Posts tagged with learning

I’ve been slacking in collating examples of maths i.r.l.

But sometimes it’s easy.

Skyrim, like any Dungeons & Dragons system, has to model certain aspects of reality.

• how likely you are to encounter a random group of bandits on the road
• what are the relevant attributes of a person?

Somewhere the computer stores some tuple that represents everything it knows about your character.
• whether someone likes your character or not

«let me see here … Nice to meet you, Fry.»
• how telepathy works. (What happens if you try to read a horse’s mind?)
• how battles work (will there be hit points? will there be `THAC0`?)
• how learning, or training works.

The result of the models must be balanced, believable, and fun.

After dragooning your GPU into computing a couple billion triangles per second on the graphics side, the designers of Skyrim decided to go easy on the maths they use to model learning of skills like

• smithing
• lockpicking
• speechcraft
• two-handed weapons

. They use a different binomial for each skill.

$\dpi{200} \bg_white \large \texttt{const} \cdot (\texttt{how good you are})^{1.95} \ + \ \texttt{const}$ determines how hard it is to get from “level 5 → level 6” versus from “level 78 → level 79”.

In addition to choosing a paradigm (existence of “levels of alchemy” and “experience points in alchemy”) and calibrating attainment grades, the game designers had to decide how much XP to reward per action.

Here again a binomial per skill, eg smithing:

• `25 + (3 ∗ item value0.65)` base XP for constructing an item.
• `25 + (8 ∗ item value delta0.6)` base XP for improving an item.

Relating this to maths terminology,

• the `25` would be the affine `b` from `y=mx+b`, allowing them to put a floor on each smithing experience;
• "Learning" is modelled by repeating a map.
• `3 ∗ 0.65`, the derivative around `item value=1`, would be the first `m` in a sequence of declining `b+m+m+m+m+m+m+…`'s.
• Three parameters; that’s almost enough to fit an elephant! And yet the designers made a hit game.
• `0.65 < 1` as an exponent makes learning concave in splendiferousness of the item crafted; repetition is more important than making one spectacular thing.

The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding.

The main point is not quantity or speed—the main point is quality of thought.
Geometry and the Imagination with Bill Thurston, John Conway, Peter Doyle, and Jane Gilman

(Source: geom.uiuc.edu)

Nature is the best teacher. Working on real problems makes you smart. … it is not by staring at a hammer that we learn about hammers.

Similarly, scientists who do nothing but abstract work in the context of funding applications are missing out. The best scientists work in the laboratory, in the field; they tinker.

By removing ourselves from the world, we risk becoming alienated. We become strangers to the world around us. Instead, we construct this incoherent virtual reality

Daniel Lemire (@lemire)

(Source: lemire.me)

The most obvious image of a laughable hipster should be a half-time art-school student whose parents are going to provide him/her with a cushy job and/or money so s/he doesn’t really have to work but can just learn some stuff, party/hang out, make some art, and do a little-of-this little-of-that. Maybe have his/her own record label or vanity company or charity or eat instagrammable food or wear cool clothes or whatever, and be beautiful.

Hey, that actually sounds like a nice life I would like to have for myself.

Since art and learning and performing and consuming of those kinds of things are ends in themselves, it’s like this stereotypical character already has what the rest of us would use up our potential leisure time working to be able to afford. In that case the hipster hatred can be just a form of envy.

Much learning does not teach understanding; else it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus.

Heraclitus (who died ∼475 BC)

via University of David

1. erudition ≠ intelligence
2. intelligence ≠ worth as a person

hi-res