Step 1 Pare the artichokes as described, cutting them in quarters and then each quarter in half again lengthwise to make 1/2-inch slices. Keep them in a bowl of lemon water until ready to use.
Step 2 Heat about 1 inch of oil in a large heavy pot over medium-high heat to about 360 degrees.
Step 3Meanwhile, drain the artichokes in a strainer and turn out into a tea towel. Pat them dry as thoroughly as you can. Return them to the strainer, and shake them, gradually pouring the flour over top. Keep shaking to remove the excess flour (it's best to do this over the trash can; all that flour is messy to clean out of the sink). The artichokes should be barely covered with a film of flour.
Step 4If you don't have a thermometer, determine if the oil is hot enough by adding a single artichoke piece to the pan; the oil should bubble merrily. Add the artichokes to the oil a small handful at a time. Don't overcrowd the pan or the oil will dip below a good frying temperature; it's much better to fry in small batches. (For a pound of artichokes, figure 3 or 4 batches.) When the artichokes are golden, about 2 to 3 minutes, remove them with a slotted spoon or Chinese skimmer. Tap the spoon against the side of the pan to shake off excess oil, then drain on a paper towel. While hot, sprinkle them with salt and serve immediately. To serve all at the same time, keep them warm on a paper towel-lined baking sheet in a 350-degree oven.