[lwfpegsf] Binary play dough

Take a lump of dough or clay and divide it in half.  Take one of the halves and divide it in half.  (Perhaps use a balance to divide precisely.)  How many times can you repeat?

Each lump, perhaps formed into a sphere, has linear dimensions 79.37% = (1/2)^(1/3) of the lump twice its size (volume).  Three halvings divide by 8, so you should a have a lump with half the linear dimensions.

Express numbers in binary as subsets of lumps.