Anton Shepelev wrote:

> David Jones:
>
> > We were later given a link to the 1933 paper, which I
> > haven't followed as my internet-safety stuff blocked the
> > link. I couldn't be bothered to avoid the block.
>
> OK, I have avoided it for you:
>
> https://freeshell.de/~antonius/file_host/Miller-EtherDrift-1933.pdf
>
> > Previous replies have said that the fitting was done using
> > a sum-of-squared-errors type of objective function
>
> Tom Roberts explained that his objective function was a sum
> a squred differences weighted with inverse errorbars.
>
> > and that, for some reason, this gave something that was a
> > discontinuous function of the model parameters.
>
> It is discontinuous in that the raw data are discontinuous
> (tabulated). The purpose of the fitting is to combine the
> eight partial drift-sequences (from the eight combined
> azimuths) into as smooth a function as possible, thus
> removing any singnal that is a function of the azimuth.

" It is discontinuous in that the raw data are discontinuous" ..
That explains nothing. An "error" that is squared is derived from an an
observed and a modelled value. Given the quantisation, the "observed"
part of this for a single observation is either just a single value
(usually the centre of the interval), or two values denoting the end
points of the interval. In either case these values are fixed and don't
depend on the mode parameters and hence cannot contribute a
discontinuity to the objective function. The basic form of the modelled
value is a continuous function of the model parameters. The usual error
comparing the modelled value with the centre of the interval gives the
error as a continuous function of the parameters. The obvious variant
of this taking explicit account of the quantisation might set the error
as zero of the modelled value is within the quantisation interval and
the distance to the closet edge otherwise. Again this gives can error
that is a continuous function of the model parameters, but the
derivative is not continuous.Now it may be that the "error" is being
constructed as a comparison of the quantised observation with a
quantised version of the continuous modelled values. This seems to be
very inadvisable, but it would produce a discontinuous objective
function. It is unfortunate that the 2006 paper provides no actual
details about what is being done by way of defining the objective
function.

>
> > There is an implication that this discontinuity was derive
> > from whatever allowance is made for the effect of
> > quantisation, but there are no details given.
>
> Can you please quote the relevant parts of the article?

Well on page 6 there is this ..

"As the data are quantized at 0.1 fringe, so are
the parameters, and instead of the usual minimization programs an
enumeration of all reasonable sets of parameters
was used with an algorithm that finds the minimum
?2. The result of the fit is a complete quantitative model of
systematic(time) for the run. This fit has 313 degrees of freedom, and
the histogram of X2 for all runs has a mean of
300, indicating that the estimate of the individual measurement
resolution (0.1 fringe) is reasonable. Fitting each run
took about 3 minutes of computer time to enumerate several million
combinations of the 7 parameters to find both
the best fit and the errorbar"

I might well have misinterpreted this use of a search over "several
million combinations" and the use of a "quantised" set of possible
parameter values as being a response to discontinuity. How the
parameters can be "quantised at 0.1 fringe" and what this means is a
mystery, but it seems to be what is being said. But perhaps this part
of the overall data analysis is not what I thought it was. But, if the
objective function is actually continuous and well-behaved, I don't see
why you would choose to do a multi-dimensional grid search.

>
> > It may well be that some of the data-manipulations have
> > been applied to the already-quantised observations, which
> > makes things difficult and, depending on the details of
> > those manipulations, maybe impractical.
>
> Yes, the original raw observations are quantized to sixteen
> fixed azimuths -- see the 1933 paper.
>
> > For example the model-structure may have a sinusoid of
> > known period and a random observation error to represent
> > what would have been observed without the quantisation.
>
> I expected some such model, too, but the device also shows a
> strong systematic drift, which too must be modelled.

Well yes, one would need to include in a model all of the effects that
need to be modelled. But the point was that the quantisation should be
treated properly as it seems to have been judged to be of such
importance. This means having a model describing what would have been
observed if there were no quantisation being done and then to treat the
consequences of the quantisation.

The above may sound a simple approach but, without thinking too deeply
about this, I am worried that the "data manipulation" that is going on
may make it infeasible. If the data-manipulation were simply that the
data actually being analysed were simply the differences of two
quantised observations, I think the approach could be carried
through.But the steps being taken seem more complicated than that ...
possibly in an attempt to remove certain effects that are of no
interest but which need to be included in a full model of the
observations actually made.

>
> > The paper does give some discussion of "error-bars" but
> > gives no details of how these are calculated.
>
> Please, see the paragraph starting with: "While Fig. 3 shows
> the inadequacy of assuming a linear drift, it is still
> useful to obtain quantitative errorbars for these data
> analyzed in this manner," and let us know whether you agree
> with the author.

Well yes error bars would be useful, but one would need to know what
they are error bars for, and one would need to know that they have been
derived in a way that is statistically valid.

>
> > There is an obvious scientifically-valid alternative to
> > all this, that is feasible in this post-modern-computing
> > world. Depending of course on what you are trying to prove
> > or disprove. You have a result from a model-fitting
> > procedure, and that procedure can be as awful as you like,
> > where that result supposedly measures the size of some
> > effect that may or may not be present. The obvious thing
> > to do is to simulate a large collection of sets of data,
> > in this case each having 5.2 million data-points, where
> > the putative effect is absent but which include a good
> > representation of all the supposed effects that your data-
> > manipulations are supposed to remove, and then to apply
> > those data manipulation steps before applying whatever
> > your model-fitting procedure is. It would of course help
> > if the model-fitting procedure is not written in an
> > interpreted language like Java.
>
> Yes, I agree, which is why I asked Thomas to please share
> his raw data, which he says is still saved on his "disk". I
> do not think Java is an interpreted language...
>

Well I did look up a description of Java. This confuses the issue, but
a summary is that the Java package itself is compiled, but that the
treatment by the package of a supplied script is that it interprets
and executes it line by line. Now there may be some version that
compiles a script into executable code, but that is not really the
point ... which is that Java is not usually counted as producing
quickly-executing code as would be the case for Fortran or C(plus?). It
may even be that there is some version of Java that is capable of
calling subroutines written in Fortran or C, as is the case with the R
package.

> > But is it worth doing any further analysis at all, given
> > that the 1933 conclusions have been disproved by later
> > experi
>
> I am rather interested in this. No later "null" experiment
> that I know of tried to reproduce the Miller experiments but
> always incorporated some important changes in the setup, but
> this is not something I have come here to discuss. My
> immediate focus in the Miller experiment and the Roberts
> reanalysis of it.

Obviously I know nothing about concepts of "Aether drift" and how this
might fit into modern versions of cosmology. But there seems to be an
assumption that, if it exists, it is in some way constant in size and
direction. Why wasn't the experiment constructed so as to determine a
direction for rthe drift if it existed? If the "drift" might vary, how
fact might it vary ... might it vary at a frequency similar to that of
visible light?
I guess the point is that there are certain mathematical theories in
which things related to reality either do or do not interact and one is
either; (a) looking for things already in the model that interact when
the theory says they do not; or (b) looking for evidence that there are
things not already in the theory that do have an effect on things that
are.