22
2020
Research
Sorting out everything
Claude E. Shannon is said to have been the first person to realise sorting problems that look enormous from an intuitive
perspective are actually small enough to be implemented in industrial practice. Unfortunately, Shannon devised a formula
for the minimal number of sorters required for a given waste flow without providing details of how to achieve this minimum
in practice. Delft University of Technology is trying to make a machine fitting the ideal profile of a Shannon sorter as a step
towards a circular use of materials.
Flake sorter being developed at Delft University of Technology in the Netherlands.
M
athematics is supposed to be the most
transparent part of science, but some
algorithms forming the basis of ad-
vanced technologies like DVDs or mobile
phone routing feel like magic. The same
is true for a mathematical theorem for the
amount of work needed for sorting a mixture
into many different materials. In 1948, Shan-
non proved that a method with a minimum
number of sorters exists – without explaining
how this method works in detail.
If we ignore the ‘how’ issue for a moment,
Shannon’s formula is truly spectacular. Sup-
pose a waste flow of 1 ton/hour contains 100
different colours of packaging plastics: after
shredding and washing, a series of machines
can sort the flakes with the help of colour sen-
sors, by ejecting flakes with certain specified
colours from the rest of the flow. Assume each
sorter has a capacity of 1 ton/hour.
Seven sorters required
Shannon’s theorem says that, provided
they are well programmed and scheduled,
just seven such machines can always sort the
waste into 100 pure products, regardless of
the concentrations of the individual colours
in the flow. Actually, for the typical concentra-
tions of different colours found in packaging,
Shannon’s formula suggests a line of just four
machines should suffice!
Obviously, Shannon’s sorting plant differs
from those we know today. Object sorting
plants for plastic packaging often contain
seven or more sensor sorters, but typically
sort into four or five different products, not
100. But then, the strategy of object sorting
plants is very simple: first remove plastic ob-
jects of type A, then remove objects of type B,
etc. Some additional sorters are used to cor-
rect mistakes in previous sorting steps.
Sorters moving around
Frankly, it’s not clear how exactly Shan-
non’s minimal sorting plant works, but Fig-
ure 1 probably comes close to the underlying
22-23_logarothmicsorting.indd 22 12-09-19 14:16
