My planes have hollows that are around 2-3 thou, as I recall. I didn't test them recently.
I've also read in the messages about plane flattening that glass can flex. So if I wanted to risk a plane with the sandpaper approach I need a piece of glass that is very flat and is 1/2 inch thick and at least 2.5 feet long so I have room to move the plane on the sand paper? (Is all glass flat to .0001" or something?) I guess part of the problem here seems like the target tolerance. If I wanted to make it flat to 10 thou or 5 thou it wouldn't seem like that difficult, but to be flat to 1 thou or less seems like a major challenge. Ivan suggested that Chinese granite plates might be affordable. I can get a small 12"x18" granite plate without spending too much, but at 85 lbs I don't think I could move it around without help, and that's not big enough for a 21" long plane. Actually looking around I see some bigger ones that appear affordable (though I expect that the cost of delivery is about 3 times the cost of the product, so maybe not as affordable as they appear). But nobody seems to sell 36" x 6 inch granite plates.
I cut some lines in a piece of MDF to test my 2 ft starrett straight edge. The results of this test are that it is perfect. I'm not sure what the accuracy limit on this test is. (I doubt it would detect a 2 thou deviation, for example--the knife would follow the previous line.) It appears that Starrett claims this item is flat to 0.0004", though I suspect the layer of wax I put on it varies in thickness by more than that...
The behavior that I observed was that there is a substantial bump on the wood but the plane won't cut at all. So it wasn't that it was cutting and cutting and the bump remained.
Is it possible that the ability to cut a bump could depend on the twist along the edge? If the edge isn't square to the face but instead twists across the length could a plane trying to make a centered cut ride the twist somehow and be unable to cut? Like if the bump is in the middle but the twist gives a high spot at both ends of the plane that hold it above the bump? (If this were happening I assume that a shorter plane would have a better chance of cutting, and presumably the best thing to do would be to remove the twist first.)
I have read all of the Charlesworth books as well. In fact, I strongly prefer books to DVDs both as a general personal preference (I read a lot) and because it's much easier to refer to them in times of need. But for some reason, I seem to find the Charlesworth books difficult to learn from. I'm not sure why. I read them all but somehow the DVD was still a revelation. But for example, I wonder if it's worth getting the DVD on shooting boards. I already improved my shooting board technique based on what he said in the book....
So I snuck down to the shop last night and tried to do some planing with the sharpened Clifton #7 and found that, lo and behold, it is now taking off the bump. I'm not sure why.
Of course, I discovered a different problem, namely that I seem to having a much harder time that before getting and staying square to the face. Before it seemed like I could just drift the plane a bit here and there and the edge would come to square and then it would stay square while I worked on the lengthwise condition of the surface.
Now I found that when the bump was gone, the edge was out of square. And I tried to adjust the plane, because it appeared that maybe it wasn't cutting in the center and so I wasn't doing what I thought I was doing, but making this adjustment seems to be difficult, but because I don't have a clear way to tell when I'm off by just a little bit, and because the adjustment lever makes small adjustments difficult. I tried the method of running a little scrap over the blade and looking for the little shavings in the plane. And that worked to a point, for getting me into the right neighborhood, but not for the final adjustment.
After a great deal of fussing and frustration I eventually got an edge that appears square and that stayed square when I turned my attention to the lengthwise direction. And I was able to remove the bump. So I don't know what was going wrong before.
We'll see how things proceed with the next board.
One thing I did notice is that the method of swiveling one end of the straight edge sometimes gives a puzzling result. There seem to be three outcomes. One outcome is that the straight edge spins freely on a point somewhere in the middle. Clearly there is a bump. The straight edge will rock. Another outcome is that the straight edge pivots on the fixed end. Clearly the surface is concave. The third outcome is that the edge pivots on a point about an inch from the other end. So if I shift the right end of the straight edge, it pivots on a point an inch in on the left. Is there a small bump at the left end? Well, if I shift the left end then the straight edge pivots on a point an inch in from the right end of the straight edge. In this case the straight edge will not rock perceptibly. Could this indicate that the surface is flat relative to the straight edge?