Appendices
275
A.5.4 Laplace’s Demon
The following observation by French polymath Pierre-Simon, Marquis de
Laplace (1749 – 1827), introduced what is now known as Laplace’s demon:
We may regard the present state of the universe as the effect of its past and the cause
of its future. An intellect which at a certain moment would know all forces that
set nature in motion, and all positions of all items of which nature is composed,
if this intellect were also vast enough to submit these data to analysis, it would
embrace in a single formula the movements of the greatest bodies of the universe
and those of the tiniest atom; for such an intellect nothing would be uncertain
and the future just like the past would be present before its eyes [8].
Even before the advent of QM, Laplace’s demon had been disputed by
physicists, using thermodynamical arguments. However, these refutations
have themselves been criticised, and debate still continues.
A.5.5 The Monty Hall Problem
When this problem was presented in a popular magazine in the U.S.,
many mathematicians wrote rude letters to the editor complaining about the
published solution, and how it demonstrated the deplorable lack of numeracy
prevailing in the U.S. Unfortunately for them, they were wrong and the
magazine solution was right.
Statisticians tackling the problem would probably use Baye’s Theorem for
conditional likelihoods. However, the rest of us can use the following argument. When the contestant makes a choice for the door the car is behind,
she has a 1 in 3 chance of being right, and a 2 in 3 chance of being wrong.
No matter what the host does, this does not change. There is always a 2 in
3 chance that the car does not lie behind the door that the contestant has
chosen. When the host, who knows where the car is, opens one of the other
doors and there is no car there, the contestant knows that there is now a 2 in
3 chance that the car is behind the other unopened door. She should therefore
change her selection.
If the reader still has difficulty believing this result, a simple experiment
should suffice to convince them. Take three cups and a coin. Turn your back,
and ask a friend to conceal a coin beneath one of them. Guess which cup
hides the coin, then ask your friend to turn up one of the other two cups
that does not hide the coin. Check whether your initial choice was right, or
whether you would have been better off to change your selection. Repeat the
275
A.5.4 Laplace’s Demon
The following observation by French polymath Pierre-Simon, Marquis de
Laplace (1749 – 1827), introduced what is now known as Laplace’s demon:
We may regard the present state of the universe as the effect of its past and the cause
of its future. An intellect which at a certain moment would know all forces that
set nature in motion, and all positions of all items of which nature is composed,
if this intellect were also vast enough to submit these data to analysis, it would
embrace in a single formula the movements of the greatest bodies of the universe
and those of the tiniest atom; for such an intellect nothing would be uncertain
and the future just like the past would be present before its eyes [8].
Even before the advent of QM, Laplace’s demon had been disputed by
physicists, using thermodynamical arguments. However, these refutations
have themselves been criticised, and debate still continues.
A.5.5 The Monty Hall Problem
When this problem was presented in a popular magazine in the U.S.,
many mathematicians wrote rude letters to the editor complaining about the
published solution, and how it demonstrated the deplorable lack of numeracy
prevailing in the U.S. Unfortunately for them, they were wrong and the
magazine solution was right.
Statisticians tackling the problem would probably use Baye’s Theorem for
conditional likelihoods. However, the rest of us can use the following argument. When the contestant makes a choice for the door the car is behind,
she has a 1 in 3 chance of being right, and a 2 in 3 chance of being wrong.
No matter what the host does, this does not change. There is always a 2 in
3 chance that the car does not lie behind the door that the contestant has
chosen. When the host, who knows where the car is, opens one of the other
doors and there is no car there, the contestant knows that there is now a 2 in
3 chance that the car is behind the other unopened door. She should therefore
change her selection.
If the reader still has difficulty believing this result, a simple experiment
should suffice to convince them. Take three cups and a coin. Turn your back,
and ask a friend to conceal a coin beneath one of them. Guess which cup
hides the coin, then ask your friend to turn up one of the other two cups
that does not hide the coin. Check whether your initial choice was right, or
whether you would have been better off to change your selection. Repeat the