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I don't know for sure but I strongly suspect that Pratchett was heavily influenced by Operation Black Buck: https://en.wikipedia.org/wiki/Operation_Black_Buck

In particular, this diagram from that page makes the process clear: https://en.wikipedia.org/wiki/Operation_Black_Buck#/media/Fi...

Hopefully the name of the original mission is enough to help you find a link to some relevant mathematics :-)

That diagram is anything but “clear”.

I find it fairly clear.

- each vertical line is the flight of an airplane

- each horizontal/diagonal line is a refueling operation

So, planes take of from Ascension Island at the bottom, only one reaches the Falkland Islands.

Ignoring the gray vertical lines (they are for ‘insurance’, in case other planes would have hit a problem), we have:

- 6 Victors taking of

- 3 of them refueling the other 3 after a short while (presumably because taking of and getting to flight height uses more fuel than steady flight), immediately returning to base afterwards.

- the bomber taking off

- a seventh Victor taking off, refueling the bomber twice, and then returning to base

- one of the 3 Victors of the first wave refuels the bomber twice, then refuels another of the three before returning to base

- that second one refuels the third one and returns to base

Etc.

Here's a bit better diagram: https://i.imgur.com/LZLSlI3.jpg

Of all the aicraft that took off, only one actually flew over the target. It had to be refueled seven times on outbound journey, and the last tanker itself had to be refueled three times to fly that far.

Yeah, OK, wow. That's ... complicated. And I think they didn't manage to get a very good return for all this effort, from a diagonal reading of the article.

Er. Sorry, I'm being thick, but your hint about the link to the relevant maths etc went way over my head. I might be missing a cultural reference? :0

I think it rather alludes to caravans and their trade with beduins accross established trade routes

Didn't the British do something similar in the Desert Campaign during WW2, burying supplies to be recovered later. The Long Range Desert Group perhaps?

Reminds me of the rescue of the Thai football team too, where the divers were dropping oxygen tanks further and further in to reach the boys.

This blog post has a great detailed description of Operation Black Buck: https://www.navalgazing.net/Falklands-Part-6

This is great, thank you for sharing!

There is an excellent book about XM607/ Operation black buck written by Rowland White. It’s not just about the actual mission it’s also about retiring the Vulcan then bringing them back and all the other bit that led up to the mission.

http://www.rowlandwhite.com/portfolio-view/vulcan-607/

If you have even a passing interest in aviation then this book is a must read. Very deep, yet incredibly compelling. I kept finding myself on edge...

I don't know about uncomputable but for intractable, I think, and as rco8786 has already pointed out, dynamic programming sorts of fit the bill. Similarly, this is what reinforcement learning does for search. Recursive or sequential monte carlo algorithms where states hold memory across transitions probably also fit this bill. And most generally, this is what humanity does with science, skills and knowledge.

No single human could discover general relativity, but generation after generation, from the first humans who worked out how to count symbolically to the definition of a Lorentzian manifold, we've been leaving caches of knowledge for each other so each next generation could reach ever farther.

Aye, found the passage from Small Gods:

Hierarchy, Vorbis said later. The Ephebians didn't think in terms of hierarchies.

No army could cross the desert. But maybe a small army could get a quarter of the way, and leave a cache of water. And do that several times. And another small army could use part of that cache to go further, maybe reach halfway, and leave a cache. And another small army . . .

It had taken months. A third of the men had died, of heat and dehydration and wild animals and worse things, the worse things that the desert held . . .

Described in idealized form here: https://en.m.wikipedia.org/wiki/Jeep_problem

The benefit of the support runners wasn't just to help him keep pace (he could probably do this with music). They also provide a drafting help to limit any head-on air resistance.

Is that significant when running?

Yes, for an attempt like this where every marginal gain is necessary https://www.runnersworld.com/training/a20823445/does-draftin...

Even a 1% benefit is significant, considering that he beat the 7200 second goal by just 20 seconds (0.28%).

It's supposed to be good for about 2% at marathon pace. I'm not quite sure how long pace makers last in a traditional marathon, but I assume at least half way. So the rotating pace makers today explain maybe 1:12 of the two minute difference to his traditional best time.

That's how a good chunk of the arctic was discovered. Previous expeditions would go in for the sole purpose of leaving caches of foods and other useful goods.

> It's a slow and costly process, but it gets the job done and it made me wonder if there are algorithms like that, that can compute results otherwise uncomputable

The catch with certain classes (maybe/probably all? disclaimer: am not theoretical computer scientist/mathematician) of uncomputable problems is that they are such that there is no notion of "getting closer" to the solution that's analogous to traversing the desert to a known location. There is no way to verify whether the next incremental step is taking you closer to or farther from the solution because calculating such is essentially the same problem as the root problem. See https://en.wikipedia.org/wiki/Undecidable_problem

No, you're right. I say "uncomputable" but that's not what's happening here. The problem is not "uncomputable" it's just that the result is negative (X men can't cross Y distance carrying Z provisions).

Thanks for pointing this out, my bad for using "uncomputable" wrong.

This is also why rockets have multiple stages. A single rocket can’t make orbital velocity with significant cargo, but a bigger rocket can get the small rocker part of the way there. It works because the second stage’s lower weight allows for smaller engines and fewer fuel tanks etc.

First thing that comes to mind is using an HP-12c calculator and only having 4 stacks available. You can go further than a regular calculator, but only a little bit at a time so you keep chipping away at a long equation and eventually your stack collapses down into the final answer across the desert ;-)

Seems similar to Conway checkers. https://en.wikipedia.org/wiki/Conway%27s_Soldiers

https://en.wikipedia.org/wiki/Operation_Black_Buck

Great example

Sounds like dynamic programming

It kind of does. I have dynamic programming in my mind also, these days hence why I'm not sure- maybe I'm seeing dynamic programming everywhere.

I don't play many video games, but when I do they tend to be military strategy games of various types. After reading your comment, it made me think if I ever deployed such a tactic in the video games that I've played and I couldn't think of a situation. I found this very interesting! Seems like an amazing dynamic to add to a video game if it were possible.

Some commenters responded saying rockets have this property... but I don't know. I'm having a hard time reconciling that mere stages model this concept. Since if so, you could argue that anything that introduces a progression satisfies this condition. Maybe there is some nuance here, for example, the caches can't be directly controlled by a player.

I've seen this problem several times expressed using camels and bananas [1]

I would also think it's related to the rocket equation - with each iteration of "grab bananas, turn around" you have fewer bananas to carry with you, but it forms a parabolic curve as you need many bananas at the start of the desert, fewer as you go onwards and don't need to make trips to retrieve the bananas you've already eaten.

[1]http://www.crazyforcode.com/camel-bananas-puzzle/

Actually sounds very similar to how the rocket equation works, too.

Solution to the Byzantine General’s Problem using proof of work is possibly an example. The basic problem is: how do you make sure that multiple entities, which are separated by distance, are in absolute full agreement before an action is taken?

If one is not trying to solve it in the fastest time, then an agreed ‘truth’ can be reached after ‘some time’ without a central entity. By deciding to go ‘slow’, a solution can be found eventually.

Another example is rockets. Most fuel in rockets is used to propell the remaining fuel up the gravity well

Maybe some kind of opportunistic prefetching if you have regular deadlines and can expect a regular complex problem deadline. But maybe concurrent threads would be easier, so this could make sense only in a super limited embedded environment.

The Tower of Hanoi!