after this this presentation I had
two possibilities to enter or not to enter
in any case he was in one of the future
possible the physics of the last century
he showed an ancient intuition of the
eastern mysticism
that is, that the world the space in which
we live is a complicated one fabric
dynamic network event button quoting
the words of Carlo Rovelli not only the
things can come into relationship but
it is precisely the relationships that
they determine the notion of what I am
a researcher at the University of Udine
I take care of the networks
they are an extremely simple model
linear satisfying but also omnipresent
internet the web
social networks our brain
what fascinates me about this model
some networks that they contain include
within them three interesting models
that I will try to illustrate you in this
linear model presentation
the branched model and the model
circular and are all represented in
this in this network or even graph like
the mathematicians call it
let’s start from the linear model what it is
the linear model is linear model
an incessant succession without
possibility of distant alternatives
corresponds to the concept of fatalism e
can be viewed using a
I walk a path then one
succession of points I will explain
this model using
the idea the phenomenon of the six degrees of
separation
someone knows the theory of the child
world well maybe my students saw it
who taught her this year and there
they are here
the theory of the small world tells us
this
take a random person on the planet
land
a tijuana mechanic in mexico or a
greengrocer of perth in australia
how many degrees of separation separate us
from these people if I knew
directly the mechanic there would be a
degree of separation
if I knew it indirectly through
another person maybe a friend of mine
he studies in Mexico there would be two degrees
separation and so on
the phenomenon of the small world tells us
that despite the world is great
network is vast in terms of a
number of actors nodes the distances between
people between actors are very small in
mathematics we say that they are logarithmic
in the number of nodes on so a lot here
at the beginning of the last century in 1929
a semi-unknown writer offer you that
be in a writer a story
entitled chains chains
from here he extracted this paragraph from him
Imagine choosing a person randomly
between one and a half billion living that
then they lived on the earth and bet
that not with more than five individuals
intermediate ie no more than six steps
he can reach through the
network of knowledge this person is the
first to guess this phenomenon though
lav intuits literary in the
sense that leaves an intuition of pure
fantasy
for me it is surprising that 40 years later
c
in 1967 an American psychologist Stanley
very famous milgram leads his
famous experiment on the small world e
in a certain sense it confirms intuition
di cali what does milgram take the list
there was no internet then
randomly choose one hundred people and
asks these people to send one
letter a package a package to a
recipient who lives a thousand kilometers
of distance
they must send through the network though
of personal knowledge
eventually he goes to his friend
collects the letters redone
of course some have been lost for
road on the letters were noted
all the steps of these chains of
these paths calculate the average of the
walk and the lengths of these paths
the number 6 comes out , that is actually 5.9 from
here the myth of the six degrees of separation
this hypothesis this idea of the child
world therefore of the fact that the world
although it is very large it is connected
from very small distances between the
individuals was then repeated was
recently confirmed in a
experiment a job done for more in
collaboration with the Milan Polytechnic
on the facebook network using a sample
much larger than the one used by
milgram a sample of one billion e
half of people just the same i
numbers that return the same number of
people who lacked imagined on the
planet earth 80 years before the gra of
separation are diminished today are 4.5
the second model I would like to
talk to a branched model implements it
realizes the concept of free will
and can be represented by a
tree the points of choice and walk
possible future a garden of paths
that fork we could say
the temporal reasoning and here we speak
of time has very ancient origins dates back
just to the Greek philosophers aristotle is
the first to question themselves on questions
thunderstorms with the problem poses the
problem of future contingent people
futile contingents are propositions that
refer to future events
aristotle wonders we take this
proposition there will be one tomorrow
Battleship
or reformulated to the present times there
it will be an earthquake tomorrow or tomorrow
the sun will rise to the state you are asking
we can define a value of
truth in a true false binary logic
for these statements today we can
to say that today these statements are
true or false in its simple wisdom
my mother would say that only the gentleman knows
the answer and a few centuries later
William of ockham did not say much
different
with all due respect to the self- response
it lies in the mind of man is not in the
mind of man but it is only in the mind
of god is actually ockham attributes
to man a very important property
the ownership of free will then
the property to choose between different
make choices and then create
different possibilities of towards paths
several possible futures and this in one
certain sense explains from a solution to the
aristotle problem of the future
contingents or these statements
they are not inconsistent as if
let’s imagine a tree structure in
which there are as future as possible
we joked at the beginning in a future
I showed up by giving this
talk in another I ‘m behind my drink
the relaxing
then it is perfectly lawful that in
some of these futures there is one
earthquake or a naval battle in
others there is not
or in all these futures it will rise
the sun tomorrow or the earth will end
curious as in the 50s a philosopher e
logical New Zealand arthur prior studies
these are mainly these reasons
those of ockham and defines the concept
of temporal logic of which you see i
four main operators of the
causality brunch in logical time the
ramified temporal logic and its
inter their interpretation on
tree structures I will not go today though
It is interesting for me to make you understand that
from these philosophical dispositions that
they may seem
in short, superficial in some ways it is
born a logic that today has important
very important applications in
artificial intelligence for example for
represent temporal knowledge e
in computer science to analyze the
behavior of reactive systems not
deterministic but the third model of
which I would like to tell you maybe that one
a little more interesting or more surprising
it is the self-referential model o
Circular is a path that returns on
his steps
a cycle we say in graph theory a
just uroborus and snake that you eat
tail
self-referentiality or recursion in
math is a concept
surprisingly present in nature and
take the shape of the fractal here you see
the Roman broccoli that besides being
very good and also a perfect one
fractal example what to treat a
fractal is a geometric figure that is
repeats to different scales on your own
right you have a fractal image
of broccoli in its entirety
your left had in particular
he sees that detail looks like everything
so there is this form and back to
this sort of self-referentiality of
circularity this is let’s say it
self-referentiality in nature this e
self-referentiality in mathematics is
always risky to show some
mathematical but mathematical equations in
a the talk and reality this equation
I care a lot about it
first of all because an equation
beautiful and I challenge anyone to say the
contrary
and this is not poetry and then it is
a useful equation to use you
everyday
this equation because the equation that
is the basis of an algorithm that is
call pagerank is pagerank
the algorithm uses more google search
the search engine to order the
pages in front of yours
interrogation in the face of your own
request
wanting to paraphrase the meaning
interpret giving an interpretation to
these mathematical symbols we could say
that we can read it this way
the equation says that an actor in the
important network if surrounded by others
important actors
you have grasped the circularity of the thing
I’m defining something in terms of if
same self referentiality almost one
tautology we will say in logic even if in
reality there is a precise solution
nicely where you see the
recital well lambda number has one
matrix an algebraic structure that
it serves to encode to represent
the exan carrier network so you can not
simplifying the x1 is someone said
Yesterday are very different structures between
of them
the recursiveness the self-referentiality
lies in the fact that
the former pump to the left and right of the
equal sign so I’m trying to
define something in terms of if
same
pure magic from my point of view one
of the work he gave me the most
satisfaction was that of
study the history of this equation
think about studying the history of
an equation to who had ever come in
mind and it seems that the first to use it not
they have been sociologists over the years
fifty affirming that a person
prestigious if it receives approvals from
other persons of prestige prayers in
1970 is also discovered in bibliometry
an influential magazine if it is mentioned by
other influential magazines in the 90s ago
peeps a team in sport too
it’s strong it beats other teams
equally strong finally in the years 2000
two doctoral students
of the American University of Stanford
sergey brin and larry page rediscover for
the umpteenth time this recursive mantra
and make it the beating heart of the engine
of google source search that will become
certainly very popular it was not
the only equation there is another but it is
also the last one at the University of Udine
we studied a variation to Mr.
colleague enrico a variant of
this equation bacchus note the
concept of power not of centrality
not important it could be
paraphrased in this way an actor
important if it is surrounded by actors
unimportant
this is also a recursive equation
as you can see the aic disappears to the right and to
we have the left of the equal sign
applied in an economic context of
negotiation must be negotiated with
someone my negotiating power
it’s high if my year contractors are
not very powerful if my contractors
they are very powerful if my contractors
they are called google apple microsoft era
puts my negotiating power
very small
in our case we have applied it to
natural gas distribution network
a Europe that you see schematically here
in an indirect graph the dimension of the
node is proportional to the power of the
knot then you see that no big ones are
close to small nodes and vice versa
This is the concept underlying
rewinding and here it is also explained the
my shirt
rewinding our uroboro our
path we can go back to the beginning and
we left saying that space
we heard this one morning
plot
the plot of reality said david 8
space is a network to a network of
events why not propose then in
this final idea a bit original the
time as a network the time network in
bottom the model of the network
contains the linearity the branching
even the circularity that they have
surely as we have seen to that
over time, make the margin
temporal that separates me from the end of
this intervention is too short for
investigate beyond this brilliant
intuition and maybe we could ask
some theoretical physicist if this
intuition makes sense
I have nothing left but to leave you with one
of the most beautiful quotes that I am
never been suggested on time and wish
to all the beauty here in this world
thank you
[Applause]
”
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