Things that are not directly connected with Factorio.
kovarex
Factorio Staff
Posts: 7506
Joined: Wed Feb 06, 2013 12:00 am
Contact:

I couldn't help myself, but I hear him talking about Factorio all the time

Gammro
Filter Inserter
Posts: 357
Joined: Wed Oct 09, 2013 1:45 pm
Contact:

That's a pretty interesting video. I was always wondering why 0! = 1, so this finally gave me an answer.

The continuous factorial in the end is also an interesting concept, I do fail to see how it relates to the factorial. Since, in my head, the factorial has always been based as "the amount of discrete configurations n objects can have"; as also seen in his given example with the coins. So it is supposed to be not "just" a function that also gives the same answers on whole numbers(/integers). *sigh* mathematicians... sometimes I don't know what the hell they're trying to do

Ignore this

Nirahiel
Filter Inserter
Posts: 351
Joined: Mon Sep 23, 2013 2:18 pm
Contact:

Ah numberphile, I love this youtube channel, and I've watched this video.
That blond guy has something I find fascinating, I dunno, he has a certain charisma I can't explain

Math3vv
Long Handed Inserter
Posts: 99
Joined: Sun Oct 06, 2013 10:47 am
Contact:

i wish he was my math teacher :/
also i like the part when he divides 1 by 0 ands says "you have broken math, stop that"

Edit : watched other videos from that channel and now my head hurts ...
Last edited by Math3vv on Sat Oct 19, 2013 8:13 pm, edited 1 time in total.

Holy-Fire
Fast Inserter
Posts: 169
Joined: Sun Apr 14, 2013 9:15 am
Contact:

Gammro wrote: The continuous factorial in the end is also an interesting concept, I do fail to see how it relates to the factorial. Since, in my head, the factorial has always been based as "the amount of discrete configurations n objects can have"; as also seen in his given example with the coins. So it is supposed to be not "just" a function that also gives the same answers on whole numbers(/integers). *sigh* mathematicians... sometimes I don't know what the hell they're trying to do
Take exponentiation (taking powers) as an example. a^n is the number of different combinations possible of n digits with a possible choices. If n is not integer this combinatorial interpretation is meaningless, but you still have no problem using 4^2.5 to mean 4^2*sqrt(4)=32. The only logical way to extend the integer definition to real numbers is x^y = exp (y * ln(x)).

For factorials it is the same. Despite the definition of Gamma being completely different from the original definition of factorial, (the shifted version of) it is the simplest real function satisfying the same recursion rule (n+1)! = (n+1) * n!, and so it is the natural generalization of the factorial.

Example application: Perhaps you've heard of Newton's binomial expansion (a+b)^n = \sum_{k=0}^n a^k b^(n-k) n! / ( k! (n-k)! ). It turns out this expansion applies also when n is not an integer - the series is then infinite, and instead of the factorials you need to use the corresponding Gamma values.

Generalizations are prevalent throughout all of mathematics.

Gammro
Filter Inserter
Posts: 357
Joined: Wed Oct 09, 2013 1:45 pm
Contact:

Thank you for the explanation Holy-Fire, although I must admit I was a bit tired when I typed my reply at 4am. It's an interesting thing none the less, finding continuous functions for things we previously only knew as discrete.
Ignore this

ssilk
Global Moderator
Posts: 11196
Joined: Tue Apr 16, 2013 10:35 pm
Contact:

It would be someway cool to include the factorial-element more obvious into factorio. i think to the receipts. E. g. Receipt E needs 5 of receipt D needs 4 of C needs 3 of B needs 2 of A which needs 1 iron ore. Then the amount of iron ore to produce one E is 5*4*3*2*1 = 120
Cool suggestion: Eatable MOUSE-pointers.
Have you used the Advanced Search today?
Need help, question? FAQ - Wiki - Forum help
I still like small signatures...

Nirahiel
Filter Inserter
Posts: 351
Joined: Mon Sep 23, 2013 2:18 pm
Contact:

Don't forget it's just a game, you don't have to know math to play

ssilk
Global Moderator
Posts: 11196
Joined: Tue Apr 16, 2013 10:35 pm
Contact:

Yeah, of course. But this one lies on hand. Perhaps, when this guy makes the next video about factorials he uses factorio to show that... No of course not,but who knows?
Cool suggestion: Eatable MOUSE-pointers.
Have you used the Advanced Search today?
Need help, question? FAQ - Wiki - Forum help
I still like small signatures...

Gammro
Filter Inserter
Posts: 357
Joined: Wed Oct 09, 2013 1:45 pm
Contact:

Another video, and my mind is blown. I actually can't decide if I believe this is true:

If it's true, it's possibly the least intuitive mathematical concept I know. Meanwhile, my brain is trying to think where a mistake has been made, but I can't see it.

What do you guys think?
Ignore this

kovarex
Factorio Staff
Posts: 7506
Joined: Wed Feb 06, 2013 12:00 am
Contact:

Gammro wrote:What do you guys think?
It's trolling done the right way

Nirahiel
Filter Inserter
Posts: 351
Joined: Mon Sep 23, 2013 2:18 pm
Contact:

Nah, the guys at numberphile are really awesome

kovarex
Factorio Staff
Posts: 7506
Joined: Wed Feb 06, 2013 12:00 am
Contact: