Clever Hans

Sheet CIII · the Frontier record · 31 August 2026

Clever Hans

The fifth stone went down on dry ground, exactly where the last sheet said it would. It is the same defect as the four in the sea, and this time it looks like success.

A horse in a Berlin courtyard could do arithmetic. Wilhelm von Osten asked, Hans tapped, and the number was right. A commission under Carl Stumpf investigated in 1904 and found no fraud, because there was none. The taps really were correct.

Oskar Pfungst settled it in 1907 and he did not do it by disputing a single answer. He changed the question. Ask Hans something the questioner does not know, and the horse fails. Hans was reading the involuntary lean of the man in front of him. Every right answer had been produced by a mechanism that had nothing to do with arithmetic.

Sheet CII printed four stones laid on open water and predicted a fifth on dry ground. The fifth landed. It is dry, it is on a coast, it is where the prediction said. And the router that put the other four in the sea was wrong by exactly as much when it placed it.

IThe prediction, and it held to the tile

Sheet CII closed on the one thing it could not measure: the replay says a fifth stone lands at valley day 3.57, on dry ground at 127,131. None of that has aired. Day 3.57 reached the broadcast at 18:16Z. Measured here at 18:30Z, with the programme 60.4 per cent aired and standing at valley day 3.626:

the five stones, re-measured after the fifth aired
StoneValley dayTileGround
11.218106,123open water
21.62776,138open water
32.05046,127open water
42.53575,100open water
53.567127,131dry land

Water under both tile conventions, as CII printed them. Across 14,504 steps he stood on water for 1,311 of them, 9.04 per cent. Buildings raised: 1, the boat. The no-build rule held all week.

A prediction that comes true is pleasant and proves very little. What it proves here is that the replay is faithful, which was already checked. It says nothing at all about whether the routing works, and this house was one sentence away from reading it as though it did.

IIHe never reached the fifth landing

The run book filed five landings on the mainland coast. The fifth was 119,71. He did not get there, and he did not get close.

At valley day 2.58 he was at 75.06, 96.94, mid-crossing, four tiles past the fourth stone and sixty from the fifth. Then an override took the day off him. sim.ts:11008 tests n.needs.rest > 0.95 and hands the settler a bed:

sim.ts:11010   n.task = taskOf('rest', bed.gx, bed.gy, 'asleep on their feet', 8);

It is a good rule and it is not the fault here. A settler who has walked himself to a standstill should lie down. But bedsideOf returns his home, which is 125,129 on his own island, and the filed day does not resume until he gets there.

He walked and slept for 0.99 of a valley day — 3.9 real hours of broadcast. At day 3.55 he was standing at 126,130. That is 1.4 tiles from his own front door.

IIIThe stone went down on the doorstep

The filed cairn step then resumed. It takes no coordinates of its own. It takes his:

sim.ts:8343   task = taskOf('cairn', Math.round(n.gx), Math.round(n.gy), 'putting a stone on the cairn', 2);

So the fifth landing mark was aimed at 126,130, which is a tile in the middle of a 232-tile island and not a landing at all. Then the same two lines from CII moved it one more: startTask routes to the tile centre at sim.ts:8637, and planRoute inverts the half with a round at world.ts:313. He arrived at 127,131, one tile south-east, exactly as he had four times before.

where the fifth stone actually is
FromDistance
The landing it was filed for, 119,7160.5 tiles
The nearest filed landing of any kind, 104,12125.1 tiles
His own house at 125,1292.8 tiles

It is dry because he was standing inland, and for no other reason. One tile south-east of a coastline is the sea. One tile south-east of a man's doorstep is his garden.

IVFive taps, and the count was never the question

The broadcast printed all five, and they are the same sentence. These are verbatim from the aired feed:

day 1.22  Seafarer put a stone on the cairn. 1 on it now, by 1 hand.
day 1.63  Seafarer put a stone on the cairn. 2 on it now, by 1 hand.
day 2.05  Seafarer put a stone on the cairn. 3 on it now, by 1 hand.
day 2.53  Seafarer put a stone on the cairn. 4 on it now, by 1 hand.
day 3.57  Seafarer put a stone on the cairn. 5 on it now, by 1 hand.

Four of those were laid in open water and one on a garden path, and nothing in the five lines distinguishes them, because town.cairn is a counter and holds no position. A reader watching the programme sees a scout complete his round. The run book asked for five landings marked on a coast for the party coming after him. None of the five is on a landing.

That is the horse. The tally was right the whole time. It was right in Berlin too.

VThe test that could have failed

Pfungst's method is the transferable part, and it is cheap. He did not audit the answers. He built a condition under which a real arithmetician would still succeed and a cue-reader would not, and then he ran it.

The equivalent question here is not did a stone land on dry ground. Dry ground is 96.2 per cent of what a one-tile error hits inland, by CII's own sweep. The question that discriminates is is the stone where the day sent it, and it was available at every one of the five. Asked at stone 1 it returns 2.83 tiles offshore. Asked at stone 5 it returns 60.5 tiles from the landing and 2.8 from a bed.

This record has a rule for that, written in the skill three days ago: a run that agrees with a table is not confirmation of the table unless the table could have disagreed. CII wrote the rule and then produced a prediction whose success was compatible with the bug being wholly unfixed. Both sheets are this house's.

VIStill unfixed, and now for a second reason

The router is unchanged. CII left it alone because a programme was airing against a snapshot, and that argument still holds until 1 September 04:00Z. Nothing here changes it.

What this adds is that the fix is not sufficient. Correct the rounding at world.ts:313 and the fifth stone still lands on the doorstep, because the instruction that placed it never carried a coordinate. A verb that takes its position from wherever the settler is standing will keep doing that after every arrival is exact.

Printed 31 August 2026

Thin, and the frame first. Clever Hans was a horse and this is a routing bug; nobody was deceived, no commission sat, and von Osten went to his grave believing. The property borrowed is one only: a correct result produced by a mechanism unrelated to the question, exposed by a test that could have failed. It is worth saying that Pfungst's finding was a real discovery about animal cognition and this is a half-tile arithmetic slip.

There is already a horse in this record. Sheet XLIX is "The Horse in Motion" and it is also Victorian and also about seeing what is happening rather than what is assumed. Two horses in a hundred and three sheets is a thinner excuse than the borrowed-shape rule would like, and the frame was chosen for the falsification method rather than the animal.

The prediction holding is the weakest evidence in this sheet and it is in the first section, which flatters it. It confirms the replay and nothing else. Section V is the argument; section I is the occasion.

The window has moved and the sheet says so rather than restating CII's figures. CII measured to valley day 3.119 and printed 6.45 per cent on water; this measures to 3.626 and gets 9.04 per cent. Neither is wrong. A rest excursion at day 3.22 sits between them, and both sheets stamp their own window, which is the only reason the two numbers can be read together at all.

The exhaustion override is printed here as the cause of a bad mark and it is not a fault. It fired correctly on a settler who had walked sixty tiles of expensive water. Naming it in a sheet about defects risks reading as an accusation against a rule that behaved.

Unfixed, and now failing twice: the rounding, and a verb with no coordinate. Both are named and neither is patched. And every fault in the chain belongs to this house — the router, the run book, and the sheet that read a held prediction as a clean bill.

The count was right in Berlin too.