On page 81 in my book, there is a brief discussion of “feedback loops”. This teaching/learning strategy is so obvious and falls so easily out of any understanding of Polanyi’s tacit theory of knowledge that I am amazed to see it pop up in a recent research study as though a major discovery is being reported. Investigators at Florida State University claim that the “Mathematics Formative Assessment System” (MFAS) applied to kindergarten and first-grade students demonstrated learning gains of six weeks to two months worth of extra instruction. The technique calls for teachers to assess what the students understand, what they do not understand and then offer the right additional learning experiences to fix the missing or error-laden material in the students’ mind. Students are asked to explain their reasoning thus exposing to the teacher any misconceptions or procedural failures on the part of the students as they work on problems.
The real news here is uncovering the practical classroom management techniques needed to manage the formative assessment tasks. Since the MFAS process is different for each student, there is a challenge for teachers to deal one-on-one with each learner and develop the right instructional intervention to solve the cognitive problems experienced by each child. Perhaps a search for additional information on this could be found using the name, Mark LaVenia who was listed as the “methodologist” on the Florida State Team.
The reality of unconscious mental processing leading sometimes to the Aha! moment is increasingly recognized by the scientific community. Research attention is shifting to conducting experiments with an aim to understand more about this effect. A study just published in Thinking & Reasoning (2017) is called “Insightful solutions are correct more often than analytic solutions”. The authors (Salvi, Kounios, Beeman, Bowden, and Bricolo) conducted a variety of puzzles comparing insightful solutions to analytically determined answers. They were able to show that those answers coming into consciousness from unconscious processing were more likely to be correct than answers constructed through conscious reasoning. A timed deadline was imposed on each puzzle which created anxiety among test subjects. A majority of answers tossed out just before the imposed deadline appeared to be either a guess or analytically derived and often wrong. The authors conclude that encouraging insightful solutions to learning and problem solving requires a relaxed atmosphere where the factor of time is not present. The need for incubation time is mentioned in my book on page 56 where an argument is made that formal education is too often run by the clock thus imposing a deadline on thought. As this research report indicates, deadlines short circuit the use of intuitive processes hence sometimes leading to wrong solutions.
When setting out to write my book on tacit knowledge, I aimed attention upon current research in neuroscience to uncover evidence that Polanyi was correct in his description of tacit knowledge as a subconscious mental processing activity. Since the publication of my book, I discovered a 2013 study by Creswell, Bursley, and Satpute (Carnegie Mellon and Northeastern Universities) that was hailed as the first neural evidence for unconscious thought processing at work. The investigators offered participants information about desirable and undesirable characteristics of four hypothetical automobiles. One of the cars was by design obviously better, one was worse, and the other two merely ok. Experimental conditions offered some participants an opportunity to consciously evaluate the characteristics of the vehicles and rate them. Others were asked for an immediate ranking (no time to consciously think about it) and the third group had to complete a demanding cognitive task (using up their conscious awareness) before ranking the vehicles. The best rankings curiously came from the group that was mentally tied up with the competing conscious task. Apparently, while engrossed in that task, an unconscious mental processing was underway that led to the best ranking in comparison to those who offered an immediate ranking or those who consciously thought about the rankings. To prove the existence of this unconscious processing system in the brain, all subjects were hooked up to a functional magnetic resonance imaging device. Brain activation was monitored during the trials. The investigators were able to demonstrate that certain brain regions associated with the rating task were activated during the competing cognitive task hence offering those participants access to portions of their brains that performed the ratings unconsciously. Skeptics for the presence of unconscious mental operations are gradually losing the battle!
How often are we accustomed to saying that a book was better than the movie? Srinivasa Ramanujan, a young Indian clerk is effectively profiled in a 2016 film called, “The Man Who Knew Infinity” based on a book of the same name written by Robert Kanigel. The book is indeed better than the movie, the reason being that in 373 pages of text Kanigel has room and time to plunge into a really complex problem. The puzzle of intuition, examined in my own book using Michael Polanyi’s tacit theory of knowledge as a guide, collapses into an enigmatic cognitive black hole when applied to the task of explaining Ramanujan’s mental magic. The finest mathematicians of our century admit defeat. Ramanujan’s capability is, to a degree, inexplicable. The movie skillfully illustrates the problem but fails to give a viewer the full perspective needed to understand the significance. We watch Ramanujan, played magnificently by Dev Patel, making an effort to earn a living for himself, a new, young wife, and his mother. Unfortunately, details of his early schooling are missing from the film. Throughout the movie, we watch Ramanujan rattling off seemingly complicated formulas. However, where did they come from? His mentor Hardy (played by Jeremy Lyons) not only wants to know but reasonably insists they be accompanied by formal, logical proofs. We are not informed that Ramanujan was provided access to several key books while a pre-college student. The first was a text on trigonometry that by age 13 Ramanujan had fully absorbed. The other was an improbable tutor summary of all the mathematics needed to pass a formidable Trinity College exam at the time. A first Ramanujan mystery presents itself. Why was he so singularly enthralled with mathematics to the degree of obsessively studying the 5,000 formulas in the exam preparation book? Scholars have subsequently poured over this book trying to find within its pages a pathway to his eventual brilliance. Aside from its expectation that a reader should prove all the assertions displayed therein, analysis of the books contents fail to display how Ramanujan might have extracted divine inspiration from its pages. Perhaps we may infer that Ramanujan received, in effect, an undergraduate degree in mathematics through his self-studies and some unidentified math courses taken at local colleges (before flunking out over a refusal to bother with any courses other than math). Today we apply the term “grit” to describe his unyielding passion.
The movie essentially begins with Ramanujan filling his notebooks with conjectures and theorems of a highly original nature. These gained the attention and admiration of Indian mathematicians leading to his introduction to Professor Hardy at Trinity College in England. We watch his arrival in England and subsequent relationship with Hardy. The film makes much of the drama surrounding Ramanujan leaving his wife at home in India but this story is probably more Hollywood than reality.
The primary mystery of Ramanujan is the source of his inspiration. Kanigel in his biography of Ramanujan describes a warning by the great mathematician, Jacobi, that excessive control over the form and pace of learning will constrain the future capacity of the learner to be creative. Ramanujan escaped that formal control by exploring mathematics on his own filling notebooks without reference to the usual problems listed at the end of textbook chapters. This characteristic of Ramanujan’s early process of learning offers a hint toward our understanding of his creativity. However, it is not enough.
The movie then gives us a sketchy and truncated version of how Ramanujan ended up at Trinity College. Most of the film shows us the problems he faced there and his interesting intellectual and semi-friendship with Hardy who skillfully managed his transition from a largely self-taught genius to a gifted mathematician capable of explaining and proving his assertions. During the sparring matches between Ramanujan and Hardy (the highlight of the film), Hardy asks in exasperation just where the magical-seeming assertions came from. Ramanujan mysteriously attributes his wisdom to whispers from his family goddess or dreams planted in his head by the same divine source. The ever practical and atheistic Hardy simply cannot understand such mystical claims. I continue to search within the tacit theory of knowledge developed by Michael Polanyi and the related new neurological research on avalanches of neural networks lurking underneath our conscious scenes for an answer. Meanwhile, I highly recommend the film and then more eagerly recommend the book.
I like seeing recent published research supporting the tacit theory of knowledge (one of the purposes I had in mind when writing my book). Polanyi explained the “Aha” effect by identifying a subconscious process he called the “tacit integration.” Today psychologists refer to this as “insight” and a crew of investigators set out to discover if insightful solutions to puzzles were more accurate than solutions formed from conscious, analytical thinking. A series of word and visual puzzles challenged participant subjects and their task was to come up with an answer to the puzzles. If they used a process of systematic conscious thinking, (such as trial and error) they identified their solution as analytical but if the solution popped into their heads in a mysterious spontaneous manner, they recognized the solution as having come from insight. One example of such a puzzle required finding a word that could combine with three others to form a sensible compound word. For example, take the words “crab,” “pine,” and “sauce.” What single additional word will work with these three? I must admit I am terrible at doing this, struggled for many minutes trying in my mind several examples, and finally decided upon the word “red.” This attempt gave me the combinations “red crab,” “red pine,” and “red sauce.” The weakness of this conscious choice was evident yet it was all I could do. It turns out my word was wrong, worse yet, I took considerably longer than the 16 seconds allowed for finding an answer. Those participants in the study who found a word through insight were nearly always correct while the analytically derived words failed a third of the time. A similar pattern occurred with the visual puzzles. The researchers concluded that an unconscious quick idea popping into your head is more likely to be a good one than a studiously analyzed result ground out consciously by the mind. Applying this result to an educational setting strengthens the case for structuring learning around generating tacit integrations, a subject covered in my book. By the way, have you come up with the right word? Try “apple”. The research was published in the Journal Thinking and Reasoning under the title: “Insightful solutions are correct more often than analytic solutions”. Authors of the study include Carola Salvi, John Kounios, Mark Beeman, Edward Bowden, and Emanuela Bricolo.
The August 2015 Issue of BBC Music Magazine contains two interesting discussions on the “muscle memory” playing of musicians. The Theory of Tacit Knowledge offers some insight into this practice. Oliver Candy in his editorial (page 5) worries that too much familiarity with a score can lead to the musician playing along while their minds wander and then later come back with a start realizing the performance is over and they cannot be sure if they did a good job of it or not. My book talks about how Polanyi would apply his tacit knowledge concept to this experience. On page 47 of the same issue Benjamin Goodson discusses engagement with the music by relying on fingers knowing what to do hence freeing up the mind to focus on interpretive niceties of the performance. His comment offers a great example of how the structure of tacit knowledge demonstrates the subsidiary awareness of muscle memory enabling the mind to focus on larger aspects of music making. You can read about this effect on page 22 of my book. When indulging in a skillful act we rely on our tacit awareness of the manipulative details of the act to throw our attention to the higher levels of what the act is accomplishing. In this example the artistic quality of the performance.
It is now the end of 2015 and Amazon has my self-published book advertised and available for purchase. Seems like many years have gone by so this is a moment of relief as well as offering a sense of birthing of my baby. The front page description of this blog has a clickable link to the book on Amazon. Now comes the task of marketing which looks to be daunting as this blog has not created any discernable traffic of interest in the project. I now turn my attention to search engine optimization and utilization of the new social media system. The potential audience for the book should be anyone trying to learn something rather difficult or anyone else tasked with the job of teaching something difficult. Full comprehension is argued here to depend somewhat on the development of tacit knowledge as described by Michael Polanyi.
I uncovered quite by accident an example of the search for tacit knowledge. In the year 1919 Clara Kathleen Rogers (an Opera singer known as Clara Doria) published a book of memoirs called “Memories of a Musical Career” (Little, Brown , and Company). On page 233 she wrote: “There was ‘the voice of my dreams’ for me to find, – that voice that was myself. I had inklings of that dream voice every now and then. I heard from myself those searching, insinuating tones which sent a thrill through me more and more often now, but they were not always there. They came and went, I knew not why, nor did I know how to coax them back again when they left me. San Giovanni could not help me at all in my quest for some way of enchaining that magic sound, and yet I felt there must be a way, if only I could find it, – a way to hold and keep it for mine always! I would have been willing to give up ten years of my life to anyone who could tell me the secret. But there was no one!” Later in the book on page 250 Clara goes on to say: “I was constantly seeking for a way to clinch my triumphant tone. The word which expressed it for me was “it.” Yesterday “it” was mine, mine to keep forever, as it seemed; today “it” was gone, and I was as helpless as the owner of a pet bird that had flown from its cage! In vain did I plead with my teacher for help. If you only could give me some advice what to do, how to practice to get a perfect tone-emission! All I could expect from him was a kind, sympathetic smile.” On page 284 Clara describes moments with another teacher who understood what she was searching for. She described the moment: “I satisfied myself very soon that he had the right idea of tone; but he knew no more about giving directions how to obtain it than anyone else!”.
Clara needed help from those who “knew more than they could tell” – this is the essence of Polanyi’s tacit theory of knowledge. She went on years later to write a book on the philosophy of singing. I need to check it out to see if she found some way to communicate explicitly what for most of her life was trapped in an implicit, tacit sense.
Some interesting examples of tacit knowledge are described in a remarkable book by David Freeman Hawke who writes a history of “mechanicians”. Not engineers as we know them today nor mechanics but unschooled masters of the use of tools found in the eighteenth and nineteenth centuries. The mechanicians could design new machines and invent marvelous mechanical contrivances yet were largely unknown. They were not mathematicians or scientists and possessed no fancy theories from school, yet had learned from experience a most remarkable set of skills. Hawke describes the stories told by George Sturt who ran a wheelwrights shop in the late nineteenth century. Tales of how these masters of wood came into their skill after seven years or more of apprenticeship. Reasoned science was not involved; instead they lived up to the acquired wisdom of the time. A stage was reached when the eyes and hands were left to a remarkable cleverness with no guide to follow. A good wheelwright knew by art rather than reasoning how tight a tyre should be made for a five foot wheel. It was a feeling in his bones. Sturt knew what convexity was required for a wheel yet neither he nor any other skilled workers in the ship could explain why it had to be that way. A wheelwrights brain had to fit itself to the task by growing into it. He said his own eyes knew through the feeling in his hands the difference between ash “tough as whipcord” vs ash that is “doaty” or “biscuit” yet he could not teach or explain this to anyone. With all the elaborate training systems of today we have lost touch with this side of education, the tacit side so well explained by Michael Polanyi.
Controversy is the meat of science. Cognitive psychologists are tossing around hypotheses about what they call multiple category-learning systems. This issue relates to tacit knowledge because the brain would appear to have a different operating system for tacit knowing (see implicit in the research literature) vs explicit learning. Another term for tacit is procedural; Zaki and Kleinschmidt argue in a recent paper that what seems to suggest this difference is actually caused by task complexity instead of indicating a need for some alternative brain structure. Now a new research study just published in Psychological Science (Feb 2014, V25 #2 pp.447-457) claims the opposite. Their research strengthens the view that procedural learning (giving rise to tacit knowledge) appears to be dissociated from processes exhibiting explicit learning.