We began with an offbeat problem, described in terms of physical objects, and
ended up with an abstract and idealized solution, expressed in terms of the sum
of an infinite series. It is important to think carefully about what we are
entitled to conclude from our ultimate answer about the original problem.
Assuming that we didn't make any mistakes along the way and that the parts of
Maple that we used are implemented correctly, then it is true that in
principle we can stack blocks so that they extend arbitrarily far beyond the
edge of a table. But in practice, with real blocks and tables, it will
be difficult to get more than a couple feet. Here are some points to ponder:
- With 100 blocks, the stack extends approximately 2.6 feet beyond the edge
of the table. But in building the stack, the blocks must be adjusted to a
tolerance of 1/200 of a foot, or about 1.5 millimeters. It rapidly becomes
difficult to precisely place the blocks.
- Furthermore, once we get into small tolerances, even small irregularities
in the densities of the blocks can begin to throw off the delicate balance.
- How much does a block weigh? Eventually, the blocks are going to crush
the table!
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah