I've been popping up at a few science festivals recently,
discussing the evidence for dark matter with particle
physicist Tom Whyntie. After a session at Cambridge Science
Festival, UK, a man in a duffle coat approached me to
explain that Einstein was wrong - that the universe is not,
in fact, expanding. (Actually, a static universe would have
pleased Einstein greatly, but that's beside the point.) As
evidence, he tried to give me his book on reinterpreting the
redshift of galaxies. When I politely refused, he accused me
of being "unscientific".
The implication is that being "scientific" means completely
digesting and testing every idea before deciding whether
it's right or wrong. But sometimes we have to make fast
decisions based on prejudice, or we'll never get anything
done. Is that OK, or does it fundamentally undermine what
we're trying to achieve?
Let's consider another recent challenge to Einstein:
faster-than-light neutrinos. Forget what we
now know - even from the moment those results were
announced, it was widely considered that they were unlikely
to be right. But while the smartest people calculated the
contradictions with results from neutrino
astronomy or the disastrous
implications for basic particle physics, the more
widespread reaction - mine included - was simple scepticism.
We can model this scepticism mathematically. The process of
making rational judgements in the presence of uncertainty
and incomplete knowledge is beautifully handled by Bayesian
statistics. It's all about assigning numerical "confidence
levels". If you assign 100 per cent confidence to true
statements, and 0 per cent confidence to false statements,
Bayesian statistics automatically boils down to normal
logical reasoning. But in science we never have such clear
situations; we have scales of plausibility.
So, based on the reams of historical evidence, you might
start by assigning 99 per cent confidence to the assertion
that "Einstein was right and nothing goes faster than the
speed of light". That means you are pretty confident it has
to be true, but you allow a generous 1 per cent margin of
doubt.
Then someone claims to have measured neutrinos breaking the
speed limit. How confident are you that the results from a
typical, carefully conducted experiment are correct? Ninety
per cent confident? That would mean that, typically, you
take experimental results at face value.
But this particular neutrino experiment has contradicted
your 99-per-cent confident "speed limit" principle.
Inserting all these previously settled-on numbers into
Bayes's theorem, you find that it's roughly 10 times more
likely that the neutrino experiment has gone awry than that
the speed of light is genuinely broken. The confidence in a
prejudice (despite being slightly eroded) has trumped the
confidence in other people's experiments.
Mathematics is hardly necessary in this case, but the point
is that there is a watertight way to model the judgements
taking place in our minds. We don't need to know anything
about the details of the experiment. We can
self-consistently use our existing knowledge to make a snap
judgement about how likely the new result is.
But does the existence of a coherent mathematical framework
tell us that rejecting ideas - without even looking at them
- is acceptable? Not really. It's a useful
tool as situations get more complicated, but it's
still only modelling what we do in our minds. In particular,
if we start with wrong prior beliefs, we'll end up making
unreasonable snap judgements. For example, I could be
blinded by my physics education, fooled into being far too
confident about statements of orthodoxy.
Once we admit that we really do operate in this world of
personal belief, what makes us "scientific"? Essentially
that we never assign any statement 100 per cent confidence
(which would make it unassailable). We try to hold beliefs
that can, given enough evidence, be overridden. For instance
an additional, independent faster-than-light neutrino result
would have beaten the 99 per cent Einstein-was-right
assertion. We can then live with snap judgements and trust
that other people will keep presenting us with new evidence
if we really are wrong.
I don't think I managed to convey all this very well to the
man in the duffle coat in Cambridge. But then, he seemed to
hold the unerodible prior belief that all scientists are
lazily arrogant with 100 per cent confidence. So, by my
definition, he's the unscientific one. Only if I'd said
that, I might have appeared arrogant.
