Basically to answer the original question a soap to be transparent must be suspended in an alcohol solution or be a composition bar of fatty acids in a sorbitol solution. The transparent natural soap bar might be pretty to look at and fine for decoration. The addition of the alcohol makes the soap drying, an attribute that most people do not want or need in their soaps for use. The difference between alcohols is based on the number of carbon atoms that make up the alcohol molecule. The lower number of carbon atoms, the alcohol is called a simple alcohol and in nature is a drying substance as it evaporates quickly.
Complex alcohols are heavy and sweet substances.
Glycerine and sorbital both are both considered safe ingredients for consumption. Many of the sugar free foods on the markets including sugar free chewing gum toothpaste, baked goods such as cookies, and candies contain sorbitol. It is very similar to glycerol in its reactions. Transparent soaps made with sorbitol and glycerine will not be drying like those made with the simpler drying alcohols. The problem is the extra energy required to produce a transparent soap made with sorbitol.