The Dropped Pebble

Glagalbagal's general-purpose information system was now serving four customers: his own livestock operation, Hjelvran the trader, Grothvik the healer, and Plomkva the architect. Records flowed in from locations across the region, carried by pterodactyls in small stone trays strapped to their legs. The system worked well — when the records arrived intact.

The Wrong Decision

The monthly report from Location 3 arrived on a windy afternoon in late Smujka. Qveshna had prepared the record carefully: a binary arrangement in a stone tray showing the herd count, animal types, health status, and feed levels. The pterodactyl assigned to the delivery was a reliable one named Grvetch, who had made the flight forty times without incident.

On this occasion, however, Grvetch hit a thermal updraft over the Brontj Ridge. The tray tilted. A single pebble — the one in position 14 of the count field — bounced out and fell into a ravine.

The record arrived at the cave missing one pebble. Position 14, which should have contained a pebble (representing a 1 in the binary count), was empty (representing a 0). The effect on the count was not subtle. The correct count was one hundred and sixty-three. With position 14 reading 0 instead of 1, the count read ninety-nine.

Glagalbagal, seeing a drop of sixty-four animals in one month, triggered the emergency protocol from Part 22. A response pterodactyl was dispatched. Additional feed was diverted from Location 1. Blortz began preparing an insurance claim. Qveshna, upon receiving the response pterodactyl, was bewildered — her herd was fine. The count was one hundred and sixty-three. Nothing had happened.

The investigation took three days. The insurance claim was retracted. The diverted feed had to be re-routed back to Location 1, arriving too late for that month's needs. The total cost of one dropped pebble was approximately forty trade-units in wasted logistics and two very angry location managers.

Qveshna (via pterodactyl): If you cannot trust the numbers you receive, why do you act on them?

Glagalbagal: Because until now, I had no way of knowing the numbers were wrong.

The Check Sum

The problem was that a corrupted record looked exactly like a valid record. A count of ninety-nine was a perfectly reasonable number. There was nothing about the arrangement itself that screamed "a pebble fell out." The receiver had no way to distinguish a legitimate record from a damaged one.

Glagalbagal needed a way for the receiver to verify that the record had arrived complete. Blortz, as usual, had the structural insight.

Blortz: When you send a basket of eight pebbles, you know it should contain eight. If it contains seven, one fell out. But that only works because you know the expected count in advance. For arbitrary records, you do not know what the count should be.

Glagalbagal: Unless the sender tells me.

Blortz: Then the sender would need to send the count alongside the record. But if the count itself gets corrupted in transit—

Glagalbagal: We need something simpler than sending the entire record twice.

The solution was a check sum — a small, separate arrangement that summarised the record. The sender would count the total number of pebbles (1s) in the entire record and encode that total in a few extra baskets appended to the end. The receiver would count the pebbles in the received record and compare the result to the check sum.

If the record contained, say, eleven pebbles across its thirty baskets, the sender would append a check sum reading "eleven" (1011 in binary — four extra baskets). The receiver would count the pebbles: if the total was eleven, the record was likely intact. If the total was ten, something had been lost.

Glagalbagal tested it on the corrupted Location 3 record. The original record had contained eleven pebbles. The check sum said eleven. The received record, missing one pebble, contained ten. Ten did not match eleven. The mismatch would have flagged the record as damaged before Glagalbagal acted on it.

The Limitation

Blortz: What if two pebbles fall out?

Glagalbagal: The count would be off by two. The check sum would catch it.

Blortz: What if one pebble falls out and another pebble shifts into a different position — slides from position 14 to position 15?

Glagalbagal paused. If a pebble moved rather than disappeared, the total count would remain the same. Eleven pebbles were still eleven pebbles. The check sum would match. But the record would be wrong — position 14 would read 0 and position 15 would read 1 when the reverse was intended.

The simple pebble-count check sum could detect lost pebbles but not rearranged ones. For the pterodactyl delivery system, lost pebbles were the primary risk — pebbles did not usually rearrange themselves in the tray. But it was not a perfect check.

Blortz: No check catches everything.

Glagalbagal: But it catches the most common error. And the cost is four extra baskets per record. That seems reasonable.

Blortz: Reasonable is not the same as sufficient. It is merely better than nothing, which is what we had before.

The Redundant Encoding

For critical records — tax filings, insurance claims, reports to the chieftain — Glagalbagal wanted stronger protection. Not just detection but correction: the ability to reconstruct a missing pebble without asking the sender to re-transmit.

The idea came from an old practice among the location managers. When Mvantika sent important messages, she would sometimes send the same message via two different pterodactyls on two different routes. If one arrived damaged, the other served as backup. This worked but was expensive — it doubled the pterodactyl cost.

Glagalbagal devised a cheaper version. Instead of sending the entire record twice, he added redundancy within the record itself. For every group of four baskets, he added a fifth basket whose value was determined by the other four: if the number of pebbles in the group was odd, the fifth basket got a pebble; if even, it stayed empty. This was a parity bit — a single basket that encoded whether the group should have an odd or even number of pebbles.

If one pebble was lost from a group of four, the parity would be wrong, and the receiver would know which group was damaged. If the receiver also knew the check sum for the whole record, the damaged position could sometimes be reconstructed.

The system was not perfect — two errors in the same group would cancel each other's parity, going undetected. But it caught and corrected single errors at the cost of one extra basket per four. For critical records, this overhead was acceptable. For routine monthly counts, the simpler check sum sufficed.

Glagalbagal: We now send more pebbles than we used to, and some of those extra pebbles exist only to verify that the others arrived correctly.

Blortz: That is the cost of not trusting the channel. If pterodactyls were perfect, you would not need any of this. They are not perfect, so you do.