Decades ago two mathematicians argued about the area of the mandelbrot set. Both argued an asymtoically approaching different numbers. They started a distributed project to calculate the area.
I donated time on PA-risc workstations to the effort and was surprised to hear that the 2 machines contributed more to the final answer then 100s of other contributors. Something about how HP's compiler/chip preserved more accurate in the intermediate results than others. That surprised me since AFAIK the PA-risc is just a normal 64 bit floating point unit, which doesn't every have more precision for intermediate results. I believe PCs at the time often used the x86, which has 80 bits of precision for the intermediate results.
I believe the project was a success, but I don't remember the conclusion.
More context here (alt.fractals discussion from February 1991) [0]:
[...] by computing the area of the M-set
using lots of terms in a series (Laurent Series?), the upper bound of
the area seems to converge about at 1.72 (the graph gets quite flat,
and seems to have an asymptote there), and by counting pixals more and
more accurately, you seem to get a lower bound of very close to 1.52.
Both these bounds are close to the values the methods would produce in
the limit - that is, it is NOT the case that these numbers would get
closer if a finer grid were used, or more terms were taken in the
series. So, why the difference of 10% or so? No one knows.
I donated time on PA-risc workstations to the effort and was surprised to hear that the 2 machines contributed more to the final answer then 100s of other contributors. Something about how HP's compiler/chip preserved more accurate in the intermediate results than others. That surprised me since AFAIK the PA-risc is just a normal 64 bit floating point unit, which doesn't every have more precision for intermediate results. I believe PCs at the time often used the x86, which has 80 bits of precision for the intermediate results.
I believe the project was a success, but I don't remember the conclusion.