So looking at many recipes for Transparent Soap and the common denominator is Alcohol, Glycerin, and Castor Oil. I understand the first 2, but does anyone understand the magic that is Castor Oil?
Is there a good alternative?
Like the other ingredients you mention, castor oil functions as a solvent. I would also point out sugar or sorbitol as powerful solubilizers for transparent soaps and the like, not to mention propylene glycol (which seems to be critical in many recipes that don't use alcohol). All things being equal, a liquid soap recipe that comes out cloudy can be clearer with as little as 3% castor oil.
The unique thing about castor oil is that it's mostly composed of ricinoleic acid. I have not yet determined whether it's the ricinoleic glycerides or free fatty acid (FFA) or soap that functions in this way. Practically speaking, it's a question of whether the castor oil soap or the castor oil superfat is the effective thing.
As for alternatives to castor, I would point out that these solvents and solubilizers are used in many different proportions and usually not all at once. They can work together and to some extent substitute for one another. There is no approach that uses all of them at once. You can find transparent soap recipes that don't use castor oil.