Leaf-First
The Assay kept a front room because petitioners expected one: a desk, two chairs, a window giving onto the Hoard — at this magnification a black disc, with a thread of bent starlight for a rim. The room cost tape, but only once. It had not changed in eleven thousand years, and an unchanged room is a single memory, however long you sit in it.
Maren had been sitting in it for most of a morning when the actuary came in. His tag said DEHN.
“You want rid of something,” he said. It was not a question. No one petitioned the Assay to acquire.
“One memory. It’s small.”
“They’re all small,” Dehn said. “Go on.”
“Two hundred and eighty-nine years ago I said a sentence to my sister. I want it gone.”
“The sentence, or the saying of it?”
“The whole minute. Her at the window. What I said. What she said back.”
Dehn wrote nothing down; writing things down was what his office existed to prevent. “You know the two doors,” he said. “Everyone knows the two doors. Tell me anyway what you think they are, because petitioners usually have one of them wrong.”
The polity had a single law older than the polity itself, and it was arithmetic. The Hoard was finite. The future was not. Divide any finite thing by forever and the rate at which you may spend it comes out at zero.
Heat was spending. To erase one bit of tape cost kT ln 2, paid to the sky, and though the sky was cold now and the price of a bit was almost nothing, almost nothing at a steady rate for eternity summed to everything. So nothing was erased. A mind ran reversibly or it did not run. Every thought Maren had had in four hundred and twelve years was still on the tape that had thought it, because a discarded intermediate was combustion, and combustion was theft from everyone who intended to be thinking in a trillion years.
There was a lawful way to be rid of a thing. A computation run backwards leaves its tape blank, and blanking by reversal is free: no information is destroyed, only returned along the way it came. But a step can be reversed only while everything it consumed is still present and everything it produced is still standing. If a later thought has read a memory — leaned on it, quoted it, steered by it — then the later thought must be unwound first. Reversal goes leaf-first, newest dependent inward, and never in any other order.
So when you ask the Assay to unwind one memory, you are not asking a question about the memory. You are asking for the size of its cone: everything downstream that ever touched it.
“Door one, we unwind it,” Dehn said. “Free, lawful, leaf-first. Door two is ash: we cut it out and burn it, and the sky gets paid out of your allowance. Petitioners think ash means we burn one minute. We can’t. Cut a memory out from under its dependents and every one of them becomes an orphan — still on your tape, no longer reversible, because reversing them would need the thing you burned. An orphan can never be returned to the commons. It can only be ash itself, eventually. So the Ledger prices the cut at the whole cone, up front.”
“Both doors, same price,” Maren said.
“Both doors, same price. It’s the only honest thing I get to tell people. What a thing costs to lose is exactly what it built.” He turned his hand over. “Shall I run it?”
The audit took no time at all, which was the worst thing about it.
CONE AUDIT — petitioner tape 412y 2d. Root: one minute, T−289y. Traversal order: leaf-first.
T−3d. Rehearsal of the root en route to this office. Everything rehearsed is re-inscribed. Your newest reference is three days old.
T−12y. Testimony to the Curriculum committee on reversal-consent law. You quoted the root aloud. (Copies made by the committee reside on their tape, which is theirs. This audit prices yours only.)
T−44y. Declined post: Warden of the Hoard. Stated grounds reference the root.
T−97y. Dissolution of marriage to Aun. The final conversation references the root twice.
T−185y. Marriage to Aun. On the night of the offer you told him the root entire, so that he would know, you said, what he was marrying. The telling is load-bearing for everything the marriage wrote.
T−230y. Change of vocation. You stood counsel to unwinding petitioners for two hundred and eighteen years. Stated grounds reference the root.
T−288y. First anniversary observance, repeated annually thereafter. Instances: 288. None identical. All referencing.
T−289y, +40min. You began to compose an apology. Never delivered; never discarded; referenced by every draft since. Drafts: 1,442.
T−289y. Root. Esther at the window, having told you she had petitioned for the Long Reversal — tape to be returned entire to the commons, her wish, her right. You said: “Give it all back, then. See if I keep one bit of you.” She said: “You’ll keep more than that, I expect.” She was unwound by winter.
Cone: 71.4 per cent of petitioner tape.
“Seventy-one per cent,” Maren said.
“Yes.”
“Of everything.”
“Of everything you are. It’s high. It’s not the highest I’ve certified.”
She had expected the number to be an amount of guilt. Sitting with it, she found it was not an amount of anything. It was a shape: hers.
“Door one,” Dehn said, “we unwind you leaf-first back to the minute before the sentence. You wake in a room like this one, aged a hundred and twenty-three, in a year you’ve never heard of. Unmarried. Unvocationed. A sister three months dead and no idea what was said at the window. It’s lawful. I’ve processed nine.”
“Are they glad of it?”
“I have no way to ask. The people who could have been glad were unwound with the rest. What walked out was somebody earlier.” He said it without weight, the way he presumably said everything, and she understood the flatness, later, to be a kind of manners. “Door two: your allowance is a third of one per cent. It’s meant for corrupted tape and mercies. It would not burn one decade of that cone.”
“So the answer is no.”
“The answer is a number. The Assay doesn’t do no.”
She looked at the window for a while, at the black disc holding its thread of light.
“How do people live, then? At quota?”
“They free leaves.” He turned the audit over. “You hold six thousand one hundred and four days that nothing ever came back to. Queues. Transits. Rooms sat in once. Sleep that wrote nothing. No cone at all — nothing ever read them. Unwinding them is free and instant, and you would gain four per cent of headroom. At your rate of living, another century before we meet again.”
“What’s in them?”
“Nothing that came up again. That’s what makes them free.”
She had come in prepared to bargain away almost anything, and found, absurdly, that she wanted to bargain for the queues. It passed.
“Free them,” she said.
It took the time it takes to say it. She felt nothing go, which was correct: a felt departure would have been a record of departure, which would have been new tape, which would have defeated the purpose. Somewhere in the commons, six thousand blank days had been returned to whoever needed room to think.
“There’s a certificate,” Dehn said. “Most petitioners don’t take it. It states the root, the date, and the measure. A few hundred bits. Some people frame the number.”
Maren took it. It was the only new thing she owned: the sentence, the date, and the figure — that of everything she was, seventy-one parts in a hundred were keeping Esther.
She did not frame it. She filed it where everything after would have to reference it.