Foreword by Gary Roskin

Measuring inclusions to determine a clarity grade has been an idea for as long as I can remember, which in actual years puts us back into the late 1970s. It was during that period of my young gemological career when I overheard a conversation between Richard Liddicoat, then president of GIA, and Dennis Foltz, then GIA director of education. They were talking about measuring inclusions, using such equipment as rotating stone holders, and referring to Okuda’s and Huddlestone’s mathematical work. I do not recall ever seeing the measuring of inclusions as part of the teachings of diamond grading, but the idea of it was something I had never forgotten.

It wasn’t until the early 1990s when I started working again with Tom Tashey, then owner of the Los Angeles European Gem Lab, that the idea of measuring inclusions became reality. Tom, who just happened to be my diamond grading supervisor at the Santa Monica GIA Gem Trade Laboratory in the late 1970s, had us using a small transparent plastic grid (transparent plastic “graph paper”) to measure the approximate size of an included crystal. It was certainly limited in nature, but it worked well enough to keep us consistent and that’s what diamond grading is all about, remaining consistent.

Over the years, Michael’s quest for finding an objective mathematical truth to diamond grading has been un-daunting. I remember our conversations starting with color grading, as Michael was trying to figure out mathematically how the grade ranges could be defined. This of course then led to talking about clarity grade ranges, how these too might be mathematically explained.

And that’s where Fibonacci and the Golden Spiral and Ratio come in. I was watching a presentation I believe at a Gem-A conference, or was it Diana Singer, New York jewelry historian and Estate Jewelry expert, talking about the Golden Ratio symmetry in a period piece, relating the beauty of an object as perceived to how the brain has calculated it as being aesthetically correct and mathematically appropriate. We say “beautiful” when our brain perceives that an art object is mathematically and aesthetically correct, as it is when proportions align with the Golden Ratio and the Fibonacci spiral.

Michael and I have been talking about the subjective and objective aspects of diamond grading for years. Anyone who has spent more than five minutes with Michael talking about the GIA’s diamond grading system has seen and heard Michael’s frustration with understanding clarity grading’s subjective and unscientific underpinnings.

Though they were experts in diamond grading, it was quite literally developed by “a bunch of guys sitting around the table saying things like ‘that looks like a solid SI1 to me. What about you?’“ This then led us directly to the question in our discussion, why? What is it that makes us feel that SI1 is more appropriate than any other grade?

What is it in our head, when looking at an emerald cut or a pear shape that says to us that the shape is “just right” or “too long” or some such seemingly subjective comment? How do we do that? I would submit that it’s our brain, in some sense mathematically determining the proportions of the stone, and liking proportions close to those in nature that obey ratios like Fibonacci’s. Whether it’s about symmetry of shape, the noticeable amount of color, or the visibility of an inclusion, our mathematical brain is signaling us to make a seemingly subjective comment, to say “it looks like a high VS2 to me.”

Our discussions eventually led us to talking about a sort of Golden Spiral of clarity grades like the Fibonacci Golden Spiral, but where the Golden Ratio relating clarity grades is 2 to 1 rather than 1.62 to 1.

Leave it to Michael to grab on to the math of the Spiral and doggedly work it until he could present a mathematical method for consistent clarity grading.

Michael’s historical research with Okuda and especially with Roy Huddleston, endeavoring to prove or correct their work, and then to refine the mathematical algorithm to give us a solid way to objectively clarity grade a diamond, is quite possibly the most significant leap forward towards developing the black box for consistent diamond clarity grading. We still believe that diamond grading is as much an art as it is a science, but what Michael has actually accomplished is to greatly increase the amount of science (the consistency) and he has revealed the natural mathematical underpinnings to the art (the subjectivity) with his System and the discovery of the “Golden Ratio of Clarity Grading.”

Someday, someone is going to take Michael’s work in this book and previous papers, develop a CADCAM program with digital imaging to mathematically clarity grade diamonds and other gemstones. My only hope is that Michael receives more than just accolades for figuring this out.