The second Project (PDF) deals with
polyhedra. They are beautiful too and related to calculus. Every network
G defines a function fG(x). The problem of computing this function
is known to be the hardest problem in computer science: it is
NP complete. We learn
here how to compute the function from local data. It is interesting that
like primes, which were studied initially for purely mathematical reasons and
which then exploded to the most important encryption and key exchange technology,
also polyhedra were studied originally since Plato for their purity but are now
part of a theory of networks which is used in tacking modern problems of communication,
computation, logistics and are at the heart of complexity theory: if we were able to compute
fG(x) effectively, we could solve essentially all hard problems in computer science
as it would settle the P versus NP problem.
Icosahedron
Echidnahedron
Tetraxishexahedron
The movie ``Travelling Salesman"
appeared in 2012. It is a stage play similarly as the Swiss play
``The physicists" written by Dürrenmatt.
[ As Singh once pointed out, WW1 was the war of the Chemists (Gas), WW2 was the war of the Physicists (A-Bomb)
WW3 most likely will be the war of Mathematicians (Communication).] In the Travelling Salemen movie, the
conversation builds on a scenario, in which the NP problem was solved affirmatively. Nobody who works in the
field however believes that P=NP holds. The goal is to prove N and NP are different. Like the scenario
that extraterrestial life exists which will be able to get in contact with us, the scenario N=NP makes good
Holliwood stuff.
