Property of Aries Alba; if found, please return

Late Ignius:

I apologize for not having the actual date; I lost track along the way here. I've spent almost every silver I had on my bow, arrows, and clothes; so I had to come to Tarishitar on foot. However, it was well worth it– this bow has saved my life more than once. It's a good thing Mom taught me how to shoot early on.

Of course, before I left, I was taught how to use a Create Food spell, so I never went hungry. However, I've tried to spare my magic. I still don't have a lot of first hand experience, so I'm not sure what my limit is. I only used it in emergencies. Otherwise, I just hunted my food.

It's hard to believe I'm finally here; Tarishitar at last. I look forward to talking to the learned people here about magic, and about what I've discovered. I left the book behind– it was far too valuable to take with me on this trip. As such, I will catalog my uses of Calculus in this journal, as I come across them. I will, however, write down the most basic formula here, just in case I like, bonk my head or something and forget everything, or in case I die and all that's left of Calculus is this journal. EVERYTHING CAN BE DERIVED FROM THIS FORMULA! 

Late Ignius, Day One After Arrival at Tarishita

I got a cat today. I named her willow, she's a beautiful calico. Mostly black all over, but still is tinged with brown, white, and orange on some spots; she really is beautiful. She appears to like me, sticking around me for the most part. Every once in a while, she'll wander off- I hope she stays safe.

As it is at the moment, I don't have much money, especially not to pay rent. However, I have holed up in a nice cave just outside the city. The entrance is rather small– you have to crawl to get in– but it opens up after about five feet. I'm doing my best to make it feel like a home. All I have right now is a single torch and a rather flat rock upon which I can set my things, and write. I also have a blanket that staves off the cold of night.

I, in a dull-witted moment, also bought a tinder box, forgetting that I could breathe fire. I suppose it could come in useful, if I ever cannot use magic for some reason. What a nightmare that would be.

Tomorrow, I'm going to go into town and see if there are any odd jobs I can do for money; perhaps someone needs a hunter or something to that effect. We'll see. Here's a list of things I need to buy to make this place feel like home. I'll also need to buy some survival supplies– I am, after all, living in a cave.

1 Blanket– to hang over the cave entrance. This will keep the cold out during the night, as well as work as a makeshift door until I'm able to craft one.

1 Canteen– I need water, after all

1 Fishing Rod– There's a rather nice river not too far off. When I can't hunt, fishing will do. 

1 Lantern– This will make the house feel a little more roomy than a torch.

1 Mining Kit– I'm living in a cave, might as well try to get something out of it. Plus, I can use these to carve areas into my house; shelves, a bed, stuff like that.

1 Whetstone– I need to be able to make arrows for myself. There are trees outside with sturdy enough branches, but I need to be able to sharpen things, which means I'll also need…

2 Daggers– Not just for sharpening wood, I also need close range protection. I think I got lucky on the way here, not running into any bandits or something to that effect. I need to begin being more careful.

The Alchemist's Handbook– I've been carrying herbs for a while, but I've no idea what exactly they do. I know they'll help me in curing some things, healing others; but I need to figure out what exactly they do, and what I can do to even make their effects stronger.

Spell: Earth Weaver– This will greatly aid me in making my cave more like home.


That's all I can think of for now. As to the development of my house, here's what I think I'll need.

Bedshelf– this can be carved from a wall. It will probably take a while, but it'll be worth it to get off the ground– I'm pretty sure I ate a spider last night.

Bathtub– I think this might just be a luxury, so it's not a high priority, but if I could just mine a little divot into the ground, I could easily fill it with water. Put a firepit next to it, so I can boil water so I don't have to bathe in the freezing water.

Shelves– Just in general, I need storage room. For food, artifacts, my journal, whatever. If I'm going to be living here, this is a priority.


I think that's it. No calculus tonight– I'm much too tired.

End Journal Entry

The Rules for Derivatives:

Now, obviously, solving the difference quotient every time you come across something you want to take the derivative of is, quite frankly, absurd. Only the gods are immortal, I don't have that kind of time. Fortunately for those of us who have a limited lifespan, all derivatives follow a set of rules. Each one, I'll give an example or two of as well, just to show that the rules work.

RULE#1: Constant Function

If f(x) = C, where C is any number belonging to the real set of numbers (i.e., C is not a variable), then f'(x) = 0

Ex: f(x) = 5

lim h->0 of [5 - 5]/h = 0/h = 0

RULE#2: Linear Function

If f(x) = Cx, where C is any number belonging to the real set of numbers, then f'(x)  = C

Ex: f(x) = 3x

lim h->0 of [3(x+h) - (3x)]/h = lim h->0 of (3x + 3h - 3x)/h = 3h/h = 3


RULE#3: Power Rule

If f(x) = Cxⁿ then f'(x) = nCx^n-1

Ex: f(x) = 4x³ 

lim h->0 of [4(x+h)³ - 4x³]/h = lim h->0 of (4x³+12x²h+12xh²+4h³-4x³)/h = lim h->0 of 12x²+12xh+4h² = 12x²


Continued on Next Page

RULE#4: The Sum/Difference Rule

If f(x) = g(x) +/- h(x) then f'(x) = g'(x) +/- h'(x)

Ex: 5x + 2x² (according to the rules: 4x + 5)

lim h->0 of (5x + 5h + 2x² + 4xh + 2h² - 5x - 2x²)/h = lim h->0 of 5 + 4x + 2h = 4x + 5


RULE#5: Trigonometric Derivatives

If f(x) = sin(x) then f'(x) = cos(x)
If f(x) = cos(x) then f'(x) = -sin(x)
If f(x) = tan(x) then f'(x) = sec²(x)

(These are difficult to prove. If I find time later on, I will prove them.)

RULE#6: Product Rule

If f(x) = g(x)h(x) then f'(x) = g'(x)h(x) + g(x)h'(x)

Ex: x²sin(x)
According to the rules, f'(x) = 2xsin(x) + x²cos(x)

As mentioned before, these are difficult to prove– I will prove them when I have time.

Continued on Next Page

RULE#7: The Quotient Rule

If f(x) = g(x)/h(x) then f'(x) = [g'(x)h(x)-g(x)h'(x)]/h(x)²

Ex: [x²-2]/[x+1] According to the rules, this will be (x²+2x+2)/(x+1)²

lim h->0 {[(x²+2xh+h²-2)/(x+h+1)]+[(-x²+2)/(x+1)]}/h

lim h->0 (x²+2x+2)/(x+1)(x+h+1) = (x²+2x+2)/(x+1)²


RULE#8: The Chain Rule

If f(x) = h(g(x)) then f'(x) = h'(g(x)) * g'(x)

Ex: f(x) = sin(x²) (h(x) = sin(x) and g(x) = x². According to the rules, this means that f'(x) = 2xcos(x²)

Those are all the rules for derivatives; as I have mentioned, I will prove all of these when I've got time. Do note that the proofs require some extensive knowledge for limits, algebra, and trigonometry.

Some addendums to my shopping list:

Spell: Water Weaving– I was thinking about that whole bathtub thing, and it'd be a bit of a hassle to carry water to and from the closest water source. I can't say that water weaving would make that entirely possible in one trip, but we'll find out, won't we?

Endapano Longbow: This would certainly be an upgrade to my current bow, which, quite frankly, sucks. It's pretty expensive, though, so I'll be saving for a bit, I think.

I'd like to enchant my weapons at some point, so I think I should learn some spells to do that. I wonder if there are any elemental spells that can do something like that… We'll find out. I think, first, though, I will focus on just getting the Weaving spells for each element, and continue onward from there. Perhaps I can figure out some ways to utilize them alongside my normal weapons; we'll find out, once I get them. 

I definitely have an affinity for air and wind spells, but I really should get some earth melding to help with my house. Really, it is quite dank in here. Definitely the table I just kind of threw together needs some work. It's all crooked and out of shape, and only SORT of flat. I promise, though, with Willow (she's so cute, she brought me a dead mouse for a present) as my witness, that this will become a fully furnished house!

I just need to finish building it.

The nice thing is that it has a little cavern leading out the back. Though, I've heard some straaaange noises back there. I think it might be a full cave system. I've only explored it a tiny bit– I'm definitely not well prepared to face whatever horrors might be down there. 

I think, with my planned line of work, greater agility would be quite useful. I've never had it cast on me, but it goes to reason that increased agility increases your thought time, right? I'll have to find out at some point. It would definitely help me with my scientific work if that were the case.

I also, while browsing, found a spell called "Magic Arrow." It's not quite all it's cracked up to be– unfortunately, it doesn't create arrows for you to fire from a bow, you just shoot them straight out. Rather strange, in my opinion, but whatever. I still prefer the ol' bow for the launching of arrows– especially since it's much more predictable.

I had an idea for a neat little home defense system, though. I think, if I were to get some rope and a crossbow, I could rig up a little trap up; just hang the crossbow (I'll have to calculate the center of gravity so I can hang it correctly for aim). After that, I set up a little tripwire near the entrance, and if someone steps on it… Well, you get the idea. I think I'll have it aim for around the upper thigh. As far as I know, those wounds aren't often fatal, and it'll also avoid things like rabbits and the like (which are definitely allowed to explore my little cave home.)

Maybe I'll draw up a schematic or something.

Either way, I was able to find some mining tools for somewhat cheap today, so I've started on the bed shelf. It's currently just a tiny divot (which is weird– I worked all day!), but I think in about a week, it'll be a full-on bed-shelf. I should probably find something more comfortable than a simple blanket to sleep on, though. That'll wreak havoc on my back.

Seriously, what I really need is Earth Weaving. I mean, it might only move small amounts, but even that would really help– just shifting things around. No pickaxes necessary. It sounds wonderful. We'll see, though.

Another thing that's beginning to get tiresome is magically summoning my food every time I need to eat. It's really taking it out of me. I can handle it for now, but I've either got to get a steady job, or start a garden. A garden COULD work… I dunno, I'll look into it.

I also need a door. You know what's weird? NO ONE HERE SELLS DOORS! It's like, a staple of home building, but noooo, no doors. Super weird. I'll see if anyone knows more about it or something. 

Finally, I've been considering picking up violin again. I know, I know, it's been FOREVER and I probably don't even remember the basics, but it gets kinda lonely around here, and I feel like maybe some music would help fill the silence. Plus, I've read that music can help you concentrate on other tasks, like thinking through a mathematical problem or something.

That'll have to wait until I'm truly settled, though.

The jobs around here are kind of bad. Mowing lawns… Watching pets (though I'll admit the wraith-watching was sufficiently terrifying enough to not be boring)… I'm hoping tomorrow will yield a better haul in terms of jobs. I only earned a dozen silver today, which I then spent on the mining tools. Ah well. Here I go back to my bed making.

(I really need to get on that bath– it may be Ignius, but the mornings are very cold. I hate bathing in cold water.)

Late Ignius

Alright, last night, I finished the bed… Sort of. I'm not anywhere near skilled with the tools I bought, and the bed is quite… Lumpy… I tried sleeping on it, but it just wreaked havoc on my back. I'll chisel at it some more today, but I feel like the only way I'll be able to flatten it out completely is to learn how to Weave Earth. Alas.

I did put all the stone I got in a large pile in the corner. I think I'm going to begin to make things. Again, most of it is going to have to wait until I can Weave Earth, but I can start on it now. A few ideas of mine:

A Comfy Chair:
For this, I'll need to get a tailoring kit, a few blankets, and other such soft things. I can easily sew cushions (thankfully, Mom taught me how to sew a bit before I left), and I'll have a nice, soft stone chair! Sounds kind of oxymoronish… But still.

Stove:
This'll be a bit trickier. It'll require more chiseling, but if I stick a divot in the wall, then that can work as the main chamber for the stove. If I got a large slab, bored holes into the wall of the cave and the slab, then looped rope through them, that would function as a pretty good door to keep the heat in. Underneath the divot would be another hole, in which I could have a fire going. This would also have a door. Perhaps I could figure out how to bore holes to the outside to give it access to air.

Bath:
I've already begun work on the hole in the ground, but I was thinking, it'll be a bit difficult to lug water to and from whatever heat source I have, so why not just build something similar to the stove? Now, I'm a little more cautious about this one, as the stove won't have me… Sitting in it, as it is. I'll have to crunch some numbers, see if it'll be safe enough for me to sit in there with a fire blazing underneath me. I wonder what the specific heat capacity for stone is?

At any rate, even with just a bed, it's starting to feel like home again. Soon, though, I'm going to make some arrows– I'm going to need to find some trees and gather sap for glue (honestly, the things they don't sell in this town). Thankfully, I still have a few left over from home, so we're good for a few more days. More good news, I did get a whetstone, and I'll be able to at least make the arrow heads for the night.

Tomorrow, I'll head out and see if I can get a nice job, get enough to buy a book on Earth Weaving. We'll see!

End Journal Entry

(Non-Journal Entry)

Aries came home to her cave, her head buried in a book. After recovering from the hunt, she'd went and bought a whole book on a bunch of the elemental weaving spells; Naota had given her enough money to buy a large elemental book that contained all the weaving spells, including stuff like electricity and shadows. Of course, what she was most interested in was Earth Weaving, at least for the moment, so she was reading up on that.

"Okay, so to cast earth weaving, you have to access the part of your mind that… Hm… Well, that's fairly straightforward." She ignored the "tips and tricks" section that followed every spell chapter; it suggested ways that you could use the spells to do neato things. She was definitely looking forward to reading those later, but for now, Aries knew what she wanted.

She raised her right hand and did what the spellbook told her to do, accessing the pieces of her mind that were "earthy"– grounding, unmoving, essentially the things about her that were always there. After wiggling her fingers a bit, a few stones on the ground shook, but did nothing else. "Dumb." She hadn't expected to become an expert instantly, but still, she was expecting a little more than that.

Aries sighed, and sat down at her makeshift table, grabbing a pebble off the ground as she did so. "Alright, come on, you dumb rock, move!" It wiggled. "Okay, now go… Up…" The rock, though Aries wouldn't detect it, became slightly less heavy for a second before she released the spell. "Hum. Hum hum hum."

After a few hours of staring at the rock, she'd been able to get an inch off the table for a few seconds. Discouraged and upset, Aries went to bed early, flames brimming at the edge of her nostrils.

(Non-Journal Entry)

After rising the next day, Aries looked at the rock, but she felt too disgusted to try it again. Instead, she grabbed the book and looked at the wind part. It said to focus on the ethereal, the changing parts of you, along with your goals and ambitions, where you wanted to go, stuff like that. To her immense surprise, when she cast the spell, a pretty large gust of wind flew through the cave, knocking over a few things. "What."

Running to the stone, she went and did what she practiced the other night; the rock, still, just barely rose when she cast her spell. Aries glanced at the book, demanding it for answers with a stare. It delivered, in the form of the "Introduction to Elemental Magic."

"There are many different approaches to casting elemental magic; this book describes one of the most organic ways of doing so, using your own personality traits, ambitions, and the like to get the material for the spell. It is believed that this is how the ancients cast such magic. The organic nature of this type of spellcasting comes with a price and reward, though, which is that everyone has different affinities for different magics.

"What this means is that someone might be able to use flame magic very well, but struggle with water magic; this makes sense, as the two are opposite in both nature and spellcraft. Everyone has a natural element, and everyone has an element that they'll need to struggle to use."

Ugh, it just figures that the one most useful to me right now is the one I struggle with. Aries used wind magic again, just seeing if that's what was really going on. Sure enough, the wind obeyed her every command, to the point where she used it to sweep the floor.

And the rock stayed resolutely on the table.

Late Ignius

Alright, so I got the magic. I'll recount the hunt later on, but right now, I just want to kind of write this down, and maybe throw some ideas out there. 

So basically, apparently the brand of elemental magic I'm using is a particular kind where if your personality doesn't fit the element, then you can't use it very well. Apparently, I'm like, the opposite of earth; wind and electricity work particularly well for me, and water and fire work with some effort. Earth, though… Earth doesn't move almost at all.

It's ruined a lot of my plans, but I think that the control of electricity might work for me a little better. I've got some ideas on how to use this stuff in some home defense things, and it should be pretty neat. I need to buy a lot of scrap metal, though. 

At any rate, I need to re-think my house. I think it'll be years before I'm able to control earth to the point where I can design my house as much as I wanted. I've been thinking that I should get a roommate, a miner or an earth user, and have them help me out. I can design stuff, get food, stuff like that; I just need the actual labor to be done. I'm going to look into it.

In the meantime, here's a few ideas I've got to use the elements I CAN use. Enchantments are obviously a good idea, and I'm going to start enchanting my stuff ASAP; for the time being, however, I'm just going to do stuff like that. Now, with water, I was thinking, I could just make it highly pressurized to do a certain amount of mining, I was thinking of going up to the river and mining a path into my house for that. I'll need to take a few measurements first, though.

I also have a few theories about the functionality of electricity. I need to do a few tests first, though, and see how it works for sure. Pretty much everyone knows about the conduction of electricity through metal; another thing it does, which a lot of people who weaponize electricity will know, is that muscles will contract when touched with electricity. I think that this combination could be used for some interesting mechanical traps and the like, but I'm going to have to collect a lot of muscles to do the necessary experimentation.

Finally, if I collect a lot of coal, or other fuel source, and use the pressurized water mining method, I can make some really neat lights, I feel. I'll also need to collect sand for glass, though, but I think it'll be pretty baller.

Anyway, that's all for now. Next entry should be the recap of the hunt, and the aftermath, obviously.