Wow, a lot of voices here. Didn't mean to open a can of worms.
Andrew, You say that Local and Global Sharpening are completely separate and independent. Agreed, up to a point. You also confirm that Local Sharpening is applied to the local area being adjusted using the settings currently set in the Global panel. Which I also agree with, but it is inconsistent with the first statement. Local and Global Sharpening always share the same settings for Radius, Detail and Masking. So, (and I apologize for seeming to beat this to death) if I have set Global Sharpening appropriately for a high-frequency image, (say for argument, radius 0.7, Detail 35, Masking 0). Local Sharpening will be applied to the image using those settings.
I think we agree on that.
Now, my original query was, "What happens when I set the Amount slider to 0 in the Detail Panel, leaving all the other sliders greyed out? I have always assumed, erroneously it seems, that this action completely turned off all Sharpening, period. Since it is still possible to apply local sharpening with the Global controls "turned off" in this way, clearly Sharpening is NOT turned off completely, it's simply NOT being applied globally. I think on balance, it's reasonable to assume that any Local Sharpening applied in this situation will be applied using whatever settings existed in the Global controls before the Amount slider was set to 0. ie. the same high-frequency settings in my example.
But that was always just a guess on my part. And I was hoping for some confirmation, or to be set straight. As I said, I prefer to be correct rather than just guessing when I respond to a student's query.
Chris, thanks for your reply. And I agree that it is possible that the Sharpening algorithms may have changed somewhat since Jeff last updated his books. With no basis for an opinion other than knowing that the Capture Sharpening algorithms are based on Bruce Fraser's work, I suspect that is unlikely. I believe, and Andrew can confirm or refute this, that the Output Sharpening algorithms are (or were) directly licensed from Pixel Genius (also based on Bruce Fraser's work) to Adobe.
I will say, however, that there is indeed actionable information in the Detail Panel sliders, but using them in this way is dependent on understanding what kind of image detail you are trying to sharpen. High frequency: lower the radius; Low-frequency: raise the radius. etc.