How Contextual Is Taste?

There is no doubt that taste is not directly accessed, but is influenced by all sorts of other factors. The question is how sensitive taste really is to that which has nothing to do with chemistry, physics, or biology. My kids, like all kids, insist that aspects of the food that adults deem irrelevant to taste, indeed consider ridiculous, are in fact crucial. Does (or can) a sandwich really taste different if it is cut into two rectangles as opposed to two triangles or four squares? Does the corn on the cob taste different from the same corn off the cob? Isn't this why restaurants garnish meals? How much of taste is a function of chemical reactions on the tongue and how much of it is psychologically constructed?