Spellbooks

Guelph stroked his beard and sat back in thought.

He'd bought all the books off a wizard, cheap. The wizard said they were useless, but in Guelph's experience, books were frequently more valuable than they appeared. So he'd bought the lot of them.

They weren't useless of course. Propping up tables, kindling. But were they worth what he paid for them, which was more than for the equivalent weight of wood? They seemed to be spellbooks. An odd mix of simple and incomprehensible. They talked about energy, work, power, but then went straight to odd symbols. The introduction pages were sensibly numbers i, ii, iii, iv, v, vi and so forth. Later chapters were 1,2,3,4 or A,B,C,D, so he assumed 1,2,3,4 were letters of a foreign alphabet called "digits". Except the "Basic Algebra I" had chapters 0,1,2,3,4, what was up with 0? His best guess was 0 was one, 1 was two, etc, but usually one was skipped because it was considered too basic.

There were a lot of references to Algebra, so he focused on the Basic Algebra I. It was talking about Set theory and monoids and Galois groups, and had wilder symbols than most of the others. Occasional simple-looking charts, but then more nonsense symbols.

The "Materials Science" had a number of tables, with long strings of the 1234 alphabet, usually things like 1.2924e10. Looking through these, he noticed a pattern: 0.7372, 0.9372, 1.0137, 1.237, 1.537, 1.927, 2.375, 2.737, 3.527, 4.273, 5.620, 6.993, 8.532, 10.52, 12.77, ... along with a graph showing as smoothly rising curve, and digits 0,1,2,3,4 along the left side. It seemed that each entry had four digits, and 0 was as common as the others. And he had it wrong: 1 was one, 2 was two, and 0 was some lack of anything. That made ten digits (thankfully), and it seemed each one on the left counted ten times as much as the next one on the right, and the period separated whole numbers from pieces. Checking a number of other tables seemed to confirm that interpretation.

Back to Basic Algebra I. It had a subchapter, 0.4, describing the natural numbers 0,1,2,3, ... Guelph figured he knew what those meant now, but it immediately launched into rings, rational numbers (WTF) and real numbers (WTF) and rings of residue classes ... skip skip skip ... Peano's axioms 0 != a+, ah, no. Later there was 0+m=m and 0m=0 and mn=nm and 1m=m. The "=" probably meant "produces". And then 0+m might be addition, and 0m multiplication, given what 0 and 1 meant. Further skimming didn't seem to contradict any of that. He still couldn't tell what 0 != a+ was, or what "a" was for that matter.

After a month Guelph had figured out the symbols for numbers, addition, multiplication, and most of "algebra". But hardly any of "Basic Algebra I". That book was probably an advanced text purposely masquerading as an introductory one. These books were still mostly incomprehensible, but it was clear they were trying hard to be comprehensible, it's just that their subject matter was extremely dense. They had tables of content, indexes, and were careful to define terms before using them. It all seemed to link real things to math, and assume you could do math easily. Doing multiplication with 74*903 was significantly easier than LXXIV*CMIII.

There were books on electricity, quantum mechanics, material science, a CRC handbook of tables. But oddly, not magic. He looked through all the indexes, and no mention of magic at all! The only reference was "Gaussian elimination is the closest thing to magic in this world". Gaussian elimination ... yes, that was a fancy stylized way of finding solutions to problems, but it required an excessive amount of multiplication and division for anything over three unknowns. And it only worked if your problem matched that exact pattern. Possibly "quantum mechanics" was their word for magic? Hum, no, it didn't seem to fit. Whole books on leverage and material strain, but no mention of magic, who ever heard of constructing a building without magical assistance?

And the physics book claimed the speed of light was nearly incomprehensibly fast, but Guelph could easily demonstrate it was slower than sound. After all you always heard thunder before you saw lightning. So, at least in some ways, the physics book was plain wrong.

So Guelph sat back in thought. Perhaps the wizard was right, they really were useless. They seemed like a very exact description of the world. But not his world. In his world there'd be a book analyzing magic by numbers. And it would give the right speed of light.

Hum. What WAS the actual speed of light, anyhow? Or sound? The book had described the experiment where they had measured it. He could measure it himself. And then once he had the right numbers, the rest of the formulas ... they were just math, right? There's no way math can be wrong no matter what world you're in. It wasn't that hard an experiment. Come to think of it, EVERYTHING had come with experiments, allowing you to confirm for yourself what was true and what was not. Even if it turned out the formulas were wrong, they'd had experiments for how they found the formulas. It wasn't like your normal spellbooks, where they told you just the result and carefully hid how they had found it. They had bent over backwards to make sure there was no need to trust them. As if they believed taking anyone's word for anything was a cardinal sin. Hum, what sort of experiment would you run to measure magic?

Guelph felt his hairs raise on end as he thought about it. The results in the books were useless. But now that Guelph knew their method, that put him above all the spell books in the world. In ANY world. If he put in the work.

He set to work setting up some experiments.

This was in response to a prompt on reddit.com r/WritingPrompts, "Due to a wizard's botched summoning attempt, an engineering college student's textbooks wind up transported to a fantasy world, whereupon they're found by a dwarf craftsman who's down on his luck."