Re: Granite, Symmetry, and ID - Summary

On Jul 5, 8:54 pm, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx> wrote:
"Seanpit" <seanpitnos...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message

news:1183677003.444080.282510@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Granite, Symmetry, and ID - Summary

This is to summarize recent discussions I've had regarding my notion
that various forms of symmetry, such as reflective symmetry, can be
used with the material of granite to hypothesize deliberate artifact
with an excellent true positive and low false positive rate.

I initially presented certain parameters that were very narrowly
defined to overwhelmingly exclude any remote possibility of a
potential false positive.

After numerous comments and sometimes heated "suggestions", I'll
summarize a few of the clarifications that seem to have solved at
least a few minor cases of some confusion.

The material in question is still granite. It is not some single
crystal that may be found in granite, but granite.

The unit of measure is still meters, centimeters, millimeters, or
whatever unit of measure, or fraction thereof, seems most appropriate
to the specimen.

The quality being measured is still reflective symmetry with regard to
surface irregularities. Spheres, cylinders, spheroid, parabolic, or
rounded off shapes do not qualify as "irregularities". For additional
clarification, though I believe I've made this abundantly clear in the
past, the type of irregularities I'm looking for are those where one
flat surface forms a sharply defined angle with another flat surface.
The angle cannot be "rounded" off to less than the degree of tolerance
described below.

This new rounding requirement eliminates practically all designed objects
that lack a blade, and blades will generally not meet the 30%/10%
requirement below (depending on what you mean by it, since it is not
entirely clear). Standard engineering practice is to round corners on
objects to a radius sufficient to prevent injury. How would you like to
lacerate your hand by rubbing it against your granite countertop? Finely
polished laboratory grade granite plates have nice rounded or beveled and
rounded corners so the inspectors don't hurt their hands.

This point could be modified somewhat, but even without modification
the point of this rule is rather obvious.

The basic method of measuring symmetry is still the same, but with a
few more clarifications. The distance of each surface point on one
half of the rock is measured from the center of the stone. This
distance is compared to the surface point exactly opposite as measured
from the center of the rock. For example, if a straight line is drawn
through the center of the rock, the surface points that it passes
through on either side of the rock are "exactly opposite" surface
points. The distance of each surface point is measured from the
center of the stone. This distance is compared to the distance of the
opposing surface point measured in the same way.
Also, the plane of symmetry really doesn't matter as long as it
is passes through the center of the stone. The reflective symmetry
will be the same regardless of the various number of ways this can be
done. And, the choice of the "center" of the stone also doesn't
matter. Any center that is chosen that actually aids in fulfilling
all the listed criteria is the better choice.

The degree of irregularity is still the same. At least 30% of the
surface points on one half of the rock must vary in distance from the
center of the rock by more than 10% of the average surface point
distance.

I strongly suggest this should be "vary in distance from a datum plane
through the geometric center of the rock." I suspect that is what you mean.
If each point is measured from the 3D geometric center, then points
equidistant from a datum plane on a perfectly flat surface are highly likely
meet the 30%/10% requirement - and I get the impression that is not what you
want.

The distances to be measured are from a center point, not a plane.
This is why it doesn't matter what "plane" of symmetry you decide to
use as long as it passes through this central point. Also, this is why
a "cube" shape does indeed fulfill the 30%/10% requirement.

The degree of tolerance previously listed (0.001%) seems to have come
under the most heat. It remains that all of the surface point
distances on one half of the rock must match all of the surface point
distances on the exact opposite side of the rock to within the stated
degree of tolerance as a fraction of the total distance from one
surface point to the opposing surface point. For example, a granite
cube measuring 500 mm on each side could sustain a variation in
surface point distance of one side compared with the other of up to 5
microns and still pass the tolerance test. For even further
clarification, if the distance between the center of the cube and one
surface point were 5 microns smaller or greater than the opposing
distance, this variation would pass the test. In other words, the
variation relative to the total distance cannot be greater than
0.001%.

I think this has gotten less clear than your original post. Initially, it
appeared that the point on each side would be measured with respect to a
datum plane.

I specifically said that each side would be measured with respect to a
central point - not a plane.

You weren't specific about that, but if "center of the object"
were generously construed as a datum plane through the geometric center of
the object, it would work. Now they are measured with respect to each other,
and both vary with respect to a datum plane. That is bad measurement
practice, and it is difficult to accuratly describe what the tolerance
means.

The have always been measured with respect to a central point and
compared with each other, with the overall variance being less than
0.001%.

Of course, the main argument hasn't been so much one over how
to measure the degree of tolerance, but that the stated degree of
tolerance is far too restrictive to allow for anything of artifactual
nature or otherwise to pass the test. As I see it, this really isn't
an issue since if this degree of tolerance were ever achieved the
artifactual nature of such a highly symmetrical granite object would
be extremely clear. The reason this conclusion would be so clear is
because there is a clearly established pattern of greater and greater
positive predictive power for finer and finer tolerances well before
the degree of 0.001% tolerance is realized. Therefore, it is quite
reasonable to induce from this pattern that the pattern will only
continue in like manner. Beyond this, there are several examples of
manufactured granite cubes that do indeed fall within this degree of
tolerance - with respect to symmetry and the measurement of tolerance
as described above (see references listed below).
Even so, because I wish to avoid as much balking over this point
as possible, I'll reduce the degree of tolerance to 0.01% - even
further, but with a corresponding decrease in positive predictive
power. Again, the point here is not so much the degree of tolerance,
but the pattern of significantly increasing true positive rate and
decreasing false positive rate (with respect to the hypothesis of
deliberate artifact) that presents itself as the degree of tolerance
is increased.

And, finally, the hypothesis is still the same. Namely, that if the
above parameters are met the prediction of deliberate artifact carries
with it very high positive predictive value (i.e., a very high true
positive rate with a correspondingly low false positive rate) that is
related to the strictness of the various parameters. Beyond this, if
the criteria of this test are not met, the possibility of deliberate
artifact is not addressed. In other words, the test does not address
negative results beyond the statement that "there is no prediction
with regard to negative results at all".
Some think this last part makes such a test worthless - that if it
is not general enough to encompass all potential artifacts and have a
good true negative rate as well as a true positive rate, why bother.
Those who make such arguments don't seem to understand that having a
test with a true positive rate that is excellent, even with a poor
true negative rate, is much much better than having no test at all.

That depends. If the test is much worse than subjective human sorting (and
this test is far worse), it is pretty much worthless.

Not when it comes to positive predictive value - which is the whole
point here. If you find a particular type and degree of symmetry in
the material of granite is the degree of symmetry somehow related to
predicting deliberate artifact? The answer is clearly yes.

Sean Pitman
www.DetectingDesign.com

References:

"Undersigned is guide to a batch of three students of Mechanical
Engineering for Masters Program I-STAR who have undertaken a project
of assessing geometrical accuracy of 3 D - CMM. During the course of
conducting project we have come across a situation which requires
certain clarifications as under. A mechanical artifact of Granite Cube
of size 500 X 500 x 500 mm (Hollow design having total mass of 140 Kg)
while being checked using First Principal for checking
perpendicularity has shown value within 5 microns for all the faces
where as flatness values for each of the six faces have been observed
within the range of 3 to 4 microns and parallelism of opposite faces
while checking with digital electronic probe ( gauge head ) are within
maximum 5 microns."

http://cr4.globalspec.com/thread/5439/Methods-for-Inspection-of-Check...

In other words, a net tolerance on the order of 13 microns with respect to a
datum plane, or 52 ppm (0.0052%) with respect to a datum through the center,
26 ppm (0.0026%) with respect to the average thickness. It fails your test.

The parallel tolerance includes the tolerance for flatness for each
opposing surface. That is why the parallel tolerance is greater than
the flatness tolerance. If the net tolerance were actually 13 microns
as you suggest, the parallel could not be known to be within just 5
microns. Also, as long as the surfaces are parallel to within 5
microns, you cannot add in the perpendicularity measurement, because
that would not have an effect on overall symmetry.

Beyond this, the measurements are well within the stated reduction in
tolerance listed above of 0.01%.

Another fair example of modern technology when it comes to the
material of granite is the Microplan Group (see link). They
manufacture, among other things, granite testing devices, to include
cubes, machined to within tolerances of 1-3 micrometers depending on
size (i.e., a um = 1/1000 of a millimeter or 0.001% of 10 cm =
0.000001 m).

http://www.microplan-group.com/pagine/prodotti_gb/cu_gb.htm

So would anybody else producing laboratory grade plates. Big deal. These are
usually about 7-8 cm thick. I know. I've used them. 1-3 microns would be 13
to 43 ppm (0.0013% to 0.0043%) of such a thickness, and that does not
include flatness (hint: the objects warp).

A 200mm cube doesn't warp appreciably in a set environment. And
again, regardless, such a cube falls well within the new 0.01%
tolerance requirement - reduced because of your complaining even
though the reduction doesn't alter the point of this test in the
least.

Sean Pitman
www.DetectingDesign.com


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Relevant Pages

  • Re: Granite, Symmetry, and ID - Summary
    ... that various forms of symmetry, such as reflective symmetry, can be ... with an excellent true positive and low false positive rate. ... The material in question is still granite. ... The distance of each surface point on one ...
    (talk.origins)
  • Re: Granite, Symmetry, and ID - Summary
    ... that various forms of symmetry, such as reflective symmetry, can be ... with an excellent true positive and low false positive rate. ... The angle cannot be "rounded" off to less than the degree of tolerance ... The distance of each surface point on one ...
    (talk.origins)
  • Re: Granite, Symmetry, and ID - Summary
    ... that various forms of symmetry, such as reflective symmetry, can be ... crystal that may be found in granite, ... The angle cannot be "rounded" off to less than the degree of tolerance ... The distance of each surface point on one ...
    (talk.origins)
  • Re: Granite, Symmetry, and ID - Summary
    ... that various forms of symmetry, such as reflective symmetry, can be ... crystal that may be found in granite, ... The angle cannot be "rounded" off to less than the degree of tolerance ... The distance of each surface point on one ...
    (talk.origins)
  • Re: Granite, Symmetry, and ID - Summary
    ... that various forms of symmetry, such as reflective symmetry, can be ... with an excellent true positive and low false positive rate. ... The angle cannot be "rounded" off to less than the degree of tolerance ... The distance of each surface point on one ...
    (talk.origins)