Discerning symmetry errors in a pattern

This group has vast knowledge about so many things. Here’s an oddball
request that I’m sure one (or more) of you will know about. While I
was making a 7-prong crown collet today, I started thinking about how
the eye/brain has an incredible ability to discern very small
differences/errors in a symmetrical pattern. I wondered how small a
difference/error must be so that the eye/brain doesn’t notice the
difference? Is there a figure (such as .01mm), or is it dependent on
certain aspects of the pattern? Is one’s “talent” for discerning
differences inborn, or can we be trained to be more discerning? Does
anyone know where I could find on this?


I started thinking about how the eye/brain has an incredible
ability to discern very small differences/errors in a symmetrical

Well, errors in symmetry are always a challenge. Human eye is more
sensitive than any instrument in jeweler’s tool box. Sometime,
measurement shows that things are the same, but eye tells you there
is a difference.

There is a parallel thread going on using microscopes. One of the
problems with using microscopes is that one loses visual perspective,
and while details may be great, the whole piece will look wrong.

To answer your question. Instead of pursuing perfect symmetry,
embrace variations and make them tasteful. Petals of a flower all
different, but the whole flower look attractive. If you understand
why is that so, you will solve the problem. The key is training your
eyes and learning from the old works.

leonid surpin


I don’t think that there is a magic number. I can measure to 0.0001"
but it still might not look right. One swipe with a file and all
looks OK.

Look counts. the numbers don’t.

Practice lots with an evil eye boss checking everything, and yes you
can be your own evil eye boss. (no cheating)

Demand Designs
Analog/Digital Modelling & Goldsmithing

or is it dependent on certain aspects of the pattern? 

Take a picture of it, you’ll see the asymmetry real quick.

But yes, it depends on the pattern. Things like 90 angles are much
easier to see because we’re used to seeing them. And derivatives like
four prong tips being out of whack. The example of seven prongs would
be a bit more challenging to the casual observer, partially because
there is no natural centerline, ie two prong tips at 180 from each

The busier the pattern is the more time it may take to discern
out-of-whackedness because the brain is distracted with froo froo.

The human eye is able to see a difference of about a tenth of one
degree. However, our brains are trainable to recognize even smaller
deviations in symmetrical patterns when we have seen those patterns
multiple times. This “pattern recognition” is why many birders can
identify birds that appear as small specks in the sky to the rest of
us. It is also used by the military to teach target recognition. So,
I would conclude that it can be taught, but there may be some innate
"talent" also required that the teaching can develop.

Try googling “pattern recognition” and see what you find.



There are tools for measuring symmetry. Here is an example which
works very well:

They discuss the interesting science of measuring symmetry,
including the measurement of radial symmetry as you describe for
jewelry. We humans are very good at assessing symmetry in human
faces, and we make the generalization “symmetrical equals beautiful”,
whereas I know a few people whose faces are fairly symmetrical but
whose hearts make them ugly!

Mark Bingham
Fourth Axis

I’ve always believed that actual “straight” is somewhere between
measured “straight” and visual “straight.”

One of the few things that I’ve done longer than make jewelry is to
play the guitar. I learned along time ago that you tune a guitar to a
pitch fork or tuner and then tune the guitar to itself.

Piano tuners have similar approach. They set the pitch on one string
with an electronic tuner or tuning fork and then tune the piano to
itself by ear. I feel that jewelry symmetry is the same.

Have fun and make lots of jewelry.
Jo Haemer

or is it dependent on certain aspects of the pattern? The pattern
causes the eye to ‘force’ it to be symmetrical. Neil was exactly
correct - take a picture and you’ll see the errors right away. There
is a foolproof way to carve a seven prong crown that I use, and teach
my students. If you’re used to working with a good carving wax and a
calculator here’s the formula. Start with your exact size circle wax
blank. Mark the center. Next measure the exact diameter X 3.14 to get
your circumference. Now divide the circumference by 7. This gives you
the spacing for seven prongs. An old “pie” (no key on my board for
this) formula for carving and measuring any perfect circle. The trick
is to mark the prongs on the top surface correctly and then scribe
the lines down the sides of the wax blank. Practice makes perfect!

Margie Mersky

If you google ‘bilateral symmetry detection’ you’ll find lots of
scholarly I read some but I won’t even try to speak to
much it here.

I did gather that we humans are best at distinguishing symmetry when
it is vertical (|), next is horizontal (-), and oblique angles (/)
taking the most time for recognition. It appears that recognition of
symmetry is measured by the accuracy of identification of a given
pattern as symmetrical and the amount of time it takes to identify
said given pattern as symmetrical.

This link has an article regarding symmetry detection that was
printed in the Journal of Vision:

Mike DeBurgh, GJG
Henderson, NV

I don’t know about any mechanical device, mathematical rule, or
textbook “method” - but when want I a discrepancy detected, a failure
of alignment found, a lack of symmetry seized upon, an eccentricity
elevated to consciousness, anything out of level or plumb pointed out
with unerring accuracy, here’s how I do it.

Without saying a word, I just let my dear wife come within eyesight
of the object and her radar immediately homes in and focuses a gimlet
eye upon the offense to propriety and good taste. She loses no time
in bringing the matter to my attention and here’s the best part - I
am always grateful. Sometimes it takes a while before my good sense
gets the better of my wishful thinking, but I am always, always

My workshop buddy and i were just talking about this area of life
and work. He opines that while we strive for the best result, there
is no getting at perfection. Them who get on their high horses, the
ones for whom nothing is ever good enough - well, some may have
higher standards than others and maybe even the higher skills to get
closer, but for everyone there is a “good enough” point. Or else,
when would anyone ever stop working?

There is no point in seeking a mathematical answer such as your
query implies when you wonder if 1 miilimeter is “good enough”. That
number would depend upon the scale of the work. Bigger work = bigger
tolerances in general, along with other practical considerations
like the distance from which an object will be viewed etc.

Listening to an inspired piece of quite funky ol’ country blues not
long ago, my fiddler friend said “Wow! You don’t have to be in tune
to be good!”

For me, personally, the greatest challenge has always been overcoming
my desire to get to the point when I can consider a piece “good
enough” and start strutting my creation about for the approval,
admiration, or cash I hope it will bring to me. I don’t want that
desire to play tricks upon my eyes or to distort my judgement. So I
am grateful to have a dear, trusted second set of eyes to help keep
me honest, along with all the measuring tools on my bench. That
second set of eyes needs to have some other good qualities attached
to it - honesty, gentleness, firmness, are just a few. And I, of
course, have to be able to abandon defensiveness and ego and just
learn to listen carefully. Being a first-born son, that last is a
damned hard skill to learn.

Good luck

I don't think that there is a magic number. I can measure to
0.0001" but it still might not look right. One swipe with a file
and all looks OK. 

Many times over the yrs, I have intentionally set things
caliwhompus(?) because straight and symmetrical simply looked wrong.
Exact measurements are not everything, but the customer’s eye is.


I would conclude that it can be taught, but there may be some
innate "talent" also required that the teaching can develop. 

I think Emie has something there. I’ve known people that could spot
a deviation in spacing or something to the nanometer or thousandth of
a degree. I’m guessing Marty’s wife is one of those. I’ve also known
people that can’t see what I’m talking about when I mention something
like prong spacing or issues of level problems with a stone, even
when it’s obviously really off. Couldn’t tell you what the difference
is, it’s not intelligence or eyesight problems, it just sort of seems
to be the way different people’s brains process

I think this is a large part of the reason some people are naturals
at the bench and others seemingly have to struggle much more to get
to the same skill level, regardless of their desire or training. It
seems similar to how some folks are blessed with perfect pitch, but
others can’t carry a tune in a bucket.

Dave Phelps

It seems similar to how some folks are blessed with perfect pitch,
but others can't carry a tune in a bucket. 

Dave-I know this is not a music forum but perfect pitch is not
necessarily a blessing. It’s genetic and when you have it, listening
to, let’s say, a school choir, you can have a heart attack from
their bad intonation. And being able to sing on pitch is about having
good relative pitch. I’ve also found that kids who were told that
they couldn’t “carry a tune”, can be taught to sing exactly on pitch.
I’ve done it with adults. One more comment that you never asked for.
When you hear singers singing flat or sharp, it’s generally not an
ear/pitch problem so much as faulty vocal technique. End of music
lesson. Back to the bench.

I was working on a cufflink commission recently which involved making
a silver cross for the cufflink face. What a faff. I found that by
eye i looked wrong until I got the arms of the cross within 10
microns of each other, and even then it was a bit ropey. However,
once I rounded the edges a bit and gave them a polish. it all looked
dandy. I suppose the learning here is that if you do the majority of
your work on a piece with crisp edges and a dull finish, you can
really see the errors and fix them, then soften and shine at the
last minute.

my theory about my own perception is that it is learned. my
ophthalmologist probably thought i was silly when i asked about the
difference in the size of my pupils. later, his optometrist told me i
was right (optometrists measure pupils.). then, when i got out of the
shower, my eye kept coming back to a mole on my back. i disregarded
it for a while but then went to a dermatologist. yep, it was skin
cancer. i had not “scanned” my skin to look for lesions; my eye kept
going to it.

my theory about my discernment: one of my majors in college was fine
arts. to draw or paint and be representative, the drawer must see the
smallest changes–and the ones that are significant. i think this
skill has remained with me even though i have not been aware that i
was “measuring.” what do you think?

jean adkins

Exact measurements are not everything, but the customer's eye is. 

It is interesting to get something in that the customer feels isn’t
straight and try to figure out what it is that they are seeing. I
think that when you spend your time making or working on jewelery
you develop practices or habits that you use to establish
straightness or symmetry to your own eye. But the customer is using
their own mysterious criteria and you need to see it through their
eyes, something that’s hard to do sometimes.


I find it pretty funny that my sweetie Tim and I can see the tiniest
imperfections in piece of jewelry and work within very tight
parameters. Yet, give us a piece of sheet rock or wall paper to cut
and measure… It’s really sad.

We are remarkably accurate with small stuff. Big stuff? Go figure.
We also can’t walk into a room, public or private, without
straightening pictures on the walls.

I’m betting that if you tested all the serious metal smiths and
jewelers a significant number would test positive for
obsessive-compulsive-anal -retentive disorder.

Have fun and make lots of Jewelry.

Jo Haemer

I know a few people whose faces are fairly symmetrical but whose
hearts make them ugly! 

OK this is too funny! I know some people like this as well - they’d
be great if only they could weld their mouths shut and I could
project all the beauty on the inside to reflect the outside!

Mary R. : )

Hi Jamie and others;

The ability of a customer to discern errors and flaws is often
mystifying. I can look at a group of.01 carat diamonds and sort
them, without measuring into 1.2, 1.3, 1.4 millimeters. If you set
enough of them, you’ll get good at that, especially if you’re bright
cutting. Carving symmetrical waxes in organic shapes, or even
fabrication using mirrored shapes, is challenging. Borel used to
sell a gadget that Doug Zaruba developed that looked like a 3 inch or
so square of plastic sheet with a grid pattern like graph paper. It
had a little 90 degree bracket at the bottom. Don’t know if they
still have that, but it was mighty handy for wax work. You can lay
things out on graph paper and it helps, or try printing a graph on a
sheet of acetate with a laser printer (maybe an ink jet would work

In the final analysis, if I can’t see it with a 10 power loupe, it
doesn’t exist for me. Not so for grading diamonds, of course.

The pickiest customers I’ve had are graphic artists (they think
anything they can make on a computer can be made in metal, no matter
how fine the detail or nonsensical the geometry. Machinists and
engineers are tough too. I tell them, this is a hand made piece of
jewelry. We can go to up to a watchmaker’s level of finish, but it’s
going to cost plenty.

Finally, your cheaper optics in magnifiers can have a lot of
spherical aberration and man, you can look at a circle and swear it’s
still oval. Look up at your overhead Dazor bench lamp with them on
(especially the higher magnifications) and you’ll see how banana-wise
it looks.

David L. Huffman

Hi David,

Once upon a time, I was one of Doug’s bench monkeys, and you’re
right, that little alignment widget is really handy. The ones we had
in the shop had steel “V” guides, and the grids were either 1 or 2mm
grid, not 2.5 like the production ones. Yes Frei’s still has those,
for about $40. I’ve had my own sitting half-finished on my 'to do’
pile for years. Maybe I’ll go finish it up. Shame I just got off the
laser cutter…

Hummm… Methinks I know why his “V” guides are plastic now…

For mine, I just bought a cheap indian ‘center ruler’, and used the
steel “V” guide from that. Rip the ruler off, attach gridded plastic,
go back to work. Just never got around to rigging up the lathe to do
the marking on the plastic grid.

Brian Meek.