[Basic] Skill of the week: Mathematics

[whswhs]

Originally Posted by Humabout

Math (Statistics) pops up in tons of fields. So does Applied. Cryptography is far narrower, and Pure may take some justification outside of inventing new physics or dealing with cthulhuluan horrors. On that note, though, it could serve as a capping skill or a crit fail saving roll for Elder Thing magic, or if using RPM, it could stand in for Thaumatology pretty easily.

Inventing new physics seems to be Mathematics (Applied). At least, that's how all the courses that talk about physical applications are categorized in math departments.

Really, there's not much more use for Mathematics (Pure) in any normal campaign than there is for Theology.

[Mailanka]

So here's something that bugs me about Mathematics: It's a TL skill. That, in and of itself is a problem, but Mathematics is also a rather abstract skill. So what does TL get you?

Consider, if you have Electronics Operation (Communications)/TL 8, then you're really good at messing with radios. If you have Electronics Operation (Communication)/TL 12^, then you're really good at thought-casting technology, or tachyonic communications, whatever. You can see what an advanced or a more primitive TL skill can do.

Mathematics definitely has a TL component because mathematics have advances. The concept of 0 or imaginary numbers or even full-on algebra comes later, and certainly calculus after that, and... well, I wouldn't even know what you could do with Mathematics nowadays.

But what does TL 9 Mathematics look like? Or TL 12? And what do you do with it? How does TL 12 Mathematics assist your adventurers, and why is it way better at that than primitive TL 8 (or even 9) Mathematics? Or what about a Super in a TL 8 setting who has invented TL 12 mathematics. What does that allow him to do?

[Polydamas]

I agree that its useful to have skills like Theology, even if their main purpose is characterizing NPCs, job rolls, and Quick Contests which affect decisions in the adventure. For example, a debate in Theology might affect whether the hero can marry the man/woman of their dreams; whether they are sentenced to death for heresy; whether they get the job which give them leisure to pursue their research into the immortality serum ...

Originally Posted by Mailanka

But what does TL 9 Mathematics look like? Or TL 12? And what do you do with it? How does TL 12 Mathematics assist your adventurers, and why is it way better at that than primitive TL 8 (or even 9) Mathematics? Or what about a Super in a TL 8 setting who has invented TL 12 mathematics. What does that allow him to do?

Like other aspects of imaginary future technology, that is up to the setting designer to invent! One likely aspect which comes to mind is that a character with Mathematics (Cryptography) can break most messages encoded at a lower TL effortlessly, barring special cases like a correctly implemented one-time pad (which itself is an invention with a date). But someone who enjoys imagining futures and reading speculations about future trends in mathematics can think of other possibilities.

Another good one would be someone with Mathematics/TL5+ using the discovery of mathematical probability to make a killing as a gambler in a low-TL setting.

[Ulzgoroth]

Originally Posted by Mailanka

But what does TL 9 Mathematics look like? Or TL 12? And what do you do with it? How does TL 12 Mathematics assist your adventurers, and why is it way better at that than primitive TL 8 (or even 9) Mathematics? Or what about a Super in a TL 8 setting who has invented TL 12 mathematics. What does that allow him to do?

You have much the same problem with other ultratech top-level science skills. What does Biology/TL10 have that we don't? Physics/TL10? Yeah, you know a bit about TL10 instruments in your respective field (also true of Mathematics, though the instruments there may be less exciting), but the main thing has to be a body of knowledge about the world that nobody has right now. And the consequences for the setting of deciding what's in that body of knowledge can be severe.

In Mathematics (Pure), honestly, I have no idea what the directions would even be, but practically the definition of Mathematics (Pure) is that nobody actually has any idea what use it is anyway. Mathematics (Computer Science) could have a P=NP proof or disproof, either of which is kind of a big deal. Mathematics (Applied), you occasionally see things like a closed-form 3-body problem solution in SF.

[whswhs]

Originally Posted by Mailanka

But what does TL 9 Mathematics look like? Or TL 12? And what do you do with it? How does TL 12 Mathematics assist your adventurers, and why is it way better at that than primitive TL 8 (or even 9) Mathematics? Or what about a Super in a TL 8 setting who has invented TL 12 mathematics. What does that allow him to do?

Well, you know, the fundamental contradiction is that if we could envision TL12 mathematics then we would HAVE TL12 mathematics. It isn't as if you needed to create new machines or synthesize new substances or anything to do the math. Math is designed to run on organic brains, and we have those brains.

Unless, I guess, you want to imagine improved organic brains with higher math ability than ours. Perhaps at TL12 every kid is born with Intuitive Mathematician.

We can imagine, for applied math, that it will enable us to view a wider range of things as mathematically necessary or obvious. Perhaps in another TL or two we will have a mathematics that predicts all possible morphologies of animal development, or all possible cell types, or a mathematics that defines beauty objectively and shows how to measure it.

[Vernon King Avaritt III]

Don't forget Mathematics (Recreational)

[johndallman]

Originally Posted by Ulzgoroth

You'd probably want some kind of interesting connection between Mathematics (Pure) and magic for a Laundry Files setting.

(Of course, you don't do that stuff in your head if you value your brain-meats.)

I made it simple for mine: Magical Aptitude and Magery were two names for the same ability. The only magician in the campaign did do it in her head, and she was very scared of critical failures.

[Polydamas]

Originally Posted by whswhs

Well, you know, the fundamental contradiction is that if we could envision TL12 mathematics then we would HAVE TL12 mathematics. It isn't as if you needed to create new machines or synthesize new substances or anything to do the math. Math is designed to run on organic brains, and we have those brains.

Unless, I guess, you want to imagine improved organic brains with higher math ability than ours. Perhaps at TL12 every kid is born with Intuitive Mathematician.

We can imagine, for applied math, that it will enable us to view a wider range of things as mathematically necessary or obvious. Perhaps in another TL or two we will have a mathematics that predicts all possible morphologies of animal development, or all possible cell types, or a mathematics that defines beauty objectively and shows how to measure it.

I like the biological and philosophical examples.

I suppose that a counter-example to "if we can envision it, we can do it" would be Fermat's Theorem: imagined as possible in the 17th century, first published proof which most peers accept in the late 20th.

I'm told that already in the middle of the 20th century, many mathematicians relied on intuitive feel for whether a proof was valid (rather than tracing the logic step by step from beginning to result), and since a few decades ago, a significant number of proofs rely on computers to check them. No human can follow all hundreds of pages of close reasoning without error. I think that may have been involved in the Fermat proof.

[whswhs]

Originally Posted by Vernon King Avaritt III

Don't forget Mathematics (Recreational)

I'd call that a Hobby skill rather than a required specialization of Mathematics. A lot of sciences have affiliated hobbies like that.

[Daigoro]

For TL12, you could start by saying that all of these problems had been solved.

No, I still don't know what that would look like or how it would be useful in-game. Maybe you could start by saying that every machine or system in every part of society works in the most economical, streamlined way possible.

(And I didn't realise this was a maths thing, I just thought it was a lame Douglas Adams joke- "The moving sofa problem – what is the largest area of a shape that can be maneuvered through a unit-width L-shaped corridor?")