The pretty word 'persimmon' comes from Native American Algonquian pessamin, strangely meaning dry fruit. I wonder if this refers to the persimmon's astringency when under-ripe, which leaves the mouth chalky-dry, thanks to the fruit's high levels of tannins. To custom-ripen or 'blet' in the home, store the persimmons in a pot with some apples, pears or bananas which exude the ethylene needed for ripening. Alternatively, persimmons can be ripened through freezing.
When a persimmon is ripe it is deep amber-orange, translucent, soft to the touch and almost oozing out of its skin and the calyx can be pulled out easily. The flesh is jelly-like and sweet with some firmer segments.
* A friend tells me that plain, blended persimmon can be frozen and stored until needed as a sauce for ice-cream: a sure-fire success.