Approximating mathematical constants using Minecraft | Hacker News Reader

Approximating mathematical constants using Minecraft

arxiv.org

38 pointsbelter54 comments

>Therefore, to approximate the value of √2, we can simply measure the time it takes for a player to travel at a constant rate along one of the legs and the time it takes for that player to travel along the hypotenuse.

In many games, moving diagonally (e.g. by pressing Left and Forward at the same time) gives the player a higher speed than moving orthogonally. The sideways and forward movements are added, rather than normalized, and so you could traverse the hypotenuse in the same amount of time as traversing a leg. I know this was the case at one time in Minecraft, but not sure if it still is. Presumably they did their measurement by just facing along the hypotenuse and walking forward, but it's the sort of weird game mechanic you have to be on guard for when doing this sort of thing.

> moving diagonally (e.g. by pressing Left and Forward at the same time) gives the player a higher speed than moving orthogonally.

Deus Ex: Human Revolution (2011) shipped that way; it was eventually patched[1].

[1]: https://store.steampowered.com/oldnews/6146

As they are using blocks (that cover a square area), I don‘t understand why use MC when you can actually compute the ratios directly based on the area covered by blocks that are less or equal some distance from a defined center - other than it being more fun to use slime ofc.

"This article is a proof of concept that Minecraft can be used in higher education. We should note that the goal of this article is not to have the most accurate approximations possible, the goal is to inspire people to have fun while learning about various mathematical topics."

I learned that 1 / e is the limit probability of a permutation not having any fixed points, nice.

Wonder if the authors are familiar with https://www.luanti.org/. Just as "fun" surely, and less nudging kids into the jaws of the proprietary toll-extracting behemoths of our world.

If you ask a random kid if they know what luanti is, they would have no clue.

Read the docs / documentation / API docs (and contribute)

Read the source

Write tests with test assertions and run them with a test runner

Learnxinyminutes > Lua: https://learnxinyminutes.com/docs/lua/

Learnxinyminutes > Python: https://learnxinyminutes.com/docs/python/

Yeah exactly, and they'll only know things that people tell them about. So tell them about Luanti.

I have given lots of classes to kids and young people, and if I followed your logic there I would have only told them about stuff I thought they already knew about. Luckily, I didn't.

Luanti (formerly minetest) is open source, written in Lua, has an API with mediawiki docs, and has a vscode extension: https://github.com/minetest/minetest

Luanti wiki > Modding intro: https://dev.minetest.net/Modding_Intro

SensorCraft is open source, written in Python, and is built on the Pyglet OpenGL library (which might compile to WASM someday) https://github.com/AFRL-RY/SensorCraft

/? Minecraft clone typescript site:github.com https://www.google.com/search?q=minecraft+clone+typescript+s...

/?hnlog minecraft:

https://news.ycombinator.com/item?id=32657066 :

> [ mcpi, pytest-minecraft, sensorcraft, ]

mcpi supports "Minecraft: Pi edition" and "RaspberryJuice" (~ Minecraft API on Bukkit server)

minecraft-pi-reborn is an open source rewrite of "Minecraft: Pi edition" that's written in C++. It looks like there's a glfw.h header in libreborn. Emscripten-glfw is a port of glfw which can be compiled to WASM. Glfw wraps OpenGL. Browsers have WebGL.

MCPI-Revival/minecraft-pi-reborn: https://github.com/MCPI-Revival/minecraft-pi-reborn docs: https://github.com/MCPI-Revival/minecraft-pi-reborn/blob/mas...

Given that it ends:

> While we chose to use Minecraft to approximate irrational numbers, we believe there are many settings where this type of experimentation is possible. We would love to hear from anyone who finds inspiration from this paper and does some exploring of their own!

I'm sure they would be happy with you testing Luanti to see if there are equivalents.

Like, how do you generate random dots in Luanti? How do you record deaths? Or do you use other methods entirely? Is velocity isotropic or is traveling on the diagonal faster/slower than horizontal/vertical?

You could go one step further and write it up.

You're missing the point - I think people involved in education should put the extra effort in to not use things like Minecraft, and should explicitly search for more "community-friendly" projects, based on Free Software.

If none existed, it'd be possible to understand.

If one did exist, and it was really well-documented, with a thriving community, and loads of care put in to modding as a primary facet of the game rather than a sort of add-on, well then... it gets harder to understand.

Whether I can play around with these ideas on luanti myself is completely beside the point.

While my point is that they can't know and do everything.

Is luanti able to even do these tasks? Depending on how it implements mobs and the physics, it might not be possible, so your "If none exists" might actually be true - you don't know!

Help them. Don't be yet another annoying FOSS fan who insists others aren't pure enough.

> While my point is that they can't know and do everything.

Indeed. If you'll relook at my initial comment, I was literally just saying, I wonder if they're aware of Luanti.

> Is luanti able to even do these tasks? Depending on how it implements mobs and the physics, it might not be possible, so your "If none exists" might actually be true - you don't know!

Again, yes, I do not know, I was really just saying, I wonder if they know about and have considered Luanti. I have been playing with Luanti now for a total of about one hour, but it seems great, and I was wondering if they knew it's there.

> Help them. Don't be yet another annoying FOSS fan who insists others aren't pure enough.

Noted. I didn't mean to be, and will be careful not to get up too high on the horse in future. Thanks for the honesty.

> and I was wondering if they knew it's there

The friendliest way is to do one of experiments in luanti, then write them to say you liked the paper, but because you don't like proprietary software, you did it in luanti, and let them know of your success/failure.

I already acquiesced to your basic point, that I should be careful about appearing too "high-horse" about the whole thing. I told you that I really did not mean to, and thanked you for sharing your perception.

And yet you're continuing, and pushing it a little step further, and implying that this is about me not liking proprietary software personally.

How weird. I don't know how I could have been more explicit. I do not think educators should use proprietary software with children if they have the choice to do otherwise. I'm making an ethical point, in the sense that I believe it should be a general rule.

Sometimes making an exception makes sense, sometimes not mentioning the whole thing at all makes sense, the world isn't black and white, sure. But I am not making a point about my personal preferences when it comes to software.

I'm sorry.

I saw that one possibility to resolve 'wondering if they knew it's there' was to email them directly and ask.

I was trying to caution you that it would be more friendly to include why you were curious, and to include some detail that tells them it you like their work enough to try it out yourself.

> I do not think educators should use proprietary software with children if they have the choice to do otherwise

The target audience is college students, not children.

Unfortunately, in my experience, mesecon (the Luanti equivalalent of redstone) mechanisms seem to be unreliable for scientific experimentation because their behavior is framerate-dependent.

Aha, ok, I didn't know that. I'm only playing around with Luanti very recently. I've made a note of this, and when I get around to experimenting with mesecon (which was on my todo list, as it looks great), I'll look into this, thanks!

FWIW 22/7 and 666/212 are Rational approximations for pi.

You can write a script to find other integer/integer approximations for pi and other transcendental numbers like e.

Hah! There's a whole Wiki page[1] about pi approximations!

[1]: https://en.wikipedia.org/wiki/Approximations_of_%CF%80

Transcendental number > Numbers proven to be transcendental: https://en.wikipedia.org/wiki/Transcendental_number#Numbers_... :

> [ π, e^a where a>0, ln(a) where a!=0 and a!=1, ]

e (Euler) https://en.wikipedia.org/wiki/E_(mathematical_constant)

Pi (Archimedes,) https://en.wikipedia.org/wiki/Pi

Avogadro constant: https://en.wikipedia.org/wiki/Avogadro_constant

Approximations of Pi: https://en.wikipedia.org/wiki/Approximations_of_%CF%80

List of representations of e: https://en.wikipedia.org/wiki/List_of_representations_of_e

Four dimensional space, 4D, Minkowski (SR), Einstein (GR) https://en.wikipedia.org/wiki/Four-dimensional_space