R
Robert Myers
I have no idea what you know of mathematics. Your comments so farRobert Myers said:I lack confidence in proofs or analysis that
I can't see through from beginning to end.
And you call me professor? This sounds very much like a
theoretical [mathematics] approach. You've gone native!
make me want to giggle at the idea of your introducing me into the
enchanted circle of mathematics.
I need premises and data, then I will perform my own analysis
or at least verifications. Wading through someone else's
analysis is a didactic insult, and you are very likely to
fall into traps like hidden assumptions made the first time.
The video Jan posted is a neat example.
**Groan**. Line-by-line analysis.
A *proof* according to some accepted formalism is a proof. Everything
else is guesswork. Since, like most of us, you've taken plane
geometry, I assume you know what a *proof* looks like.
Proofs are available to us only under the most constrained of
circumstances, and even there we have good reason to have doubts.
The only thing validated by "validation" is the certainty of futureYou might complain this is not possible with CFD and similarly
complex computer models. I've been dealing professionally with
such for 30 years and the rules are always the same: validate
the model and input against known conditions and step-outs.
Watch the tweaking. When I can't, the model is just like a
Picasso -- maybe you like it, maybe you don't, but you have no
way to determine validity. "Trust" is reliance, not validation.
funding by the snakeoil salesman peddling it.
Possibly I was permanently soured by the military, which loves to
"validate" things. Once something is "validated," it becomes an
oracle, which is what the military (along with Wall Street) really
wants.
Once someone starts talking about validating (making valid?) computer
models, I stop listening.
The shuttle debris damage model is an example of a "validated"
computer model that led to spectacular miscalculation and death.
I've done some engineering in my life. You need a number, and you get
it any way you can. You don't have that number because it's
necessarily reliable, but because you *need* it to complete the
analysis. That's one reality of engineering. If the number you
grabbed out of the air leads to disaster, you don't start inventing
excuses about the housing market. You tried, and you failed. It
happens.
As to CFD models, I was introduced to CFD through spectral and
pseudospectral methods, where the connection between the differential
operators and their finite-dimensional representations is particularly
clean.
If you do non-trivial fluid mechanics, you eventually run into the
problem of renormalization. The nature of this problem is obscured in
most CFD models, but it is perfectly clear in pseudospectral
calculations: energy that has nowhere to go is aliased. Most CFD
models "solve" this problem by a crude and inapparent renormalization
that gives reasonable-looking results with an unknowable relationship
to solutions to the underlying differential equations.
Simply saying that the models are complex and therefore beyond
comprehension is a lazy evasion that reveals that the speaker doesn't
know what he's talking about.
So why, exactly, are you so certain of your own methods and so quickThere is tremendous value in orthogonal ("cold eyes")
analysis. And for including diversity in general.
Omissions are usually worse than errors.
to sneer at anyone who does not recognize their universal validity?
Robert.