|
|
[NOTE: This is a direct translation from
Spanish using atla-vista, please excuse the
English.]
COMPLUTENSIAN NEWSPAPER 19 of October of
1999
INVESTIGATION
A mathematical model that gives much
game
The paradox of Parrondo: to lose +
to lose = to win
Juan Manuel Rodriguez Parrondo, titular
professor of the Department of Atomic, Molecular and Nuclear Physics
of the Faculty of Physical Sciences, has devised two simple
mathematical games of chance that are interesting to experts in very
diverse areas of science. Their results are surprising in
statistical terms, to play anyone of the two separately supposes to
lose. However, if the player alternates both, in certain or random
combinations, it wins. An effect that in articles specialised
already is known like "the Parrondo’s Paradox".
Professor Rodriguez Parrondo found inspiration of
games in his investigations on motors of Brown or motors brownianos,
models of study in Physics that must his name to botanist Robert
Brown, who it observed in the last century that an immersed particle
very small in a fluid moves of erratic form, with abrupt changes of
direction which they do not obey to any guideline pretends
(browniano movement). Einstein explained east phenomenon in 1905,
supposing that that movement must to that the particle continuously
receives molecule collisions coming from all the points.
Motors of Brown
Much more recently it has been begun to study the
behavior of these particles submissive the combat operation: for
example, placing them in an electric field that can be connected and
become disconnected. To greater tempetatura, greater agitation takes
place in the fluid and more impacts receive the browniana particle.
When being made studies with a great number of particles tin has
been discovered peculiar effect: if the field is connected and
disconnected alternatively, these move slowly in a direction.
These systems, that turn a
chaotic fluctuation into a determined movement, are now known in
Physics like motors Brown or recrificadores (Brownian ratchets,
Brownian motors or recrifiers in English), and thinks that they can
be used in Biology for the molecule transport within a cell. |
Already almost two years ago to
professor Parrondo it was happened to him to make a luck of
simplified mathematical version of the operation of these
rectifiers, and almost as curiosity devised two games of probability
whose results presented/displayed in diverse seminaries, without
seting out at least to publish them. With time they have given rise
to diverse scientific studies in which already they are known like
the paradoxical Parrondós games.
The process is significant from
the point of view of the sociology of science: changing the notion
of browniano rectifier by the one of game, and the magnitudes of
time and space by most manageable of I number of played times and
points or obterudo capital, Parrondo has managed to interest to
experts of Optics or Climatology in tin phenomenon that before a
scientific community very reduced only investigated.
A game of probabilities
The great virtue of the games is that they are
easily comprehensible for anyone. To play can be compared with
sending a currency to the air and, starting off of a determined
capital, to be making or losing money according to it leaves face or
cross (for example, 1,000 pesetas in each occasion).
In the game To we have a
currency slightly pocketed a ball to lose: concretely, p=l/2– m
gains with a probability and p=l/2+ m is lost with probability (to
see superior graph). In game B in fact we have two currencies: good
and a very bad other. If the amount of capital that we have is
multiple of three, game with the bad one, whose propabilidad is
p1=l/lO- m. If he is not multiple of three, one gambles with the
good currency, whose probability is p2=3/4– m. Thus, if we began
playing with 10,000 pesetas, we will have to send the good currency.
If we won, we will have 11,000 pesetas already and it will be called
on to continue sending the good currency to us. However, if we lose
we remain with 9,000 pesetas and, to the being this amount multiple
of three, we will change to the other currency.
|
It is possible to be verified
that if m =0 both games are right; that is to say, which in average
neither one gains nor it loses. But if m is positive, in both games
it is lost. Therefore, any person who plays, by means of
sencillísimo computer science program, a sufficiently high number of
times to anyone of the two games, will end up losing inexorably. The
surprising thing is that if however combines both, in series ABAB,
AABB or even of totally random form, it will end up winning with the
same inexorabilidad (to see inferior graph).
The reason is intuited easily.
When one gambles only game B, the good currency and the bad one are
compensated, with a slight advantage for this last one. However, the
games, the currency are alternated To, that she is bad in himself,
modifies the things so that professor Parrondo is used plus the good
currency of game B. and the investigators interested in this
mechanism create now that he can be present in physical systems,
biological or even climatologic.
Scientific applications
The games have monopolized the attention in a
congress to multidiscipline celebrated east summer in Australia,
where they were presented/displayed by the organizer of the same
one, the engineer Derek Abbott. Also, the mathematician Charles
Pearce presented/displayed two works in which he demonstrates that
the example of professor Parrondo, very simple, can be generalized
to other many cases. A review of the Nature magazine the past
emphasized month the value of the games for the understanding of the
phenomena of rectification in general, as well as his possible
future application in as different fields as the genetic Econornía
or studies on Theory of the Evolution: the case could occur, to put
an example very simple, of which the complexity of the biological
Earth systems decreased separately in two certain supposed ones
taken but it increased when being combined both. Once described the
theoretical model the exciting possibility is opened of tracking it
in the real world. |
|
TO
REMOVE PARTY
In
general, at random, any physical system pequer6no has magnitudes
that behave of erratic form, that is to say, that presents/displays
random fluctuations. In Physics noise to these fluctuations is
denominated, because of the real noise that takes place in the
loudspeakers like result of the fluctuations produced by the
components of an amplifier. Until recently one thought that the
noise only could destroy the order and the complexity of a system,
but in the last decade have been situations in that it has the
opposite effect: it can help to that a system has a more complex
behaviour. It is the case, for example, of the transport induced by
noise that takes place in the systems known like Brownian motors, in
which it is managed to rectify particles, leading them in a
direction. Professor Parrondo has been dedicating itself for years
to the study of these motors, investigating, for example, the energy
interchange that takes place in them, area in which has obtained
important |
It arrives, both games. In the B different
probabilities are used according to we have an amount multiple of
three or no. Down, results of playing separately the games and in
different combinations (2 times To and twice B, etc.). 50,000 games
have been
simulated. |
|