chuft-captain wrote:
sjohn,
As Fridger has already made the decision to use stochastic methods for visualization of objects at cosmological distances (which is his decision to make), we should reserve this thread for discussion of the details of how this can be correctly achieved (scientifically) in the software.
Let me close this not very useful debate with sjohn with just a few general comments:
After reading sjohn's posts again carefully, it seemed to me that he firmly believes that my statistical approach in celestia.Sci is
pure theory, i.e. being not based on any direct experimental measurements whatsoever..
This is of course entirely wrong, since all used probability densities in celestia.Sci rely on best-fit approximations to the respective existing experimental data like luminosity densities, spacial star densities, color-magnitude distributions etc!
Before entering such a discussion on inherent uncertainties, It is indispensable to know the precise meaning of experimental error bars that accompany EVERY kind of experimental measurement! Firstly, there are only two types of experimental errors:
- so-called statistical errors (with identical definition in conventional experimental measurements and stochastic methods). These decrease with the number of measurements or with the number of objects involved.
- so-called systematic errors. These typically characterize (hardware) imperfections of the measuring apparatus or other deteriorationg effects that do NOT decrease with the number of measurements.
The basic "axiom" in case of statistical errors is that all measurement errors are distributed in a Gaussian manner (<=> Normal distribution). The error bars then result as the
standard deviation of this distribution. Thus experimental uncertainties quantify the spread of the results of measurements when these are repeated many times or when many objects are involved. The familiar error bars are defined in terms of the width of the underlying Normal distribution.
Since systematic errors are NOT normal distributed, it is generally not allowed to add systematic and statistical errors in square to form the total experimental error.
Last not least:
A great concern of mine is to implement an intuitive and transparent visual scheme of displaying experimental uncertainties in
celestia.Sci. This is all but easy and good ideas would be much appreciated!
A typical example are the orbits of multiple star systems. Since the measured orbital parameters partly involve large errors, the graphical display of the resulting orbit lines should make this unambiguously clear, without messing up the clarity of the display!
Fridger