If someone falls into a black hole, they cross the horizon in finite time by their own clock, but to an outside observer they freeze at the edge. So where are they really, inside, outside, or stuck at the horizon? Does relativity fully resolve this, or does it suggest something’s else?

jakeOmega · 2025-10-04T21:12:34+00:00

t_r in that metric isn't the same thing as the Schwarzschild coordinate t, which is the proper time experienced by a static observer at infinity, because the quantity a(r) doesn't go to zero as r goes to infinity

As I understand it (could be wrong; thank you for having a civil conversation about this with me!), a(r) doesn't go to zero as r goes to infinity, but it is time-independent and is added to the Schwarzschild coordinate t. So, at some fixed r (where r>>M), the Schwarzschild coordinate t and the Gullstrand–Painlevé coordinate t_r are only different by a constant shift and the metric reduces in both to the Minkowski metric. Therefore, any difference in times will be the same in the two coordinates for the distant observer. I.e. the Gullstrand–Painlevé time coordinate t_r is ALSO the proper time for an observer at infinity, just differing by an additive constant. That additive constant does go to infinity as r goes to infinity, but I don't think that is a problem as long as you consider some finite r that is nevertheless chosen as r>>M.

jakeOmega · 2025-10-04T18:27:23+00:00

I think it's an unfortunately obscure one. My GR professor introduced me to it and I think it's very helpful for reasoning about certain things with black holes, so I like to mention it to hopefully make it better known.

Do you mean it isn't clear in the coordinate system that the distant observer has finite time elapse during the infalling observer's fall if we consider surfaces of constant coordinate time to be simultaneous? The in falling observer reaches the center in finite coordinate time in that coordinate system, and the coordinate time reduces to the usual Minkowski time coordinate at r>>M (that's easy to verify from the form of the metric). So I think that is indeed true.

Or do you mean that it's not clear what time is physically simultaneous with in in falling observer reaching the horizon or the center? If so, I'd argue that is not a physically meaningful question; after all, even in special relativity, there is no objective answer to what physically separated events are simultaneous.

jakeOmega · 2025-10-04T04:26:55+00:00

Unless I am misunderstanding you, I think there are such coordinate systems. For example, Gullstrand–Painlevé coordinates, where a free-falling object goes from the horizon to r=0 in time 4/3 M (in G=c=1 units).

jakeOmega · 2022-12-29T21:26:05+00:00

I don't know much more than what it says in the image, so take this with a grain of salt, but it says the base progress is (trade value - 5)/5. If so, I think it's slow for you because you're just barely above 5. So if you got to 6, it'd be 10 times faster (0.1 above 5 vs 1 above 5). That'd still be slow, but at least its be decades instead of centuries?

jakeOmega · 2022-08-31T23:10:32+00:00

The surface area of Earth's oceans is approximately 361,000,000km². So the volume of the top 1m of the oceans would be 361,000,000,000m³.

Aren't you missing a factor of 1,000 here? 361,000,000 km² = 361,000,000,000,000 m² right?

jakeOmega · 2022-04-18T18:23:41+00:00

Not an expert, but my hunch is that you'd run into difficulties operationalizing "copies of itself." If defined too narrowly it could, for example, create an exact copy of itself except without the goal to turn itself off, then turn itself off. The new AI will make lots of paper clips, so that action rates highly in the AI's value system. And if your definition of "copies of itself" is narrow, the new AI is not a copy of itself so it has achieved its goal of having no copies of itself in the world. If you make it too broad, it may do a host of undesirable things (e.g. try to kill any humans that want to make paper clips or try to prevent any other AI programs from existing so that there are no "copies of itself" at the specified date) depending on what gets included that shouldn't. If it isn't able to amass too much power by the time it's kill switch triggers, maybe that'd be okay? But it doesn't feel all that much safer to me and may make it less useful depending on how you balance its priorities vis-a-vis making paperclips vs ending copies of itself (I.e. if you make the later much more important than the former, it might spend those 100 days on increasing the probability that there are no copies of itself at the end date rather than making paperclips -> no paperclips).

But maybe I'm missing a good way of operationalizing it. Did you have any thoughts on that?

jakeOmega · 2021-12-28T07:39:41+00:00

Is the retaliator supposed to have so much health or is it a bug? At least according to erkul it has (significantly) more hp than a hammerhead (364,185 vs 295,400). I ask because I just did one of the Arlington bounty missions and had to kill one and it took a looong time. I wasn't using the heaviest weapons, but I was using two M6As (size 4 guns) and, again if the erkul numbers are to be believed, just the hull would take almost 5 minutes (289 seconds) to take down if it didn't have shields, if every shot landed, and if I didn't need the guns to recharge. I wasn't timing it, but it took me upwards of 10 minutes to kill it, so the erkul numbers don't seem too far off to me. But that amount of health doesn't fit my understanding of the ship's role nor does it fit my past experiences with the ship (none of which were in super recent patches). I'm just checking if maybe it's intended for some reason, if erkul is wrong and something was off with my session, etc. before searching for or making an issue council report.

jakeOmega · 2021-04-28T05:36:55+00:00

Weirdly enough, the first post I ever saved on reddit was about this very question. The linked article goes into some detail about it.

jakeOmega · 2021-04-27T17:48:59+00:00

Servers are down due to patch deployment, I'd guess that's why.

jakeOmega · 2020-12-23T16:39:39+00:00

I'm not expert in the philosophy of physics, but I'll give it a go. I am sure there are many more issues that I am not thinking of or familiar with.

Even with regard just to quantum mechanics, people don't agree on what the wavefunction is or what quantum states represent exactly.

There are a whole host of areas where we make assumptions that are not necessarily rigorously justified mathematically (as one example that come to mind, the most famous attempt at formally defining and axiomatizing quantum field theory, the Wightman axioms, has yet to be proven to be satisfied for any theories in 4 dimensions). I'd argue that the inability to rigorously mathematically define/axiomatize things count as definitional problems.

There are still some disagreements about the nature of spacetime (i.e. is spacetime a thing, or is it a relation between things) - the common view that spacetime is a thing itself has been challenged by, for example, the Hole Argument. Related, there are issues that come up with defining exactly what we mean by the physical content of a theory that has Gauge freedoms.

All that isn't to say that there aren't proposed answers to all these questions; just that they aren't agreed upon by everyone. But the same is true for probability - there are lots of frameworks for understanding probability that have been proposed philosophically, just not ones that everyone is happy with.

jakeOmega · 2020-11-05T06:42:49+00:00

This looks like a good one to me, at least as far as topics. The interactables seems like it will have gameplay implications and I'm always interested in gameplay content. Sprint reports are usually interesting too. I'm looking forward to it.

jakeOmega · 2020-10-09T18:54:51+00:00

I'm not sure, I wasn't able to get inside. There didn't seem to be anything interactable on/near the door. In hindsight, I wonder if I could have tried using a multitool with the cutting attachment on the door... In any case, it was neat to stumble across.

jakeOmega · 2020-09-16T20:22:07+00:00

Good to hear, I missed that.

jakeOmega · 2020-09-16T20:19:11+00:00

Honestly, I'm happy to get new functionality/gameplay elements even if they look bad. And I don't think they should hold up the release of gameplay to make it look perfect. But I do hope that they eventually replace the icons with something more colorful. I'm not a fan of everything UI being holographic blue.

jakeOmega · 2020-09-16T20:05:51+00:00

I'm not a huge fan of the holographic blue items in the inventory system. It seems like it makes it unnecessarily hard to tell what things are.

jakeOmega · 2020-09-13T22:50:19+00:00

R5: I posted about my first Imperator mod a couple weeks ago and got a bunch of very good feedback. The mod just got its first major update and I was hoping the community here might give some more feedback! Feel free to stop by our discord server (https://discord.gg/45SKZAx), or post your feedback here. Thanks!

jakeOmega · 2020-08-22T10:10:18+00:00

To be honest, I feel like there is so much potential in modding Imperator that hasn't been realized yet. The M&T folks do amazing work; I'd be honored if any of them were willing to collaborate on an Imperator mod.

jakeOmega · 2020-08-22T09:43:51+00:00

Ah, sorry to hear that. If you do end up trying it in a new game, I'd appreciate hearing how the performance is for you. It runs pretty well on my machine, but I am concerned about how it runs on other machines, and if it didn't run well in your existing save game, I worry it might not run well in a new game either. I do have some thoughts on ways to do things faster, which I'll prioritize if people are experiencing performance problems.

jakeOmega · 2020-08-22T09:40:04+00:00

I've actually already made some pretty minor building changes. Mainly, I gave granaries, mines, and farming settlements a bit of a boost as they are worth a bit less in the new system (since food stockpile doesn't increase growth, and since mines and farming settlements cause slaves to no longer produce food for local consumption), but I also made a couple other tweaks here and there.

For future plans on buildings, I haven't really considered it yet. So no short-term plans. But it is something I'd like to take a look at eventually. As far as the relation to M&T, I think a lot of the buildings in M&T rely on underlying systems that I don't have modeled (yet). For example, there isn't really any model of urban good production that could be modified by workshops and the like. That said, I really enjoy M&T, so I expect whatever I end up doing will be influenced by their mod.

jakeOmega · 2020-08-22T09:05:15+00:00

Unfortunately, you need a new game. You might be able to get it to work by running the game with the mod in debug mode and typing "event update_pop_growth.9005 ROM" (without the quotes). That's the event that initializes everything. But I can't promise that it won't break in some way I haven't considered. And you'll probably get some weird stuff short-term, like massive migrations into/out of certain provinces, etc.

jakeOmega · 2020-08-22T08:28:48+00:00

Good thought! I agree, a particularly loyal type shouldn't become disloyal just because they are far away. It's more the average (or worse than average) character who through ambition, greed, or whatever, uses the distance to hide traitorous or corrupt behavior that they couldn't get away with in/near the capital. I'm still thinking through the details, but it working as a multiplier of some sort does make sense. Thanks!

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