Gold from base metals anyone?
Start by putting lipstick on the sow. Then register it to run in your local Republican primary.
+1 (at least the local Republicans will believe it is a silk purse because they would rather believe Satan himself has been redeemed than tolerate a well-educated, socially minded, empathetic Democrat, Libertarian, etc...)
Use the sow's ears as an incentive/reward in the training of an attack dog. Take the dog for frequent walks until you see someone who has a nice silk purse. Threaten to set the dog on them if they don't give you the purse.
Feed sow's ear(s) to maggots. Feed mature maggots (flies) to spider. 'Harvest' silk from spider (it's done, or used to be, for cross-hairs on high precision instruments). Spin and weave (or felt) silk into cloth. Sew cloth into purse.
Get enough sows ears and sell them for dog treats. Then take the money and buy that silk purse that you like.
There aren't enough letters, never mind the ones you need... L
Search Instructables for 'junk', 'trash', 'recycle', 'garbage', or 'rubbish' and you'll come up with hundreds of silk purses made from sows' ears (metaphorically speaking).
You can't. Silk comes from a caterpillar. You'd just have a pig ear purse.