I think a lot about creativity and my current series about intellectual creativity and AI has me thinking about it specifically and in some detail. In this effort I decided to take a look at an article recommended by my colleague, Ramesh Viswanathan, Rick Mammone, Will AI Ever Think Like Einstein or Create Like Picasso?—Imagination is All You need, The Quantastic Journal, July 7, 2025. The article is interesting, and I agree with the premise.
But Mammone offered a simple model for creativity that seemed dubious to me, one based on a phase of divergent thinking followed by one of convergent thinking. It’s a common idea, but I find it problematic because it assumes that one has a specific objective in mind, something for which you are seeking a creative idea. That I don’t think we always have a specific goal in mind when we begin a process that has a creative result. The process might begin with an open-ended search that has no specific goal. Coming up with a specific goal, then, becomes an objective. Once you have that, then you can set about achieving the goal.
So I decided to put the question to ChatGPT. Here’s the resulting dialog. Major topics:
Creativity in Science
Arts and Humanities
Kubla Khan
Engineering and Architecture
Limitations of the divergent-convergent model
AI and Benchmarking
I’ve highlighted my prompts in light orange.
* * * * *
I’ve taken the following characterization of creativity
from a recent article by Rick Mammone (Will AI Ever Think Like Einstein or
Create Like Picasso?—Imagination is All You need):
“Creativity is often described as involving two distinct
modes: divergent and convergent thinking. Divergent thinking is the process of
generating a wide range of ideas and possibilities, for example by
brainstorming, while convergent thinking is about focusing on and evaluating
those ideas to arrive at a solution. By combining these two approaches,
individuals and teams can effectively harness their creative potential to solve
problems and generate new ideas.”
Do we have any documented cases of creativity in any
intellectual field that look like that? Such cases would explicitly list the
ideas and hypotheses under consideration and then trace the process by which
one idea finally won out.
Yes, there are
documented cases of creativity in intellectual fields where a
combination of divergent
and convergent thinking is explicitly visible—though not always
in such a neat or schematic form. The clearest examples come from fields
like mathematics, science, and sometimes literature or philosophy, especially
when thinkers have left behind detailed notebooks, correspondence, or retrospective
reflections. Below are some instructive cases:
1. Charles
Darwin – The Origin of Species
Domain:
Biology
Documentation:
Darwin’s notebooks and correspondence
· Divergent Thinking:
Darwin explored a broad array of hypotheses about variation, inheritance,
species divergence, and extinction. His notebooks are filled with sketches,
alternative explanations, and speculative ideas—including the now-famous “I
think” evolutionary tree sketch.
· Convergent Thinking:
Over time, he evaluated these ideas through systematic observation (e.g.,
pigeon breeding), empirical data from the Beagle
voyage, and Malthusian population theory. He gradually rejected alternatives
and synthesized natural selection as the core mechanism.
· Traceable Process:
The transition is well-documented in his notebooks and later works. Scholars
like Howard Gruber (Darwin on Man) trace
these steps carefully.
2. Albert
Einstein – Special and General Relativity
Domain:
Physics
Documentation:
Einstein’s letters, memoirs, and drafts
· Divergent Thinking:
Einstein entertained multiple lines of reasoning about simultaneity, reference
frames, the ether, and gravitation. His thought experiments (e.g., chasing a
light beam) are examples of conceptual divergence.
· Convergent Thinking:
He eventually focused on the constancy of the speed of light and the
equivalence principle, using rigorous mathematics to formalize his intuitions.
· Traceable Process:
Many stages of this process are documented in his correspondence (e.g., with
Michele Besso) and in secondary studies such as Abraham Pais’s Subtle is the Lord and John
Stachel’s editorial work.
3. Claude
Shannon – Information Theory
Domain:
Mathematics / Electrical Engineering
Documentation:
Shannon’s master's thesis and 1948 paper, plus interviews and Bell Labs memos
· Divergent Thinking:
Shannon drew on a wide range of fields: Boolean algebra, cryptography,
thermodynamics, telephony, and symbolic logic.
· Convergent Thinking:
He honed in on the mathematical formulation of entropy and channel capacity,
rejecting less rigorous or less generalizable approaches.
· Traceable Process:
His writings and the intellectual context at Bell Labs allow for reconstruction
of his thinking. Notably, his master's thesis already foreshadows key concepts.
4. Barbara
McClintock – Jumping Genes
Domain:
Genetics
Documentation:
Laboratory notebooks, experimental records, and Evelyn Fox Keller’s biography (A Feeling for the Organism)
· Divergent Thinking:
She explored non-Mendelian patterns of inheritance in maize, testing and
discarding various mechanistic explanations.
· Convergent Thinking:
Eventually, she identified the phenomenon of transposable elements (jumping
genes), a radically new idea at the time.
· Traceable Process:
Keller’s account highlights how her experimental reasoning combined divergent
hypotheses with a keen intuitive feel for patterns.
5. Poincaré
– Mathematical Discovery
Domain:
Mathematics
Documentation:
Poincaré’s own reflections in “Mathematical Creation”
· Divergent Thinking:
He describes producing a wide range of possible function forms and
transformations during conscious work.
· Convergent Thinking:
He claims the final successful combination came to him in a moment of
unconscious insight, followed by conscious verification.
· Traceable Process:
Though not as structured as a lab notebook, his account shows a clear sequence:
generation, incubation, insight, and evaluation.
Bonus: Thomas
Edison’s Invention Process
Domain:
Invention / Engineering
Documentation:
Lab notebooks, business records, and biographies
· Edison's
labs ran on a kind of industrialized divergence: many variations on filaments
or circuits were tested.
· Then
came convergence: systematic evaluation of durability, cost, and
manufacturability.
· This
process is documented in Edison’s notebooks and the work of Paul Israel and
others at the Edison Papers project.
Summary
In all of these cases, we find:
· Divergence:
A documented stage of idea generation—often experimental, speculative, or
exploratory
· Convergence:
A subsequent process of testing, evaluating, selecting, and refining
· Traceability:
Enough documentation (notebooks, letters, essays, retrospective accounts) to
reconstruct the creative trajectory
So yes—while creativity is often messy and retrospective, there are empirically rich, traceable
cases that match the divergent/convergent
model, particularly in the sciences. Would you like a comparison table of these
cases or more from the arts/humanities side?
