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<p>[QUOTE=&quot;Publius2, post: 8044106, member: 105571&quot;]Here&#039;s a common definition of the verb:</p><p><br /></p><p>&quot;score or mark the surface of (something) with a sharp or pointed object.&quot;</p><p><br /></p><p>Of course, all the terms in this definition are vague.&nbsp; What is sharp?&nbsp; It&#039;s all relational.&nbsp; A cat&#039;s claw is sharp but not with respect to a bee&#039;s stinger.&nbsp; What makes something pointed?&nbsp; All it has to be is somewhat conical in shape with the angle of the tip tending more towards 5 degrees than 80 degrees.</p><p><br /></p><p>But we, in a very general sense, agree that a scratch must be considerably longer than it is wide.&nbsp; Call it the L/W ratio.&nbsp; It also should be relatively shallow.&nbsp; Call this the length/depth (L/D) ratio.&nbsp; If not shallow, then we use the term &quot;gouge&quot; to differentiate from &quot;scratch&quot;, although the term gouge includes indentations that don&#039;t always follow the &quot;longer than wider&quot; dictum.</p><p><br /></p><p>So, a scratch should have a large L/W ratio and a large L/D ratio.&nbsp; Would it be a scratch if the L/W ratio were 2?&nbsp; i.e. the length were only two times the width?&nbsp; Most of us would agree that would not constitute a scratch. </p><p><br /></p><p>How about L/W=20.&nbsp; Let&#039;s put some actual numbers to that:&nbsp; If the width of a mark on a coin were 1/64&quot; (0.0156&quot;) then a L/W of 20 would give a scratch length of 0.3125&quot; (5/16&quot;).&nbsp; That&#039;s not what most of us would think of as much of a scratch although it would certainly be very visible and maybe many of us might think of it rather as a gouge.</p><p><br /></p><p>An L/W of 100 with a width of 1/128&quot; (0.0078&quot;) yields a length of 0.7813&quot;.&nbsp; Now this is recognizably a scratch over which few would disagree.</p><p><br /></p><p>So, a scratch is geometrically characterized by its length divided by width ratio as something in the neighborhood of 50 to 60.&nbsp; The actual number is highly debatable as is this entire exercise, but let&#039;s not let that stop us.</p><p><br /></p><p>Now to depth.&nbsp; I think most people would agree that the nature of a scratch is to not be deep, whatever that means since the terms are relational.&nbsp; For example, the Grand Canyon is merely a scratch on the earth&#039;s surface in that it is long when compared to its width and it is shallow when compared to its length.&nbsp; So what is a proper L/D ratio?&nbsp; Let&#039;s take our previous example with a L/W of 100 with a width of 0.0078&quot; and a corresponding length of 0.7813&quot;.&nbsp; For this scratch to be a scratch, it needs to be shallow in relation to its length so the L/D ratio needs to be large.&nbsp; How large?&nbsp; If the depth were equal to the width in this example, 0.0078&quot;, then the ratio L/W would be 100.&nbsp; It&#039;s almost looking like the geometric definition of a scratch is a mark that meets L/D and L/W ratios somewhere in the neighborhood of 50 to 100.</p><p><br /></p><p>Let&#039;s take a slightly different tack based upon what&#039;s been developed so far.&nbsp; How wide does a mark have to be before the unaided 20/20 human eye can even detect it?&nbsp; Well, a quick search on the net tells me that number is about 10 microns or 0.00039&quot;.&nbsp; So, if a &quot;scratch&quot; narrower than 0.0004&quot; is not detectable to the unaided human eye, then is it even a scratch?&nbsp; I say no so let&#039;s proceed from there.&nbsp; W=0.0004&quot;.&nbsp; For a L/W of 50, the scratch length would be 0.02&quot;, not much of a scratch at all.&nbsp; For L/W of 100, the length would be 0.04&quot;, certainly detectable but we might not call it a scratch but some other kind of a mark.&nbsp; These kinds of extremely narrow scratches are probably more in the category of what numismatists call &quot;hairlines&quot; which are a special category of scratches and not what I think Insider is getting at.</p><p><br /></p><p>We could also take a look at the length of the mark in relation to the diameter of the coin.&nbsp; Again, a dimensionless ratio might work in this regard.</p><p><br /></p><p>We could work this further looking at the W/D ratio to see if that made any sense but you should have a sense of what I&#039;m getting at here - is there a dimensionless ratio or ratios that more or less captures what we all generally agree constitutes a scratch?&nbsp; </p><p><br /></p><p>Of course, we can add non-numerical descriptors to further tighten the definition such as &quot;displaced metal to one or more sides of the scratch and/or at the beginning and end of the scratch.&quot;</p><p><br /></p><p>And finally, congratulations to anyone who&#039;s had the stamina to wade through all this late-night rambling.[/QUOTE]</p><p><br /></p>

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