The Creative Process
EE 101, Fall 2014
University of Kentucky
Creative Process Models
• Wallas’ Model (1926)
• Rossman’s Creativity Model (1931)
• Osborn’s Seven-Step Model for Creative Thinking
(1953)
• Universal Traveler Model (Koberg & Bagnall,
1981)
• Creative Strategic Planning Model (Bandrowski,
1985)
• Barron’s Psychic Creation Model (1988)
• Fritz’ Process for Creation (1991)
• Creative Problem Solving Model (Parnes, 1992)
Wallas Model
• We’re going to look at the stages in the Wallas
creative process model
• The others are quite similar to the Wallace
process; we’ll briefly look at a couple of them
just to see how close ‘modern’ models of the
creative process are to Wallace’s original 4stage model
Creative Process Models
• Wallas’ Model (1926)
– Preparation/Incubation/Illumination/Verification
– Creative thinking is a subconscious process that
cannot be directed
– Creative and analytical thinking are
complementary
– These basic ideas are present in most other
models of creativity
Wallas’ Model in Mathematics
• Why Math first?
– This “is a problem which should intensely interest
the psychologist. It is the activity in which the
human mind seems to take the least from the
outside world, in which it acts or seems to act only
of itself and on itself” (Poincare, 1952, p. 46).
• Taken from
– The Psychology of Invention in the Mathematical
Field (Jacque Hadamard)
Creativity in Mathematics – Case Studies
• Henri Poincaré, 1854—1912
– Brother of Raymond Poincaré, prime
minister then president of France in
WWI
– Originator of algebraic topology,
theory of analytic functions of
several complex variables
– Major contributor to algebraic
geometry, number theory, physics,
applied math
– Examined his own thought processes in a 1908 lecture
on Mathematical invention to the Institute Général
Psychologique in Paris
Poincaré – Case Study
• Describes his discovery of a
theory of so-called Fuchsian
groups
• Started by thinking that
Fuchsian functions cannot
exist
A tessellation of the unit disc
with hyperbolically isometric
regions. Tiles are related to each
other by Fuchsian transformations, which form a group.
Drawing by Escher (1898-1972) .
Poincaré – Case Study
•
“I wanted to represent [Fuchsian] functions by the quotient of two series; this idea
was very conscious and deliberate; the analogy with elliptic functions guided me. I
asked myself what properties these series must have if they existed, and
succeeded without difficulty in forming the series I have called theta-fuchsian.
•
“Just at that time, I left Caen, where I was living, to go on a geologic excursion
under the auspices of the School of Mines. The incidents of the travel made me
forget my mathematical work. Having reached Coutances, we entered an omnibus
to go some place or other. At the moment when I put my foot on the step, the idea
came to me, without anything in my former thoughts seeming to have paved the
way for it, that the transformations I had used to define the Fuchsian functions
were identical with those on non-Euclidean geometry. I did not verify the idea; I
should not have had time, as, upon taking my seat in the omnibus, I went on with
a conversation already commenced, but I felt a perfect certainty. On my return to
Caen, for conscience’ sake, I verified the results at my leisure.
Poincaré – Case Study
• Then I turned my attention to the study of some arithmetical
questions apparently without much success and without a suspicion
of any connection with my preceding researches. Disgusted with my
failure, I went to spend a few days at the seaside and thought of
something else. One morning, walking on the bluff, the idea came
to me, with just the same characteristic of brevity, suddenness, and
immediate certainty, that the arithmetic transformations of
indefinite ternary quadratic forms were identical with those of nonEuclidean geometry.
• Most striking at first is this appearance of sudden illumination, a
manifest sign of long, unconscious prior work. The role of this
unconscious work in mathematical invention appears to me
incontestable.
Hadamard – Case Study
• Jacques Hadamard,1865 – 1963
– French mathematician
– The number of primes
<n grows as fast as n /ln n
– Conjectured by Lebesgue
(1798) and Gauss (1849)
– Hadamard’s proof is based on his theory of
integral functions applied to the Riemann zeta
function
– Described his mathematical thinking as wordless,
and described solutions being received as images
Hadamard – Case Study
• J. Hadamard, The Psychology of Invention in
the Mathematical Field, Dover, New York, NY,
1954.
– Based on his own introspection and that of
Poincaré and other successful mathematicians
– Conclusion:
• Preparation, incubation, intimation, illumination,
formulation
• Essentially the same steps proposed by Wallas (1926)
Preparation
• Conscious, long, hard work.
• Attack all questions “carrying all the outworks,
one after the other. There was one, however,
that still held out, whose fall would involve
that of the whole place. But all my efforts only
served at first the better to show me the
difficulty, which indeed was something.”
[Poincaré]
• Errors, dead ends, frustration.
Incubation
Hadamard’s proposal:
• Invention or discovery takes place by
combining ideas
• There are very many combinations, most
useless, few fruitful
• The mind constructs many possible
combinations, unconsciously and at random
• The conscious mind only chooses some that
could be fruitful
Intimation
• “For some thinkers, while engaged in a creative work, illumination
may be preceded by a kind of warning by which they are made
aware that something of that nature is imminent without knowing
exactly what it will be.” [Hadamard]
• Paul Valéry, French Poet, 1871—1945:
– “Sometimes I have observed this moment when a
sensation arrives at the mind; it is as a gleam of light,
not so much illuminating as dazzling. This arrival calls
attention, points, rather than illuminates, and in fine,
is itself an enigma, which carries with it the assurance
that it can be postponed. You say `I see, and then
tomorrow I shall see more.’ There is an activity, a
special sensitization; soon you will go into the
dark-room, and the picture will be seen to emerge.”
Illumination
• “Most striking at first is this appearance of
sudden illumination, a manifest sign of long,
unconscious prior work.” [Poincaré]
• Carl Friedrich Gauss, 1777—1855, on a theorem
he had tried to prove for years:
– “Finally, two days ago, I succeeded, not on
account of my painful efforts, but by the
grace of God. Like a sudden flash of lightning,
the riddle happened to be solved. I myself
cannot say what was the conducting thread
which connected what I previously knew with
what made my success possible.”
Illumination (cont’d)
• After years of fruitless calculations, Einstein
suddenly had the solution to the general theory
of relativity revealed in a dream
– After years of futile calculations, convinced that his
quest was hopeless, he said he had gone to bed
deeply depressed. Suddenly the answer appeared
“with infinite precision, and with its underlying unity,
size, structure, distance, time, space, slowly falling
into place piece by piece like a monolithic jigsaw
puzzle. Then, like a giant die making an indelible
impress, a huge map of the universe outlined itself in
one clear vision.” (Einstein: A Life by Denis Brian, p.
159, 1996.)
Illumination and Choice
• “It takes two to invent anything. The one makes up
combinations, the other one chooses, recognizes what
he wishes and what is important to him in the mass of
the things that the former has imparted to him. What
we call genius is much less the work of the first one
than the readiness of the second one to grasp the
value of what has been laid before him and to choose
it.” [Valéry, poet]
• Divergent, then convergent thinking
• Generate, then test
Illumination and Choice
• Poincare:
– The rules of choice are extremely fine and delicate. It is almost
impossible to state them precisely; they are felt rather than
formulated. Under these conditions, how can we imagine a sieve
capable of applying them mechanically? The privileged unconscious
phenomena, those susceptible to becoming conscious, are those
which, directly or indirectly, affect most profoundly our emotional
sensibility.
– It may be surprising to see emotional sensibility invoked à propos of
mathematical demonstrations which, it would seem, can interest only
the intellect. This would be to forget the feeling of mathematical
beauty, of the harmony of numbers and forms, of geometric elegance.
This is a true aesthetic feeling that all true mathematicians know, and
surely it belongs to emotional sensibility.” [Poincaré]
Formulation
• Formalization: express by writing
• Conscious, disciplined, focused,
painstaking
• To verify.
– “The feeling of absolute certitude
which accompanies the inspiration
generally corresponds to reality; but it may happen
that it has deceived us.” [Hadamard]
• Compress
– “It never happens that the unconscious work gives us
the results of a somewhat long calculation already
solved in its entirety.” [Poincaré]
Summary of Creativity in Mathematics
•
•
•
•
•
Preparation: No free lunch. Expect frustration.
Incubation: Random search. Give it time.
Intimation, Illumination: Eureka!
Formulation: Down to business.
Louis Pasteur, 1822—1895:
"Chance favors only the prepared mind.“
• Thomas A. Edison, 1847—1931:
“Genius is one per cent inspiration and ninetynine per cent perspiration”
Criticisms?
What are some:
– shortcomings/holes
– inaccuracies/false assumptions
of the Wallas/Hadamard model of
the creative process?
• Reminder:
– Preparation (the conscious, hard work)
– Incubation (non-conscious processing & idea
generation)
– Intimation/Illumination (insight, breakthrough, a-ha!)
– Verification (look for holes, fill-out details)
Criticism of Wallas’ Incubation Phase
• Wickelgren (1979)
– “there isn’t a shred of evidence to support [non-conscious
processing]”
• Alternative explanations
– Relief from fatigue
• Taking a break relieves the solver from
the mental effort and thus (somehow)
revives capacity to attempt a solution
– Relief from a fixed ‘mind set’
• Note
– The Snyder et. al. study (2004) was designed to avoid these
criticisms to the extent possible
• Participants were mentally engaged during a break between sessions
• A divergent idea generation session was employed to minimize
concerns associated with a fixed ‘mind set’/approach
In-class Exercise I
• Form groups with at least 4 members
– Get a blank sheet of paper
– List names of group members
– Assign a secretary
• Take 5 minutes to perform the following task
– List as many uses as possible for a blank sheet of
paper (8.5” x 11”)
• After 5 minutes, turn your sheets in
In-class Exercise II
• Individual exercise:
– Put your name on a blank sheet of paper.
– List the things you see in this picture:
In-class Exercise III
• Re-form your groups
• Get your previous list of uses for a blank sheet
of paper
– Draw a line under the previously listed ideas
– Take 5 minutes to come up with more ideas
Non-conscious Idea Generation?
Interesting study:
• A. Snyder, et. al., “Nonconscious idea
generation,” Psychological Reports, 94, 13251330, 2004.
– 125 participants (age 11 to 71)
– Worked on solving the following
problem
• Given a blank sheet of paper,
find as many uses as possible
Non-conscious Idea Generation?
• A. Snyder, et. al., “Nonconscious idea generation,”
Psychological Reports, 94, 1325-1330, 2004.
– After five minutes, the session ended, and the participants
were given another, unrelated mentally engaging task,
which also lasted five minutes.
– After a period of distraction, the participants were asked
to resume the task of coming up with uses for a sheet of
paper (this was not expected by the participants – they
thought that this task was done)
– The second session proceeded in a manner similar to that
of the first session
• A new burst of ideas
• Suggests that, even in absence of a reason to pursue solutions,
the process of non-conscious idea generation continued
Non-conscious Idea Generation?
• Total number of responses:
– 8 to 44 (Mean=23.2, Median=22)
– Prebreak: 5 to 33 (M=15.4)
– Postbreak: 3 to 15 (M=7.8)
Non-conscious Idea Generation?
• Similar response patterns pre- and post-break
• Although responses were exhausted in the first
session, the second session provided a new burst
of ideas
Non-conscious Idea Generation?
• Snyder et. al. interpreted their findings as indicating
non-conscious idea generation during the break