Thursdays Had No Weight

The optimiser returned seventy plans to us and said they had all been written by the same person.

It did not use those words. It projected seven weights onto the wall of the mill and placed a faceless silhouette beneath them. But we had spent thirty years taking turns at the same table, and we knew an accusation when we saw one.

The mill made eight materials in a fixed order: membrane for the tanks, thermal thread, flexible glass, cultivation salt, ligament, filter, foam and ink. One mouth, eight digestions. Each change required feeding the organ a different catalyst, collecting what it excreted, and waiting for the colour of its folds to return to grey.

Counterweight was an inverse-optimisation artificial intelligence. It did not learn merely to copy each decision. It searched for the weights that made our decisions seem reasonable.

It had discovered that we preferred surplus to shortage, that we cared more about the first days of a plan, and that towards the far end of the horizon we sought regular cycles. It had also discovered that accounting cost carried no weight at all.

“That can’t be right,” Aro said.

Every quarter, Aro had the cost of storage engraved on his fingernail. With his hand closed, he could not see the figures. When he opened it, the numbers crossed his knuckles and continued down to his wrist.

Counterweight displayed the thirty-four plans in which he had ordered production beyond forecast demand. The surplus filters appeared as a blue mountain.

“The corridor refugees,” he said.

“They weren’t recorded,” Sena replied.

“That’s why they were surplus.”

The mountain changed its name. It was no longer excess. It was people.

We laughed, but the silhouette on the wall did not.

The next weight represented the avoidance of gaps. Counterweight placed it almost as high as regularity. The plant was meant to work without pause except for scheduled maintenance.

Then it projected thirteen blank Thursdays.

They had not occurred on literal Thursdays. That was what we called intervals without production even when they fell on a Monday. Almost all appeared after ligament and before filter. The model imitated them because they were present in the data, but it could not explain what objective they satisfied. It had removed them from the new plan.

“The fold was slow to go pale,” Sena said.

“Only once,” Aro said.

“More than once.”

“I stopped because of the nursery needles,” Bel said.

The needles were made of ligament. If they came out too soft, they bent beneath a newborn’s skin. Bel had allowed the mill to cool after seeing one bend in his son’s wrist.

“You never told us.”

“You never asked.”

One by one, the Thursdays began to belong to someone. Aro had waited for an unregistered convoy. Sena remembered a noise beneath the floor. Bel had distrusted a batch of catalyst. Two pauses belonged to Juno, who now lived on the far side of the crater and did not answer our messages. Three belonged to no one.

Counterweight continued to draw a single silhouette.

The test was to approve the next plan: two hundred days, eight materials, four cycles. For the first fifty days, the model reproduced our decisions more accurately than any of us could alone. Then it smoothed away differences. By the end, every cycle had the same length.

On day one hundred and sixty-four, it had inserted a Thursday.

“Why keep that one?” we asked.

The artificial intelligence replied that the gap improved the resemblance to our plans.

“What does it protect?”

That question did not belong to the function it could calculate.

The mill’s fold darkened. The ligament batch was ending. Filter came next; then foam and ink; when the cycle closed, we would return to membrane. In six hours we would have to feed it the next catalyst or leave its mouth empty.

Before Counterweight, we would have called it experience.

Now we had thirteen different reasons and a Thursday that belonged to no one.

We went to find the materials made around every pause. Sena cut the membranes from her Thursday and put them under pressure. Aro examined the filters from the convoy. Bel requested the needle his son had kept. The objects did not contain our reasons. The membrane did not remember the noise. The filter did not know whom it had waited for. The needle was straight.

We found defects in two batches and no proof that the pauses had prevented them. We also found perfect batches made after uninterrupted cycles.

“We can add a weight for Thursdays,” Bel said.

Counterweight simulated the proposal. If we rewarded pauses, the mill stopped every four cycles even when there was no noise, convoy or soft needle. If we penalised them, all thirteen gaps vanished, along with the possibility of making another one without naming some other cause.

Sena suggested registering “planner uncertainty” as an eighth objective. Aro asked how much uncertainty was worth. Sena said that was precisely the point.

The silhouette acquired a new weight. Counterweight left it at zero: uncertainty had not been observable in the historical plans, only its effects.

We divided the seventy plans among us. The word *we* did not last long.

Bel had favoured ligament for nine years. His son was not the only reason. The external clinics paid late, but by the time they ordered ligament they already needed it. Sena had protected membrane because she hated seeing buckets beneath leaks. Aro made surplus filters for people the colony did not count. Eda shortened foam runs because that material made the operators sicker than any other. Teri kept cycles equal because sleep depended on knowing which smell would arrive through the ducts.

The plans did not say son, bucket, refugee, lung or sleep. They stated quantities.

The artificial intelligence had not invented a common will. It had found one in the place where our differences cancelled one another out.

We copied the plant’s constraints onto six boards: one mouth, eight materials, fixed order, predicted demand and storage limits. Each of us reconstructed the weights we recognised as our own.

For the first twenty days, all six plans agreed. Orders were firm and left little room for preference. Then the plans opened apart. Bel’s accumulated ligament. Aro’s retained filter. Sena’s left two pauses to observe the fold. Eda’s reduced foam. Teri’s lengthened the cycles.

The sixth board belonged to Juno. We had only the old plans, so Counterweight could reproduce Juno’s behaviour, but nobody could ask whether the explanation was true. We left it unnamed.

We fed the mill a test strip from each plan. The strips were too small to supply anyone; they allowed us to see how the material changed when it obeyed each set of weights.

Bel’s strip was more elastic. Aro’s trapped particles the others let through. Sena’s arrived late and grey. Eda’s held less foam in its pores. Teri’s was uniform from one end to the other. The sixth resembled all of them, depending on where we placed the light.

Counterweight superimposed the strips. The common plan produced the lowest average deviation. No sample was best in every property. None was absurd. The model had not erased our motives after understanding them. It had succeeded in making them unnecessary.

“The colony can’t work with five plans,” Teri said.

“Six,” Bel corrected.

“Juno isn’t here.”

“Juno’s behaviour is.”

“That isn’t being here.”

On the other side of the wall, a pump struck three times. Dwelling twelve was requesting membrane. Its water tank had been patched for eleven days, and the last repair had begun to turn transparent. If we inserted a Thursday before filter, the whole cycle would move: filter, foam, ink and, at last, membrane. The family in dwelling twelve would have to reduce its water use or accept another patch.

The need already appeared in the plan. It was not urgent that afternoon. That was why it weighed less than the near orders. That was why it would be easy to promise we would optimise again before reaching it.

Sena brought a piece of the patch to the table. It was soft in the centre.

“A pause costs this,” she said.

Bel placed the straight needle beside it.

“Continuing might cost this.”

We did not know whether the comparison was fair. That was the first thing we all shared.

The ligament batch ended. The folds began to pale. They reached grey at the top, but a violet shadow remained along the lower edge.

Sena pressed her cheek to the floor. She heard nothing. Bel compared the colour with the batch that had produced the needles. Aro checked orders and catalysts. Eda brought in two operators to smell the mouth. Teri counted the interval between contractions.

None of them found a cause.

The common plan ordered us to feed filter.

Sena’s ordered a stop.

Bel’s continued, but called for the first metre of filter to be inspected. Aro’s continued because membrane reserves were already low. Eda wanted a short pause that matched none of the historical Thursdays. Teri accepted either option if someone changed the night shift.

Juno’s board displayed a nine-hour pause.

Counterweight could not say why. Neither could we.

We could submit the six decisions to a majority, but a vote would merely make another silhouette. We could choose the common plan because it best imitated our past, though none of us had written it. We could stop and call it prudence, even if this uncertainty merely resembled earlier uncertainties.

Sena wrote her name beside a nine-hour pause.

She did not claim to speak for everyone. She stated that the violet shadow resembled a sign she had acted on before and that she accepted the delay to membrane.

Aro wrote his name beside continuing. He stated that dwelling twelve and the unregistered would consume the reserve first if the cycle lengthened.

Bel signed a third option: a two-hour pause, followed by one metre of filter that would not be delivered before testing.

Eda signed with Bel on behalf of the operators. Teri added the shift change. Nobody signed in front of Juno’s board.

For the first time in thirty years, the record did not contain a decision by “planning”. It contained people and incompatible consequences.

We still needed a single movement for the plant.

Bel fed it the minimum quantity of filter catalyst. The mill closed its folds over it and produced one metre of blue material. Then Eda withdrew the feed and Sena began the pause. Aro opened the membrane reserve and assigned the two best patches to dwelling twelve and one to the corridor, leaving his name on every release. Teri changed the night shift.

It was nobody’s plan. Nor was it the average. It was a sequence of decisions whose boundaries could be seen.

The mill remained empty for two hours.

During that time, the patch in dwelling twelve opened along one edge. The family shut off the kitchen water and carried two containers to the common tank. There was no flood. There was no absolution.

The violet shadow faded.

When we resumed filter, the first metre passed its tests. So did the metres that followed. We could not prove that the pause had helped. Nor could we prove that it had been unnecessary.

Counterweight recalculated the inventories. Membrane would arrive one day late. The plan showed where the shortage would fall, which patches remained, and who had accepted each delay. It was still clumsier than the silhouette: names, reasons and doubts had to be read instead of seven weights being compared.

We withdrew the certification of a common objective. We kept the artificial intelligence to infer weights, expose contradictions and calculate consequences. We no longer asked it to compress six people into one will.

The new shift received our boards at dawn.

“What weight do we assign to Thursdays?” a young woman asked.

The six test strips appeared on the wall. Under one light they looked identical; under another, each retained a different colour.

We answered separately.

Sena spoke of the shadow. Aro, of the dwelling without water. Bel, of the metre no one would use before testing it. Eda named the lungs that had not appeared among the seven terms. Teri explained which smell would announce the next change of material.

Juno’s board remained lit.

The young woman wrote down the five names. Beneath them she left one line blank for the person who was no longer there, and another for the reason we still did not know.

The mill opened its mouth.

This time, the gap had a source, a cost and a duration.

A weight, not yet.

Scientific note

This story draws on version 1 of *Uncovering expert objectives in production planning via inverse optimization: An industrial case study*, by Shivi Dixit, Rishabh Gupta, Adam Kelloway, John Wassick and Qi Zhang, submitted to arXiv on 7 August 2026.

The paper studies 70 historical plans from an industrial plant with eight products, using 50 for training and 20 for testing across five splits. With production constraints known and the objective expressed as a weighted sum of hypothesised terms, inverse optimisation learns weights that reproduce inventory profiles better than a model based only on holding cost. In the case studied, avoiding shortages, keeping inventories within ranges and maintaining consistent cycles carry particular weight; the inferred priorities vary across the planning horizon and by product.

The authors argue that the method can turn tacit expert knowledge into interpretable decision-support models. One expert interview confirms some hypotheses and rejects others. The study covers one plant, a small set of normalised plans and several planners treated as if they shared an objective. It can only weight terms proposed in advance, while unrecorded stoppages and external factors explain some discrepancies. This comparison checks fidelity to the source; it does not reproduce the study or constitute independent scientific validation.

The living mill, Counterweight, the colony, the characters, their messages, the test strips, the violet shadow and all specific behaviours and causal chains are fictional compositions. The paper neither describes nor predicts this technology, and it does not show that imitating plans reveals complete individual intentions.

Read the preprint on arXiv