Thread: I could use some advice here

Originally Posted by Hammett

On the practical side, yes, you're absolutely right that it is very odd to have a smiling edge that makes full contact across the edge at the same time, thus the need for rocketing X strokes.

If the edge is appropriately contacting the hone, what is the resoning re the need for exotic sharpening strokes?



ed

Because the edge has a smile and second, because the blade rockets on the hone, hence the need for the "exotic" sharpening strokes.

Originally Posted by Hammett

Because the edge has a smile and second, because the blade rockets on the hone, hence the need for the "exotic" sharpening strokes.

Apologies, misread the thread (missed the bit about "an old W&B"), and thought you were talking of the same razor.



ed

Originally Posted by Hammett

I am sorry but that statement is wrong. You are seeing the blade as a single plane.

Uhm, no, the statement is correct, your understanding of math isn't. A 'curved plane' is called 2-dimensional space or surface and generally is not made from interjections of planes. If the 2-dimensional space is a manifold yes, locally it resembles Euclidian space, which is what you're thinking. An ideal edge is obviously not a manifold. the two sides of the bevel are two completely different tangent spaces attached to the same point/line.

Originally Posted by Hammett

That if 2 straight lines (edge and spine) can have contact on a hone (flat surface), a curved line (if properly done) can too, as the curve is just a sum of straight lines.

First there are three lines, the edge and the spines on the two sides of the razor. Second straight doesn't describe your razor.

Any three points form a plane, whole lines belonging to the same plane puts a lot of restrictions. If your edge (a line) and the spine on one side of the razor (another line) belong in a single plane, the spine on the other side of the razor (third line) is not in the same plane and therefore cannot be in a plane with the edge.

It the math is too abstract you can take a piece of paper and convince yourself that you cannot fold it to form a 'smiling' edge without crumpling or tearing it.

BTW English isn't my native language either, hence using math which is invariant, to explain your issue.

Originally Posted by gugi

It the math is too abstract you can take a piece of paper and convince yourself that you cannot fold it to form a 'smiling' edge without crumpling or tearing it.

True, I cannot make a smile from a single piece of paper, but I can get a bunch of papers and make a smile, and that's my point.

Originally Posted by gugi

Any three points form a plane, whole lines belonging to the same plane puts a lot of restrictions. If your edge (a line) and the spine on one side of the razor (another line) belong in a single plane, the spine on the other side of the razor (third line) is not in the same plane and therefore cannot be in a plane with the edge.

Sorry, I am not a math geek (though I understand what you say). I am speaking of what I am remembering from primary school, hence I admit I might be wrong.

But, if we can imagine a half-moon 3D object and we cut it with 2D planes at any angle, we will end up with 2 edges made by the intersection of the 2 planes and the object. If we can narrow those 2 edges to a minimum (just a line), that new edge will share the same plane from the 2 sides of the spine.

Originally Posted by Hammett

True, I cannot make a smile from a single piece of paper, but I can get a bunch of papers and make a smile, and that's my point.

And that's the reason why you cannot have a smiling edge lay on a flat hone. If you can make it with a single piece of paper you'd be done.

Originally Posted by Hammett

But, if we can imagine a half-moon 3D object and we cut it with 2D planes at any angle, we will end up with 2 edges made by the intersection of the 2 planes and the object. If we can narrow those 2 edges to a minimum (just a line), that new edge will share the same plane from the 2 sides of the spine.

If I understand correctly your proposition, the part in red is what you cannot make happen. I mean you can make it in a single case and that is when the two planes coincide, but that's not a razor.

Anyways, the whole point of talking about the math is to convince you that there is only one way to get a shaving edge on that razor. If you aren't convinced you'll still have to do it the only possible way, but it may take you a lot of time trying to make something happen that is impossible to happen.
You can do x-pattern strokes, you can do scything strokes, rocking strokes, they accomplish the exact same thing which is to abrade metal from every section of the bevel, one at a time. I personally find it easiest to focus on the goal and the means are just whatever it is necessary to achieve it. Of course, other people prefer to use set prescriptions without worrying too much what exactly is happening and that can get them to the same end too.

All I'm saying is that if getting into the math is becoming a distraction it may be better to refocus back on how to sharpen that razor.


And yes, I've got a proven record as a math nerd, my math skills put me somewhere in the top 0.05% of people. I suppose just the fact that I calculated it gets me a third of the way there

Just for the record, because it gets clear you know way better than me what you talking about, my assumptions to my point were 2:

1.- A single line belongs to an infinite number of planes
2.- A curve is the sum of tangent lines at a given reference point

Using these 2 assumptions, I can make a curve that will belong to an infinite number of planes, which will include the razor. I guess there is something wrong in those assumptions that would make my point not valid. And I guess this forum is not the place for this kind of discussion :P

Originally Posted by Hammett

1.- A single line belongs to an infinite number of planes
2.- A curve is the sum of tangent lines at a given reference point

(1.) is true only if the line is straight.
(2.) is somewhat imprecise, but close enough for a working definition.

And, just for completeness, a plane is a flat surface. I just took a look at the wikipedia entry and it's pretty good: http://en.wikipedia.org/wiki/Plane_(geometry)

The issue is geometrical, once you stray from flat surfaces and straight lines certain things are not true anymore.
The restrictions your are facing are (1) your hone surface is flat (2) you have two different and distinct surfaces on both sides of the bevel.
When these surfaces are flat and your edge is a straight line everything you are saying is correct, but any amount of curvature on any of them necessitates curvatures in at least one more, but your hone remains flat.