What is sharp?

One question that nags me as a knife maker is what counts as sharp?  How do we quantify sharp?  I've had people hand me a 'sharp' knife and wondered what counted as dull for them - a rolling pin perhaps?  I've watched lots of demonstrations that show how sharp some implement is, but they all have their problems.

The best demo I ever saw was a swordsman take a katana and slice a bamboo pole wrapped in a japanese mat into multiple pieces. "This is why people think the katana is such a good sword" he said "because it is so sharp.  But watch this..."  He pulled out a medieval broadsword with an edge like a typical butter knife, and proceeded to do the exact same slicing demo.  He cut the mat-wrapped pole into multiple pieces.
To me, what this demo shows is that it's very hard to know what's sharp because demos involve way to many other factors, and the fact that sharp is invisible to the naked eye.

Howard Schechter of The Perfect Edge crystallized this thought for me at a demo he gave.  He also showed me how to get past this problem - a digital USB microscope.  Now I have some way to judge sharpness - I can look at it!  So here's a few 'sharp' things I've seen with my microscope:

The first thing on the left is a hair.  It's for scale.  All these shots are taken at the same ~207x that my cheapie microscope focuses at.
Next is a steak knife we use all the time.  When people tell me they have a sharp kitchen knife at best about this sharp.  It goes through steak just fine, and my daughter cut her finger with it just the other day.  But here it looks round.
Next is a knife I sharpened on a 220grit stone.  It's sharp enough to shave hair.  Very grabby - it feels sharp.  Most people I know would describe this as "wicked sharp".  It's definitely better than the steak knife, but look at that white line.  That's the light bouncing back off the flat spots on the edge.
The next edge is sharpened down to 600 grit, and the flat spots on the edge are much thinner.  At this point the edge is smooth enough that it doesn't feel sharp anymore.  The grabbiness is gone, but it cuts very well.
This trend continue down the 16,000 grit edge where the flat spots on the edge have almost disappeared.  Sharp is becoming invisible again.  This level of sharpness is scary, because you don't feel it cutting you anymore - you just start bleeding.  Then it starts hurting  I sharpen my woodworking chisels to this level so I know this from experience.
The last shot is a typical single edge razor blade like you scrape paint with.  Sharp has gone invisible again.

The important part for me is now I have a way to judge sharpness & edge-holding.  Sharpen the knife, take a picture of the edge, do a prescribed set of cutting activities (like cutting shipping tubing), and then take another picture of the edge and see what happened!
What does happen?  That will be another post, where I do the same cutting with one of my knives and a couple very expensive commercial kitchen knives...