Perhaps you’ve seen this image floating about the internet?
Fellow capper Sans Serif
reposted it to his fb, where one of his friends suggested there might be a sweet spot where an elephant could still breathe without being crushed. To see if that’s so, we first need to know how much weight that elephant column puts on an elephant at a given height. [If this were basic cable, this is where we'd put a "science content" warning. Since it's not, we won't. If you flunked out of AP Physics, just ignore the formulas and you should get the gist.]
Adapting from the first source I found, the weight of a column of height h would be
W(h) = R * h * We / He * (R + h)
where R is the radius of the earth at the bottom of the stack, and We and He are the respective weight and height of a unit elephant. So, if we take Ht as the total height of the stack, the total weight would be
Wt = W (Ht) = R * Ht * We / He * (R + Ht)
To find the weight, WA, pressing down at height h, we just subtract the weight below from the total weight and do some mild algebra to get:
WA(h) = Wt – W(h) = C * (Ht – h) / ((R + Ht) *(R + h))
where C is a constant defined as
C = R2 * We / He
So, let’s see if the first space elephant, sitting at the so-called edge of the atmosphere, the Kármán line, h = 100 km, might have survived the weight on top of it. We’ll treat the earth as a perfect sphere and use R = 6,371 km. To get a (relatively) short stack of elephants, we’ll go with the more pessimistic results of our casual googling and put “every elephant in the world” at 326,000. We’ll also go with an average height of He = 3.4 m, which puts the whole stack at Ht= 1,108 km. Plugging these all in, we find a weight of just under a quarter million elephants pressing down on the first space elephant. Without looking up the compressive strength of an elephant, I’m going to say that’s still well in the crushed elephant range. So, there’s no sweet spot in the breathable but uncrushed range. I’d further wager that’s not just crushed, but liquified too. So, in addition to the space elevator we’d probably have to build to carry this all out, we’ll also need a tube extending up into orbit to hold our Dumbo gumbo. Which would be some pretty advanced technology, bu wasn’t it Arthur C. Clarke who said that any sufficiently advanced technology is indistinguishable from a slurry of elephants?