Fall 2026 · Week 02

Three Numbers

A sequence and a hidden rule.

Last week's task

Did every answer come with a confidence?

Who did it? — And how sure are you about that?

A game

I have a rule in my head. A sequence of three numbers either fits it or does not.

In pairs, propose any three numbers. I tell you: fits, or does not fit.
When you think you know the rule, announce it.
First, on your own card, write the rule you guess right now. Do not show your partner.

2, 4, 6 fits.

Testing · up to 8 triples per pair

Before every triple

1. Write the three numbers on the card
2. Write your prediction:  fits / does not fit
3. Raise a hand. I answer with one word.

2   4   6   →  fits

I say "fits" or "does not fit". Nothing else.

Announce

Write your final rule, and a confidence

Each pair announces in turn.

50% — a guess
70% — fairly sure
90% — almost certain

The rule

Any three increasing numbers.

1, 2, 3 fits. 7, 100, 1000 fits. 6, 4, 2 does not.

What just happened

Triples proposed:              __
Predicted "fits":              __
Judged "fits":                 __
Pairs with the right rule:     __ / 3
Average confidence:            __ %

Typically: 24 triples, 20 predicted to fit, 21 judged to fit, zero or one pair right, confidence above 80%.

What does a "fits" tell you?

You ran twenty-some experiments. Twenty were "I think this fits." And they did fit. Then you were ninety percent sure. And wrong.

An experiment you expected to fit, that fit, tells you almost nothing. A hundred different rules would all say "fits".

One step

How to kill a hypothesis

Your guess:        "even numbers, add 2"
Best experiment:   1, 2, 3
You predict:       does not fit
I say:             fits

One step. The hypothesis is dead.

You ran eight experiments each. Not one hypothesis died.

Three names

Confirmation bias · Counterexample · Falsification

The brain naturally looks for evidence that agrees with it. "Fits" feels good; "does not fit" feels bad. That habit is called confirmation bias. There is only one cure: the counterexample.

See a thousand white swans and say "all swans are white". How sure are you? One black swan, and it drops to zero.

Scientists do not try to prove themselves right. They try hard to prove themselves wrong. What survives, stays. That is falsification.

One case

Two thousand years, one counterexample

Bloodletting was used for two thousand years. Every doctor had seen patients get better after it. Those were the "fits" experiments.

Nobody ran the uncomfortable one: leave half the patients alone, and compare. In the 1830s someone did. Bloodletting did not help. Sometimes it made things worse.

Back to last week

What confidence should grow from

Supporting examples, however many, raise it slowly.

Surviving one counterexample you honestly expected to break it raises it fast.

Your 90% was worth 40%. Now you know why: you pumped it up with supporting examples.

And AI

It follows the way you ask

Ask "why is X right?" and it gives you ten reasons. Ask "where might X be wrong?" and it gives you ten more.

How you ask decides whether you see confirmation or a counterexample. Week 6 is about asking.

Now be a scientist. I have a law of nature in my head. Find it with blocks.

Blocks · how to play

Find the rule

I am the host. The rule is about how the blocks are arranged.
I build two examples first: one fits (white card), one does not (black card).
Pairs take turns building a new arrangement. Say your prediction before you build. I give it a white or black card.

Blocks · scoring

Coins and guesses

Right prediction: one coin. One coin buys one guess at the rule.
A wrong guess costs nothing, but I immediately build a counterexample for everyone to see.
A right guess ends the round: 3 points. Ten experiments per round, then I reveal.

Round 1 · up to 10 experiments

Go

Say the prediction. Then build.

Round 1

What you did

Experiments:                 __
Predicted "does not fit":    __
Rule found:                  yes / no

I had just finished explaining confirmation bias. And you did it again.

Two new rules

From now on

At least half of your experiments must be ones you predict "does not fit". Three "fits" predictions in a row and I stop you.
Change a dimension. Cannot think of a counterexample? Move something you have not touched yet.

Five dimensions

Colour
Count
Orientation     flat, or standing
Position        high, low, left, right
Touching        or not

Which of these have your experiments changed so far? Which have you never touched?

Round 2 · up to 10 experiments

Same shape of rule. New dimension.

"At least one…" again, so the two rounds compare fairly. Both new rules apply.

Round 3

You host

One pair writes a rule and shows it to me first. One sentence, judged in three seconds.
Template: "at least one block…" / "all blocks…" / "more … than …".
Build two examples. The other pairs experiment; same rules as before.
Host: build a correct counterexample within 20 seconds and earn 2 points.

Round 1 vs Round 2

Round 1:   __ experiments   predicted ✗ __   rule  found / not found
Round 2:   __ experiments   predicted ✗ __   rule  found / not found

Ten "fits" are worth less than one "does not fit". That is not a rule of the block game. That is the rule of science.

The rule

Read it together

Everyday version: when you feel sure you are right, ask "what would make me wrong?"

This week: pick something you are very sure of. The strongest character in a game, the best restaurant, something about a classmate. Go find a real counterexample. Found or not, write it in the notebook. Or try it on an AI: have it state an opinion, then order it to give three examples that would overturn it.

Look for a counterexample first, not one more supporting example.

Same as last week

The calibration scoreboard

Confidence	Correct	Wrong
50%	+1	0
70%	+2	−2
90%	+3	−6

Five questions. Pick A, B, or C, and write how sure you are.

1 / 5

Four cards each have a letter on one side and a number on the other. Rule: "If one side is a vowel, the other side is an even number." On the table: E, K, 4, 7. Which cards, at minimum, must you turn over to test the rule?

AE and 4
BE and 7
COnly E