Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
Years ago I watched a weird cartoon.
There was a big friendly creature sitting at the top of a hill with a circular plate in front of it and a whole chocolate cake. It’s just about to tuck in when a little friend turns up with a plate in its hand.
The big friendly creature cuts the cake in half and gives half to its little friend. Fair’s fair, right? It’s just about to tuck in when another little friend shows up with an empty plate. The big friendly creature says “half for me, half for you”, cuts the cake in front of it in half and gives it to its friend. Except it’s now left with a quarter cake.
This keeps happening until the big friendly creature is paring down ever thinner wedges of cake. We pan out to see a queue of little friends leading all the way down the hill with no end in sight.
Weird right? I thought it was a bit short sighted of the big guy, and I thought it wasn’t fair that it never gets to eat anything while the first little guy is presumably chowing down on an entire half but anyway I digress…
“When will the cake run out?” is not a useful question in this case because the answer is “technically, never”. “When is there so little cake left there’s no point bothering with it?” is what we’re actually getting at, but that’s too subjective.
So if I just tell you how long each “round” takes (how long it takes the big friendly creature to cut and serve half of whatever’s left) you can take that information and do what you want with it. For example if you decide a 1/32 piece isn’t worth bothering with you can work out how long it will take to get there.
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