The Creative Process

EE 101, Fall 2014University of Kentucky

• 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)

Creative Process Models

• 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 4-stage model

Wallas Model

• 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

Creative Process Models

• 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)

Wallas’ Model in Mathematics

• 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

Creativity in Mathematics – Case Studies

• Describes his discovery of a theory of so-called Fuchsian groups

• Started by thinking that Fuchsian functions cannot exist

Poincaré – Case Study

A tessellation of the unit discwith hyperbolically isometric regions. Tiles are related to each other by Fuchsian transfor-mations, which form a group.Drawing by Escher (1898-1972) .

• “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 non-Euclidean 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.

Poincaré – 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)

Hadamard – Case Study

• 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.

Preparation

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

Incubation

• “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.”

Intimation

• “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

• 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 (cont’d)

• “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]

Illumination and Choice

• 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]

Formulation

• 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 ninety-nine per cent perspiration”

Summary of Creativity in Mathematics

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)

Criticisms?

• 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

Criticism of Wallas’ Incubation Phase

• 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 I

• Individual exercise:– Put your name on a blank sheet of paper.– List the things you see in this picture:

In-class Exercise II

• 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

In-class Exercise III

Interesting study:• A. Snyder, et. al., “Nonconscious idea generation,”

Psychological Reports, 94, 1325-1330, 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

Non-conscious Idea Generation?