Jochen Bern wrote:
Sorry for the delay, I'm *still* not back to my usual workplace ...
On 01/21/2015 11:39 AM, Mike Cook wrote:
I couldn’t find a definition of a monotonous function. Does it exist?
As David already suggested, I learnt my math in Germany - and switched
to CS before taking a shot at a PhD, which would have required me to
tear into actual current research, which would have been written in
English. So yes, "(streng) monoton" should have been translated as
"(strictly) monotonic", not "(strictly) monotonous".
(Quick terminology recap: A function takes inputs from one set (domain)
and assigns an output/result from another set (codomain) to them. In
order to define "continuous", both domain and codomain need to be
ordered and have a notion of "distance" or "difference" (metric).)
The function can be non-linear. See below.
Yes. In particular, implementing a leap second by decelerating your "all
minutes have 60 seconds" "clock" results in a conversion function that
is monotonic and continuous, but not linear. In the case of having it
run at half its normal speed for two seconds, it would qualify as
"piecewise linear" - and not have a defined derivative at the switchover
points.
One of the good points about Google's smear is the fact that they use a
half cosine to distribute the offset, which means that they have a time
function which is both continuous and monotonic, as well as having an
infinite number of defined derivatives, i.e. it is maximally smooth.
The _huge_ problem with their approach is that they have to make d***
sure there will never be any time leaks between their internal smeared
timebase and any external UTC/TAI clocks as long as the adjustment is
taking place.
Again, what you are highlighting is the inability or unwillingness of
engineers to create sufficiently robust conversion functions.
Well, if you want to put it that way, yes. Though unavailability of leap
second info within whatever system they're designing (say, a mechanic
wrist watch worn by an average human) is a pretty *solid* reason to
claim inability to do so.
:-)
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"
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