Consider definitions from the Merriam-Webster dictionary:
sharp
adjective \shärp\
: having a thin edge that is able to cut things
keen
adjective \kēn\
: having a fine edge or point
These two adjectives will serve to describe
A) The thinness of the edge (sharpness) as quantified by the edge width at 3 microns from the apex.
B) The edge width or fineness of the edge (keenness) as measured at the very apex of the bevel.
These two words are colloquially synonyms; however, we require more precise definitions reflecting the subtle differences in the meanings of the two words.
scienceofsharp 
4 responses to “Definitions of Sharp and Keen”
I’m trying to visualize this but isn’t sharpness, according to the definition, a function of bevel angle? Won’t a 16° degree bevel angle have the same width 3 microns from the apex regardless of thickness of the steel (assuming no micro convexity and same hones used)? For any given bevel angle, the width at 3 microns should be the same… right?
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For a triangular bevel, if we know two of; the edge width, the width at 3 microns or the bevel angle, we can calculate the third. For example, a 16 degree triangle has a thickness of 0.85 microns at 3 microns, and if the edge width is 0.15 microns, the thickness at 3 microns is 0.85+0.15=1.0 microns. Since we never have a perfect triangle – there is always finite edge width (or a radius of curvature) to the apex, the angle is not constant, and not straightforward to measure. For these reasons, I measure the apex width and the width at 3 microns. After extensive experimentation, I determined that 3 microns is a good predictor of shaving & shallow cutting behaviour. This quantity is representative of the “thickness behind the edge” for this type of cutting. For other applications, such as food preparation, thickness millimeters behind the edge may be more representative. The key point is that thickness behind the edge determines the volume of material that is displaced as the blade penetrates – thinner is better, provided the blade is not damaged.
These measurements do not factor in the advantages of an irregular edge in enhancing draw-cutting performance; they are representative of push-cutting performance.
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[…] ” These two words are colloquially synonyms; however, we require more precise definitions reflecting the subtle differences in the meanings of the two words.” – Todd Simpson, Scienceofsharp (Definitions of Sharp and Keen) […]
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Great post. I have a question, and hope its not a silly one. If I hone with tape, do I leave the tape on when I go to a felt paddle strop? Or is there enough give in the felt to compensate for the missing tape? I understand that tape only changed the angle by a degree, but if I strop with tape would this dull my edge? Or if I don’t leave the tape on will the apex contact the substrate?
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