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[NOTE:
This is a direct translation from Italian using atla-vista, please excuse
the English.]
THE PARADOX OF PARRONDO, THE FASCINATING THEORY OF A SPANISH
PHYSICIST
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| From the gamblings we learn to win
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| 23 past December the prestigious British scientific review Natures published an
article of a page that has interested and intrigued biologi, mathematicians,
logical and statistical. The author is an Australian engineer, Derek Abbott, that he has illustrated therefore said paradox of Parrondo. Costui - the prof.
Juan Manuel Rodriguez
Parrondo - he is a physicist of the university of Madrid and has shown like can be gained
with emergency participating to two gamblings iniqui (in everyone of which the
probability us sfavorisce). Firm all: applications of this theory to the games
offers from the casinos and, much less, to Lotto and Superenalotto are not
previewed - irrimediabilmente iniqui. The Spanish physicist has escogitato this
application of its theories to the competitive games in order to illustrate the
methods of its searches on the transport of proteine within the cells, on sure
peculiarities of the browniano motion of molecules of a fluid or a gas and on
sure problems of thermodynamics. Juan Parrondo describes two gamblings based on
the launch of coins. To head or cross, if the coins are balanced (that is the
game are honest) the probability to win are 50%. Instead in the game To di
Parrondo, we bet that head comes, but the currency is unbalanced: in average it
falls on single head 495 times on 1000. Therefore, playing to the game To, in
the long run we lose sure. In the game B we bet equally on head, but we use 2
coins (which we assign numbers 2 and 3). The currency 2 us sfavorisce a lot: it
once gives to single head 50 times on 1000 (on 20). Currency 3 - finally -
favors, gives to head 700 times to us on 1000. Other rule of the game B is that
we aim at the currency 2 solos if we have in pocket an exactly divisible number
of coins for 3. If this number is not divisible for 3, uses currency 3. Also to
the game B in the long run one gets lost. In fact the probability to win is 1/3
(the percentage of the times that we use currency 2 that is) multiplied 0.05
(twentieth) that it gives 0.01666... more 2/3 multiplied for 0.7 that are worth
0.46666... The sum of the 2 probabilities is worth 0.48333: less of 50%. We
conclude that does not convene to us to play neither to the game To, neither to
the game B. the discovery of Parrondo is strabiliante: if we play 2 times to the
game To and 2 times to the game B and we continue therefore - or we choose every
time to case some time To and some time B, instead losing, we win. Much more to
along we play, much more we win. Parrondo has demonstrated to this its
conclusion resorting to reasonings rather sophisticated mathematicians - and not
them bringing back. Also it has simulated on computer several sequences very
50.000 played and has confirmed this amazing result that seems to brutally
contradict our common sense and our intuition. In order to explain as this
probabilistica analysis finds a formal parallel in thermodynamics experiences,
we would have to go still more on the difficult one. It is not sure possible
farlo within the space of the 4000 struck that me it has been assigned. You
take, therefore (for faith), how much follows as a similitudine - even if is
something more: it is a faithful model. The situation of the two gamblings is
formally identical to that one of a ratchet gear that comes made to turn from a
shovel wheel moved from molecules of a gas that goes to us accidentally to blink
(a ratchet gear is a dentata slanted tooth wheel like those of one saws, that it
can turn in one of the two senses, but not in the opposite sense because there
is a harpoon or nottolino that impunta in the socket between two teeth and jams
the wheel. In the sense allowed, instead, the harpoon slides on the advanced
surface of the teeth and the spin does not hinder). Ideally a structure
therefore could take energy from molecules of the gas that goes to case in the
just sense and to be insensitive to that they go in opposite sense. From the
first moment it could appear that this apparatus would be able of violare
According to Principle of the thermodynamics, because would draw energy from a
gas to one single temperature, without to take advantage of a jump from warmth
to cold. Naturally it is not therefore. Nobody can violare According to
Principle. The thin reasonings of Parrondo will serve to explain complex
mechanisms of the nature. Arricchiranno only who makes the effort of capirli,
not who sight to beccarsi some jackpot. |
