o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o (01)
PDM = Paola Di Maio (02)
Paola, (03)
Information and uncertainty are opposite aspects of
every doubtful situation -- the more information we
have about a situation the less uncertainty we have
about it. Indeed, that is what defines information. (04)
Defining information and uncertainty as concepts and
measuring information and uncertainty as quantities
requires the concept of a probability distribution. (05)
A "wide" probability distribution like the following
depicts a situation where it's anybody's guess where
the actual value of a variable ''x'' happens to lie.
Thus it represents a situation of high uncertainty
and low information. (06)
1 o
|
|
+-------------------o
| |
| |
0 o----+----+----+----+ X (07)
A "thinner" probability distribution like the following
pictures a situation where we know with certainty that
''x'' lies in a narrower band of values than the above.
Thus it represents a situation of comparatively less
uncertainty and comparatively more information. (08)
1 o o---------o
| | |
| | |
+ | |
| | |
| | |
0 o----+----+----+----+ X (09)
More later, maybe ... (010)
Jon Awbrey (011)
paola.dimaio@xxxxxxxxx wrote:
>
> HI Ed
>
> > I don't understand how to build an X factor to protect from a beast you have
> > never seen. Engineers build in "margin for error" factors, to accommodate
> > less than ideal materials, cumulative errors of approximation in estimating
> > impacts of factors they understand, and unexpected usage behaviors that are
> > only somewhat outside conventional guidelines.
>
> I knew after I wrote that sentence that I would need more thinking. I think
>what
> I am trying to say here is that we have to model uncerntainty.
>
> > Most cases of failure involve shoddy material or poor/dangerous design. And
> > those cases can be described as simple malpractice -- deliberately failing
>to
> > have the expertise and materials to do the job adequately.
>
> Okay, failure due to malpractice is predictable to some extent
> (although some bad buildings can stay up indefinitely, mysteriously)
>
> >
> > But the surprise failures are those that involve a factor that was not
> > considered at all, and not commonly considered in the trade. How do you
>build
> > an "X factor" defense for that?
>
> Simply like this: certainties+X = do not assume that because the
> bridge is built according to a sound model it will stay up, because
> there are factors out there that we dont yet know.
> Then stick that somewhere prominent in the engineering book.
>
> What I am trying to stress here, is that some science has the
> presumption to be 'exact' (haha} simply because it ignores the
> 'unknown factor' by not including uncertainty in the model, But
> uncertainty exists even when we ignore it. The fact that we can build
> a solid and sound bridge today, does not mean that the bridge can
> adapt to change.
>
> We do the analysis of these failures in order
> > to learn from them! And the approach is pure Sherlock Holmes: When you
>have
> > eliminated the impossible, whatever is left, however unlikely, must be the
> > explanation. The scientific requirement, however, is then to show that that
> > hypothesis leads to the result that was observed. The end is advancement of
> > our knowledge, not a better "X factor".
>
> I think we all agree that 'what is to be known' is infinite, while our
> 'ability to know' is finite, al
>
> To work towards perfect knowledge, okay, improved knowledge would be enough
> we have to stop relying solely on what we can know,
> and we have to learn how to study what we cant know for sure, cause it seems
>to
> cause so much trouble , I accept if you find this cognitive method a
> little disconcerting at first. It is also called 'possibility theory'
> (
>
> http://en.wikipedia.org/wiki/Possibility_theory
>
> There is some interesting work under 'uncertainty and fuzzy modeling n
> civil engineering' approach somewhere. I am sure some will find
> fuzzyness objectionable in hard science,
>
> Our Models are based on simplified assumptions, such as:
>
> "For simplicity, assume that the universe of discourse Ω is a finite
> set, and assume that all subsets are measurable."
>
> Too bad that the universe of discourse is infinite, and only a few of
> the subsets are
> measurable - thats the real world
>
> You are assuming that you can place certainty upon certain factors,
> while there is some uncertainty lurkin benerath your assmption of
> certainty that I think we should put in our equations
>
> > > The stability factor in a model can only be a temporary , and must be
> > > balanced with the 'uncertainty' factors at application stage
>
> We cannot accommodate factors we know nothing about,
> > or do not understand.
>
> I think we can, But then again, I am not a civil engineer
>
> Paola Di Maio (012)
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