Re: history of knife sharpening
John, the softer the stone is, the larger the grain size. Works just like sandpaper. Soft stone - large grain size - like one of them cheap carborundum stones you see at flea markets for a buck - take a lot of metal off quickly, but leave gouges in your blade edge. Think of them like 60-grit. Puts a sorta-edge on a really dull knife, fairly quickly.
Then you got your medium stones - like a soft Arkansas. Think of it like 240-grit. You can take that same really dull knife and put an edge on it, but it takes a lot longer since you are removing less metal with each pass. But if you have a knife with any kind of an edge already on it, it will make that edge better.
Hard Arkansas is like a 600-grit. Very fine grain. Very smooth to the touch. If you took your dull knife and tried to sharpen it with that, it'd take you a week or so, but you would eventually get there. If, however, you have a sharp knife already, this stone will polish the edge and make it sharper.
The last one is a Black Arkansas. 1200-grit. Takes that fine edge you got off your Hard Arkansas and polishes it even finer. You're getting up there into straight-razor sharpness.
Normally, the coarser the stone, the bigger it is. You might get a set with a soft stone that's 6" x 2" x 1/2" thick, a hard stone that's 2 1/2" x 1 1/4" x 3/8" thick, and a black stone that's 1 1/2" x 3/4" x 1/4" thick. Since you use the coarser stone more, they make it bigger. Also the finer stones are rarer, and they cost more, so you don't get as big a piece.
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