[Basic] Skill of the week: Mathematics

[johndallman]

Mathematics is the IQ/Hard TL skill of the various fields of reasoning and study that get labelled "mathematics" in current academic practice. The definition on B207 is pretty good, but I'm not sure if it's complete. Specialisation is required, and the specialisations in Basic are (Applied), (Computer Science), (Cryptology), (Pure), (Statistics) and (Surveying). These all default to each other at -5, and there is a general default of IQ-6. Most of the specialisations also have defaults to other skills that use mathematics. For example, (Applied) defaults to Physics-5 or Engineering (any)-5; some of these skills have an appropriate Mathematics specialisation as a prerequisite. A few more skills have Mathematics as a prerequisite, or a default; if you were to build a tree structure for GURPS skills, Mathematics would be one of the root skills. Mathematics appeared at GURPS 1e, but the structure of specialisations is from 4e.

Mathematics also allows for optional specialisations or Hyper-specialisation perks within its compulsory specialisations. It's a skill where reversing the optional specialisation rules to create an IQ/VH Mathematics (all) skill seems legitimate for any settings that aren't harshly realistic. A point where GURPS does default to realism is in player-made maps: B491 describes what you can map in a dungeon without spending a lot of time and making a Mathematics (Surveying) roll.

Mathematics shows up on templates for engineers, sages, scientists and teachers. Some fantasy traditions also make it important for magicians. Bio-Tech prescribes it for ecological engineers and epidemiologists, and Fantasy makes it an option for artificers, battle wizards, enchanters, scholars, and utility spell-casters, plus Roman engineers and philosophers, and explains the usefulness of the abacus in working around the limitations of Roman numerals. Fantasy-Tech 1 has devices to ease low-tech calculations, and High-Tech has surveying tools. Locations: Worminghall places Mathematics within the quadrivium of classical learning. Low-Tech and LTC1 have a lot on low-tech tools for calculations and the development of mathematics through history. Monster Hunters requires (Applied) for paraphysics and technomagic. Power-Ups volumes 2, 3, 6, 7 and 8 all have examples that use Mathematics. Powers: Enhanced Senses has the Triangulation technique, and Social Engineering covers opinion polling, media surveys and Sociometry. Thaumatology covers mathematics' many possible uses in magic, and Magical Styles and Urban Magics provide examples, including the (Numerology) specialisation. Underground Adventures has applications to surveying, mining and underground navigation.

Mathematics isn't often a key skill in adventuring, but it can happen. The Infinite Cabal characters are currently trying to work out who's a really good historical mathematician for a problem they have: given their access to a wide range of worlds at different points in history, they plan to just go and recruit their target once they've worked out who it is.

What have you done with Mathematics within a game?

[RogerBW]

As I understand it, the division into pure and applied is the top-level one; other things come under that (as described in the book they're all fields of Applied, though one could make a good case for crypto being Pure).

I think that if I were designing from scratch I'd be inclined to treat Pure and Applied as the basic compulsory specialisations, with the other three being optional specialisations on top of that, and maybe more from https://en.wikipedia.org/wiki/Mathem...of_mathematics or something like it. "Applied" as listed is really Mechanics. At that point, though, pretty much any PC would take Applied rather than Pure.

(Yes, you can stack an optional specialisation on top of a compulsory specialisation, and the listing under Pure proves it.)

As a GM I tend to ask for a roll on maths when the problem is anything more than I can trivially do in my head - things like "how long will it take this 1G-constant-thrust spaceship to go 2AU if it decelerates at the other end" or "we want to point our boat so as to catch theirs at the exact moment when they're most likely to be changing fuel tanks".

[Celti]

My GM has a school with revolutionary teaching techniques in one of his settings, that teaches (among other things) the trifecta of Mathematics (Statistics), Meditation, Philosophy (Reason) — and allows rolls against the first two as Complementary Skill rolls for the last one's "what course of action feels right" option, as a sort of trained Common Sense.

[Flameblade]

Originally Posted by Celti

My GM has a school with revolutionary teaching techniques in one of his settings, that teaches (among other things) the trifecta of Mathematics (Statistics), Meditation, Philosophy (Reason) — and allows rolls against the first two as Complementary Skill rolls for the last one's "what course of action feels right" option, as a sort of trained Common Sense.

Also, Psychology (Applied). The point of it is to try to address the normal ways that humans fool themselves about things through various cognitive biases. Anyone who has read Eliezer Yudkowsky's stuff ought to recognize the inspiration for the idea.

[Mithlas]

Originally Posted by Flameblade

Also, Psychology (Applied). The point of it is to try to address the normal ways that humans fool themselves about things through various cognitive biases.

I think Psychology would be just as good as statistics.

I'm inclined to treat math as one of those culturally-aspected perks that characters may or may not have. My reasoning revolves around the core book's statement that a roll should only be made "when the results of success or failure could be interesting or dramatic". Like 'housekeeping' which I think would rarely if ever result in something interesting, most uses of 'math' itself don't seem like they'd overlap with 'dramatic'. Almost any use that would be is better handled by Mechanics, Engineering, or some other skill.

[Polydamas]

The games I have run were all low-tech aventures without any scholarly characters, so I don't think that Mathematics ever came up. With a physics major and a biology major in the group, running anything like SF was right out!

Originally Posted by Mithlas

I think Psychology would be just as good as statistics.

I'm inclined to treat math as one of those culturally-aspected perks that characters may or may not have. My reasoning revolves around the core book's statement that a roll should only be made "when the results of success or failure could be interesting or dramatic". Like 'housekeeping' which I think would rarely if ever result in something interesting, most uses of 'math' itself don't seem like they'd overlap with 'dramatic'. Almost any use that would be is better handled by Mechanics, Engineering, or some other skill.

One classic adventuring use of Housekeeping is cleaning up a crime scene to defend against TL 7+ Forensics. In SF games dealing with an epidemic it can be very important too.

Using basic surveying trigonometry to figure out how much rope you will need to descend at night into the secret valley, as in a Gordon Dickson novel, is a good adventuring use of Mathematics (Suveying). So is making sure that your claim to the gold strike/asteroid you just found actually covers the lode. Does anyone want to give other examples?

Mathematics (Statistics) is a classic investigative skill at TL 6+, along with Accounting. It lest characters spot fishy numbers and analyse data to tell them where to go have face-to-face adventures, what power plant to blow up, what the evil empire is trying to hide, ...

Cryptography and Navigation can be very important in adventure stories, and at TL 5+ they require Mathematics.

[Ulzgoroth]

Originally Posted by Polydamas

Cryptography and Navigation can be very important in adventure stories, and at TL 5+ they require Mathematics.

Neither skill asserts any such requirement.

It's certainly true that both of them involve mathematics. But there's no suggestion that either Cryptography or Navigation without a Mathematics skill is a problem.

[Humabout]

Originally Posted by Polydamas

Using basic surveying trigonometry to figure out how much rope you will need to descend at night into the secret valley, as in a Gordon Dickson novel, is a good adventuring use of Mathematics (Suveying). So is making sure that your claim to the gold strike/asteroid you just found actually covers the lode. Does anyone want to give other examples?

Using it to discover clues about where Elder Thing portals lead seems an interesting use of Mathematics (Pure).

I would also allow it as a complimentary roll for a WIDE variety of skills - Engineering, Physics, Chemistry, Cryptography, Navigation, Accounting, Finance, Economics, Administration, Politics, Marketing, Merchant, Pharmacy, and Physician just off the top of my head.

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.

[malloyd]

Originally Posted by Humabout

I would also allow it as a complimentary roll for a WIDE variety of skills - Engineering, Physics, Chemistry, Cryptography, Navigation, Accounting, Finance, Economics, Administration, Politics, Marketing, Merchant, Pharmacy, and Physician just off the top of my head.

This is the main barrier to making Mathematics useful - most of the things you could roll against it are better rolled against some other skill. In principle you could use another skill to know what you need to solve (that is to set up the problem) and Mathematics to actually solve it, but there doesn't seem to be a good reason to break a task like that.

[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.)