[ExI] A Working Quantum Computer by 2017?
anders at aleph.se
Mon Sep 5 09:35:07 UTC 2016
On 2016-09-05 00:06, William Flynn Wallace wrote:
> This may be too complicated to answer: what, if any, ways are there
> to validate simulations? Well, let the world go by and see what
> really happens, I suppose. What else? Do real world experiments? In
> short, why trust simulations? We should primie facie distrust them
> (like the null hypothesis). At least two problems arise: GIGO for
> one. Not putting in crucial variables (because you don't know that
> they are crucial) is another.
This is a big thing in the world of simulating stuff. It depends on what
kind of system you are modelling.
Many physics problems have conserved quantities like energy, so you can
validate your code by checking the energy stays constant. Or you run it
for systems with known behavior and compare. But often the right
approach is to first write down the maths and figure out an
approximation scheme that have guaranteed error bounds: a lot of awesome
numerical analysis exist, including stuff like symplectic methods that
allows virtually error-free prediction of planetary orbits over very
You can also empirically change the resolution or stepsize in the
simulation to see how it responds: if there is a noticeable change in
output, you better increase the resolution or do things another way.
Same thing for parameters: if everything changes if you twiddle the
knobs of the model slightly, you should be skeptical.
In neuroscience things are harder, since the systems are more complex
and not everything is known. You can still build a simulation and
compare to reality though: if it doesn't fit, your model (either the
theory or the code) is not right. You can also validate things by making
virtual experiments to get predictions and then check them in the lab -
this has produced some very solid results.
But many neuroscience models do not aim at perfect fits, but rather to
see if our theory produces the right behavior. That can sometimes
involve making very simple models rather than complex ones: my rule of
thumb is that you better get more results out of the model than you have
free parameters, otherwise it is suspect. This is why many computational
neuroscientists are somewhat skeptical of large scale computer
simulations: we might not learn much from them.
Now, in systems like climate you have a bit of the physics side - we
know pretty well how air, heat and water move - but also a bit of the
neuroscience mess - clouds are hard to model, vegetation changes in
complex ways. So there is a fair bit of uncertainty (many climate
modellers are *really* good at statistics and the theory of
uncertainty). That is not a major problem; one can handle it. The thing
that worries me most is that many of the scientific codes are vast,
messy systems with subroutines written by a postdoc that left years ago
- I think many parts of science ought to have a code review, but nobody
will like the answers. This is likely true for the simulations
underlying much of our economy too: I know enough about how insurance
risk models work to not want to look too much under the hood. Often the
bugs and errors get averaged out by the complex dynamics so that they do
not matter as much as they would in simple models, which I guess is a
kind of relief.
Many models are trusted just because they fit what people believe, which
is often based on running models. In science people actually do perform
comparisons with data, experiments or even mathematical analysis to keep
the models in the vicinity of reality.
The key thing to remember is that "all models are wrong, but some are
useful". You should not select a model because it promises perfect
answers (that is frequently dangerous) but rather than it gives you the
information that matters with a high probability.
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
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