Hey guys spirit of the law here in this video
I want to take a look at a question related to the forest noting map. If you don't know what it is
It's basically a map where there's nothing, but forest kind of self-explanatory really
You have to chop in order to make a clear space for farms and then use the market to get other resources
You can think of it as a cross between solitary confinement and a forced labor camp
anyway
It got me wondering how long would it take a lone Dark Age villager to chop all the wood on a giant map
Just one villager. No upgrades. No new lumber camps
No breaks
no vacation days and definitely no overtime take a guess at which option you think is closest to the
Real-world time it would take on a game running at fast speed and hang on to that guess for the moment
We'll see if you're right now to find the answer
I'll set up a villager with a lumber camp in the middle of a giant map and I'll time-lapse it at
2,000 times speed while I go out for a walk
On second thought this is gonna take a while. In fact, that's as far as he got in four-and-a-half real life hours
This isn't gonna work. We're gonna have to do it with math
so first of all
If this is a giant map, its 240 tiles along each edge giving us fifty seven thousand six hundred trees
That's almost six million wood for him to collect Dark Age Lumberjacks
Collect a little over 23 wood per minute which gives around two hundred and forty seven thousand minutes to collect just the wood
Assuming he can teleport to new trees
It also takes two and a half seconds to cut down a tree so adding that time in as well gives us another twenty four
Hundred minutes now we need to think about the total walking time
This is not as easy to figure out though one nice thing is we don't really have to factor in what order he cuts them
But it still leaves us with the question of how can you add up the distance to every tree on the map?
well to start with finding the distance to any particular tree from the lumber camp can be seen as just the
hypotenuse of a right triangle
So all we need to do is calculate the distance using Pythagorean theorem
now just do that fifty seven thousand five hundred and ninety four more times to get it for every tree on the map and then
Add them all together
The problem is even calculating those at one per second would still be over sixteen hours
If you think about it, though, we don't really need to calculate all of them
We can reduce that work by cutting the grid into four quadrants
Assuming our lumber camp is in the middle and then just use the Pythagorean
Theorem for every tree in that quadrant and just multiply by four
All we need is a process to automate that if we just think about the grid within a quadrant as well
Any tree we pick has a unique tile that can be described by some number to the right and some number down from the lumber camp
Every tree is going to have a unique combination of those numbers which makes the two sides of a triangle
the fact that every tree is just a different coordinate of right and down movements means that we can automate the
calculation with an Excel spreadsheet
Won't get into it too much but basically it's doing the Pythagorean theorem with the trees row and column number
The point is each cell represents a tree and is telling us how many tiles it is directly away from the lumber camp
you can see the example that was seven to the right and two down gives us the same distance as before but much faster than
Calculating by hand the giant map extends 119 tiles away from the lumber camp in each direction
So we just add all the numbers going out that far and you get a sum of just over 1.3 million tiles
That's the distance to visit each tree one way or at least a reasonable estimate
Multiply it by 2 for a round-trip
times 10 for the number of trips per tree without wheelbarrow
And then times 4 since this is just for one quadrant in the end
We get a total walking distance of over a hundred and five million tiles I get the sense
He'll probably reach his Fitbit goal for the day
Villagers walk point 8 tiles per second meaning to walk back and forth 10 times from every tree would take him over 2 million minutes
Adding that to our overall count before we get a total of about 2.4 million minutes or a little over 40,000 hours of game time
since we're doing this on fast speed we'd divide that by 2 and get a final answer of
About 2 years 3 months and 3 weeks of real time almost 90% of which is taken up by walking
Sounds like he's got his work cut out for him or actually, he'll be the one cutting but you know what I mean
If anyone would like to verify that experimentally you're more than welcome to do so
On the plus side, you'll end up with more than five and a half million wood
so you're really going to be set up for a Post-Imperial trash war
Just for curiosity's sake here are the results for some other map sizes as well
They can range from just under four months to over 17 real life years
Just looking at the Ludacris size map on its own a tree in the corner as far away from the lumber camp as possible takes
An hour and 14 minutes of real time to cut and that's just one tree out of over
230,000. So how close was your guess the correct answer for a giant map was of course option D for me the walking distance added
Up faster than I expected. But certainly makes sense in retrospect and it was a fun problem to try to work out
That's all for this one though. Thanks for watching guys, and I'll see you next time