[Basic] Skill of the week: Mathematics

[whswhs]

Originally Posted by johndallman

To add a few more things on the relationship between mathematics and technology, the simple concept of a computing machine that Turing devised, for the pure mathematics purpose of trying to discover what can and can't be calculated, was immensely influential in the design of actual machines, because it told would-be inventors that a particular design would be able to do useful work.

Something else that was very influential was Shannon's master's thesis, which showed that Boolean logic, which had existed for decades, could be used to simplify the design of electronic circuits that calculated logical and mathematical functions. This mean that there was a sound basis for engineering them, rather than just making them up. Eleven years later, Shannon also created a sound theory for communication, which identified the limits of what's possible.

Those results from the 1930s and 1940s still form the basis of modern computing and communications.

Yes. This was TL6 mathematics that created the basis for digital electronics, as Maxwell's TL5-6 mathematics created the basis for analog electronics earlier. (As I understand it, Maxwell himself created electromagnetic theory without the benefit of vector or tensor analysis, using purely TL5 notation to express nascent TL6 concepts. But Maxwell was one of the most brilliant physicists ever. People like Heaviside came up with math that made it possible to state electromagnetic theory simply and elegantly.)

[johndallman]

Originally Posted by Phil Masters

How much does any of that relate to, derive from, or feed into the recognisable technologies of those TLs? Could many or any of those changes plausibly have come sooner or waited until later, without serious consequences for the physical technologies in use?

A lot of the new mathematics of TL6 was and is vital for analogue electronics. You need that mathematics to engineer electronics that will work predictably and reliably.

[gmillerd]

Originally Posted by malloyd

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.

I use the skill to augment other rolls, its not like Maths is a first responder for action scenes. Its integral to quality control, validation, risk assessment, etc.

In projects, Long Tasks, I ask for Research and Math rolls. Success in each yields doubling the Extra Time bonuses or halving the Extra Time duration for the normal bonuses. When including Team Efforts, this is quite profitable.

From magical formula research, ley line charting with big data, weapons development, etc ... useful. You can watch a few episodes of STTNG and see Geordi and company do exactly this (if your not familiar with testing and experimentation), in crazy Cinematic episodes he basically indemnifies himself that he wasn't given the time to perform these actions.

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The TL discussion is interesting, is -TL really a thing for this? Would TL10 people see TL8 math all that of a problem? We might have issue with some tools, but that is more likely a cultural familiarity issue. (not having zeros, odd base maths units, lacking proofs and using route tables, etc)

Andrew Wiles wasn't using Wolfram tools or similar, but rather Pen-Paper and Chaulk (as a matter of preference, although he is familiar and validations were consulted) to work out all the number theory relations with Fermat's Last Theorem. Sort of addresses some of the TL language regarding tools. Yes, the higher the TL the more the tools and techniques are ... technical.

The RAR reads ... "There is a penalty to your skill roll when you use these skills with the equipment of a higher TL (which relies on scientific and engineering principles unknown to you) or a lower TL (which depends on principles that were, at best, a “historical footnote” during your training)."

But math's background (like many sciences) isn't a "historical footnote" it would seem. A TL3 math problem is really -9 to TL8 (I guess we might get +10 for trivial contest - no roll needed) ... Damn me for selling Ice Age at GenCon so long ago.

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Similarly quick at the Skills List for TL skills, low tech Criminology, Farming, Sewing might be odd to higher tech people ... but is it really distinct? (might be that +10 again for the tasks I can imagine).

[whswhs]

Originally Posted by gmillerd

The TL discussion is interesting, is -TL really a thing for this? Would TL10 people see TL8 math all that of a problem? We might have issue with some tools, but that is more likely a cultural familiarity issue. (not having zeros, odd base maths units, lacking proofs and using route tables, etc)

Some math becomes unfamiliar and even obsolete. Can you multiply two numbers by successively doubling one and halving the other? Or do Euclidean compass and straightedge constructions? Or use a slide rule? Or take square roots by performing the classical square root algorithm that looks like mutant long division? (For me it's yes, no, sorta, and yes—for example, I've done design in GURPS Vehicles using a slide rule when I couldn't find my calculator.) I suggest that a lot of mathematicians in 2016 don't have those techniques at their fingertips.

[RogerBW]

The approach I'd be inclined to take is to allow the player to decide how the PC approaches the problem. Take the GURPS Vehicles design calculations as an example (which are mostly +-×÷, plus the occasional exponentiation); doing that at TL8 means using a calculator or computer. Doing it at TL6 means using a slide rule, and if you don't have the computer or calculator handy you have to make a choice between taking the lack-of-equipment penalties or the down-TL penalties.

[whswhs]

Originally Posted by RogerBW

The approach I'd be inclined to take is to allow the player to decide how the PC approaches the problem. Take the GURPS Vehicles design calculations as an example (which are mostly +-×÷, plus the occasional exponentiation); doing that at TL8 means using a calculator or computer. Doing it at TL6 means using a slide rule, and if you don't have the computer or calculator handy you have to make a choice between taking the lack-of-equipment penalties or the down-TL penalties.

And in the same way, adding up multidigit numbers in ancient Rome means using an abacus and then writing down the results in roman numerals. And if you don't have an abacus you have to struggle with pebbles in the sand, or tally marks, or counting on your fingers, and take penalties.

[Þorkell]

Originally Posted by whswhs

Some math becomes unfamiliar and even obsolete. Can you multiply two numbers by successively doubling one and halving the other? Or do Euclidean compass and straightedge constructions? Or use a slide rule? Or take square roots by performing the classical square root algorithm that looks like mutant long division? (For me it's yes, no, sorta, and yes—for example, I've done design in GURPS Vehicles using a slide rule when I couldn't find my calculator.) I suggest that a lot of mathematicians in 2016 don't have those techniques at their fingertips.

I can't answer those questions for myself, I am by my own admission not terribly good at math. But I also might be having an English-to-math-to-Icelandic problem with the question. However the question that came to mid is this, assuming someone with Math/TL8 how hard would it be to explain the methods above to him, Would it require one demonstration or something way more?

[ericthered]

Originally Posted by Þorkell

I can't answer those questions for myself, I am by my own admission not terribly good at math. But I also might be having an English-to-math-to-Icelandic problem with the question. However the question that came to mid is this, assuming someone with Math/TL8 how hard would it be to explain the methods above to him, Would it require one demonstration or something way more?

some are easier, some are harder. Compass and straitedge is its own little thing, and its not something where you see it once and get it -- each construction is its own little trick, and there are a number of little tricks. Someone with proper geometry training can probably hack some of it -- but very slowly.

The square root thing is an awsome trick, but it takes some doing to get used to. Its also a single trick, and can be written down without too much trouble. But if you're not good with math, its tricky and hard and nasty.

[whswhs]

Originally Posted by Þorkell

I can't answer those questions for myself, I am by my own admission not terribly good at math. But I also might be having an English-to-math-to-Icelandic problem with the question. However the question that came to mid is this, assuming someone with Math/TL8 how hard would it be to explain the methods above to him, Would it require one demonstration or something way more?

It depends on the method being used. The square root algorithm is a bit arcane. Anyone with a couple of points in Math/TL8 ought to be able to follow it without much trouble, but they would need practice to do it quickly and get all the steps right, I think. Isn't the penalty for lower tech about -1? That suggests that doubling the time would buy off the penalty, and represent your having to go slowly and remind yourself of what the next step was.

[malloyd]

Originally Posted by ericthered

some are easier, some are harder. Compass and straitedge is its own little thing, and its not something where you see it once and get it -- each construction is its own little trick, and there are a number of little tricks. Someone with proper geometry training can probably hack some of it -- but very slowly.

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....