For example, Johnny's mom bakes a wonderful cheese flavored bread, and in Johnny's context, his mom is a creative wonder. But Johnny's mom simply followed Grandma's recipe, so in her context, there was nothing creative at all in what she did to realize her product. A machine can be built (a bread-maker) that blindly follows the same recipe, or algorithm, to achieve the same result.
But now we ask whether Grandma, who devised the recipe, was being truly creative. Wasn't Grandma also possibly following some algorithm in coming up with her creation. After a lifetime of baking she was familiar with many bread recipes and knew very well what tastes please her. She might well have experimented with known recipes, altering various ingredients until finally reaching something she liked. Using taste as a criterion, she likely varied the recipe, using a systematic trial-and-error process to ultimately maximize her taste response. This is not unlike what a computer can do, clearly a procedure that could also be implemented in some machine.
We might even suppose that Johnny's mom produced her bread unaware of Grandma's recipe. Whatever her knowledge base, even she might well have followed some logical procedure, though it would undoubtedly been far more lengthy and involved, assuming she isn't the bread expert that Grandma is.
Most people would probably agree that there is no creativity involved if one achieves some end by simply following a fixed set of instructions, even those that suggest a trial and error process. But this is exactly all that machines and computers are capable of doing. Even the most complex learning machines, ones that can alter their behavior dependent upon their experience, generate an output that is ultimately predictable, since their code is specific. There is no randomness or "free will" in what they do, and it would seem that only living organisms have that potential, whatever it is.
So when can a human task be considered creative? Let T be the task to be performed by our human, H, and let H' represent the mental process by which H performs T .
Thus human creativity, if it truly exists, must involve some kind of insight or glow that cannot be explained by a rational argument or logical procedure. It's like an unknown and unexpected spark that suddenly ignites a gaseous mixture, a spark that is only recognized after the fact, and can only thereafter become part of our database to be used in a future algorithmic way, should we desire it. The true source of this mental spark may, perhaps, be understood more fully only once we humans move a bit further along our evolutionary path.
The first bulleted item above is often easy to show, whereas the second is, as yet, outside our reach, since modeling the mind of our human is a research in its primal infancy. The third item is also generally inaccessible, a common occurrence in trying to prove a negative. However, one result of a theorem by Godel in 1931 did seem to show that humans can know things that algorithmic machines cannot, and thus humans are more than just logic processors responding to the mental criteria of the moment1,2. The AI community still questions the direct application of this theorem to computer programs3, which many feel could ultimately explain all mental activity, even consciousness and first person experiences, i.e. the qualia (joy, pain, lust, love, hate, envy, understanding, etc.). This is strongly disputed by others, particularly John Searle with his Chinese Room argument4.
Consider Gary Kasparov, former world chess champion for many years, and widely regarded as a highly creative chess genius. Contrast him with the equally capable IBM chess program Deep Blue, simply a machine following a fixed program, and clearly not creative at all. We levy different qualities on Kasparov and Deep Blue, though they achieve the same dominating result. Given a state of the chess board, both contemplate the results of several potential moves, and then select that which best satisfies some internal criterion. Does Kasparov do more than that, perhaps something that is not algorithmic, and subject to computer replication? Is Kasparov really creative?
What about Deep Blue, which, in following a fixed set of rules, or program, is clearly not creative, as no machine can be. Is the development of Deep Blue's program, call it A, however, a creative effort of some human programmer, call him/her A'? We simply ask the same question as before. Can the process, say B, that A' used to develop A, be expressed as an algorithm, namely have B be a program that writes the program A? If so, a new machine can be constructed that develops A using the set procedure B, and the effort of A' was clearly not creative. We can now go on to ask whether program B is a creative effort, namely the result of a process that is not entirely algorithmic. If not, we can then delve one level deeper (program C), and so on, until we finally reach a creative (non algorithmic) effort, thus finding the true seed of creativity. Of course, this process might be unending, and true creativity never found.
In the real world, our feel for creativity is far less precise. Deep Blue is clearly not creative, but the author (call him/her A') of its program (call it A) may be. It is likely that a key element of the process for generating Deep Blue's program involved the establishment of one or more figures of merit regarding chess positions, combined with a search routine that looks forward several steps in order to select the best possible move at any stage of the game. Thus, quite possibly, a program, B, could be developed that writes Deep Blue's program A. Thus A is not a creative effort in an absolute sense, and should B mimic the process employed by A', the program's author, then A' fails the human creativity test as well. But I am not sure that the development of a suitable B is in the cards as yet, so I attribute at least some true creativity to our programmer A'. Going one step further, writing a program that writes another program that writes the program A seems even more difficult, so I would attribute even greater creativity to such an endeavor. But, in fact, it may still turn out that a machine could ultimately be built to accomplish this task, and true creativity not emerge.
So, at its most fundamental, the existence and nature of creativity seems open to debate, and in the category of other mind elements, such as consciousness, awareness, first person experiences, and free will. In everyday life, we are a bit more relaxed and consider creativity as some kind of magic that some people display in certain endeavors, and draw a lesser distinction between a creation and the creative effort needed to get there.
1. Godel's Theorem and its proof are quite complicated, but several simple overviews are provided at http://www.miskatonic.org/godel.html , particularly the offering of Rucker.
2. Penrose, R., Shadows of the Mind, Chapter 2
3. Nagel and Newman (editor Hofstadter) Godel's Proof, page xv
4. Searle, John, Mind , page 88