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Which of the three forms of creativity is GAI capable of?

This is a useful summary from Margaret Boden in AI: Its nature and future. It seems clear to me that Claude and ChatGPT can do combinatorial creativity with a range and speed that exceeds human beings, can undertake exploratory creativity with sufficiently careful prompting but at a vastly sub-human standard and could potentially be capable of occasional instance of transformational creativity but it would be a trial and error process to bring it about.

Moreover, AI concepts help to explain human creativity. They enable us to distinguish three types: combinational, exploratory, and transformational. These involve different psychological mechanisms, eliciting different sorts of surprise. In combinational creativity, familiar ideas are combined in unfamiliar ways. Examples include visual collage, poetic imagery, and scientific analogies (the heart as a pump, the atom as a solar system). The new combination provides a statistical surprise: it was improbable, like an outsider winning the Derby. But it’s intelligible, so valuable. Just how valuable depends on judgements of relevance, discussed above. Exploratory creativity is less idiosyncratic, for it exploits some culturally valued way of thinking (e.g. styles of painting or music, or sub-areas of chemistry or mathematics). The stylistic rules are used (largely unconsciously) to produce the new idea—much as English grammar generates new sentences. The artist/scientist may explore the style’s potential in an unquestioning way. Or they may deliberately push and test it, discovering what it can and cannot generate. It may even be tweaked, by slightly altering (e.g. weakening/strengthening) a rule. The novel structure, despite its novelty, will be recognized as lying within a familiar stylistic family. Transformational creativity is a successor of exploratory creativity, usually triggered by frustration at the limits of the existing style. Here, one or more stylistic constraints are radically altered (dropped, negated, complemented, substituted, added … ), so that novel structures are generated which could not have been generated before. These new ideas are deeply surprising, because they’re seemingly impossible. They’re often initially unintelligible, for they can’t be fully understood in terms of the previously accepted way of thinking. However, they must be intelligibly close to the previous way of thinking if they are to be accepted. (Sometimes, this recognition takes many years.)

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