I know we’re derailing, but I desperately want to go back in time and get a short story from Lacer’s POV. Growing up, Uni, Red Guard, etc. Maybe we will eventually get something like that.
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I know Professor Burberry said “Well, I suppose by your age Thaddeus Lacer was already at four or five thousand thaums.”. But I read this as hyperbole. Why would this professor know Lacers thaumic capacity when he was 20? Then again war is horrible, and we don’t know when Lacer was drafted. Maybe he really did have 4-5000 thaums by that time. It just seems unlikely to me.
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Given the current pace of Siobhan’s progress it’s not that far fetched if he started young too which he most definitely did.
And he was in a much better situation, Siobhan lost her teacher barely 2 years after she started, then spent 2 years (and iirc 6 months before Ennis found her) without being able to cast because of her nightmares, then she was always moving around with Ennis so that probably limited her too.
And now she almost tripled her capacity in ~9 months.
On another note, I bet training to apply glyphs with her Will, and particularly doing 2 at once is going to help tremendously when it comes to free casting.
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So, I redid the calcs based on the date in the new chap. Siobahn gained on average 11 thaums per week given (assuming we take out the days she wasnt really casting due to will strain).
Now, based off a comment in one of the chaps (See here), Siobahn’s actual capacity when she was originally tested at the beginning of the story was about 234 thaums (rather than the 203 thaums she was tested at). If we remove say 12 -14 or so days of practice (a pure guestimate on the upper limit of what to remove to get the base rate because of will strain and other factors), Siobahn gained around 9.5 thaums a week on average.
So currently, she is getting better, though not quite at the astonishing level I had initially thought. Of course, a lot of practice right now is not really growing her capacity, (Myrddins book is excellent training for her, but is just not the type of training that grows capacity as it does not need thaumic capacity, it instead trains other aspects). This will change later though as the topics of research change.
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It’s still a lot, while she gained 370 thaums Damien who wasn’t new to casting either and had a solid base only gained 210 in the same period of time.
And he really has it a lot easier than her and come from a big crown family, but despite that she progressed 75% faster than him.
I’ll try to analyse her progress more in depth when I have the time though, because it’s not linear and sorcerer gain thaums faster as they improve.
Oh Damien has been doing fantastic too. His rate of growth is quite excellent. He works very hard and like he isn’t just monofocused on casting. He has also done a ton of research into the red guard and aberrant incidents.
He is a pretty good comparison point too since they weren’t thaaaaat far apart initially. 234 vs 166 is a difference of just 68 thaums. Yet Siobahn has grown from 234 to 618 while Damien has grown from 166 to 370. The gap between them has grown larger at 218 thaums between the two
And yeah you are right that Sorcerers don’t just gain thaums at a constant rate. Their growth is not linear. Azalea said the growth is exponential (with a gentle slope) somewhere but ngl, I suspect she is wrong and the growth is actually quadratic because it fits her universe better. Exponential growth doesn’t actually fit it well because it’s constantly multiplying capacity when in fact it’s implied it’s because you gain thaums faster because time to do get an additional one decreases as you practice more which really imo fits a quadratic.
I have some math I’m working out on modeling growth for sorcerers. It fits pretty well with what we are given as possible, but I need to like fully write it out
So I keep a spreadsheet that helps me calculate where S (and some others) are at certain times in the story. I have a formula that works partially off of hours spent casting.
(It uses an exponent. Is it really exponential, or quadratic? I think it’s the former, but one of the reasons I couldn’t make Siobhan really amazing at math is because I’m not. I’ve gone through Calculus and all that but I don’t have the same instinct for math that those who are really good have, and I’ve forgotten most of the stuff that I don’t use in my daily life.)
However, there are also hidden mechanics at play that may skew your calculations in one way or the other. Things I keep track of that increase or decrease the Will growth.
That’s not to say you shouldn’t “investigate” these things. It’s just the kind of thing I’m likely to do when reading a fantasy story I love, and you might be able to pick up underlying Will-mechanics clues…
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FWIW, if the equation is something like 2^x then it’s exponential. If it’s x^2, then it’s polynomial instead. Quadratic means the exponent is 2 specifically, but something like x^1.25 is still polynomial.
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Yeah, the actual calculations are something thats gonna be biased heavily by circumstances. I chose to make it based on a weekly rate, with it increasing slightly over time in a predictable manner, because it seems like that fits the mathematics of what you wrote about will grows and it makes it feasible to calculate. For feasibilities sake, I generally assume the best unit of time is a term, which makes quick calculations for university students really easy to make. (I assume this model would perform worse for graduates)
The basics seem to be in the short term growth is linear (which is obv true of most functions including polynomial and exponential functions). And growth increases consistently as you handle stronger and more powerful magic as well as more novel magic. There is a rather gentle change in the increase in speed over time.
A big reason I chose to model Siobahns (and others) growths using this approach is it seems to fit the story well. Growth is based on the novelty and strength of magic used. Its implied the process is additive with increasing speed on adding new thaums, which fits something polynomial growth well, rather than exponential, which is all about multiplying the pool more and more over time.
Main reason I use weeks is its something I can standardize. I don’t know how much others practice, I don’t know how much Siobahn practices, but I can know that if the one mage gains 2 thaums in a week and Siobahn gains 11, she is growing faster according to graph. Siobahn practice more, uses more varied, and stronger magic than a mediocre low level mage.
Some things I’ve noticed based on my calculations. The apprentice threshold is just high enough that most of the classmates who had prior training should be able to easily make their apprentice certification level (250 thaums) after three terms considering the starting will, without having to practice on their vacations. However for those who just got in with no training, its a hard threshold to get to, especially for those with little talent initially and they will need to probably practice a ton during their vacations to make that threshold. Its possible, but its set high enough that for many commoners, they really need at least another semester for it to be “safe”.
Taylor,
Copied from the web site chapter 19…
“Two hundred three thaums,” Burberry announced.
…
???
Where do you see 234?
Right here I already posted the source. Check the comments of the linked chapter
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“…And just as a little tidbit, her real capacity in Chapter 19, Intro to Modern Magics, was 233.99 thaums.” (Azalea)
Ok… its an Azalea Comment, Below the chapter text…sorry i missed that.
Enough said , of course she is correct , no disputing that.
Using only the data points from the book we wouldn’t know that, only that Siobhan was slacking a bit on her first test… somewhere above 203 and below 250 (shattered conduit)
Great catch 
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In something interesting, we actually have a new way to estimate approximate thaumic growth for Siobahn.
It takes Damien roughly 5 hours to gain 1 thaum according to the most recent chapter. It takes Achmage Zard roughly 2.5-3 hours to gain one thaum.
Siobahn practices actively for about ten hours a day according to herself. She passively controls her shadow constantly, though one wonders how much this will affect her growth considering Will growth require novel and varied use. One can expect her to be very consistent with her practice especially now that she doesn’t have to sleep.
I also wonder how much her working with the journals affects her Thaumic Capacity. This takes up practice time as she can only use her will for so long. Its straining certainly but, does it strain her in a way that causes Thaumic growth or simply improves other faculties of her will.
Regardless one can estimate her potential will growth. Since she actively practices roughly 10 hours a day, she should roughly gain around 2 thaums each day. This is roughly 14 thaums in a given week.
Note, assuming Archmage Zard actively practices around 6 hours a day (a reasonable guess given he is an archmage) and takes 3 hours to gain one Thaum (as Damien believes), he gains roughly 2 thaums in a day.
So Siobahn is quite possibly gonna grow her Will in Archmage level amounts. Its quite possible her Will may grow Faster than Professor Lacer’s in the same time period.
Is this a reasonable estimate? Lets check.
Between January 9 and March 26 there were 76 days. She gained 97 thaums during that time period. This gives an estimate of Roughly 1.27 thaums gained per day. If she practiced on average 6 hours a day and gained a thaumic every 5 hours, she should gain roughly 1.2 thaums a day.
The estimate seems plausible, though an underestimate.
I chose this time period because iirc Siobahn was able to consistently practice without too many issues of things like conduit breaking, will strain, etc or things interrupting her practice.
Math aside - because I’ve stared at too many spreadsheets in the last day and automatically opened up Excel to rough out analysis - what’s everyone’s take on her constant use of the Shadow-familiar spell, does that count as practise?
Or is it the focussed, dedicated stretching of her will and limits?
And if she (eh, looking for a better term but failing) “Juices Up” the Shadow Familiar spell, constantly, on top of her actual Practise practise, apart from possible Will-strain, would this count as hardcore Will-grinding for her magical capacity?
Also, sorry if this was covered in another post - if so, let me know and will disappear it.
I thought it was one hundred and ninety six spoilers and had to check
Haha, chapter 196 spoilers