The last post got a lot of feedback since we all love math, but this is also quite interesting. I didn't realize that quartering troops was such a common practice as I had imagined more armies acting like the Romans setting up their own camps - however it seems common based on the authors writing. He mentions a few times how this probably impacted the writing of the American 3rd amendment - no quartering troops in civilian homes
The third amendment was a response to the British quartering troops in American houses. This was often done as punishment or harassment, and the soldiers were often not well behaved.
Edit: From my reading of history, none of this is unique to the British American Colonial experience. Forms of it are ongoing in occupied countries.
And frankly, I believe we would've seen similar levels of civilian violence and sexual violence in American occupations of other countries had Americans not generally fed and housed their own and therefore avoided that kind of close contact and dependence.
Probably, I wasn’t implying it was specific to Britain, just that the 3rd Amendment (like most of the Constitution) was a direct response to abuses incurred from the Crown in (their) recent history.
I love “the tyranny of the Wagon Equation,” what a great way to put it. I’d never thought through this before, but it provides a lot of context on the way wars unfolded throughout history.
It would have been fun to see the exponential behavior unfold. Want to supply one soldier for one week? No big deal. Want to supply one soldier for n weeks without resupply? Better have a huge amount of resources dedicated to just supply.
Except I suspect the wagon equation is actually worse than the rocket equation. Rockets can have large fuel tanks, and rockets can throw away their stages en route. But if you like your army to continue to exist, you can’t throw away your wagon drivers, etc. So you have worse than exponential behavior — eventually any food-carrying resource runs out of the ability to carry its own food, and it can’t go farther even with exponential blowup.
I suppose that, if setting up supply caches is in the cards, then the rocket equation might emerge again. If one person can carry enough for a 10-day round trip, then they could walk 4 days, deposit 2 days of food, and walk home. Repeat five times and there’s a full resupply at the cache. Now the person can deplete the cache by visiting it, filling their pack, walking four more days, caching two days of food, and walking all the way home. So they can go on a 4n-day one-way trip by doing ~5^n advance supply trips.
At least once you boost a rocket to escape velocity, it keeps going!
The keys that makes the desert problem finite bounded are "can't leave supplies in the desert to pick up later" and "without starving any traveler on the way". Relax either restriction and you're back to exponential behavior, either by taking extra trips or leaving a lot of dead travelers.
I don’t see how that matters if you can have arbitrarily many carriers.
Let’s say a carrier carries food for 3 days. To get one carrier 4 units out, send out 2 carriers, let them walk for one day, have one of them load up the other. The first has food for 1 day left and can return to base, the second has 3 days supplies and can walk to the finish.
To get one carrier 5 days out, do the first part twice to get 2 carriers at distance 1 with a day of supplies and 2 with 3 days of supplies. The first two can return to base, the other two can walk to distance 2, reload, and let one carrier reach distance 5. The other has food to return to distance 1. There, it can be met by a carrier who left base just in time with 2 days rations left, and both can return to base.
I think this scheme extends infinitely. To get one carrier N+1 days out, get 2 fully loaded N-3 days out, have one dash for the finish, and have one return to N days out, where they can be supplied with one day’ rations to return to N-1 days, etc.
This seems like so much more effort than war in modern times. Wonder what future generations 100 to 200 years from now would think and write about our current happenings.
Modern war requires even more effort. Hundreds of thousands of Russians and Ukrainians are consuming much more than a Roman legion or a Spanish army in the Netherlands. They need a constant stream of fuel and bullets and shells and more food than just bread. It's just that trucks and trains and oceangoing ships make logistics possible at this scale.
Some of it is pretty specific, but decisions like:
* Heavy or light foraging?
* Forage with smaller groups of cavalry or large groups of infantry?
* Terrorize the people in the countryside or try to stay on their relative good side?
* Do you have handmills?
* When is your campaign going to happen?
seem like the type of choices that could intuitively be included in a board game (although some of the content bumps it out of comfortable family game night fare) or even maybe hacked into a pen and paper RPG (I say hacked in because usually players aren't in charge of huge armies anyway, so we're already pretty far from, like, standard d&d).
It would be neat to play a game about logistics with tactics as an afterthought, for once.
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[ 2.1 ms ] story [ 43.7 ms ] threadAnd frankly, I believe we would've seen similar levels of civilian violence and sexual violence in American occupations of other countries had Americans not generally fed and housed their own and therefore avoided that kind of close contact and dependence.
Except I suspect the wagon equation is actually worse than the rocket equation. Rockets can have large fuel tanks, and rockets can throw away their stages en route. But if you like your army to continue to exist, you can’t throw away your wagon drivers, etc. So you have worse than exponential behavior — eventually any food-carrying resource runs out of the ability to carry its own food, and it can’t go farther even with exponential blowup.
I suppose that, if setting up supply caches is in the cards, then the rocket equation might emerge again. If one person can carry enough for a 10-day round trip, then they could walk 4 days, deposit 2 days of food, and walk home. Repeat five times and there’s a full resupply at the cache. Now the person can deplete the cache by visiting it, filling their pack, walking four more days, caching two days of food, and walking all the way home. So they can go on a 4n-day one-way trip by doing ~5^n advance supply trips.
At least once you boost a rocket to escape velocity, it keeps going!
That problem is called the “travelers across the desert problem” (https://en.wikipedia.org/wiki/Jeep_problem)
I would think it can reach arbitrarily far, but can’t think of an easy proof, or find one.
Let’s say a carrier carries food for 3 days. To get one carrier 4 units out, send out 2 carriers, let them walk for one day, have one of them load up the other. The first has food for 1 day left and can return to base, the second has 3 days supplies and can walk to the finish.
To get one carrier 5 days out, do the first part twice to get 2 carriers at distance 1 with a day of supplies and 2 with 3 days of supplies. The first two can return to base, the other two can walk to distance 2, reload, and let one carrier reach distance 5. The other has food to return to distance 1. There, it can be met by a carrier who left base just in time with 2 days rations left, and both can return to base.
I think this scheme extends infinitely. To get one carrier N+1 days out, get 2 fully loaded N-3 days out, have one dash for the finish, and have one return to N days out, where they can be supplied with one day’ rations to return to N-1 days, etc.
(Given the description of https://puzzling.stackexchange.com/questions/233/travellers-... and https://www.mathsisfun.com/puzzles/cars-across-the-desert-so..., I think “get at least one carrier across” is the correct interpretation of the somewhat imprecise text on Wikipedia. It certainly can’t be “get all across”, as that’s trivial if you don’t allow intermediate dumps)
* Heavy or light foraging?
* Forage with smaller groups of cavalry or large groups of infantry?
* Terrorize the people in the countryside or try to stay on their relative good side?
* Do you have handmills?
* When is your campaign going to happen?
seem like the type of choices that could intuitively be included in a board game (although some of the content bumps it out of comfortable family game night fare) or even maybe hacked into a pen and paper RPG (I say hacked in because usually players aren't in charge of huge armies anyway, so we're already pretty far from, like, standard d&d).
It would be neat to play a game about logistics with tactics as an afterthought, for once.