab

Chaos Divergence Explorer

A compact lab for seeing when near-identical forecasts stop agreeing.

This lab compares near-identical forecasts under a known rule. Pick a simulation, load a preset, run the model, then adjust one control at a time to see when the paths split.

What this tests

The explorer compares near-identical forecasts under known rules. It is designed to separate pattern recognition from precise prediction.

Simulation modes

  • Feedback maps show compounding mismatch.
  • Attractor flows show bounded systems with unstable paths.
  • Local cascades show how small differences spread through connected rules.
  • Gravity flybys show near-miss paths changing direction.
  • Basin boundaries show small input changes landing in different outcomes.

How to read it

The useful readout is the predictability horizon: the first point where the forecasts are no longer close enough to trust as one answer.

Why it matters

Many business and technical systems are not random, but they can still become hard to forecast after enough feedback, unresolved variables, or hidden rule drift.

Limits

The lab is an explanatory model, not a production forecasting engine or scientific simulation package.

Related

Use Probability Signal Simulator for probability updating, or Systems Field Notes for operational examples where small changes can cascade.

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Interactive lab

AI Token Budget Lab

A local simulator for teaching token usage, context pressure, retrieval overhead, retries, agent loops, latency, and classroom-scale cost.

This browser lab estimates how prompt anatomy, retrieval, tool output, retries, model assumptions, and repeated classroom or team use can change an AI workflow budget.

Boundary

The lab is deterministic and local. It does not call an AI API, use an API key, contact a tokenizer service, or send user-entered text out of the browser.

How to read it

Token counts, context pressure, latency, and cost are approximations. Real tokenizers, billing rules, infrastructure, model behavior, and application designs vary. The editable profiles are teaching assumptions, not provider claims.

What it teaches

  • Prompt sections compete for the same context window.
  • Retrieval can help when the signal is focused, but noisy chunks can bury the useful material.
  • Retries and agent loops can multiply both cost and latency.
  • Small per-run estimates can become meaningful when many students, teams, or sessions repeat the workflow.

Related

Use Probability Signal Simulator for probability updating, Chaos Divergence Explorer for feedback and forecast limits, and Practical AI Implementation for the adoption context behind token budgets.

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