I've been trying to figure out what useful mathematical functions can be computed arithmetically like in this challenge with primality testing. I've found you can compute binomial coefficients, Fibonacci numbers, and GCD. I'm looking for ways to do factorial, indicator function of being a perfect square, and count of divisors.

@xnor at first I was confused, but then it makes sense: You don't allow loops

because factorial is trivial if you allow loops :)

@xnor neat challenge:)

Just thought about how the "learning curve" is used in english.

It just does not make sense

first of all, a lot of things that you cannot do immediately have a learning curve to them

(according to how this phrase is used today)

I think it makes sense. Often you hear "steep learning curve" or "shallow learning curve"

but then many people also seem to think that a steep learning curve refers to something that is very hard to learn, and takes a lot of effort

What else could it mean?

To me, its a graph of time vs Knowledge required

but I think the majority would agree that a learning curve shows how much you've learned as a function of effort or time

in this sense a steep curve would describe something that takes very little time or effort to learn

No, it means you have to learn the most before you can progress

the highest amount of learning in that period of time

which is harder

I think of it as the independent variable being how much you can do with the thing and the dependent variable being how much knowledge/effort it requires.

oh, really?

so according to you both the learning curve measures the productivity as a function of effort?

We have the same dependent variables

my independent variable is the time/effort put into it

effort isn't a good term

time is though

@El'endiaStarman I don't think that parametric curves help in this discussion =P

@flawr Bahahaha just....ignore that one. [waves hand]

I actually thing that that last graph means it requires time travel

or a superposition of multiple states =P

anyway, would you agree that the independent variable should be the time you spend learning/trying to do something?

I don't because different people will take different amounts of time, but I would consider learning curves to be fairly intrinsic to the thing itself.

Oooh, one has to consider that progress on prior learning curves can affect one's progress on current learning curves!

Primes and Squares: Where linguistics is turned into maths.

lol

Deep down, it's all the same thing.

@El'endiaStarman I don't buy the "people are different" argument. Not because they aren't, but because you can generalize the average person, and you can have individual learning curve

I agree

For that VS graph above, if I were to say "How much do I have to learn VS today", and measure that each day, I'd get my learning curve

(assuming I'm spending 8 hours on VS each day)

I'd consider that the derivative of the learning curve

That doesn't make sense for Notepad though. (Honestly, I would consider all learning curves to be strictly monotonically increasing.)

@El'endiaStarman yeah, I can go along with this as well (because to me, its more about knowledge over time vs learning over time)

Knowledge required over time

Anyway, I guess I can get on board with time being the independent variable since there's a sort of time/effort equivalence relationship (akin to E = MC^2).

That said, what one wants to do with the thing has to be considered as well.

that's very true

I use vim all the time. Simply because of git, but I've learned nothing about it then how to press i and :wq

E.g. Python. Fairly easy to learn, meaning a shallow learning curve, but if you want to get into e.g. interpreters for languages, you have to learn quite a bit more. And then one might need to use metaclasses...

so what is the independent variable then?

Yeah, vim was another example I thought of. I know how to do pretty basic stuff because I don't try to do much more.

maybe the graph is knowledge vs effort?

where knowledge is the independent variable?

you choose how much knowledge you want and it tells you how much effort is required to learn it?

Actually, ability.

For a given ability level, how much effort is required?

then it's a skill curve

I wouldn't say that a baseball pitcher has a steep learning curve (though that may be true)

Hmm. I had a good friend that was a pitcher in high school. There's quite a lot that goes into pitching if you're doing anything beyond getting it to the catcher's mitt. Elbow extension, grip location, release point, velocity, etc.

In that case, the learning is more physical but I think it still applies.

And really, don't most people mean skill when they talk about learning curves? It's how much you have to learn to achieve a particular skill.

Too bad I know nothing about baseball, except that there is at least one base and at least one ball.

Actually, don't the muscles learn as well?

so it is skill(time)?

as well as nerves and stuff?

like, how reflexes wrk

Yeah, muscle memory.

@flawr Can't be just pure time. Could be some normalized concept of time though, so that one hour of intense focus is equivalent to a day of mild focus.

This gif is quite neat, incidentally. Five pitches from the same release point: link.

@El'endiaStarman sure, your constitution changes every day, so you probably cannot measure it exactly

so I'd still consider the red one a steep curve, and the green one a shallow one

right

I agree

I would as well, at least initially.

of course

so something with a red ("steep") curve is learned more quickly than something with a green ("shallow") curve, right?

(I think we're always primarily considering the very start of a learning process.)

(Because over time, all learning curves will get more horizontal.)

@flawr Yeah, that does not make intuitive sense to me.

Maybe the axes should be flipped. time(skill)

why would anyone want to put time on the vertical axis D:

We target a specific skill, yes? Then we want to know how long it'll take to get there.

right. Time required

right, but I think the skill(time) formulation makes more sense, as you can put in as much time as you want and you will always have some kind of skill level, while on the other hand you might never achieve a certain level of skill

I think we can at least agree that if something is said to "have a learning curve" it technically says nothing about the "difficulty" of learning it, as every learnable thing has a learning curve.

we could continue with my other pet peeve (I like this expression a lot btw:) that everything that everything that grows supposedly has an exponential growth according to the colloquial use of it:)

Yeah, I like my sinusoidal learning curve

I think we've established that learning curves are monotone? :P

Yes, yes, ignore the troll.

lol

Actually, come to think of it, you could have non-monotone learning curves if learning more makes it harder to do stuff.

I thought about that as a subjective or perceived learning curve.

At some point in school just after we learned to divide I asked myself why we have so many more years of math to come, because we now know everything there is, right?

And right now I have the impression that I know next to nothing about math

It can be quite interesting how what one knows affects what one thinks one doesn't know.