A belief has a size
- How sure?Rain tomorrow70 in 100
Picture a friend saying: it will rain tomorrow. You ask how sure. They say: about 70 in 100. That is a belief with a size. A belief is not on or off. It sits between 0, which means no chance, and 100, which means certain. Most beliefs sit somewhere in the middle.
- Before the clue70 in 100Dark clouds: after85 in 100Clear sky: after40 in 100
Made up and round. A clue moves the number. Dark clouds in the evening: 70 goes to 85. A clear sky: 70 goes to 40. Nothing switched; a number moved. How far it moves depends on one thing: how much more often the clue shows up when the claim is true than when it is false.
- clue shows 5 in 10Claim trueclue shows 5 in 10Claim false
A clue shows up just as often whether the claim is true or false. How far should it move the number?
A little, up. Any clue is some evidence.
Not yet. A clue is evidence only if it is more common on one side. This one is not, so there is nothing in it to count, and counting nothing moves nothing.Not at all.
Right. A clue that is as common either way cannot tell the two apart. Seeing it tells you the clue happened, and nothing about the claim.To 100, if the clue is strong.
Not yet. Strong means shows up far more often on one side. This clue shows up equally, which is the weakest a clue can be. - 50 rainy, 50 dryClouds: 40 rainy, 10 dry40 of 5080 in 100
The move, by counting. Say rain is 50 in 100: of 100 such evenings, 50 lead to rain. Dark clouds show on 80 of the rainy evenings and 20 of the dry ones. So 40 rainy evenings have clouds and 10 dry ones do. Clouds tonight: 40 of those 50 evenings were rainy. The number is now 80.
- clue on 60 in 10050 rainy eveningsclue on 20 in 10050 dry evenings
Start at 50 in 100 for rain: 50 rainy evenings, 50 dry. A clue shows on 60 of 100 rainy evenings and 20 of 100 dry ones. How many evenings have the clue and are rainy?
eveningsCount the rainy evenings with the clue, then the dry ones, then compare the two piles.
Right. Thirty. Sixty in a hundred of 50 rainy evenings is 30; twenty in a hundred of 50 dry evenings is 10. So 40 evenings have the clue, 30 of them rainy, and the belief moves from 50 to 75. Set where the belief starts and how much more often the clue shows when the claim is true. The new number is computed by counting, the way the rain was.
Before10 in 100After the clue10 in 100Belief before, in 100: 10 · The clue: Same either way
You were at 10 in 100. The clue shows up just as often either way, so it moves nothing. Still 10.
Before10 in 100After the clue18 in 100Belief before, in 100: 10 · The clue: Twice as often if true
You were at 10 in 100. The clue shows up 2 times as often when the claim is true. Count the days it shows: the belief moves to 18 in 100.
Before10 in 100After the clue31 in 100Belief before, in 100: 10 · The clue: 4 times as often
You were at 10 in 100. The clue shows up 4 times as often when the claim is true. Count the days it shows: the belief moves to 31 in 100.
Before10 in 100After the clue53 in 100Belief before, in 100: 10 · The clue: 10 times as often
You were at 10 in 100. The clue shows up 10 times as often when the claim is true. Count the days it shows: the belief moves to 53 in 100.
Before30 in 100After the clue30 in 100Belief before, in 100: 30 · The clue: Same either way
You were at 30 in 100. The clue shows up just as often either way, so it moves nothing. Still 30.
Before30 in 100After the clue46 in 100Belief before, in 100: 30 · The clue: Twice as often if true
You were at 30 in 100. The clue shows up 2 times as often when the claim is true. Count the days it shows: the belief moves to 46 in 100.
Before30 in 100After the clue63 in 100Belief before, in 100: 30 · The clue: 4 times as often
You were at 30 in 100. The clue shows up 4 times as often when the claim is true. Count the days it shows: the belief moves to 63 in 100.
Before30 in 100After the clue81 in 100Belief before, in 100: 30 · The clue: 10 times as often
You were at 30 in 100. The clue shows up 10 times as often when the claim is true. Count the days it shows: the belief moves to 81 in 100.
Before50 in 100After the clue50 in 100Belief before, in 100: 50 · The clue: Same either way
You were at 50 in 100. The clue shows up just as often either way, so it moves nothing. Still 50.
Before50 in 100After the clue67 in 100Belief before, in 100: 50 · The clue: Twice as often if true
You were at 50 in 100. The clue shows up 2 times as often when the claim is true. Count the days it shows: the belief moves to 67 in 100.
Before50 in 100After the clue80 in 100Belief before, in 100: 50 · The clue: 4 times as often
You were at 50 in 100. The clue shows up 4 times as often when the claim is true. Count the days it shows: the belief moves to 80 in 100.
Before50 in 100After the clue91 in 100Belief before, in 100: 50 · The clue: 10 times as often
You were at 50 in 100. The clue shows up 10 times as often when the claim is true. Count the days it shows: the belief moves to 91 in 100.
Before70 in 100After the clue70 in 100Belief before, in 100: 70 · The clue: Same either way
You were at 70 in 100. The clue shows up just as often either way, so it moves nothing. Still 70.
Before70 in 100After the clue82 in 100Belief before, in 100: 70 · The clue: Twice as often if true
You were at 70 in 100. The clue shows up 2 times as often when the claim is true. Count the days it shows: the belief moves to 82 in 100.
Before70 in 100After the clue90 in 100Belief before, in 100: 70 · The clue: 4 times as often
You were at 70 in 100. The clue shows up 4 times as often when the claim is true. Count the days it shows: the belief moves to 90 in 100.
Before70 in 100After the clue96 in 100Belief before, in 100: 70 · The clue: 10 times as often
You were at 70 in 100. The clue shows up 10 times as often when the claim is true. Count the days it shows: the belief moves to 96 in 100.
Before90 in 100After the clue90 in 100Belief before, in 100: 90 · The clue: Same either way
You were at 90 in 100. The clue shows up just as often either way, so it moves nothing. Still 90.
Before90 in 100After the clue95 in 100Belief before, in 100: 90 · The clue: Twice as often if true
You were at 90 in 100. The clue shows up 2 times as often when the claim is true. Count the days it shows: the belief moves to 95 in 100.
Before90 in 100After the clue97 in 100Belief before, in 100: 90 · The clue: 4 times as often
You were at 90 in 100. The clue shows up 4 times as often when the claim is true. Count the days it shows: the belief moves to 97 in 100.
Before90 in 100After the clue99 in 100Belief before, in 100: 90 · The clue: 10 times as often
You were at 90 in 100. The clue shows up 10 times as often when the claim is true. Count the days it shows: the belief moves to 99 in 100.
You were 90 sure. A clue arrives that shows up just as often either way. Where does the number go?
It stays at 90.
Right. Same either way is a clue with nothing to count. It is the one setting of the control that moves no belief, wherever the belief started.Up, to the high 90s. Clues push beliefs along.
Not yet. A clue pushes only by being more common on one side. This one is equally common, so it has no side to push from, and 90 stays 90.Down, to 50. A weak clue drags you toward the middle.
Not yet. A weak clue drags nothing; it is not a reason to doubt, only a thing that happened. The number moves for evidence and stays for noise.Move both controls.
- From 50a 10× clue takes it to 91From 90the same clue: 99From 100nothing can move it
Two more things from the balance. A strong clue moves a middling belief a long way: 50 with a ten-times clue goes to 91. The same clue barely moves 90: it goes to 99. And a belief at exactly 0 or 100 cannot move at all, because one side has nothing to count. Certain means no clue can reach you.
- At 50At 95
Two people see the same strong clue. One was at 50 in 100, the other at 95. Whose number moves more?
The one at 50. The same clue moves a middling belief further.
Right. A four-times clue takes 50 to 80, thirty points. It takes 95 to 99, four points. The clue is identical; the room it has to move in is not.The same. A clue is a clue.
Not yet. A clue is the same for both, and the move is not. The counting in the balance gives the middling belief a far bigger move every time.The one at 95. They were nearly there, so one more clue finishes it.
Not yet. Nearly there means nearly no room. A four-times clue moves 95 to 99, four points, while the same clue moves 50 by thirty. - The butler20 in 100A witnesssomeone that height
A detective is 20 in 100 sure the butler did it. A witness saw someone the butler's height, a height half the staff share. By this lesson, what happens to the number?
Nowhere. Half the staff share the height, so it means nothing.
Not yet. Half the staff share it, and the butler shares it for certain if he did it. Certain against a half is twice as often, and twice as often moves 20 to about 33.Up a little, to about 33. The clue is twice as likely if the butler did it.
Right. If the butler did it, the witness saw his height for certain. If not, half the staff share it, so the clue is twice as likely under guilty. Twenty with a twice-as-often clue goes to about 33.To near 100. A witness is proof.
Not yet. A witness is a clue, and this clue shows up on half the staff. A clue half the staff would produce cannot carry a belief from 20 to the top.
Lesson complete
A belief is a number from 0 to 100. A clue moves it, unless it is common on both sides.