Notes on probabilistic planning from the team building Topolog: why deadlines should be distributions, what a planning language buys you, and how budgets trade against the odds.
A Pareto frontier is the set of options where improving one objective requires giving up another. The definition, dominance in one table, and what the frontier means for project budgets and success odds.
Read the articleA planning language is a formal, text-based notation for describing plans: tasks, dependencies, uncertainties, decisions, and endings, with semantics a machine can check and execute. Definition, properties, and why totality matters.
Read the articleThe planning fallacy is the systematic human tendency to underestimate how long work will take, even with full knowledge of past overruns. The definition, the inside-versus-outside view, and the corrections that actually work.
Read the articleThe critical path is the longest chain of dependent tasks through a project, the sequence that sets the earliest possible finish date. The definition, how it is computed, and why a slip on it costs the whole project a day.
Read the articleA near-critical path is a dependency chain whose slack is small enough that ordinary estimate error can make it the critical path. The definition, the probabilistic version (criticality rate), and why these chains cause most schedule surprises.
Read the articleMonte Carlo project forecasting simulates a plan thousands of times, drawing each task's duration from a distribution, to produce the full range of possible finish dates with probabilities, instead of a single guessed date.
Read the articleThe per-seat AI add-on quietly charges your whole team for capability a few people use heavily. Pooled credits price the actual resource: the compute. A short economics argument with a worked example.
Read the articleA planning graph is a directed acyclic graph whose nodes are tasks and whose edges are dependencies. A plain definition, why acyclicity matters, and how Gantt charts, Kanban boards, and to-do lists are all views of one.
Read the articleGoal decomposition is the process of breaking a large objective into smaller, dependency-linked pieces until each piece is estimable and executable. The definition, the working-memory rule that governs it, and where AI fits.
Read the articleThe fear with AI planning is real: plausible-looking structure with subtle nonsense inside. The fix is architectural, not promissory. Generation and verification must be different systems, and only one of them gets to say what is true.
Read the articleThe blank canvas is where planning actually fails. What happens between "I want to launch a course by September" and a validated, forecast-ready dependency graph, and why the journey goes level by level.
Read the articleThe hands-on bring-your-own-AI workflow, end to end: hand your model the TOL handbook, let it draft a plan, feed the validator's errors back, and watch the loop converge to zero. No Topolog AI credits involved.
Read the articleOvercommitment is invisible at the moment it happens, because each yes looks affordable alone. Treating the team's painted hours as one pool, drawn down by every active plan, makes "can we take this on?" a computable question.
Read the articleEvery tool now claims AI and intelligence. Here is a buyer's checklist that cuts through it, including the question vendors least want asked: when is your product the wrong choice?
Read the articleEvery schedule rests on an assumption about your hours, and most tools assume a fiction. Painting your actual week, including the school runs, the day job, and the Tuesday evenings, is the difference between a forecast and a wish.
Read the articleManagers want the roadmap, contributors want today's list, finance wants the burn. The classic answer is three tools and a sync meeting. The better answer is one object and nine computed views of it.
Read the articleThe Sunday-night ritual of dragging Gantt bars exists because plans store conclusions instead of logic. When the schedule is computed, marking work done is the only status input the system needs, and the forecast learns your real pace from it.
Read the article"Looks fine" is not a property. A plan that is about to govern months of work deserves the same treatment as code that is about to run in production: a compiler pass, with named rules, line numbers, and severities.
Read the articleReal work loops: revise until approved, test until green, pitch until funded. Dependency graphs forbid cycles. The resolution is a bounded iteration whose length is a random variable, and the engine forecasts it as one.
Read the articleThe working-memory result from 1956 turns out to be the right constraint for breaking down projects, and it is precise enough to enforce mechanically. Topolog's validator literally warns when a plan level exceeds seven children.
Read the articleBefore a single estimate is typed, a plan's structure already commits it to a risk profile. Long chains, wide fans, diamond joins, and lonely bridges each fail in characteristic ways, and you can learn to see them.
Read the articleThe critical path tells you what is setting the pace today. The near-critical paths tell you what will ambush you tomorrow. Dependency-aware planning means watching both, and under uncertainty the difference between them is only ever a bad week wide.
Read the articlePlans mix two kinds of uncertainty that behave nothing alike: things the world will decide, and things you will. Most tools model neither. Making decisions first-class changes what a plan can tell you.
Read the articleA plan can complete every task and still fail, because the money ran out on the way. Wiring solvency into the definition of success makes the forecast tell the truth about both.
Read the articleFifty years of research says humans systematically underestimate how long work takes, and knowing about the bias does not remove it. Stop trying to fix the human. Build the correction into the system.
Read the articleSchedule risk gets all the attention, but the fatal project risk is usually financial: the balance crossing zero before the work crosses the line. How a Monte Carlo cash trajectory puts a probability on running out.
Read the articlePortfolio scenario planning usually means a spreadsheet copy named final_v3_really. When the plan is an executable graph, "what if we cut this feature" is a question you ask the engine, and the answer comes back as a forecast.
Read the articleEvery PM tool added an AI button and a per-seat AI price. There is another way: publish the planning language, let any model author plans, and let a deterministic engine be the judge of what is correct.
Read the articleA point estimate throws away the most useful thing you know about a task: how wrong you might be. How lognormal durations and a coefficient of variation capture honest uncertainty, and what the research says about real task times.
Read the articleMost tools treat a budget as a wall. It is actually a lever, and the relationship between spend and probability of success is a curve you can compute, plot, and pick a point on.
Read the articleA single date is the most common lie in project management. Here is what a Monte Carlo completion forecast looks like instead, with real numbers from a real engine, and how to read one.
Read the articleThe three classic planning views never agree because teams maintain them separately. They are all projections of one structure, a directed acyclic graph, and treating them that way ends the disagreement permanently.
Read the articleYour plan is already a program; most tools just refuse to let you read it. What a small, total, deliberately not Turing-complete language buys you: diffs, reviews, version control, and forecasts that are computed rather than guessed.
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