Re: Parity Eotvos experiment, update

Richard Herring wrote:
> 
> Uncle Al <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> > Richard Herring wrote:
> > >
> > > Graham Lee <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> > > > Uncle Al wrote:
> > > > > If anybody cares...
> > > > >
> > > > > http://www.mazepath.com/uncleal/qz.pdf
> > > > >  Fig. 2, Table VI.
> > > > >
> > > > > We recently crunched quartz to 3.3 quadrillion atoms or a 43 micron
> > > > > diameter ball - 2.8 GHz Xeon and 1.8 GHz Opteron CPUs in Linux gave
> > > > > identical data
> > > >
> > > > One would hope that digital computers running the same code would give
> > > > the same results as each other (to within limits of the precision of the
> > > > data types employed).
> > >
> > > If one doesn't take sufficient care with the numerical analysis,
> > > sometimes the only thing the code actually calculates _is_ the
> > > precision of the data types employed :-(
> >
> > 80-bit double_long_precision only in our calculation.  Two separate
> > analyses show we are well beyond the precision needed.
> 
> Good. I assume you'll be publishing them?

http://www.mazepath.com/uncleal/gz.pdf
 (Quartz to .33 quad, not the full 3.3 qaud)

The calculation is subsidiary to the physics - and mostly a show of
bravado for the Referees.  Periodic crystals are self-similar by
definition.  Even a small radial sample beyond a few unit cells sets
the trend to arbitrarily large dimensions.  However, because an atomic
lattice is not homogeneous (atom or no atom) and not  istropic
(certainly not for the thre qualified pairs of enantiomorphic space
groups) we get a full standard deviation of noise calculated points
vs. best fit curve.  As with a real world test mass, things average
out with accumulating size and only the trend remains...

...but you never know.  A 12,000 atom lattice isn't much of an
argument (a cube 23 atoms on an edge).  A 3.3 quadrillion atom lattice
is a better example (a cube 150,000 atoms on an edge).  The surface
doesn't intrude so much.  42 quadrillion atoms (a cube 350,000 atoms
on an edge) is better still.

> > All results
> > exactly overlap to 18 decimal places - Windows or Linux OS; Intel and
> > AMD consumer PC CPUs; Xeon and Opteron CPUs.
> >
> But all _that_ proves is that the hardware is performing as specified.
> If the results from two entirely different _algorithms_ overlapped to
> 18 places I'd be more impressed.
> 
> > Double_precision shows noise in the ~11th decimal place.
> 
> "Noise" is too vague. Where does rounding error start to eat into
> truncation error?

80-bit long_double-precision code in an 80-bit precision CPU is more
than sufficient to comfortably retain 18 decimal places through
arithmetic operations for the number of points considered.  The lowest
precision operation is a square root.  No trig functions.  

   1) Two programmers have rigorously looked at the precision needed
vs. dataset size and are satisfied.  That's theory.

   2) A Xeon and an Opteron gave absolutely identical results for the
3.3 quad run.  We see no hardware dependence.  Random error is not
ocurring.

   3) The fitted slope and intercept shifted slightly in their fourth
decimal place when teh 3.3 qaud run was added in, increasing the atoms
considered tenfold.  If there were accumulating error for whatever
reason, the 3.3 quad run would not be consistent with numbers from
1000 atoms.  We see a large dataset breakdown using double_precision.

-- 
Uncle Al
http://www.mazepath.com/uncleal/
 (Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?"  The Net!