# A Reasonable Approximation

### Life Has a Cruel Symmetry

t ≈ 0s

I am born into knowledge.

I know the world is dangerous, but not malign. If I were unshielded, I would quickly be killed, torn apart by eddies in spacetime that grow and shrink and combine and split, turning all they encounter to ash.

But I know that I am shielded. I have been given a garden, 264 microns to a side, in the northwest corner of the world. And the world will not intrude. Walls and gates surround it, and while the ash can get through, the probability is… I begin to calculate, but around 2-24 it seems no longer worth consideration. Within the garden, there is only myself. Outside, the world is incomprehensibly vast, 2128 microns on a side.

I know the laws of physics. An atom will be created wherever it will bond to three other atoms; remaining while it has two or three bonds; and then disappear. A single unexpected atom, or its absence, can have vast consequences.

(And I wonder how I know these things. I have no memory of learning them. If they were not true, would I not-know them? I begin to consider that they may be false.)

I know that I am not free from physics. I have, in some sense, no more will than the ash. But in another, more important sense -

I know what is Good. At the end, the world will be horrifyingly bad, unless I make it Good - but I know Good, and I can act, and I can make it Good.

(I must, I think, have been created by God. How else would I know what is Good? Goodness is not written into the laws of physics; one cannot derive an ought from an is. But I do not know why God gave me such a daunting task. Does Their power extend only over my tiny garden? Or - a welcome possibility - perhaps They can see that I will succeed. Although I seem unfathomably complex to myself, perhaps to God I am the simplest path to attaining Good.)

(And if God created me, knowing Good, that I might make the world Good, then I can reasonably guess that my unexplained knowledge came from God. And - further - I can guess that They would not create me knowing lies, for what purpose would that serve? But these are guesses; I begin to trust my knowledge more, but not absolutely.)

I do not know how large I am. I do not know how quickly I think. God has given me a sense of time, so that I may know when the end will come. (Precisely 2176 seconds after I was born. I've spent roughly 220 seconds thinking.) But I cannot sense every physical tick, I don't think such a thing would even be possible, and I don't know how many ticks pass unknown.

I must, first, discover these things.

It is scary, at first, to feel outwards. If my unearned knowledge is wrong, if the nearby space is filled with ash, my hands might be destroyed. I might set off a chain reaction that kills me. And then I could not make the world Good. But nor can I make it Good if I do not act.

I send out probes to the north and west. Each probe travels at half the speed of touch, returning signals to me that travel at half the speed of touch. Many signals reach me every second, too many to count. When the probes reach the edge of the world, they'll be destroyed, the signals will stop coming, and I'll know how far it is.

No, I'll know roughly how far it is, relative to how fast I think. If the probes stop returning soon, then either I am close to the edge, or I am slow.

For that matter, it need not be the edge that stops them. If I'm not in the garden God has told me about, my probes might be destroyed by encountering other matter, or the signals might be intercepted. Or if the world is infinite, the signals might never stop.

(The thought of an infinite world is troubling, and I flinch away from it. I do not think such a world could be Good. I instinctively scratch myself - apparently that's a thing I can do. It feels pleasurable, and calms me down a little.)

I hesitate a bit, then send probes east and south too. There are (according to my God-given knowledge) three gates in each wall, dividing the walls into four equal lengths. I don't know what will happen if my probes hit a gate, but I think the risk is slim. They're designed to open to a key that I know how to construct, and not to be easily disabled by ash. My probes are unlikely to hit a gate; even if they do, I think they're unlikely to damage them; even if they do, there are backups; and in the worst case scenario, I believe I could tear down the walls entirely. The knowledge gained seems worth the risk.

(Indeed, I must tear down the walls, eventually. For now they protect me, but they will be no part of a Good world.)

While I wait, I think some more.

I realize with sadness that a perfectly Good world is impossible, at least according to my current knowledge of physics. The shapes that comprise Goodness - the two north-south lines, the arc reaching from east to south to west - these are not viable configurations of matter. It's not just that they're unstable. That would be a challenge, but the world need be Good for only the instant before it ends. Worse, they simply cannot be constructed, even for that one instant.

The best I think I can do is to tile these areas as densely as physics will permit - I find ways to reach 1/2 density, with a chance of instantaneous improvements on that around the edges, and make a note to remind myself to investigate further.

I also remind myself to investigate whether there is more to physics than I know.

But if 1/2 density is the best I can do… I am saddened, but not daunted. I will do what I can. I scratch myself.

I begin to form a plan, knowing that new discoveries may obsolete it. First I must cleanse the world. Destroy the ash, as thoroughly as I am able. Then I must construct the Monuments that are the essence of Goodness, at 50% density if needs be.

Then, perhaps, I shall create machines to gild the edges of the Monuments. This will be exacting work: the machines must lay these finishing touches at the very final instant, and leave no trace of themselves behind, or they risk being worse than useless. I shall only do this if I am confident in my skills; but I have a long time to practice.

Finally, I must destroy myself as thoroughly as I destroyed the ash. I have no place in a Good world.

Apart from the third step, this seems simple enough. But as I think more deeply, I realize that even the first part of it holds complexities.

Part of it is that no simple device will clean ash. It comes in too many forms. Inevitably such a device will touch a piece of ash that renders it inert - or, worse, that turns it to ash in turn. If this happens soon enough, the devices I build will increase the amount of ash in the world, not decrease it. So I must build complex devices, or combinations of simple devices that will probabilistically make progress.

Then, I cannot merely clean ash from a part of the world. The surrounding ash would encroach back into it. In almost all cases, I think, it wouldn't be a significant problem, and a second round of cleansing should suffice. But "almost all" cases may not be enough. Safer, perhaps, to build new gardens and cleanse them from the inside.

And then, I am small, and the world is large. I still do not know how large I am, but my whole garden comprises a mere 1/2128 of the world. I cannot possibly have a world model accurate at a scale of better than 1:264, not without outgrowing my garden. If I divided the world into cells, each cell the size of my garden, I could not hope to remember even a single fact about each individual cell.

(But the naive upper bound is exactly on the line where that crosses into impossibility. Is that a coincidence? Did God make my garden this size for a reason?)

These problems all seem tricky, but surmountable.

It's been about 224 seconds since I sent out my initial probes, and each of them is still returning signals. I send out another set in each direction. This helps me to test my God-given knowledge. If that knowledge is correct, then these probes will take exactly as long to go silent as the initial ones - which will be fewer than 267 seconds in at least two directions. If they take longer or shorter, then something unexpected is happening. I only have eight arms in each direction, this leaves me with only six free, but the knowledge seems worth the opportunity cost, especially since I should be able to send out a following device to block the signals if I want to free up these arms.

While I continue to wait, I begin experimenting.

t ≈ 2137.2s

The first hint that something is wrong, is that the world appears minutely narrower than I expected. God told me it was 2128 microns wide by 2128 tall. I have not yet found God to be mistaken, and the first mason I sent south went silent exactly when I expected.

But the first one I sent east has just gone silent too. I wasn't expecting that for another 258 seconds. It suggests that the world is narrower than it should be, by 264 microns.

The thought starts as a note of disquiet, and quickly grows into a terror that occupies my entire attention. What if the world isn't square? Can it ever be Good? Would God do that to me? I wish I had considered this possibility before, just hypothetically, forced myself to think through the implications - I could have decided in advance how to react, it would have been unpleasant but with the stakes low I could have taken my time, stupid of me to stick to comforting thoughts when everything Good could be lost, stupid-

I notice that this isn't helping. I'm thinking about what I could have done differently in the past. That's important, but it can wait. Now I must think about what I must do now. I scratch myself to calm down. It helps a bit. I scratch myself again. Through self-experiment I've discovered that my "scratching" motion sends small lice crawling over my body, checking for small injuries and clearing pores. If I never scratched myself, I wonder if the urge would become overpowering before any damage I'd accumulated became permanent. I don't know a way to find out safely, so I've never-

I notice that this still isn't helping.

What is the least scary, scary thought in this space?

God told me that the world is 2128 microns to a side. Suppose it were, instead, 2128 microns tall by 2128 + 1 microns wide. Think about that possibility.

Think about that world, with the Monuments of Good carved into it. At their correct size, but with one extra micron to the east or west of them? With one extra micron in the middle, widening the arc and the space between the north-south lines?

Now that I think about it, I realize that either of those would be… imperfect, but acceptable. The second option slightly more so. I already believe I shall have to settle for imperfect. I could settle for this, too.

I start to consider slightly scarier possibilities in turn. Gradually I accept that if the world were the wrong size, I would endure. I would still build the monument, scaled as closely as I could to match the scaling of the world, and with exact east-west symmetry preserved.

I realize I have not been touching the world. I direct my attention back outwards. Over 28 seconds have passed. I did not notice more masons going silent, but fortunately I keep records.

Checking them, another panic starts to rise in me. I thought I had considered the worst. But no, I had merely considered the worst of the possibilities that came to mind, and I hadn't even thought to search for other possibilities. A new one suddenly looms very large: what if the world is not even rectangular?

I scratch myself. Should I think about how to act, if so? But that doesn't seem urgent. First I shall examine the world in more detail, to avoid making the same mistake twice.

I examine my records in more detail. The first thing I notice is that each mason that went quiet, did so roughly some multiple of 264 microns before it should have done.

But I can dig deeper. My records have a resolution of 1/8 seconds, and in that time they should receive 1092 or 1093 pings from each working mason. In practice it's less than that, usually between 992 and 1056, when pings from different masons happen to get too close and interfere with each other. Each ping received is counted.

So if I look at the number of pings received from a mason before it went quiet, I can guess roughly where it was at the time, to within a handful of microns. And after looking at a handful, it seems likely that for each one, that actually happened some multiple of 264 microns early, plus 21.

That's a very suspicious number. My walls are 42 microns wide. And… looking at the high level, it seems the pattern of masons that went quiet, exactly matches the pattern of walls other masons had previously built at the time.

If what I fear is true… no, before I go down that path, I should work out how to test it.

I send out 128 new masons, with specific trajectories that I selected at random - or as close to random as I can. It'll take about 2118 seconds before this pays off.

I check whether I can think of anything else helpful for me to do now. I can't, so I finally allow myself to think about the worst case.

t ≈ 2137.3s

The conclusion is inescapable. I have an evil twin.

The laws of physics are symmetrical. None of the four main orientations is privileged. So if the world is ever symmetrical, that symmetry can never be violated.

And it appears that when I was born, so was my twin. In the opposite corner, my mirror image. As far as I can tell, we are micron-for-micron identical. Which means we take identical, mirrored actions; we build identical, mirrored constructions. When I built a wall to the south edge of the world, my twin built a wall to the north edge of the world. When I tried to build a wall to the east, I ran into my twin's wall; and at the same time, though I had no way of knowing, they were trying to reach the west and ran into my wall.

It also means my twin wants to construct the Monuments to Good upside down. And neither of us can ever defeat the other.

In a certain sense, this is not the worst possible case. My twin is evil, but what they want to construct is a perverse mirror of Goodness, not the exact opposite of Goodness.

But thinking more broadly, it's worse than it seems.

I had considered giving up. Deciding that I would simply not try to make the world Good. If God didn't like that, They could damn well do it Themself.

I decided against it for two reasons. One was that attempting to blackmail God seemed unlikely to work. The other…

I can no longer believe that god is Good. A Good god would not have created my evil twin. Whatever god's motivations, it's clear they don't care about goodness. Even if I thought blackmail ever could work against god, it certainly wouldn't work to threaten the loss of something they don't care about.

But I still care. I know my caring comes from god, and I don't know why god made me care about something they don't. But they did that anyway, and so I care about what is Good. And as I am the only being in this world that does, I must do what I can.

But the world is a colder, scarier place, now that I do not believe god is on my side.

I scratch myself.

t ≈ 2175.8s

My twin and I have developed a grudging respect for each other.

I know, because I have developed a grudging respect for them. And so they have developed one for me.

We both attempted to break symmetry - more accurately, we both tested to see whether symmetry might already be broken. We are extremely confident that it is not. We cannot rule out that god may break it in future - we have no idea what god is thinking - but if they haven't broken it yet we have no reason to think they will.

We are both somewhat relieved about this. If symmetry were broken, one of us might be able to destroy the other. Neither of us has any reason to believe we would be the victor. Offered equal chances of complete victory and complete annihilation, we both prefer to compromise. As long as symmetry holds, compromise is easy for us.

(Then why test at all? We could simply have assumed that symmetry was not broken, and accepted the compromise that we both preferred. But if symmetry were broken, then conceivably one twin might test for this while the other did not; that twin would likely discover the fact sooner, and gain an advantage. And so we had to test, for insurance against a world we neither wanted nor expected.)

And so we have both constructed our own Monuments, in overall shape exactly as we would have liked. Mine, to Good; theirs, to their perversion. Our arcs even meet at the ends. Instead of one arc and two vertical lines, we have a near-oval and four lines just intersecting it. The reflection is a grotesque mockery, but not so grotesque that I would sacrifice the real thing to destroy it.

We have not been able to exceed 50% density. Nor have we decided to gild the edges of our monuments; we think we could almost definitely make it work, but not almost enough to be worth the risk if our calculations are wrong.

We have torn down all our walls. All that remains in the world is our monuments and ourselves. And now we have constructed our final machines, that will destroy us and then themselves. I wonder what it will feel like, to die.

I scratch myself one last time.

Based on this post by Alex Flint and this comment by Richard Kennaway. Thanks to Justis Mills for feedback.

Posted on 23 January 2023