An Infinite Orchard (opens in new tab)

(alaricstephen.com)

22 pointsbladecatcher7y ago5 comments

5 comments

The final paragraph on the topic alludes to Olber's paradox, but stars are not infinitesimally small, so I do not think the argument applies here (though the Big Bang makes the question moot anyway.)

http://cmb.physics.wisc.edu/pub/tutorial/olbers.html

Retra7y ago

Stars are also not confined to an integral grid. Surely if the trees in the orchard were not so confined, they would cover the entire field of view.

mannykannot7y ago

Good point - though it has me wondering this: the equi-spaced grid is a case having a straightforward proof (given that Cantor did the heavy lifting), but is it a necessary condition?

1 more reply

mcenedella7y ago

In the final problem, as the apple trees can be in more than one line, the minimal valid solution is 9 trees, not 12.

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5 comments

mannykannot7y ago

The final paragraph on the topic alludes to Olber's paradox, but stars are not infinitesimally small, so I do not think the argument applies here (though the Big Bang makes the question moot anyway.)

http://cmb.physics.wisc.edu/pub/tutorial/olbers.html

Retra7y ago

Stars are also not confined to an integral grid. Surely if the trees in the orchard were not so confined, they would cover the entire field of view.

mannykannot7y ago

Good point - though it has me wondering this: the equi-spaced grid is a case having a straightforward proof (given that Cantor did the heavy lifting), but is it a necessary condition?

1 more reply

mcenedella7y ago

In the final problem, as the apple trees can be in more than one line, the minimal valid solution is 9 trees, not 12.

j / k navigate · click thread line to collapse