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Old 05-02-2016, 08:12 PM   #51
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Default Re: [Basic] Skill of the week: Mathematics

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Originally Posted by malloyd View Post
Thinking about it though, that was 40 years ago. I suppose it's possible nobody draws the figures by hand anymore.
In my experience the figures are usually drawn by hand...at least for ones drawn during class rather than on handouts...but they don't need to be drawn with much precision.
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Old 05-03-2016, 07:30 AM   #52
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Default Re: [Basic] Skill of the week: Mathematics

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Originally Posted by malloyd View Post
Is geometry not taught that way anymore? When I last took it the proofs were perhaps more rigorous than those in Elements, but mostly quite similar. The compass we used for the chalkboard was even the traditional kind you had to hold open yourself.

Thinking about it though, that was 40 years ago. I suppose it's possible nobody draws the figures by hand anymore. There has been a little technological change since - I bought my first calculator (a 10 digit red LED display one from Radio Shack that was about the side of my current tablet, only 3 times as thick) for electronics class that same year....
You might get one or two days a year from the folks who like it. The world is going very very digital. I graduated high school in 07, and went to colledge from 09 to 13 and took a good deal of math (5 classes short of a major). Saw it, but only a few time. I suspect those techniques are becoming more and more rare.
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Old 01-07-2024, 09:08 AM   #53
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Default Re: [Basic] Skill of the week: Mathematics

The sciences are traditionally divided into three main branches: natural sciences (Astronomy, Biology, Chemistry, Geology, and Physics), social sciences (Anthropology, Archaeology, Psychology, Sociology, and so on), and formal sciences (Cryptology, Logic, Mathematics, Computer Science, and Systems Science). GURPS presents Cryptology and Computer Science among the required specializations of Mathematics; and what's traditionally called Mathematics is treated in GURPS as the Pure specialization of Mathematics; so it seems to me that GURPS may be, in effect, using the Mathematics skill as an umbrella skill that encompasses all of the formal sciences. If that's the case, then I'd add two more options to the list of required specializations: Logic, and Systems Science.

I don't personally know much about Systems Science, so I wouldn't be able to comment on how it might be used in-game, though I suspect that it might be related to Market Analysis in a similar way to how Mathematics (Cryptology) is related to Cryptography. On the other hand, Market Analysis might be a better match for Mathematics (Statistics).

But I see Mathematics (Logic) being used for Sherlock Holmes type characters. Possibly relate it to Intelligence Analysis?
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Old 01-07-2024, 09:24 AM   #54
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Default Re: [Basic] Skill of the week: Mathematics

Sherlock Holmes understands induction but isn't, by profession, a logician.
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Old 01-07-2024, 09:30 AM   #55
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Default Re: [Basic] Skill of the week: Mathematics

Not by profession, no. But who says you need to be a professional to study logic?
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Old 01-07-2024, 09:46 AM   #56
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Sherlock Holmes never demonstrates anything about logic, the academic discipline, you couldn't glean from an introductory text. And in fact, by his own admission, he ignores things like astronomy that might clutter up his knowledge and take time away from concentrating on his detection methods.
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Old 01-07-2024, 10:49 AM   #57
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Default Re: [Basic] Skill of the week: Mathematics

Mostly, what I actually use formal logic for would involve rolls at +4 (or more).
Know the difference between exclusive and inclusive OR, recognize that mostly "all p is q" is taken not to have existential implications, be closely attuned to the difference between not Sing p and Sing not p (e.g., for knowledge), knowing various features of S5 modal logic, and being able to use the square of opposition.

Roll with various modifiers to understand such strings as:
□((∃!x)((y)(Py ⊃ Qxy)) ≡ ~(∃y)(Ry & ~Rx)) once you know what the predicates P, Q, R mean. Also roll to manipulate such a sentence to derive various claims from it. That one should have a decent positive modifier, but some might have penalties depending on how obscure the symbols are and how complicated the string is.

There are some interesting proofs about soundness and completeness, the upward and downward Lowenheim-Skolem theorems, and such, most of which I barely recall from the required graduate logic course I took. They just aren't that useful for the kind of thinking I actually do (and Sherlock, I imagine, would have even less of a use for them: he's never dealing with Beth-2 possible worlds!).
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Old 01-07-2024, 01:13 PM   #58
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Default Re: [Basic] Skill of the week: Mathematics

That that's the one drawback with putting Logic under Mathematics: it's far too easy to assume that this is referring solely to Mathematical Logic. But while what I'm referring to would include that, it would also include things like knowing that arguing from authority is a logical fallacy, or how inductive reasoning works. You know; logic. Worminghall addresses this as Dialectic, or Philosophy (Scholastic), when it describes the seven classical liberal arts.

Though I'm not sold on all of the associations that book makes: the writer puts Arithmetic under Mathematics (Applied) which, based on its default association with Physics and Engineering, probably shouldn't even be a thing multiple centuries before Newton gave us a firm mathematical basis for physics. I'd be more inclined to have it under Mathematics (Pure) or Mathematics (Statistics), the latter because of its connection to Accounting.

So: should it be Mathematics (Logic), or Philosophy (Scholastic)?
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Old 01-07-2024, 02:08 PM   #59
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Default Re: [Basic] Skill of the week: Mathematics

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That that's the one drawback with putting Logic under Mathematics: it's far too easy to assume that this is referring solely to Mathematical Logic. But while what I'm referring to would include that, it would also include things like knowing that arguing from authority is a logical fallacy, or how inductive reasoning works. You know; logic.
That's a form of logic in the general sense, but not academic logic. ALL fields require that kind of logic. What you are talking about sounds more like Rhetoric.
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Old 01-07-2024, 02:14 PM   #60
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Default Re: [Basic] Skill of the week: Mathematics

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Originally Posted by dataweaver View Post
That that's the one drawback with putting Logic under Mathematics: it's far too easy to assume that this is referring solely to Mathematical Logic. But while what I'm referring to would include that, it would also include things like knowing that arguing from authority is a logical fallacy, or how inductive reasoning works. You know; logic.
Much of this is probably just IQ.

I knew circular reasoning was a bad way of reasoning when I was 5 and my Sunday School teacher told me we knew the Bible was true because the Bible said so. Most reasoning is stuff you do without being (explicitly) trained; it's just easy to get confused in some contexts--sometimes that's failing a Will roll against Fast-Talk or similar, sometimes it's a combination of the other guy failing a Writing roll and you failing an IQ roll to understand their complicated sentence, and sometimes it's a failed Speed-Reading roll.

Other informal fallacies are difficult to detect without some subject-matter expertise. Most are distortions of proper modes of reasoning. An argument from authority may be totally fine if the authority is actually in a better position to know. What counts as a proper authority, however, can be a vexed question in some contexts. Similarly, there are arguments about whether circular reasoning is always bad and why. All of that complexity I'd fold into skill in the particular domain of reasoning.

Other informal fallacies are just lack of pedantry and would be fine in typical conversational contexts--we just forget we aren't in them. For instance, denying the Antecedent and Affirming the Consequent work fine if someone tells you "If I go to the grocery store, I'll buy ice cream" in most circumstances because usually there's a background assumption that this is the most likely way they'd wind up getting ice cream.

Quote:
Worminghall addresses this as Dialectic, or Philosophy (Scholastic), when it describes the seven classical liberal arts.
I take it that's skill in reasoning in the scholastic style, using the conceptual resources the Scholastics employ (Note, "based on Aristotle"). So, it probably includes Aristotelian conceptions of essence, actuality, potentiality, being, etc.

Quote:
Though I'm not sold on all of the associations that book makes: the writer puts Arithmetic under Mathematics (Applied) which, based on its default association with Physics and Engineering, probably shouldn't even be a thing multiple centuries before Newton gave us a firm mathematical basis for physics. I'd be more inclined to have it under Mathematics (Pure) or Mathematics (Statistics), the latter because of its connection to Accounting.
Archimedes would like a word...

I'd treat what we call basic arithmetic as part of learning defaults for Mathematics. The mathematics of levers, pulleys, etc., would all be Mathematics (Applied). Part of being lower TL might be uncorrected errors, e.g., about how gravity and energy transfer work. But Mathematics (Pure) has errors about magnitudes of infinity, too.

Quote:
So: should it be Mathematics (Logic), or Philosophy (Scholastic)?
The latter, at least, covers the square of opposition, since that's Aristotle. At Worminghall, Philosophy (Scholastic) reasonably covers pretty much all the formal logic (Aristotle's).

Contemporarily: Mathematics (Logic) for formal deductive and mathematical logic. Statistics for Bayesian logic. Most of the rest fall into IQ or subject-matter-specific skill. Some of this falls into there not being strict borders between skills: if a player has a skill, I'd generally assume they had enough logic to understand the literature. I can read modal logic because I work in areas where it gets used, such as debates about free will, not (I think) because I have skill in Mathematics (Logic).
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