Xiaofan Chen wrote:

>> Maybe the unknowable does have its place in engineering?
> 
> The unknowable and the knowable are relative. A 1K Ohm with +/-5%
> tolerance resistance is of unknown value and unpredicatble exact value,
> but it is of known boundary value. It is knowable in one sense yet
> unknowable in another. ;-) 

This resistor is not really of known boundary value. The spec only means
that the probability that its value falls within the +-5% band is /much/
higher than that it falls outside of it. There are few manufacturers that
guarantee you that the value won't be outside the range; and by "guarantee"
I mean more than just replacing a resistor that falls outside. Think life
support -- would somebody go to jail for life (or on the chair in some
places in the USA) if the value were outside the range and somebody died
because of that? /That/ would be a guarantee. (This is a mere and grossly
simplified thought experiment, of course -- in reality there's more
involved with that.) And there's no manufacturer that guarantees you that
the value remains inside the band in your application, no matter how simple
that application may be. So if not even the manufacturer guarantees it, the
"know" part must be /quite/ relative...

IMO we get away most of the time, and in some cases often enough to make a
living off it, with assuming that it'll be in the target range, whatever it
may be. And the better the engineering, the more often one gets away with
it. But generally I put a higher mark on "knowing" than just getting away
with it...


> Mathematics is suppose to be the subject who needs precision. However a
> mathematics theory needs only to be coherent (or self-contained) to make
> it a valid theory. One have to agree on some atoms/base theorem and then
> based the whole theory on those. Again this base theorem can not be
> proved or disproved. 

Exactly. Mathematics has knowables, by definition, because it has no
relation to real life; it is a well-defined, completely contained space of
pure thought. Anything in real life has no actual knowables -- at least
that's what I suspect (I wouldn't know even if I knew it :)


> Engineering is even more so. All theories are accurate (or even only good
> enough) only under certain conditions. That is good enough for people to
> make use of it. 

Thing is the conditions are usually not known. Some are known, but I think
not all, usually. So what do we do with something we know is only valid
under certain conditions, but we don't know whether the conditions we think
we know are all there are? Do we "know" that? :)

Gerhard

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