Rubbing your body with lard and ashes

I remember one time I was at one of those historical re-enactment places. I think it was colonial Williamsburg. Everything was all colonial american-y, which means that there was traditional clothing, persons, food, and soap. Especially the soap. While a Colonial lady was doing a demonstration on colonial american crafts, she mentioned that she had save the fireplace ashes so she could make soap. I asked about it (oh, i shouldnt have).
Soap is apparently made from fat and ashes. I find it counterintuitive that rubbing lard and charcoal over your hands makes them cleaner, but who am I to question colonial logic.
I wonder who it was that discovered that this mixture made soap. I mean, some of those "old" inventions make sense. Milk makes sense. You see young cows drinking at the udders. You realize that it must be nutritous, as young animals consume it and get bigger. You make the connection. In this way, the discovery of milk seems totally logical.
Soap is not. Who was it that discovered that this odd mixture made scum and dirt come off? I suppose some pre-colonial woman could have been cleaning her fireplace out with a pot of fatty pork cooling above when some of the fat could have drabbled out, mixing with the ashes. I then suppose her daughter could have come in the door, dirty from playing out in the fields. In a loving gesture, the colonial woman could have tried to brush the dirt from her daughters face, forgetting the fat/ash mixture on her hands. However, when she brushed her daughter, she may have realized that the dirt came off.
Anyways, thats my take on it. There is no other possible way people could have figured out that mixing beef fat and ash could make soap. Its almost as illogical as extracting an enzyme from bull liver, putting it in a thai energy drink, and marketing it as red bull.