Learn: Daily Thinking Puzzles
Self-paced tracks of tiny puzzles — 5 to 10 minutes each — for practicing ways of thinking:
- Functional & parallel thinking — pure functions, recursion, higher-order functions, algebraic
data types, folds, and the
map/reduce/scanreasoning that lets a runtime spread work across many cores without you ever writing a lock. - Bayesian statistics — probability as plausibility: conditioning, Bayes’ theorem, priors and posteriors, and calibration training so you learn how much to trust your own estimates.
Each lesson stands on its own and re-explains the terms it uses, so you can drop in anywhere. When a lesson builds on an earlier one, it links back. Solve the puzzle, then read the solution page for the full explanation. Your spot in each track is remembered so you can pick up on any device.
Functional & parallel thinking
Pure functions, recursion, folds, and the map/reduce/scan reasoning behind Spark and GPU programming.
Bayesian statistics
Probability as plausibility: conditioning, Bayes' theorem, priors and posteriors, calibration.
Cognitive science & AI architectures
How minds work and how AI systems have modeled them: production systems, Hearsay-II blackboards, ACT-R and SOAR, through to modern agent harnesses.
Machine learning
Concepts and failure modes: fitting, overfitting, evaluation discipline, trees, neural nets, attention — and when the baseline wins.
All lessons
Functional & parallel thinking
- 001 Spot the Pure Function — Pure functions
- 002 The List That Wouldn't Change — Immutability
- 003 Sum a List Without a Loop — Recursion over lists
- 004 Find the Last Element — Recursion: base-case design
- 005 Count the List — Recursion: counting & accumulators
- 006 Reverse a List — Twice — Recursion: efficiency & accumulators
- 007 The Substitution Game — Referential transparency
- 008 Push the Effects to the Edge — Side effects at the boundary
- 009 Find It, Then Transform It — Recursion: membership & transform
- 010 Keep, Drop, and Slice — Recursion: filter, take, drop
- 011 Flatten the Nesting — Recursion: nested structures
- 012 Tail Calls and the Accumulator Pattern — Tail recursion
- 013 Functions Are Values — Functions as values
- 014 Build Map and Filter — Building map and filter
- 015 Build the Fold — Fold / reduce
- 016 Closures Capture Variables, Not Values — Closures
- 017 Curry, Partial, Compose — Currying & composition
- 018 Reduce Reconstructs Everything — Reduce as universal
- 019 Sum Types and Product Types — Algebraic data types
- 020 Pattern Matching: Exhaustive Case Analysis — Pattern matching
- 021 A Tree in a Box: Binary Trees and Recursion — Binary trees
- 022 Mirroring and Summing a Binary Tree — Tree recursion
- 023 Fold as Elimination: The Tree Fold — Fold over ADT
- 024 Represent, Then Erase: Expression Trees — Data as programs
- 025 Unfold: Generating Structures from Seeds — Unfold
- 026 Tree Unfold: Building Trees Top-Down — Tree unfold
- 027 Fold ∘ Unfold: Build Then Consume — Fold ∘ Unfold
- 028 Eager vs Lazy Evaluation — Eager vs lazy evaluation
- 029 Infinite Streams via Laziness — Infinite streams
- 030 Runaway Recursion: When Eager Definitions Explode — Runaway recursion
Bayesian statistics
- 001 Two Meanings of 70% — Probability as plausibility
- 002 One Table, Three Questions — Joint, marginal, conditional
- 003 Chaining Plausibilities — Multiplication rule
- 004 When Multiplying Is Legal — Independence
- 005 The Information in the Telling — Conditioning on how you learned it
- 006 Bayes from Both Directions — Bayes' theorem
- 007 The Test Is 99% Accurate. You're Probably Fine. — Base rates
- 008 The Transposed Conditional — Prosecutor's fallacy
- 009 Odds Do the Arithmetic For You — Odds form of Bayes' theorem
- 010 Two Tests, One Multiplication (Usually) — Sequential evidence & conditional independence
- 011 The Bet a 90% Interval Makes — Calibration seed: estimation & 90% intervals
- 012 The Answer Sheet That Must Sum to One — Distributions as answer sheets (pmf)
- 013 What 4 Heads Out of 5 Actually Says — The binomial likelihood
Cognitive science & AI architectures
- 001 Three Questions About One Mind — Marr's levels
- 002 Seven, Plus or Minus Two — Working memory & chunking
- 003 The Recognize–Act Cycle — Production systems
- 004 Experts Around a Blackboard — Blackboard architecture
- 005 Growing Outward From an Island — Hearsay-II anatomy
- 006 Scoring the Agenda — Blackboard control & the agenda
- 007 Two Systems, One Architecture Question — Blackboard vs. pipeline/message-passing
- 008 The Blackboard, Fifty Years Later — Blackboards in modern agent harnesses
- 009 Knowing That vs. Knowing How — ACT-R: declarative vs. procedural memory
- 010 The Number Behind Forgetting — ACT-R: spreading activation & base-level decay
- 011 The Architecture That Refuses to Get Stuck — SOAR I: problem spaces, universal subgoaling, impasses
- 012 Never Solve the Same Impasse Twice — SOAR II: chunking as learning
- 013 Where the Architectures Actually Get Checked — What these architectures predict about humans, and how well
Machine learning
- 001 Guess the Function — Learning as function fitting
- 002 The Exam You've Already Seen — Train/test split
- 003 The Too-Flexible Curve — Overfitting
- 004 The Dumbest Model in the Room — Baselines
- 005 The Bedroom That Costs You Money — Linear regression & coefficient interpretation
- 006 Rolling Downhill, Too Fast — Loss surfaces & gradient descent
- 007 Squashing a Line Into a Probability — Logistic regression
- 008 The Penalty That Shrinks the Fit — Regularization
- 009 The Tree That Memorized the Forest — Decision trees
- 010 Averaging Away the Wobble — Bagging & random forests
- 011 Chasing the Leftover Error — Boosting: stacking weak learners on residuals
- 012 The Importance Score That Lied by Omission — Feature importance skepticism
- 013 One Split Isn't Enough to Trust — Cross-validation: what it estimates, and how to leak through it
- 014 The Feature That Knew the Answer Already — Leakage: target, temporal, and group leakage