first section of this part is given to knots: if you make a knot
with a rope and then you secure it by joining the two ends, you
fix it in something that cannot be untied (unless you made a false
knot that by means of manipulation could be reduced to the shape
of a circumference). There are simple knots and very complicated
ones and the work Continuo infinito presente, by Remo Salvadori,
is an example of artistic employment of knots.
First of all the visitor is invited to recognize what are the knots
that represent some of the models hung up all along the way. He
has got two instruments at his disposal: on a first table there
are the same models hung up so that
he can hold them and look at them from different points of view,
till he recognizes them; on a second table there are some "special"
ropes: the visitor can knot them at will and, furthermore, he can
join their ends (magnetic) so that each knot can be disposed on
a table by flattening it in various positions, each one giving a
different way of portraying the same knot.
The same ropes can be also used to reproduce some artistic knots that you
can see in Milan (from capitals in Sant' Ambrogio to Borromeo family
coat of arms) and that are reproduced on a poster. It is particularly
curious to observe that the three
rings of Borromeo family coat of arms were not always drawn
in the same way and these seemingly "little" changes in the drawing
generate completely different knots as a matter of fact.
table shows the drawing of a rope carved into a wooden
framework; by following the track in the wood it is possible to
"make" this knot thanks to available ropes and then fix it by joining
the two ends; the result is a knot which looks rather elaborate:
if you slip it from the track and you manage it, you can realise
how, as a matter of fact, it has a much simpler shape and it is
even one of the hung up knots.
Finally two knots are placed in front of a mirror:
by means of two available ropes, it is possible to realize that some knots are identical to their mirror image while others are not.
the second part, the plan of Milan is a good opportunity to propose
two classical topological problems.
On a first table there are a good number of maps where some itineraries
are marked with different colours: it is a matter of understanding
if and how it is possible to go along each itinerary without detaching
the pencil from the paper (that is to say, without "flying") and
without going along the same street twice (that is to say that you
do not want to see things a second time). And trying to understand
why some times it is possible to do it and other times it is impossible.
The so-called problem of the "three houses" is shown on a second
table: it is a question of linking three landmarks (in our example
three stations: Centrale, Nord and Garibaldi) up to three others
(in this case: the Duomo, the Linate airport, the Meazza stadium)
by means of itineraries that do not intersect. A first map proposes
this problem using a "normal" plan of Milan, while a second one
let the visitor fly of fancy and presents the same problem in a...
science fiction situation: the map is the same but now it is possible
to go out from one of its sides, ON CONDITION that you go back into
again following some rules (for instance on the opposite side and
at the same height) that recall what happens in some video games,
when the cursor leaves the screen and reappears on the other side.
Some tridimensional models show also how these "rules" are equivalent
in the reality to draw the plan of Milan on a surface different
from a plane one (a doughnut surface and
a Moebius strip surface);
an interactive animation proposes the same question on the workstations
(from computer screens).
map of the old Milan with its town walls takes the opportunity to
another observation: it is possible to compare the plane map with
its transposition on two other exhibited models, a double doughnut and another
Moebius strip: of course the
distortion is wide but some elements are still clearly recognizable.
An animation allows visitors to understand the procedure and the way
the map of Milan has been shifted on the double doughnut or on the Moebius strip.