A New "Hilbert" Problem

Y. B. Karasik
Thought Guiding Systems Corp.,
Ottawa, Canada.
e-mail:karasik@sympatico.ca

The info by Genady Filkovsky about octopuses caused me to search for an explanation to why the arm of an octopus reaches the food the way it is described in the note. It is quite possible that octopus does it in order to minimize the effort of reaching food. (The "effort" is yet to be defined.) To verify this hypothesis one has to solve the following problem.

Suppose that muscles are evenly distributed along a completely flexible arm. How should they be flexed in order for the arm to reach the food with the minimum effort ?

If the solution is that the muscles have to be flexed to form three rigid joints, then this would confirm the hypothesis.

However, it is not clear what mathematical apparatus has to be employed in order to solve the problem. It looks quite formidable. Not sure if the calculus of variations can help. It seems that the problem is a good candidate for yet another "Hilbert" problem.