Bodley Head, London 2009
Predictioneer was highly recommended by one of my
correspondents as a ‘must read’ – and so I did.
And was
astounded right from the start, when reading in Game Theory 101:
“Bayes’ Theorem provides a way to calculate how people digest new
information. It assumes that everyone uses such information to check whether
what they believe is consistent with their new knowledge….in response to new
information that reinforces or contradicts what we thought was true. In that
way, the theorem, and the game theorists who rely on it, view beliefs as
malleable rather than as unalterable biases lurking in a person’s head.
“In real life there are plenty of incentives for others (and for us)
to lie… Therefore, to predict the future we have to reflect on when people are
likely to lie and when they are most likely to tell the truth. In engineering
the future, our task is to find the right incentives so that people tell the
truth, or so that, when it helps our cause, they believe our lies.”
Definitely a
book for me, I thought – great lacunae in my knowledge here.
So I read it
cover to cover in one day (and a TYGER night).
And then a
single line on page 215 hit me smack on with full mental tsunami power:
“Let’s take a look at the
inconvenient truth that won Al Gore the Nobel Peace Prize.”
I’m surely not
the only one remembering that UK courts ruled at the time that Al Gore was, in
fact, so ‘economical with the truth’ that his advocacy was forbidden to be
shown in schools.
Not only in my
opinion is the whole fable of man-made global warming (AGW) not just
‘irrational’, but amounts to no less than the biggest political and intellectual
fraud ever.
[1] [2] [3].
And there I was, thinking to be on terra firma with my smatterings
of thermodynamics, armed with Thomas Payne’s advice on sources of ‘truth’ in his
Age of Reason [4]
”The Creation speaketh an universal
language, independently of human speech or human language, multiplied and
various as they may be. It is an ever-existing original, which every man can
read. It cannot be forged; it cannot be counterfeited; it cannot be lost; it
cannot be altered; it cannot be suppressed. It does not depend upon the will of
man whether it shall be published or not; it publishes itself from one end of
the earth to the other;”
all further supported by Sir
Karl Popper who deserves special mention by referring if only to these five
tokens from his legacy, from The Logic of
Scientific Discovery [1934], to The Open Society and its Enemies [1945],
to Conjectures and Refutations
[1963], to the latest and most important summaries: The Lessons of this Century [1997] and All Life is Problem Solving [1994,1999]. [4].
And then recalling Bruce
Bueno de Mesquita:
“In real life there are plenty of incentives for others (and for us)
to lie… Therefore, to predict the future we have to reflect on when people are
likely to lie and when they are most likely to tell the truth. In engineering
the future (1), our task is to find the right incentives so that
people tell the truth, or so that, when it helps our cause, they believe our
lies.”
(1) and not
least the future of energy supplies.
So here I found this gaping
black hole – the lacuna of my Baysean ignorance – which needed diving into. Starting from Meinong’s base tenet – Truth is only a human construct, but facts
are eternal – but now remembering again not only that PANTA RHEI was written in big letters above the entrance portal of my
erstwhile alma mater, Technical University Munich (TH in 1954), translating in
the 1960s into “No Man can step into the
same river twice”, or the current definition of Information I=log1/p,
where p is the probability of any event occurring (and inevitably leading to
inquisitions, autodafes and worse when claimed by the powers that be, that 'p' amounts to 100%).
Still diving
and still on the way down, I discovered two things to start with:
An Intuitive Explanation of Eliezer
Yudkowsky’s Explanation of Bayes’ Theorem
– by Luke
Muehlhauser at: http://commonsenseatheism.com/?p=13156#sthash.2TSZhf75.dpuf
Where Luke Muehlhauser ends
by quoting Yudkowsky further, at [5]:
“The Bayesian
revolution in the sciences is fuelled, not only by more and more cognitive
scientists suddenly noticing that mental phenomena have Bayesian structure in
them; not only by scientists in every field learning to judge their statistical
methods by comparison with the Bayesian method; but also by the idea that science itself is a special case of Bayes’
Theorem; experimental evidence is Bayesian evidence. The Bayesian
revolutionaries hold that when you perform an experiment and get evidence that
“confirms” or “disconfirms” your theory, this confirmation and disconfirmation
is governed by the Bayesian rules. For example, you have to take into
account, not only whether your theory predicts the phenomenon, but whether
other possible explanations also predict the phenomenon.
“Previously, the most
popular philosophy of science was probably Karl
Popper’s falsificationism - this is the old philosophy that the
Bayesian revolution is currently dethroning Karl Popper’s idea that
theories can be definitely falsified, but never definitely confirmed, is yet
another special case of the Bayesian rules; if p(X|A) ~ 1 - if the
theory makes a definite prediction – then observing ~X very strongly falsifies
A. On the other hand, if p(X|A) ~ 1, and we observe X, this
doesn’t definitely confirm the theory; there might be some other condition B
such that p(X|B) ~ 1, in which case observing X doesn’t favor A over
B. For observing X to definitely confirm A, we would have to know, not
that p(X|A) ~ 1, but that p(X|~A) ~ 0, which is something that we
can’t know because we can’t range over all possible alternative
explanations. For example, when Einstein’s theory of General Relativity
toppled Newton’s incredibly well-confirmed theory of gravity, it turned out
that all of Newton’s predictions were just a special case of Einstein’s
predictions.
You can even formalize
Popper’s philosophy mathematically. The likelihood ratio for
X, p(X|A)/p(X|~A), determines how much observing X slides the probability
for A; the likelihood ratio is what says how strong X is as
evidence. Well, in your theory A, you can predict X with probability 1,
if you like; but you can’t control the denominator of the likelihood
ratio, p(X|~A) - there will always be some alternative theories that
also predict X, and while we go with the simplest theory that fits the current
evidence, you may someday encounter some evidence that an alternative theory
predicts but your theory does not. That’s the hidden gotcha that toppled
Newton’s theory of gravity. So there’s a limit on how much mileage you
can get from successful predictions; there’s a limit on how high the likelihood
ratio goes for confirmatory evidence.
On the other hand, if you
encounter some piece of evidence Y that is definitely not predicted
by your theory, this is enormously strong
evidence against your theory. If p(Y|A) is
infinitesimal, then the likelihood ratio will also be infinitesimal. For
example, if p(Y|A) is 0.0001%, and p(Y|~A) is 1%, then the
likelihood ratio p(Y|A)/p(Y|~A) will be 1:10000. -40 decibels
of evidence! Or flipping the likelihood ratio,
if p(Y|A) is very small, then p(Y|~A)/p(Y|A) will
be very large, meaning that observing Y greatly favours ~A over A. Falsification is much
stronger than confirmation. This is a consequence of the earlier point
that very strong evidence is not the product of a very high
probability that A leads to X, but the product of a
very low probability that not-A could have led to X.
This is the precise Bayesian rule that underlies the heuristic value of
Popper’s falsificationism.
“Similarly, Popper’s
dictum that an idea must be falsifiable can be interpreted as a manifestation
of the Bayesian conservation-of-probability rule; if a result X is positive
evidence for the theory, then the result ~X would have disconfirmed the theory
to some extent. If you try to interpret both X and ~X as “confirming” the
theory, the Bayesian rules say this is impossible! To increase the
probability of a theory you must expose it to tests that can
potentially decrease its probability; this is not just a rule for detecting
would-be cheaters in the social process of science, but a consequence of
Bayesian probability theory. On the other hand, Popper’s idea that there
is only falsification and no such thing as confirmation
turns out to be incorrect. Bayes’ Theorem shows that falsification
is very strong evidence compared to confirmation, but falsification is
still probabilistic in nature; it is not governed by fundamentally different
rules from confirmation, as Popper argued.
“So we find that many
phenomena in the cognitive sciences, plus the statistical methods used
by scientists, plus the scientific method itself, are all turning out to
be special cases of Bayes’ Theorem. Hence the Bayesian revolution.”
I have to come
up for air now before diving again farther down – and learning what everyone should at
least have been acquainted with before leaving school – any school. But however inadequately, I needed saying and
posting this a.s.a.p.
Meanwhile, sincere
thanks to Werner, Philip and Bruce.
oooOOOooo
