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 :-)
- 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.
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.
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
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.
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 . . .
Even a 1% benefit is significant, considering that he beat the 7200 second goal by just 20 seconds (0.28%).
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
Thanks for pointing this out, my bad for using "uncomputable" wrong.
Great example
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 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.
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.
This reminded me of an episode from Terry Pratchett's Small Gods. This is mostly from memory, but he describes an invasion of the country Ephebe where the invasion force comes from the side of a desert considered impassable, because no expeditionary force could carry enough provisions to make it through the desert. The trick is that a number of expeditions have preceded the invasion whose function was to leave caches of provisions for the actual invasion force to use. Each expedition only has to carry enough provisions to make it to a cache location and back and of course multiple expeditions can deposit provisions to the same cache location, until it is sufficiently stocked for the invading force.
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. I'm pretty sure there are- in fact I'm pretty sure it's something blindingly obvious that I'm missing because I'm thinking of it in terms of runners and soldiers crossing deserts... Maybe divide and conquer strategies, or dynamic programming?