Your next move
Follow your curiosity.
Start with a question. Each route gives you a result you can inspect and challenge.
One Move / today's exact puzzle
Five readings. One reversal.
Change one reading to make the other estimate closer to the fixed target. Can you find the smallest strict flip?
Make a challenge image ↓
Share or download a 1200 × 630 PNG with today's five readings, target, and the address of this exact date. It hides the closer estimate and the winning move. The image is made in this browser; the link above remains a blind invitation without the inputs.
Want a lesson? Read the five-minute guide or print the worksheet. To see what the mathematics can prove, inspect three exact proofs. Explore the Discovery Archive for checked counterexamples, or run your own exact finite conjecture search. Analyze your own 3–21 readings, odd or even with exact fractions, then vary the target across an interval. Build and verify an exact certificate when several readings can vary at once. Try Shape the Data, Flip Levers, Flip Point, Target Lens, and the Outcome Atlas.
Start here / three revealing cases
Choose a question. See the evidence.
Each case loads seed 42 and one fifth estimate. Change the controls afterward to challenge the example.
Your data / local workbench
See what one value does to your numbers.
Paste 3–40 numbers, separated by commas or spaces. Add a known target if you have one. The result shows what changes when the value farthest from the median is removed. Analysis runs in this browser. Creating a challenge link puts the selected values in its URL.
Finite values from −1,000,000 to 1,000,000; use a period for decimals. The examples are invented. Do not treat a removed value as invalid simply because it is far from the median.
A link to another experiment needs exactly five readings and a supplied target, each from 0 to 100 with at most four decimal places. Its URL contains those values and may appear in browser history or hosting logs. Use invented or public data only.
The mean is the sum divided by the number of observations. The median is the middle sorted value, or the average of the two middle values. “Farthest” means greatest absolute distance from the original median; ties use the first entered value. Removing a point is a counterfactual, not a recommendation to discard data. A target you enter is a reference you supplied, not one verified by this page.
Experiment 01
Remembrance Calculus™
Set the pull strength, add a shock, then watch the point return toward a fixed target. Pause to inspect exact steps.
Paused at step 0.
See one step ahead ↗
From the current state, add the pull term to velocity and multiply by 0.92. Opening this view does not advance the model. A faint ring marks the next position while paused.
v ← 0.92(v + 0.008α(target − position)); position ← position + v. A shock adds one seeded impulse to velocity. “Settled” means distance < 4 and speed < 0.5 for 45 consecutive steps.Experiment 02
Witness Geometry™
Four seeded observers estimate a known target of 50. Move a fifth observer and compare the two estimates on the same data.
Experiment 01 · observed pathTrace the path behind you ↗
Freeze up to 150 recent positions from the actual run. Scrub the captured steps to inspect distance and position; rose and lavender marks show where shocks and pull changes occurred. Copy a link to open a selected step paused in this view. Opening or refreshing this view does not change the live model.
Distance through time
Where the point traveled
Experiment 01 · side studyCompare two futures ↗
Fork this exact position and velocity into two 60-update paths. Both use the same target and damping, with no new shocks. Previewing does not change the live run.
Which path is nearer at each update?
Experiment 02 / sensitivity sweep
Where does each estimator win?
Hold the four seeded values fixed and try every whole-number fifth estimate from 0 to 100. Each curve is absolute error against the known target of 50. The dashed line marks your current slider position.
| Fifth estimate | Mean error | Median error | Lower error |
|---|---|---|---|
| Current: — | — | — | — |
| 0 | — | — | — |
| 25 | — | — | — |
| 50 | — | — | — |
| 75 | — | — | — |
| 100 | — | — | — |
Reading this sweep: Counts describe these 101 evenly spaced inputs, not the chance of an estimator winning in the world. A different seed changes the four fixed estimates. The reported maximum errors refer only to this 0–100 grid.
Experiment 02 / seed cohort
Does the pattern survive a seed change?
Repeat the same 101-position sweep across 128 generated seeds, starting at the selected seed. The curves average absolute error over those seeds; the counts report how many individual seeds favor each estimator at your current fifth estimate.
| Fifth estimate | Mean avg. error | Median avg. error | Median lower in seeds | Lower average |
|---|---|---|---|---|
| Current: — | — | — | — | — |
| 0 | — | — | — | — |
| 25 | — | — | — | — |
| 50 | — | — | — | — |
| 75 | — | — | — | — |
| 100 | — | — | — | — |
Protocol: seeds = (selected seed + 0 through 127) modulo 232. Four estimates per seed come from successive draws of the documented pseudorandom generator, scaled to [42, 58); the same fifth estimate is tested for all 128. Press Reset seed & state to apply a new seed. Averages and seed counts answer different questions; this fixed generated cohort is not a population estimate or external validation.
Experiment artifactMake a visual run receipt ↗
Capture the current trajectory, seed, and model readings as a PNG. The picture is a snapshot of a toy run; use the replay link below for the exact event history. Refresh after the run changes.
Experiment notebook
Keep the inputs and outcome
Export the seed, parameters, shock events, exact state, the 101-point sweep, and the 128-seed cohort as JSON. Or copy a link that replays this toy run and opens it paused. The link contains the seed, selected fifth reading, pull changes, shock strengths, and step count; URLs can appear in browser history or hosting logs. Use invented values only.