So what is the measure of sharpness to go by?

I'm curious. I tend to disagree with marcinek and agree with proton. I think marcinek is just being an ass to stir crap up like he normally does. I believe the statement is true that given the right tools and technology an edge can be taken as sharp as the steel molecules on the edge allow, in theory at least.

I'd like to hear what a physicist says about it.

I'm not a physicist but here is my two cents anyway.

I have always said that sharpness is defined by the thickness of the apex. If you have tools to measure the thickness then that data is empirical. We can call the measurement whatever we wish but as it stands now, a sharp knife by necessity has a thin apex.

I differentiate sharpness from cutting performance which is influenced by many factors like blade thickness, blade grind, thickness behind the edge, and of course how perfectly formed the apex is. A well formed apex is also by definition, as thin as we can make it. A rounded apex which is not well formed, is also dull as compared to a well formed one.
 
I'm not a physicist but here is my two cents anyway.

I have always said that sharpness is defined by the thickness of the apex. If you have tools to measure the thickness then that data is empirical. We can call the measurement whatever we wish but as it stands now, a sharp knife by necessity has a thin apex.

I differentiate sharpness from cutting performance which is influenced by many factors like blade thickness, blade grind, thickness behind the edge, and of course how perfectly formed the apex is. A well formed apex is also by definition, as thin as we can make it. A rounded apex which is not well formed, is also dull as compared to a well formed one.

Yeah, I agree. Leaving all other factors aside there is a measurable width at the apex which, in my opinion, is what defines what sharp is. I'm probably opening myself up to attack, especially from marcinek because that's what he does, but as long as there's any kind of angle there can and will be some width to the actual angle vertex. The thinner the actual vertex and more acute the angle, the more precise it will cut. In theory if you were able to form a steel sheet one molecule wide, then you couldn't get any sharper and there'd never be a need to sharpen in order to refine the vertex width, only to smooth the length.

And before I'm attacked for saying it, I don't believe a chunk of steel that's bent at a 179 degree angle but with an apex that's taken to 1 molecule in width will do anything. I do believe it can be done though, and that apex would cut anything that's bigger that the size of the molecules that form the steel. You couldn't expect it to cut deeply though.
 
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Does the word "keen" have a more precise definition than "sharp"? In my vocabulary it does not. As far as the most suitable word for geometry or thickness behind the edge, what about geometry or...thickness behind the edge. I just don't see the need for assuming that sharpness doesn't mean what it does only to replace it with a word that is no more "precise". Again, you may have been taught different meanings to these words than I was so we may not be able to get anywhere with this discussion, but those are my thoughts. You are welcome to tell me yours again but I believe we are going to find ourselves in disagreement on this subject...and that is fine. :)

As a Physicist, my preference is to use precise wording to avoid ambiguity. However, we are discussing the word "sharp" and what we interpret it to mean.

In practice, there are two aspects of a blade geometry that determine the ability to cut - the "edge width" or "radius of curvature of the apex" and the thickness of the blade at some or several distances behind the apex (which is usually simplified/approximated by the bevel angle(s)). You are correct, we can use those rather unwieldy terms to avoid confusion.
I have chosen to assign the short-hand term of "keen" to the radius of curvature of the apex. After studying the colloquial use of the word and definitions from various sources, I am comfortable with the consistency of this choice. I simply do not get paid more if you agree.

The lack of precision in the word "sharp" is essentially due to the larger number of somewhat inconsistent uses and definitions that exist. My position is that the meaning of the word, when applied to a blade, is most often referring to the general cutting performance. In terms of measurable geometry, both the radius of curvature of the apex and bevel angle contribute to our perception of cutting performance - to different degrees for different media being severed.
 

You can cut a hair, but can you whittle it?

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Does it make me a pleb if I don't sharpen my knives to hair shaving sharp?

Not at all...

I don't either, but I have before. I dull my edges too fast to worry about whittling hair, and there isn't any advantage over a moderately sharp knife when it comes to real-world cutting tasks.
 
Not at all...

I don't either, but I have before. I dull my edges too fast to worry about whittling hair, and there isn't any advantage over a moderately sharp knife when it comes to real-world cutting tasks.

This line of thinking seems to be in line with my experiences. Trying to maintain a razor edge on all my knives started to drive me insane as I used to be very nit picky about it. Now I enjoy just touching up my EDC once or twice a week and maintaining a moderately sharp working edge.
 
I was out cutting a bunch of bailing twine today, not to test any edges, just doing some work and even though the knife I was using easily shaves hair the edge was gliding across the old twine. So I got the smiths pocket pal that rides in the pouch on the sheath out and hit the edge a couple passes on both sides to rough it up and give it a toothy edge and got instant better cutting results on the twine.

Depends on what you are doing what will define how you judge how sharp the edge is.
 
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