Copy, merge, choose your clock

Leans on Big minds are slow minds, The cost of forgetting.

What does it mean that a mind is a file?

In the Vigil, a resident runs as a program: a large pattern of ones and zeros held in memory banks and updated by processors. This fictional premise allows residents to copy themselves, merge their experiences and choose their processing speed.

The first is copying. A pattern can be written into a second memory, and the copy runs. Both wake up with all your memories up to that moment, and both think they are you. It is the same fact that lets a mind cross the dark on a laser beam (Bits travel, atoms do not): bits can be copied, and the sender keeps theirs.

The second is merging. Two copies that have gone their own ways for a while hold mostly the same things and a few different ones. A resident can lay the two side by side, keep what each learned and let the rest go. The copies become one again, and the one remembers both afternoons. Nothing in physics forbids it, though how it would be done for a real mind is a guess frontier. It is closer to reconciling two versions of a document than to anything that happens to a body.

The third is choosing a clock. A program runs as fast as you give it energy. Ten times the pace costs ten times the power. So a resident decides how fast to live. Run quick and you get more thinking out of each year of the universe. Run slow and you save energy, and you stay in step with friends far across the swarm. Light needs about 13 minutes for a question to cross the computing zone, zone C, and its answer to come back. A fast thinker feels that wait as days, or years. The slow residents are not slow by accident. They are matching their pace to their friends'.

Guess first You run a thousand times faster than a person, and a friend on the far side of zone C answers you after the light delay. How long does the wait feel?

About 9 days. The round trip is 13 minutes of ordinary time, and at a thousand times the pace every one of those minutes is a thousand of yours. At a million times the pace it would feel like 25 years.

The calculations below estimate storage, power and subjective waiting time under stated assumptions. Whether a human brain can be captured as a program, how two minds could be merged, and whether a running copy preserves identity or consciousness remain unresolved. These claims carry the frontier marker, and the last fold discusses them. There is no accepted test for consciousness in such a program.

One mind copies into three that run at different clocks, each gathering its own new memories, then merges. Only what differs has to be reconciled.

How big is a mind, and what does it cost to run, copy and merge?

Start with size. This site takes a resident's whole state to be about 1 × 10¹⁷ bits, the size used on Bits travel, atoms do not illustrative, inside a range from 5 × 10¹⁵ to 1 × 10¹⁸ bits that comes from estimates of what it takes to describe a human brain frontier. The table prices each size. Erasing a state of N bits once costs at least

energy ≥ N × k T ln 2

(the floor from The cost of forgetting), and moving it over the 28-light-year link takes N divided by the link's rate.

State size	Floor to erase it once at 30 K	Full rewrites a second per watt, at the floor	Time to pour it into the beam
5 × 10¹⁵ bits	1.3 × 10⁻⁶ J	7.4 × 10⁵	0.45 s
1 × 10¹⁶ bits	2.9 × 10⁻⁶ J	3.5 × 10⁵	0.95 s
1 × 10¹⁷ bits	2.9 × 10⁻⁵ J	3.5 × 10⁴	9.5 s
1 × 10¹⁸ bits	2.9 × 10⁻⁴ J	3,500	95 s

At 300 K the floor is ten times higher. Either way, the price of a copy is tiny at every size: making blank room for a 1 × 10¹⁷-bit mind costs at least 2.9 × 10⁻⁵ joules. What costs is the light-time, and above all the running.

Running is about speed. By the 2008 estimate this page leans on, a brain-like program at the level called a spiking neural network needs about 1 × 10¹⁸ operations a second to keep human pace frontier. Take the upper end and say every one of those operations forgets a bit. The floor at 30 K is then 2.9 × 10⁻⁴ watts. The Vigil's logic is mostly reversible and forgets far less, so that is the most the floor could ask, not a fixed price. Real hardware sits far above it anyway. Charge a single gate switch per operation (a real operation takes many) at the cheap end of the chips of the 2020s, 1 × 10⁻¹⁶ joules, and the same pace costs 100 watts, 3 × 10⁵ times the floor. Speeding up multiplies the bill:

Pace, against a human	Floor power, one bit forgotten per operation	One zone-C round trip feels like
1 times	2.9 × 10⁻⁴ W	13 minutes
1,000 times	0.29 W	9 days
1 × 10⁶ times	287 W	25 years

Faster processing also increases the subjective delay of communication. A resident at a million times human pace still waits 13 minutes for a reply from a friend across the zone, equivalent to 25 subjective years. Over the Saturn link, a question and its answer need 56 years of ordinary time at any processing pace. Big minds are slow minds explains the light-speed constraint.

Merging is cheap because only the differences need work. In 1986 the psychologist Thomas Landauer (not the physicist of the floor) estimated that a person's long-term memory holds roughly 1 × 10⁹ bits of what has been learned. Spread that evenly over a 70-year life, which is this page's assumption and not his, and lasting new memories come in at about 0.45 bit a second. A copy that lives one subjective year therefore brings back about 1.4 × 10⁷ new bits, a fraction 1 × 10⁻¹⁰ of a 1 × 10¹⁷-bit mind. Throwing away all of it would cost at least 4.1 × 10⁻¹⁵ joules, and keeping all of it costs nothing at the floor. The copy's pace does not change this count, because the year is the copy's own.

Open everything

How do you get from a brain to a number of bits and operations per second?Counting parts, state per part and updates per second; the cost of a thought at the floor

Three ways to count

An estimate of what a brain-like program needs has three inputs, and every published number comes from choosing them:

How many parts the program has to track: neurons, connections, compartments inside neurons, molecules.
How much state each part carries, in bits.
How often each part updates, per second.

Memory is parts times state. Compute is parts times work per update times updates per second:

$M = N_{\text{parts}}\, b, \qquad C = N_{\text{parts}}\, w\, r$

Here $b$ is bits of state per part, $w$ is operations per update and $r$ is updates per second.

The levels

Sandberg and Bostrom's 2008 Whole Brain Emulation: A Roadmap organizes the choices as levels of detail. At level 3, populations of neurons are tracked as averages: 4 × 10¹⁴ bits and 1 × 10¹⁵ operations a second. At level 4, individual spiking neurons: 1 × 10¹¹ neurons and 1 × 10¹⁵ connections, 6 × 10¹⁶ bits of state and 1 × 10¹⁸ operations a second. At level 5, the electrical state of every compartment of every neuron: 8 × 10¹⁶ bits and 1 × 10²² operations a second. At level 6, the chemistry too: 8 × 10¹⁸ bits and 1 × 10²⁵ operations a second.

From level 4 to level 6 the memory grows about a hundredfold, from 6 × 10¹⁶ to 8 × 10¹⁸ bits. The compute grows by a factor of 1 × 10⁷, because there are far more things to track, each needs more work per update, and the updates come more often. The choice of level moves the compute far more than the storage. The Roadmap's guess at the level came from a workshop poll, and the answer was a range, levels 4 to 6, with two participants more optimistic and two thinking that detail at levels 8 or 9 might be needed. This site's range of 5 × 10¹⁵ to 1 × 10¹⁸ bits covers levels 4 and 5 and stops short of level 6.

A count from synaptic strengths

A second way to count looks at the information a synapse can hold. Bartol and colleagues (2015) found at least 26 distinguishable synaptic strengths in rat hippocampus, which they put at 4.7 bits per synapse. Across 1 × 10¹⁵ connections that is 5 × 10¹⁵ bits, the strengths alone, with no wiring diagram. That is above the first row of the table and near the low end of the range, so the lowest row assumes less than a full reading of every strength. It was measured in one region of a rat's brain, so extending it to every synapse of a human brain is an assumption frontier.

A third way counts what a person has learned. Thomas Landauer's 1986 estimates of the functional content of human long-term memory came out around 1 × 10⁹ bits. The mind size used on this site is 1 × 10⁸ times larger because it includes the structure and working state needed to run the mind, beyond the facts it remembers.

The cost of a thought at the floor

Run the program at a pace $s$ times human. Its work per second scales as $s$ . With $C_1$ operations a second at human pace, and, at the upper end, each operation erasing one bit at temperature $T$ :

$P(s) \ge s\, C_1\, k_B T \ln 2$

For $C_1$ = 1 × 10¹⁸ and $T$ = 30 K, that is 2.9 × 10⁻⁴ W at $s = 1$ . At level 6 the same pace needs 2,871 W, even at the floor. Reversible computing (Computing without forgetting) goes below this: Charles Bennett showed in 1973 that any computation can be done reversibly, by keeping a record of every step, copying out the answer and running backwards to clean up. The bound above is for a mind that forgets as it goes.

Why copying and merging are cheap

Writing a state into blank memory can be reversible: copy each bit with a gate that leaves the source untouched. What is expensive in principle is making blank memory, which means erasing, and that is the second column of the first table.

Merging is the same accounting in reverse. Two copies that share an ancestor hold the shared part twice. The second holding can be cancelled by computing it from the first, without erasing anything. The information that must go is whatever part of the differences the mind decides not to keep. That is at most the $D$ bits the fork learned, and the floor on discarding them is

$E_{\text{merge}} \ge D\, k_B T \ln 2$

The clock against the light

The light delay $\tau = 2d/c$ between two friends at distance $d$ is fixed in the world. A mind at pace $s$ feels $s\tau$ . For a mind spread over a region of size $L$ , the argument of Big minds are slow minds gives a step time of at least $L/c$ for anything that needs the whole mind to agree. A faster pace is therefore possible only for a smaller mind, or for a mind that asks less of itself at once.

Can a brain really be captured, and is the copy you?The roadmap, substrate independence, Parfit's cases, and the limits of this page

The roadmap, and what it did not try to settle

The 2008 Roadmap came out of a workshop the Future of Humanity Institute held in Oxford in 2007, on how a brain might be scanned, turned into a model and run. It gives the level table used above and a rough date for each level, assuming computing power per dollar keeps growing at its past rate. It set aside identity and ethics on purpose, and it calls its own figures order-of-magnitude estimates that are quite debatable. By 2026 complete wiring diagrams had been mapped for a worm's nervous system and a fly's brain, and for no mammal.

The Roadmap's survey gives widely different estimates of brain computation, converted to common units: 2 × 10¹⁶ operations a second from a count of neurons and connections (Kurzweil, 1999), and 1 × 10²⁸ from treating the states of microtubule proteins as bits (Tuszynski, 2006), a factor of 5 × 10¹¹ apart. On memory the same table runs from 5 × 10¹⁵ bits (Leitl, 1995) to 8 × 10¹⁹ for the microtubules. The estimates differ in which brain processes they treat as computationally necessary. The required level of detail remains unresolved frontier.

Substrate independence

The idea that a mind could run on something other than a brain rests on two claims that are easy to confuse. The physical one comes from David Deutsch's 1985 paper, which states the Church-Turing principle as a law of physics: every finitely realizable physical system can be perfectly simulated by a universal computing machine operating by finite means. If that holds, a brain's behavior can be simulated, on a quantum computer if need be. The philosophical claim is that the simulation would have a mind, or would be the person. Deutsch's principle says nothing about that, nor about whether it would be conscious, and no accepted test could settle either. Every number on this page is the same on any answer frontier.

The no-cloning theorem forbids copying an unknown quantum state, so a brain could not be copied if its function depended on quantum states that cannot be read out as classical bits. Such a dependence has neither been established nor ruled out. Bits travel, atoms do not has the details.

Which one is you?

Derek Parfit's Reasons and Persons (1984) is the standard source for the puzzle a resident meets every time they fork. In his cases a person is scanned and rebuilt, and in the branch-line version the original carries on too, so that two people each remember stepping into the machine. Parfit argued that "which one is really me?" can be an empty question even when every fact is known, and that what matters in survival is psychological continuity and connectedness, which branching can preserve in two places at once. Others hold that identity is a further fact, or that it follows the body or the unbroken running of one process. The disagreement is not about physics frontier.

A merge runs the puzzle backwards: when two minds with different recent memories become one, whose continuation is it? The Vigil's residents live with that question, and the physics gives them no way to answer it.

Still argued

What level of detail is enough? A factor of 1 × 10⁷ in compute rides on the answer.
Can a human brain be scanned at all? The Roadmap lists what would have to be built; in 2026 most of it is still missing.
Does a mind keep its size? A mind that learns for centuries may grow; this site's range is for a human-sized start.
Is a faster mind the same mind? Running a thousand times faster changes how much of the world each thought can wait for. Whether that changes what thinking is has not been tested frontier.