Goldmage

[cbhacking]

Time to see if I can get a good feel for the costs of the various kinds of goldmage magic. I really should have done this a long time ago, but I remember trying and getting results I couldn't make sense of, then never working through that problem. So, trying again. Ok... Apparently, a fully-scheduled goldmage who never needs to do more than pause can live past 50 (Chapter 7 prologue). If they use almost no magic before ten and we assume normal lifespans of ~80 - probably optimistic given the tech level, but they do have whitemages - then that means 40 years of basically perfect work burns away 30 years of lifespan. We were also told for the cost ratio of coexistence to freezing (10x-20x).

We have another data point, though. Apparently a ten-year-old has the potential for ~36 hours of coexistence (Chapter 3, Meea's prodigal sister). For the purposes of this calculation, I'm assigning pessimistic values to the costs; we will assume that the one who had *not* jumped was killed, and that there had been no other magic used. That works out to about two years per hour, or two months for five minutes, or about a day every five seconds (all values in Earth units). Freezing is a tenth as much (for maximally pessimistic costs), actually going forward or back is somewhere in between (and probably not the same). Apparently kids can *maybe* manage as far as a week into the past, so call it a decade per day, which is five months per hour, which is five days for two minutes, which is an hour per second (roughly 1/5th the cost of coexistence, or twice the cost of freezing). All of this is of course very wishy-washy (though the numbers turn out quite nicely with only a little rounding, unless I screwed up my math).

Huh. That's actually a less-atrocious rate than I expected. Meea *probably* lost no more than a decade or two in that misadventure, and possibly much less (the time from when that servant gave the utterly unhelpful message to come with him to when they were in the room and the jumped self was killed is probably less than an hour?) Pretty sure she lost years, could have been decades, and she's spent some magic before (and some since; if she froze for 25 minutes when she was fleeing then she lost another month doing that). It's not unreasonable that she could live to 40 or so, though, if she avoids other magic *extremely* well now. Given the sort of adventure she finds herself on at this time, though, that seems highly unlikely.

Of course, then we come to the thing that was probably the reason I had trouble with the numbers in the first place: apparently jumping backward and going on *really* severely caps your lifespan. As in, "jumping backward is very expensive. Jumping selves who've gone on don't usually make it past thirty even if they do scarcely any pausing, even if the jump was only a minute" which introduces a huge discrepancy into the concept of how jump costs work, since that should have only cost a few minutes. Plausible explanations time!

1) Lifespan is non-linear. The rate at which you burn it decreases drastically as you age, so if you take two hypothetical goldmages who have never used their magic, and one is 70 (ten years left, if nature takes its course) while the other is ten (70 years left), the 70-year-old would have way less than one-seventh as much lifespan as the ten-year-old. There are variations on this, of course; does a six-year-old who has burned the vast majority of her lifespan through coexistence use up the rest at the typical six-year-old rate, or at the rate as if they were actually 76 now? In any case, if this is the actual explanation, the derived costs above can be disregarded and the computations will need to be made more complex. This could explain the bit where it's said (of costs) that "we don't even know for sure if they're the same for everyone".

2) Jump costs are non-linear. This seems like the most plausible explanation for the thing where jumping back two minutes and then going on caps your life expectancy at less than half but it's even *possible* to jump a few days back. For example, if the simple act of jumping back - regardless of duration - imposes a massive cost and then you pay the duration at a more sane rate. 20 years up front would work into the values that we have fairly well; they'd need to be damn careful about who they ever send back, but most goldmages who are under 30 could manage it if it wasn't far. This does a lot to explain why Meea was removed from the position of bodyguard; she can no longer be certain she has enough lifespan to jump back by a millisecond, even though she could go on pausing and such for probably years of normal duties.

3) Various other explanations, such as that "lifespan" is something that you use up as you live and die instantly if you run out of, but it's not correlated with actual life expectancy. That is, non-goldmages who live longer than normal and then die of heart attacks at 90 died because of physical causes, not because they'd used up their hypothetically-could-have-been-200-years lifespan. In that case it's really hard to tell whether there even is a typical amount of lifespan, much less what it is, with the data we have.

Anyhow, I invite speculation (and corrections, either to my math or to my assumptions).

[Alicorn]

oh god math help aaaaaaah

[cbhacking]

Hahahaha. Umm... sorry? I mean, I expect that you have some master version of all this information somewhere. I'm just trying to figure it out without outright asking for spoilers, because hey, puzzle!

[Alicorn]

I actually don't. I decided to write a goddamn time travel story without a clear idea of the math behind it and hope there was enough wiggle room. I've had to add epicycles since then to make it work. My betas have tried to help me and I'm sure there's some candidate explanation that makes mathematical sense of everything, but I don't have a notes file which contains it XD It helps that the characters don't have exhaustive knowledge.

[cbhacking]

Well like I said, the numbers work out pretty well just from a couple data points aside from the thing where jumping back and then going on is so severe, and that's easily accounted for in a few different possible ways. Of course, that then implies that even "never-make-a-mistake" goldmages must still pause a lot - 30 years lost to pausing is 150 hours if we're pessimistic, 300 hours if it's only one twentieth as bad as coexistence (assuming my coexistence numbers are sane). In retrospect, though, that's reasonable; that's around four hours paused per year on average. Depending on how many people need killing or whatever and how spread out they are, that's possibly only a handful of combats (less than 10-20?) per year.

OK, I'll stop math-ing at you. Unless you want me to go on, in which case let me know. I like figuring out stuff like this. Either way, I'm enjoying the heck out of Goldmage and hope you're able to keep working on it. I really can't wait to see where the plot (both in the story-sense and the conspiracy-sense) is going... I could speculate, but I'm just going to sit here and hope chapters fall into my lap instead. I really like when that happens. :-D

[tau]

I had the math of this worked out once in a way that makes sense, from back when we were beta-ing it. I forget what I worked out, though. I could spend some time re-working it out if someone wants me to? But it looks like other people are doing/have done already, so maybe not.

[DanielH]

Yay! More goldmage! Where we learn that things are worse than we thought but seem like they will soon improve at the end of the chapter! And we get to hear the fairy tale!

The fairytale works very well in the larger Goldmage setting and I like it as part of the larger book. I wouldn’t like it if I lived in the Goldmage universe and it were a real fairytale for me to read/have read to me there, but that’s a completely different issue.

Although there do seem to be some formatting problems with the end-of-chapter links. On Chapter 2, the “first” link is on its own line because you accidentally start their div twice, the “last” button still leads to chapter nine on at least four of the chapters, and you include “next” and “last” links at the bottom of the most recent chapter. I was dissappointed when those didn’t take me to a Chapter 11.

EDIT: I accidentally used present-tense for what I said about the end of the chapter.

[Alicorn]

Fixed chapter 2 and the "last". Not having next/last buttons on the most recent chapter would be one more thing for me to forget to fix with each update, sorry.

[DanielH]

I see the fix in Ch. 2. All ten of the last buttons take me to Chapter 9 still.

EDIT: That’s just my browser being stupid. I see that it should take me to the right chapter.

[Lambda]

I thought of a Best Idea: if you know in advance that you're going to need to jump back to a particular moment, then you should jump forward across that moment, thereby avoiding coexistence. This both spares you the coexistence cost, and avoids creating a can't-go-back-any-farther block.

You usually don't know that in advance, though, so it's possibly of somewhat limited application. It might make jump chains possible, though.

Obvious patch: you count as existing during jumped-forward-over gaps for purposes of coexistence.