HUMAN AND COMPUTER CREATIVITY Bisociation of Koestler (1964) as the Theory of the!aha!-moment.

Transcription

1 HUMAN AND COMPUTER CREATIVITY Bisociation of Koestler (1964) as the Theory of the!aha!-moment. Chinese National Association of Mathematics Education Conference Lanzhow, Gansu, China June 2014 Bronislaw Czarnocha Hostos Community College City University of New York NYC,USA

2 Arthur Koestler, The Act of Creation, 1964 I have coined the term bisociation in order to make a distinction between the routine skills of thinking on a single plane as it were, and the creative act, which always operates on more than one plane p. 36 for Koestler, bisociation represents a spontaneous flash of insight...which connects previously unconnected matrices of experience (p.45)

3 Reminder from CTRAS 5: Wu Zhipeng The Construction of High School Mathematics Wisdom Class Professor Cheng Shangrong synthesized research about intelligence in and out of China, and came to the conclusion that intelligence is a typical character produced and expressed in education situations, and it is directed by virtue and creativity. The purpose of obtaining intelligence is to cultivate and develop the students capability, mathematics sensitivity and sudden enlightenment.

4 Mao Tse Tung: On Practice, July 1937, p.68 As social practice continues, things that give rise to man s perception and impressions in the course of his practice are repeated many times; then a sudden change, (a leap) takes place in the brain in the process of cognition, and concepts are formed. Concepts are not longer the phenomena, the separate aspects and external relations of things; the grasp the essence, the totality and the internal relations of things.

5 Albert Einstein (1949) Autobiographical Notes, p.7 Notes. P.7 lbert. P.7 What exactly is thinking? When at the reception of sense impressions, a memory picture emerges, this is not yet thinking, and when such pictures form series, each member of which calls for another, this too is not yet thinking. When however, a certain picture turns up in many of such series then precisely through such a return it becomes an ordering element for such series, in that it connects series, which in themselves are unconnected, such an element becomes an instrument, a concept.

6 Bisociation: When two habitually independent matrices of perception or reasoning interact with each other the result is either: a collision ending in laughter A Raymond Smullyan joke: A visitor who wants to investigate life of prisoners comes to a prison and is led around by the prison s chief. They walk along the prison corridor and look, unnoticed, into cells through small, so called Judas windows placed within the doors. In one of the cells, 4,5 cellmates are sitting on their beds, from time to time one of them states a number, like for example sixteen (16) and the rest are laughing. After observing it for a while, the visitor asks the prison s chief: What s happening here? What are those numbers and why they laugh? The chief says, it s simple. They tell jokes; they made a list of jokes, each joke has a number and they heard it so many times they know it by heart. hey continue watching as several numbers are shouted by different prisoners. At some point one of them says 56, they laugh and stop for awhile, but one of them laughs so much, he falls under the table laughing. The visitor is asking, what happened to this one? Oh the chief answers- he heard it for the first time! A fusion of intellectual synthesis. Poincare fusion For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations, and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination A confrontation through esthetic experience

7 Examples of bisociation: Guttenberg Press (Koestler, p.123)printing Press Here, then, we have matrix or skill No. I: the printing from wood blocks by means of rubbing. It leads Gutenberg, by way of analogy, to the seal: 'When you apply to the vellum or paper the seal of your community, everything has been said, everything is done, everything is there. Do you not see that you can repeat as many times as necessary, the seal covered with signs and characters?' Yet all this is insufficient. I took part in the wine harvest. I watched the wine flowing, and going back from the effect to the cause, I studied the power of this press which nothing can resist... At this moment it occurs to him that the same, steady pressure might be applied by a seal or coin-preferably of lead, which is easy to cast on paper, and that owing to the pressure, the lead would leave a trace on the paper - Eureka! A simple substitution which is a ray of light... To work then! God has revealed to me the secret that I demanded of Him.

8 Koestler s Triptych an example of the triptych assignment used by Introductory Statistics class: Trailblazer Outlier O Sampling Probability Confidence Interva Law of Large Numbe Lurker/Lurking Variable Correlat The triptych below is an example of student wo Trailblazer OUTLIER Random SAMPLING Chance PROBABILITY Lurking Variable CORRELATIO Testing CONFIDENCE INTERV Sample Mean LAW OF LARGE NUM

9 Classroom of Algebra: 0 The teacher asked the students during the review: Can all real values of be used for the domain of the function X + 3? 1 Student: No, negative X s cannot be used. (The student habitually confuses the general rule which states that for the function only positive-valued can be used as the domain of definition, with the particular application of this rule to.) 2 Teacher: How about -5? 3 Student: No good. 4 Teacher: How about -4? 5 Student: No good either. 6 Teacher: How about -3? 7 Student, after a minute of thought: It works here. 8 Teacher: How about -2? 9 Student: It works here too. 10 A moment later Student adds: Those X s which are smaller than -3 can t be used here. (Elimination of the habit through original creative generalization.) 11 Teacher: How about X 1? 12 Student, after a minute of thought: Smaller than 1 can t be used. 13 Teacher: In that case, how about X a? 14 Student: Smaller than a can t be used. (Second creative generalization)

10 Act of Creation is the defeat of habit by originality. (Koestler,p 96) That means that bisociation not only is the cognitive reorganization of the concept by an immediate perception of relations, but also it can be an affective catalyzer of the transformation of habit into originality. Liljedahl (2004) metafindings: Aha experience has a helpful and strongly transformative effect on student s beliefs and attitudes towards mathematics (p.213). The presence of this cognitive/affective duality of creativity, of the Aha moment, can provide the intrinsic motivation to bridge the Achievement Gap in US (Prabhu, 2014) and in other centres of educational inequality, such as Poland (PISA in Focus,36).

11 How to facilitate bisociation- Aha! Moment in the classroom? The dual character of bisociation as cognitive restructuring and as an affective act of liberation makes it an excellent classroom tool for classroom teaching in the contemporary era. Since minor, subjective bisociative processes do occur on all levels, and are the main vehicles of untutored learning. (p.658). Therefore, in order to approximate the conditions of untutored learning in the mathematics classroom necessary for Koestler s bisociation we, as teacher-researchers are led to the guided inquiry leading to discovery method, which allows us to find, within the classroom discourse, the space for intellectual freedom within which these conditions are met.

12 Why and how utilize the bisociation in the mathematics classroom? WHY Students in remedial mathematics at community colleges are at risk. Their success in higher education depends on overcoming obstacles to learning, many of which are attitudinal, related to affect perception, and detrimental to cognition. (Prabhu, 2014) WHY Mathematical creativity may be the only gate through which to reactivate the interest and the value of mathematics among contemporary youth whose engagement in the field is hampered by disempowering habits expressed as I can t do it, I am not good in math, thinking tires me (Czarnocha et al, 2011). WHY Habits are indispensable core of stability and ordered behavior; they also have a tendency to become mechanized and to reduce a man to the status of conditioned automaton. The creative act, by connecting unrelated dimensions of experience, enables him [the man, or her, the woman] to attain to a higher level of mental evolution. (Koestler, p641)

13 Achievement gap is the persistence difference in student scholastic achievement between different social groups, classes, genders. Analysis of PISA 2012 exam revealed that whereas many participatnts solidified its lead (Shanghai, China) in overall achievement or have made significant advances (Poland from 25 th to 14 th position), at the same time equally significant Achievement Gaps between children of different social classes were observed. (PISA 2012 News #36). The degree of achievement gap was measured in the table below by the difference in the average scores of the top social class (professionals, managers) and the average scores of the lowest social class (elementary professions, blue collar workers). In US, teaching with the help of the Act of Creation that is facilitation of the Aha moment is one of the routes through which the Achievement Gap can be closed. The second route comes from Texas and is described in (NYTimes, 5/15/14)

14 Achievement Gaps revealed by PISA Korea Japan Norway Canada Estonia Latvia Russia Finland UK Lithuania Ireland USA Spain Sweden Italy Denmark Netherland Vietnam Malayasia Mexico Costa Rica Kazachstan Poland Germany France Luxemburg Portugal Israel Belgium Shangai Taipei Slovakia

15 Achievement Gap in USA

16 Computational Creativity, from M.R. Berthold (ed) Bisociative Knowledge Discovery, LNAI 7250, 2012 Along with other essentially human abilities, such as intelligence, creativity has long been viewed as one of the unassailable bastions of the human condition. Since the advent of the computer age this monopoly has been challenged. A new scientific discipline called computational creativity aims to model, simulate or replicate creativity with a computer (Boden,1999;Dubitsky et al, 2012). Computational Creativity = Bisociation (minus) leap of insight.

17 Computational Creativity types of bisociation 1 Bridging Concept 3.Bridging by Graph Structural Similarity

18 Computational Creativity/Human Creativity

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20 Possibility of the new type of collaboration between Mathematics Education and Informatics The situation is interesting: we have one precise principle underlying both Human and Computer creativity. Each domain is in the beginning of its development. A collaboration in the investigation of both and their mutual impact promises, in the spirit of Bisociation to bring a wealth of new results and discoveries for both. On one hand The ability of humans to perform creative reasoning like bisociative thinking outstrips that of machines by far, and on the other hand, the generality of computer creativity offer wealth of applications to the classroom..the re-introduction of creativity into mathematics classroom might be the only way through which our students will get back interest in, and enjoyment with mathematics. Our respective tasks, facilitation of the discovery in the classroom and sensitizing computers to habitually separate domains, although different bear, a similarity, which could be the basis of new type collaboration between Math Ed and Informatics.