Re: Granite, Symmetry, and ID - Summary
- From: bdbryant@xxxxxxxxxxx (Bobby Bryant)
- Date: Sat, 07 Jul 2007 15:41:21 GMT
In article <1183677003.444080.282510@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Seanpit <seanpitnospam@xxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:
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.
At least you _assumed_ they would.
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.
And we care about detecting ID in granite blocks because...?
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.
That's an epicycle that I haven't seen previously. What false positive
did you need it to rule out?
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.
Center of mass, center of volume, center of minimal enclosing convex
hull, or what?
You need to define what you mean by 'center'. One interpretation
would make your symmetry trivially true for all measurements!
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.
No, that's not true. There are infinitely many ways you can pass a
plane through the center of {mass,volume} of a hen's egg that would
result in a bilateral symmetry, but also an infinite number of ways
of doing it to get an asymmetrical result.
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.
Boy, you're _really_ piling on the epicycles now, aren't you.
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%.
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.
Anyone know what the tolerance on a quartz crystal is?
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).
I think you've reduced the metric to trivially satisfiable again.
Suppose you are checking a wooden fence post. You don't expect
manufacture to that kind of tolerance, right? But since it doesn't
have to be symmetrical in _every_ measurement, you just work your way
down and around, one femtometer at a time -- yielding a seemingly
infinite number of possible measurements -- and keep the ones that
match while throwing out the ones that don't.
The problem with your argument and the seemingly infinite number of
patches to rule out the potential false positives you want to rule
out, is that you aren't developing the argument from any principle.
You're starting with some claim that you _want_ to be true, and
trying to patch it up until it is. (Or perhaps merely looks like
it is.)
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.
Can you quantify that? It's hardly useful as a design detection
tool otherwise.
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)
What do you mean by "very high true positive rate? Surely your
method is going to miss almost all intelligently designed stone
artifacts.
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".
That's fair enough, but -
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.
The problem is that you can always make a test strict enough to give
few false positives, because it gives few positives at all.
Can you quantify any of that for us?
Heck, can you tell us what principles your method is built on? You
started with a simple claim that symmetry was indicative of design,
and now you've got the whole pile of crap above. Why should we
believe it actually detects design, other than because you say so?
And now that you've narrowed it down to the point that it can only
be applied to finely machined granite blocks, why should anyone
care about your method even if they thought it actually worked?
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-Checking-Reference-Granite-Cube
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
And what are you going to say when someone produces a naturally
occuring object with even higher precision? Got any more epicycles
left in the back of the closet?
--
Bobby Bryant
Reno, Nevada
Remove your hat to reply by e-mail.
.
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- Granite, Symmetry, and ID - Summary
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