Teaching-mechanic library

replication_chamber · math · simulator.reach_state

Concept: Exponential growth

Player does: Set the growth factor so the colony hits the target on day n

Breaks: Exponential growth is fast linear growth

Exponential growth multiplies by a constant factor each step, which eventually outpaces any linear growth no matter how fast.

inheritance_machine · math · simulator.reach_state

Concept: Recursive sequences

Player does: Set a₁ and the rule so generation 5 matches

Breaks: Recursive and explicit rules can't describe the same sequence

A recursive rule and an explicit formula can generate exactly the same sequence, just computed differently.

repeat_experiment · math · simulator.sample

Concept: Variability

Player does: Rerun the identical experiment; predict the spread

Breaks: Same setup, same result

Random variation means identical setups can still produce different results from trial to trial.

prediction_stabilizer · math · simulator.sample

Concept: Law of large numbers

Player does: Choose how many trials until the estimate stays in the band

Breaks: After five heads, tails is due

Independent trials have no memory, so past outcomes don't change future odds; the law of large numbers only stabilizes averages over many trials.

long_run_casino · math · simulator.sample

Concept: Expected value

Player does: Pick the table with the best long-run payoff, then watch 1,000 plays

Breaks: The biggest prize is the best bet

Expected value weighs each payoff by its probability, so a rare huge prize can still be a worse bet than a smaller frequent one.

population_collector · math · simulator.sample

Concept: Sampling bias

Player does: Sample only reachable districts; explain why the estimate drifts

Breaks: A bigger biased sample fixes the bias

A biased sampling method stays biased no matter how large the sample gets; only fixing the method removes the bias.

capture_the_parameter · math · simulator.sample

Concept: Confidence intervals

Player does: Throw interval nets; predict how many catch the hidden true value

Breaks: There's a 95% chance this one interval holds the value

A 95% confidence level describes the method's long-run capture rate across many intervals, not the chance for one already-computed interval.

odds_forge · math · simulator.sample

Concept: Probability & counting

Player does: Choose the fork with the best odds of loot

Breaks: Two outcomes means 50/50

Probability depends on how many ways each outcome can occur, not just how many outcomes are listed.

recoil_movement · physics · simulator.intervene

Concept: Newton's 3rd law

Player does: Move only by throwing mass the opposite way

Breaks: The bigger object pushes harder

Newton's third law pairs are always equal and opposite in force, regardless of the objects' relative size.

orbit_slingshot · physics · simulator.reach_state

Concept: Gravity & orbits

Player does: Set the launch speed that reaches a stable orbit

Breaks: There's no gravity in space

Orbiting objects are in continuous free fall under gravity; an orbit is a balance of gravity and sideways speed, not an absence of gravity.

heat_flow_rooms · physics · simulator.predict

Concept: Thermal equilibrium

Player does: Predict final temperatures when rooms share a wall

Breaks: Cold flows into warm objects

Heat flows from the warmer object to the cooler one until both reach thermal equilibrium; cold itself does not flow.

dynamic_reaction_arena · chemistry · simulator.predict

Concept: Dynamic equilibrium

Player does: Watch forward and reverse reactions; predict when counts stop changing

Breaks: At equilibrium the reaction stops

At equilibrium, the forward and reverse reactions still run, just at equal rates, so concentrations stop changing but the reaction never stops.

energy_barrier · chemistry · simulator.reach_state

Concept: Activation energy

Player does: Heat until enough molecules clear the barrier

Breaks: Exothermic reactions need no energy to start

Even an exothermic reaction needs activation energy to get started, before it releases net energy overall.

particle_spread · biology · simulator.predict

Concept: Diffusion

Player does: Predict how particles spread from the crowded chamber

Breaks: Particles move toward empty space on purpose

Particles move randomly and simply spread out net from high to low concentration; they have no destination in mind.

membrane_balance · biology · simulator.predict

Concept: Osmosis

Player does: Predict which way water crosses and whether the cell swells or shrinks

Breaks: Salt crosses the membrane instead of water

In osmosis, water crosses the semipermeable membrane toward the higher solute concentration; the solute itself often cannot cross.

atp_gate · biology · simulator.intervene

Concept: Active transport

Player does: Spend ATP to pump ions against the gradient before the budget runs out

Breaks: Transport always goes down the gradient

Active transport uses ATP to move substances against their concentration gradient, unlike passive diffusion.

dock_blocker · biology · simulator.predict

Concept: Competitive inhibition

Player does: Decoys occupy sites; predict how much more substrate restores the rate

Breaks: Inhibitors destroy enzymes

A competitive inhibitor blocks the active site reversibly; adding more substrate can outcompete it and restore the reaction rate.

meiosis_shuffle · biology · simulator.sample

Concept: Meiosis & variation

Player does: Shuffle homolog pairs; predict how many gamete types appear

Breaks: Meiosis makes identical cells

Meiosis shuffles homologous chromosomes to produce genetically varied gametes, not identical cells.

survival_sim · biology · simulator.predict

Concept: Natural selection

Player does: Change the environment; predict which trait spreads

Breaks: Individuals evolve because they need to

Natural selection acts on existing variation across a population over generations; individuals themselves do not evolve by need.

drift_sim · biology · simulator.sample

Concept: Genetic drift

Player does: Run tiny populations and watch alleles vanish by chance

Breaks: Evolution always improves fitness

Genetic drift changes allele frequencies by random chance, especially in small populations, regardless of fitness.

feedback_controller · biology · simulator.intervene

Concept: Homeostasis

Player does: Release insulin or glucagon to keep glucose in the safe band

Breaks: Hormones switch on and stay on

Hormonal control in homeostasis is a continuous feedback loop, releasing and easing off as the level shifts, not an on/off switch.

threshold_pulse · biology · simulator.intervene

Concept: Action potentials

Player does: Stack inputs until threshold fires an all-or-none spike

Breaks: Stronger stimuli make bigger action potentials

An action potential is all-or-none once it fires; a stronger stimulus raises firing frequency, not the spike's size.

vaccine_memory · biology · simulator.predict

Concept: Immunological memory

Player does: Predict how fast the second infection is cleared

Breaks: Vaccines give you the disease

A vaccine trains memory cells to recognize a pathogen without causing the actual disease.

greenhouse_dial · earth_space · simulator.intervene

Concept: Greenhouse effect

Player does: Adjust emissions to keep temperature in the band

Breaks: The greenhouse effect is the ozone hole

The greenhouse effect traps heat via gases like CO2, which is a separate process from ozone depletion.

path_prediction · engineering · simulator.sample

Concept: Branch prediction

Player does: Guess each branch; watch the pipeline flush on a miss

Breaks: Mispredictions cost nothing

A branch misprediction forces the pipeline to flush and restart, costing real cycles.

antibiotic_resistance · health · simulator.predict

Concept: Resistance evolution

Player does: Stop treatment early; predict which bacteria survive

Breaks: People become resistant to antibiotics

Antibiotic resistance evolves in the bacteria population, as the drug-tolerant survivors of an incomplete course multiply.

population_pyramid · geography · simulator.predict

Concept: Demographic transition

Player does: Predict the pyramid's shape a generation later

Breaks: Population always grows

As birth and death rates fall through the demographic transition, a population's growth can slow, plateau, or shrink.

living_marketplace · economics · simulator.predict

Concept: Supply & demand

Player does: Shift supply or demand; predict the new price and quantity

Breaks: Higher prices increase demand

Higher prices reduce quantity demanded along the demand curve; only a shift of the whole curve changes demand itself.

hidden_spillover · economics · simulator.predict

Concept: Externalities

Player does: Your factory's costs land on neighbors; predict the true social cost

Breaks: The market price captures every cost

An externality falls on people outside the transaction, so the market price can miss part of the true social cost.

money_multiplier · economics · simulator.reach_state

Concept: Money creation (textbook model)

Player does: Set the reserve ratio so deposits expand to the target

Breaks: Banks keep every deposit in the vault

Banks lend out most of a deposit and keep only a fraction in reserve, which is what expands the money supply.

diversification_sim · finance · simulator.sample

Concept: Risk & diversification

Player does: Build portfolios; watch thousands of market years

Breaks: Diversifying lowers returns without lowering risk

Diversification spreads risk across uncorrelated assets, which can lower volatility without a matching loss in expected return.

reinforcement_schedule · psychology · simulator.predict

Concept: Reinforcement schedules

Player does: Predict response persistence under fixed vs variable schedules

Breaks: Rewarding every time builds the most persistent habit

Variable schedules of reinforcement produce more persistent behavior than rewarding every single response.

marketing_funnel · business · simulator.reach_state

Concept: Conversion funnel

Player does: Tune conversion at each stage to hit the sales target

Breaks: More traffic always fixes low sales

Sales depend on the conversion rate at every funnel stage, so more traffic cannot fix a leak further down the funnel.