Chapter 1 – Rethinking Thinking
Invention presupposes imagination. Einstein once revealed to his friend, “The words of the language, as they are written or spoken, do not seem to play any role in my mechanism of thought” Some scientists insist that thinking in feelings and mental images can be rationally manipulated.
MIT Prof. Richard Feynman (Nobel Prize winner) told once, “Mathematics is the form in which we express our understanding of nature, but it is not the content of that understanding”
In Creating minds and Frames of mind, scientists are logico-mathamatical thinkers, poets and writers are highly verbal thinkers, psychologists as intrapersonal thinkers and politicians as interpersonal thinkers.
Poincre (greatest mathematician in19th century) once said, “it is by logic we prove, but by intuition that we discover...”
French physician Armand Trousseau agreed, “All science touches on art; all art has its scientific side. The worst scientist is he who is not an artist; the worst artist is he who is no scientist.
Sculptor Naum Gabo once wrote. “Every great scientist has experiences a moment when the artist in him saved the scientist.”
Various professions including medicine are beginning to recognize intuition as a necessary part of disciplinary thinking.
Chapter 2 – Schooling the Imagination
Takes about something Indian philosophy where it is based on ‘Maya’ – virtual reality. It is easier to see things with eye closed as you can imagine things.
Einstein stated categorically “In creative work, imagination is more important than knowledge.
Our perception of reality depends upon the kind and quality of Illusions we conjure. This is what Picasso meant when he said, “Art is a like that makes us realize the truth”.
The problem with current education is, it does not connect different knowledge to solve problems.
Harvard psychologist “In so distinguished institution like MIT, a student can learn and have mastered calculus to the satisfaction of the teacher by having solved the problem set on the final examination. On entering the physics course, he cannot see how to apply calculus to the solution of problems in physics. Sort of one-sided education.”
This being the case, the task for educators, self-learners and parents is simply put to reunite the two. And the world’s most creative people tell us how in their own words and deeds; in their own explorations of their own mind at work. What they find as individuals, when taken as a whole, is a common set of thinking tools at the heart of creative thinking/understanding. These tools include (bit are not necessarily limited to)
Observing: Initially, all knowledge about the world is acquired through observing, paying attention to what we seen, heard, touched, smelled, tasted, or felt within the body.
Imaging: the ability to recall or imaging these feelings and sensations is also an important tool.
Abstracting: Because sense experience and sense imagery are rich and complex, creative people in all disciplines also use abstracting as an essential tool. – The process of paring down complicated things to simple principles is the same.
Recognizing Patters: It is involved in the discovery of nature’s law and the structure of mathematics, but also the rhymes and rhythms of language, dance, music and the formal intentions of the painter. Recognizing patterns is also the first step toward creating new ones.
Pattern forming whether in music, art, engineering or dance almost always begins with combining simple elements in unexpected ways.
Analogizing: The realization that two apparently different things share important properties or functions lies in the heart of the world’s greatest works of art and literature and the most enduring scientific and engineering inventions.
Body thinking: Thinking that occurs through the sensations and awareness of muscle, sinew, and skin. Well before they have found the words or the formulas to express themselves, many creative people ‘feel’ ideas emerging. Bodily sensations, muscular movements and emotions act as a springboard for more formal thought.
Empathizing: It is related to body thinking. Many creative people describe ‘losing’ themselves in the things they study, integrating ‘I’ and ‘it’.
Dimensional thinking is the imaginative ability to take thing mentally from a flat plane into three dimensions ore more, from earth into outer space, through time, even to alternate worlds. It is essential in engineering, sculpture, visual art, medicine, mathematics and astronomy – indeed in any activity that involves interpreting pictures, in one set of dimensions as objects in another set.
One can learn and practice each of the above tools (first 9 out of 13) somewhat independently of the others. The last four, however are clearly high-order tools that integrate and rely upon the primary tools.
Modeling objects and concepts require some combination of dimensional thinking, abstracting, analogizing and manipulative or body skill.
Playing is another integrative tool, build upon body thinking, empathizing and play-acting and modeling
Transforming is the process of translating between one tool for thinking and another and between imaginative tools and formal language of communication.
Synthesizing completes the imagination’s tool key, for understanding is always synthetic, combining many ways of experiencing.
There are 2 fundamentals components to the synthetic thinking. One is synesthesia, a neurological and artistic term for experiencing sensations in multiple ways at once. (E.g. a sound may provoke colors; a taste may call up tactile sensations or memories..) . Synthesizing also supposes an integration of knowledge in which observing, imaging, and empathizing and the other tools all work together organically – not serially as in transformational thinking, but simultaneously, such as everything – memory knowledge, imagination, feeling is understood in a holistic way.
We call this unified understanding linking mind and body, sense and sensibility, - synosia – and it is the ultimate goal of tools-for thinking education.
Each of the rest of the chapters is dedicated to each of these 13 tools.
Chapter 3 – Observing.
Many can recall a key moment when they learned he difference between looking and seeing. (There are few visual examples shown in the book, which show hidden view that cannot detect by just looking.)
Picasso says, “ I recall my father saying to me - I am quite willing for you to become a painter, but you must not begin to paint until you are able to draw well and that is very difficult”-. Then he gave me a pigeon’s foot to practice on” . Having learned to observe one thing, he had learned the keys to observing and describing everything.
Vincet van Gogh’s goal was to be able to draw in such a way that it goes as easily as something writing down… to see in such a way that one can reproduce at will what one sees on a larger or smaller scale.
However, simply looking, even patiently, is not sufficient. Part of seeing as the camouflaged ptarmigan demonstrates knows what it look at or for. It is kind of comparable to some people who , if they are given a book in which some word occur only once, can flip through it and find it.
An interesting story of observation – “A Manchester physician, while teaching a ward class of students, took a sample of diabetic urine and dipped a finger in it to taste it. He then asked all the students’ to repeat his action. This they reluctantly did, making grimaces, but agreeing that it tasted sweet. “I did this’ said the physician with smile, ‘to teach you the importance of observing detail. If you had watched me carefully you would have noticed that I put my first finger in the urine, but licked my second finger’.
(from the book - the art of Scientific Investigation.)
Unlike other fruits, why Orange does not turn black on being damaged or there is no color change when it got hurt? That was the observation done by Biochemist Albert Szent-Gyorgy. The answer was that those plants contained vitamin C, a sugar like compound that prevents oxygen from oxidizing the polyphenols into brown or black protective compounds. You can actually gauge the vitamin C content of different fruits fairly accurately simply by noting which ones turn brown when damaged(e.g. banana) and which do not (e.g. orange).
Harvard psychologist Rudolf Arnheim said in his 1969 book – Visual thinking – “The cognitive operations called thinking are not the privilege of mental process above and beyond perception but the essential ingredients of perception itself”. As Herbert Read documented in his classic – Education through art-“Part of the activity of art is one of the exercise and an activity that keeps faculties lively whatever the discipline touches on: the mind, the ear, whatever.
As with Sherlock Homes, “success rests with the powers of observation…”
Close one’s eyes and construct what is going on nearby through sound alone. Listening TV without looking at it or watching it without sound is also an educational experience in observing; all too often either the visual aspect or the sound is irrelevant.
Collecting things, whether stamps, coins, insects,… is another excellent way to improve visual observations.
Chapter 4 – Imaging.
Numerous studies have found significant correlations between the aptitude for visual imaging and career success in engineering.
Many examples listed in Brook Hindle’s famous book – Emulation and invention.
Henry Petroski’s book – Invention by design.
Max Wertheimer – Productive thinking
Horace Barlow, Colin Blakemore & Miranda Weston-Smith – Images & understanding
Beethoven says, “I carry my thoughts about with me for a long time, often for a very long time, before writing them down…. I change many things, discard others, and try again and again until I am satisfied; then in my head, I begin to elaborate the work in its breadth, its narrowness, its heights, its depth…. I hear and see the image in front of me from every angle, as if it had been cast (like sculpture), and only the labor of writing it down remains”.
Beethoven’s mastery of mental imagery surely explains how he was able to compose some of his greatest music long after he had become profoundly deaf.
At Kanton Schule attended by Einstein, students practice the ABCs of visual thinking as rigorously as the ABC’s of language. The young Einstein was thoroughly schooled in what modern scientists would call ‘thought experiments’’ seeing and feeling a physical situation almost tangibly, manipulating its elements, observing their changes – all of this imagined in the mind.
Professors of visual thinking at MIT & Stanford, suggests that any kind of formal training in design, draftsmanship, drawing, painting or photography can improve adult visualizing skills.
Aural imagining skills can clearly be learned by practicing. Listening to poetry and literature read out loud can also improve imaging skills, according to poet Amy Lowell. Perhaps this is one of the reasons that reading to young children has been found to stimulate their intelligence.
Good example on treating algebra problems geometrically and treating geometrical problems algebraically.
Problem – A man rowing a boat when his hat falls into the river which is flowing at 3 km per hour downstream. He is rowing upstream 2 km per hour faster than the stream is taking him down. He discovers his hat is missing on half-hour after it has fallen in the river. If he turns around and rows back at the same speed relative to the river to fetch his hat, how long will it take to catch up to it?
The algebraic approach to this problem is to abstract out the key parameters in order to setup an equation and solve he for the unknown
Hat is dropped and moves at 3km /hr for 0.5 hour, so it travels 1.5km downriver. With the same time (0.5 hour), man rows at 2km/hr and travels 1 km upriver. Hence man is 2.5km away from his hat when he discovers its loss. He travels back to catch the hat. In order to travel 2km/hr upriver, he had to be moving 5km/hr relative to the river; so if he rows at the same rate downriver, his total velocity will be 5km/hr + 3km/hr that river moves on or 8km/hr. The hat is still moving at 3km/hr. Let t be the time necessary for the man to catch his hat. Then the time it takes the man to catch his hat is (8km/hr)t= 2.5km+(3km/hr)t. Solving the equation yields (8km/hr)t-(3km/hr)t=2.5km or t=.5hr.
The geometric approach to this problem is to visualize it.
Instead of imagining a man riding on a boat, as if it was a swiftly moving train. Suppose you drop your hat as you are walking through one of the cars in the same direction the train is travelling. You walk for thirty seconds before you discover your hat is missing. You turn around and walk for 30 sec before you discover your hat. How long will it take if you walk back through the cars at the same constant speed? 30 sec. The fact that the train or the river is moving with respects to the ground outside turns out to be irreverent to the physical problem. Treating the river as if it were a train and the man in the boast as if he were walking on the river/train quickly yields 30 min to the solution to our problem as before.
Although both provides same result, but have two separate approaches. Einstein’s and Feynman’s conundrum was that they thought as geometricians, but needed to communicate their results in analytical,, algebraic form to satisfy the rigorous demands of physical proof. Only few people can switch with ease between 2 approaches.
Chapter 5 – Abstracting.
Although all abstractions are simplifications, the best abstractions are likely Picasso’s Wilson’s and Cumming’s in that they yield new and often multiple insights and meanings, using simplicity to reveal inobvious properties and hidden connections.
Mark Twain and Earnest Hemmingway have written to their editors that they regretted the extreme length of their manuscripts; if they had had more time, the work has been half as long. Winston Churchill is supposed to have said that he could talk for a day with 5 min of notice, but needed a day to prepare if he had only 5 min in which to speak.
As physicist and inventor Mitchell Wilson wrote half-century ago “I’ll tell you what you need to be a great scientist. You don’t have to be able to understand very complicated things. It’s just opposite. You have to be able to see what looks like the most complicated thing in the world and in a flash, find the underlying simplicity. That’s what you need; a talent for simplicity”.
Knowing what abstracting is and why it is important is half the problem. The other half is learning how to find the simple concepts hiding among complex expressions.
Picasso says, “To arrive at abstractions, it is always necessary to begin with a concrete reality…You must start with something. Afterwards you can remove all the traces of reality. It is what started the artist off, excited his ideas and stirred his emotions (refer. Picasso’s Bull series (Merrill Lynch’s icon?)
Learning how to abstract in one discipline provides the key to understanding the abstractions of all disciplines.
Chapter 6 – recognizing Patterns.
Recognizing patterns within the patterns has stimulated many artists.
“ A way of stimulating and arousing the mind to various inventions,” Leonardo da Vinci advised himself and others to “ look at a wall spotted with stains or with a mixture of different kinds of stones , if you have to invent some scene, you may discover a similarity with different kinds of landscapes, embellished with mountains, rivers rocks, trees, plants, wide valley and hills in varied arrangement: or again you may see variety of objects which you could reduce to complete and well drawn forms.
The solution of much more complicated problems can sometimes be reduced to similarly straight forward calculations. For example, what is the sum of infinite series x=1+1/2+1/4+1/8+1/16….
This may looks complicated or even impossible, but with a bit of clever manipulations, the problem is trivial. If x is as given above, x/2 will be ½=1/4+1/8+1/16…
x-x/2= (1+1/2+1/4+1/8+1/16..) – (1/4+1/8+1/16…)
x-x/2 = 1 + (1/2-1/2)+(1/4-1/4)+(1/8-1/8)+(1/16-1/16)…
Every even numbers can be described as sum of 2 prime numbers. That pattern recognition by Goldbach is still not broken. All even numbers known can be summed as 2 prime numbers.
Playing with jigsaw puzzle also exercise pattern recognition as does puzzle making. Many eminent people in every field are puzzle addicts or puzzle inventors.
Chapter 7 – Forming Patterns.
Learning to create patterns is one of the keys to innovating in every discipline and it is wise to learn this skill early on. You can do this easily in writing by taking a very limited number of words and exploring all the possible ways of making sense with them.
Similar exercise can be performed with kinesthetic and auditory patterns and rhythms. People who have difficulty with the physical elaboration of multiple contrasting patterns may find it easier to explore such patterns graphically. As a starting point, we highly recommend, René Paola’s Optical Art: theory and practice.
Looking through the history of almost any scientific field or studying any scientific controversy will show that scientists always try many ways of expressing their insights before some standardized textbook formulation ossifies thinking in that area.
Making patterns for oneself is a lot more fun than memorizing – and lot more valuable. Teasing apart one pattern and composing another require real understanding of the basic elements of phenomenon and process. More, it opens up whole new worlds of knowledge.
Chapter 8 – Analogizing.
It is critical to understand the difference between analogy and similarity. Analogies recognize a correspondence of inner relationship or of function between two or more different phenomena or complex set of phenomena. Similarities are resemblance between things based upon observed characteristics such as color or form.
‘Her lips like berries” is an example for similarities, because comparison is simply links the observed property of redness. A child or poet compares a baseball to the sun might however make a valid analogy based on the fact that each rises and falls though the sky in an arc. Comparing orange to sweetness of life is also analogy.
The critical part of interesting analogies is that they reveal not mere resemeblence but inapparent relationships between abstract functions, one of which is understood, the other not.
How is possible to learn about things such as quantum mechanics or logic or democracy or goodness in the first place? How can we learn about or explain anything that we can’t directly, physically sense? And how it it possible to apply knowledge learned in one content to another very different one? How do we realize that musical resonance has some applications to atoms or atomic resonance to medicine?
Without being identical, ideas can resonate too, just like the strings of musical instruments or the electrons and nuclei of atoms.
Mental leaps: Analogy in creative thought, - a book on analogy. It mentions many such examples from history in different fields. Even Darwin’s theory of evolution is based on several analogies. Newton’s theory of gravitation originated when he suddenly realized that the moon like an apple dropping from a tree, must be falling.
Jacob Bronowski says, “The discoveries of science, the works of art are explorations – more of explosion, of a hidden likeness”.
William Wordsworth wrote of “the pleasure the mind derives from the perception of similitude in dissimilitude’.
Todd Siler greatly expands this approach, comparing the growth of our minds to the growth of trees and onions. His book – Think like Genius- provides dozens of exercise, some of which specifically develop and metaphorical thinking.
Chapter 9 – Body Thinking
This is about 6th sense. It is possible to conjure up feelings of body tension or touch or movement in the mind, but most of us overlook these imaginative feelings because we are trained so early to see them or translate them into descriptive words.
Few books on this mentioned on this topic
Howard Gardner – Frame of mind
Vera Johns Steiner – Notebooks of mind
Surprisingly, musical feeling, physical sensations, manipulative skill, and their mental imaging play an important role in scientific thinking too which may be related to the fact that many eminent scientists are also excellent artists or musicians.
Encyclopedia Britannica defines mime as the first and only truly universal language.
Like the other types of thinking discussed, body thinking combines objective and subjective ways of knowing. Body thinking exercise can also be made an explicit part of disciplinary and transdisciplinary studies.
When children play out choreography of movements representing fundamental elements f narrative, they remember it better. Additionally students can be encouraged to pay attention to their bodily feelings when a class problem does not make sense and use this discomfort as the basis for asking questions. Sensitive teachers can teach them it identify and work with these feelings by reading postures and facial expressions, just as we read a mime.
Sort of kinesthetic explorers
With practice, we may all expand our imagination with the sensations of movement, tension and touch that we experience, imitate model and project.
“I hear and I forget. I see and I remember. I do and I understand”, says a Chinese proverb.
Doing and remembering how it feels to have done is inseparable from learning to think with the body. So don’t just sit there. Monkey around and just might find yourself solving problem only your body knows how to answer.
Chapter 10 – Empathizing.
Willa Cather once wrote that novelists, actors and physicians have the ‘unique and marvelous of entering into the very skin of another human being’.
Cather continues to say , “ You must enter into the person you are describing into his very skin and see the world through his eye ad feel it through his senses”.
C.P.E. Bach argues, “ A musician cannot move others unless he too is moved. He must feel all the emotions that he hopes to arouse in his audience, for the revealing of his own humor will stimulate a like mood in the listener.”
Empathizing is “key skill for the practice of any helping relationship’.
Many creative individuals argue that theatrical experience encourages and promotes the empathic imagination.
Practice “inner attention which centers on things we see, hear, touch and feel” in real and imaginary circumstances. This means observing your own responses to the world and also remembering physical and emotional memories of your responses.
Practice “ external attention” to people and things outside yourself.
Imagine what the object of your external attention is sensing and feeling get close to it.
Emulation is always a useful way to empathize. This is certainly the educational approach used by PBS TV program ‘ Kratt’s Creatures’.
All of these examples show us that understanding is most complete when you are not you but the things you wish to understand. In fact, when it comes to empathizing, the whole world is a stage for the imagination.
Chapter 11 – Dimensional Thinking.
Dimensional thinking involve moving from 2-D to 3-D and vice versa.; mapping or transforming information provided in one set of dimensions to another set; scaling or alerting the proportions of an object or process within one set of dimensions and conceptualizing dimensions beyond space and time as know of them.
Another aspect of moving from plans to reality involves the dimensional skill of scaling. Philip and Phylis Morrison and the office of Charles and Ray Eames produced a wonderful movie and book called ‘Powers of Ten’ that provides a useful scale running from smallest to largest.
Scale and time certainly matter. Massive buildings connote power; small rooms connote intimacy and privacy. A six inch model of Eiffel tower has none of the impact of the original. Some things has to be seen in the acute angle, to see it understand it. (Writing SHORT in a paper and writing the same word, covering the entire A4 sheet will have different experience for a reader. However, if the reader see it from a long distance, the word that written in very large size can be seen, but not the word written in normal size.
Einstein showed that the passage of time or what is sometimes called as 4th dimension is not absolute but relative to observer and observed. All of us have experience by looking at the clock and wondering where the time went (too fast). We have been so bored that every second is like a minute and every minute is like an hour. When we mediate, time seems not to exist at all. Physical time, physiological time, mental time appear to be different; perhaps there are dimensions of time as unexpected and surprising as fractal dimensions in space.
Is a month the same to one-year old who experiences that unit of time as one twelfth of his life as it is it to centenarian for whom it is a mere one one-hundred-twentieth? Is time, then a single dimension or set of dimensions?
Granted the need for dimensional thinking skills, not only in science but in arts, engineering, manufacturing and daily life, how might they be taught?
One method is to play with geometric shaped and connect them to objects in real world.
Reid one of consummate mathematics popularizes of this century, outlined one approach in her 1963 book, ‘A long way from Euclid’ which she used with high school teachers and education students. Reid goes on to show that although we can see only shadows of our hypercube, we can still know its properties by extrapolating. A point has no angles, edges, or faces and one vertex (the point itself). A line segment has no angles, no faces, one-edge (1-D form) and two vertices (points at the end of the segment). A square has 4 vertices (points) , 4 edges(1-D form), 4 angles, and a single face (2-D form). A cube has 8 vertices and angles, 12 edges (1-D forms), 6 faces (2-D form), one 3-D form. As dimensions increases, the number of vertices increases; one, two four, eight. As dimensions increases, the number of angles increases from 0 to 0 to 4 to 8. If we want to extrapolate further, we could even describe the characteristics of a 5-D or a 6-D without even being able to visualize. Such is the power of dimensional imagination.
Chapter 12 – Modeling.
Models can be smaller than life-size or bigger; physical or mathematical; realistic or not; depending on their intended uses. In almost all cases, the point of modeling is to make accessible something that is difficult to experience easily.
Modeling requires and therefore teaches many imaginative skills. Models can be formulated only after a real system or situation has been intensively observed, simplified by abstracting critical features, rescaled for human manipulation and embodied physically or expressed in some verbal, mathematical or artistic form.
Perhaps the most important thing that modeling does is to provide the modeler with complete control of a situation, object or idea – or, conversely to reveal explicitly where control or understanding is lacking. As Picasso said, “To model an object is to possess it.”
The earlier a student learns that every equation has its physical manifestation and every physical phenomenon its mathematical model, the better equipped he or she is to be inventive. Visual thinking can also be improved by modeling, because there is a direct connection between the kinesthetic sense and vision.
Develop spatial skill by modeling your school, house or neighborhood. Because it requires figuring out how things work, modeling is a great way to learn, no matter your age. Make modeling is a lifelong habit and you hold a key to a lifetime of fun and learning.
Chapter 13 – Playing
Considering the sheer joy of fooling around, not to mention its potential rewards, it is not surprising that many scientists have galumphed with their subjects.
Playing with distinctions, boundaries, unassailable truths and the limits of utility is in fact what many of the most innovative people in all disciplines do. When the rules of grammar are systematically broken, logic overturned or perceptions puzzled, we know that a ‘game’s afoot’ and something interesting will happen. No better examples exist than in the topsy-turvy worlds of those masters of play, Edward Lear, Lewis Carroll and M.C. Escher.
Wordplay and inventions came naturally to Lear and his ‘boshblobberbosh (meaning particularly foolish foolishness) was well enough appreciated to make his book of ‘Nonsense and Laughable Lyrics’ enduring bestsellers. One reason that does this book have appealed to generations of children and adults alike is that they break all boundaries of word to use, exploring connotations, combinations and sounds as few have done before or since.
Lewis played a nonsense poems and whimsical stories for children at photography and at logical games and puzzles that reached the heights in ‘Alice in the wonderland’.
Lear’s verbal nonsense, Carroll’s logical conundrums, Escher’s perceptual puzzles and Penrose’s periodic tiling challenges our conceptions of nature and reality. But as play of the most creative art, they do more than that. The games they invented have practical applications.
There is more to the study of piano or violin than just reproducing the tons and more to making music than musical conventions or contemporary taste might suggest. Play with patterns of all kinds can improve skills in composition and improvisation.
Reference to the ‘Oxford Guide to World Games’ shows that amusements come in a huge variety; perhaps the most popular is the making of anagrams – taking a word and seeing how many other words can be made from its letters: OWN, NOW, WON.. It is also possible to form words that read same forward and backwards as a mirror image without turning the word upside down. These are called plaindromes: NOON, DAD, BOB.
“Madam. I’m Adam’’, “ Tis Ivan, on a visit” areplaindromic sentences. Most of these words games have direct analogues in music.
Word games, board games, musical games, visual games, puzzles, toys and almost any other intellectual amusement imaginable all develop some skill, knowledge or concept that can be turned to good account and often in more than one discipline or endeavor.
Chapter 14 – Transforming
We call the serial or simultaneous use of multiple imaginative tools in such a way that one (set of) tool(s) acts upon another (set) transforming or transformational thinking.
Take a look at any creative endeavor and you will invariably find ideas and insights transformed through many tools for thinking and translated into one or more expressive languages. Most creative people handle complex transformational thinking with ease.
Sir Francis Galton, one of the founders of modern psychology, documented in his classic ‘Inquiries and Human Faculty and Its Development (1883)’ that mnemonic devices are extremely common. “Persons who are imaginative almost invariably think of numerals in some form of visual imagery’.
Sometimes people collaborate on a mnemonic transformation that integrates concepts from many disciplines. For centuries, students of music & poetry in India have memorized a nonsense word in order to learn and remember all of the basic patters of sound rhythm The word is ‘yamatarajabhanasalagam’ which when written according to its spoken rhythm of stresses look like this: yaMATARAjaBHAnasalaGAM. George Perle has explained it, “There is a lot in those 10 syllables. As you pronounce the word you weep out all possible triplets of short and long beats. The first syllables, ya MA TA have the rhythm short, long, long. The second through the fourth are MA TA RA: long, long, long. The you have TA RA ja: long, long, short. Next there is RA ja BHA: long, short, long. And so on.” Thus a simple word, when pronounced properly condenses a huge amount of pattern information that can be applied to many of the arts.
Perle’s friend Sherman Stein (mathematician) , took the transformation another step. He pointed out that the basic pattern in the Indian word is digital. By assigning ‘0’ for short and ‘1’ for long, the word will become ‘0111010001’ (=465 in decimal). Since there are 10 digits in the number, the number may be turned into a physical mneme with the thumb and little finger of the left hand bent and the three middle fingers of the right hand bent. The bend digits represent ‘0’ and unbend, ‘1’. All of these mnemes are logically equivalent to the original Hindu word.
Significantly the digital numerical sequence presents possibilities that the original Hindu word does not. Imagine, Stein suggests, a kinetic analogy in which this string of numbers is a snake that grabs itself by the tail. Visualizing this “snake” that the first 01 (its ‘mouth’) will overlap the last 01 (its tail) and a continuous circle of numbers will be formed. Although the number sequence has now lost 2 digits, the circle still has all of the possible combinations of three pairs of elements – whether they are musical beats, syllabic accents in words, numbers, the result or flipping three pennies ways of grouping three people of either sex or a great many other things. This numerical snake is therefore the most concise description of such information that is possible. Notably it has the same pattern as entities known to mathematicians since the 1880s as ‘memory wheel’ which can store all the possible parts of things, triplets of things, quadruplets things and so on, in the most condensed form. The power of transformational thinking is that it can reveal meta-patterns connecting music, genes, telegraphy, poetry and math or any other set of disciplines.
A Yale political science professor Edward Tufte has pointed out in a series of stunningly beautiful books, including ‘The Visual Display of Quantitative Information (1983) and ‘Envisioning Information (1990), data in every field are converted into graphs and visual images of one sort or another.
Ears can observe complexity that eyes cannot. Eyes can follow only a single line, one pattern at a time. When we listen to a musical ensemble, however, we hear each individual instrument even as we hear the harmony that results from their interaction.
Many universities are experiencing with transformations with complex databases – for instances economic indicators – into a music that allows analysts to hear the synthetic patterns while simultaneously following individual trends.
The point is that different transformations of an idea or a set of data will have different characteristics and uses. The more unexpected the transformation, the greater the likelihood that a surprising insight will result.
The 3 notations that are generally used today are Labanotation invented by Rudolf Laban in 1928, Benseh Movement Notation by Rudolf Benesh and his dancer wife Joan in 1955. & Eshkol-Wachmann Notation (1958)
Rebuses, representations of words by pictures, sounds, or symbols are perhaps the most developed type of puzzle that builds word-number-image transforming skills. When we become aware of the transformations our ideas undergo, we are well on the road to an awareness of creative imagining as a process we can play with and control.
Chapter 15 – Synthesizing.
The inevitable result of transformational thinking is synthetic understanding, in which sensory impressions, feelings, knowledge, and memories ocme together in a multimodal, unified way. Vladimir Nabokove wrote in his extraordinary memoir “Speak, Memory (1947). “I may be inordinately fond of my earliest impressions, but then I have reasons to be grateful to them., They led the way to a veritable Eden of visual and tactile sensations.”
Associational synesthesia occurs in about half of all young children and from 5 to 15 % of adult’s population. The huge difference between children and adults suggests that the typical educational focus on unisensory experiences and express stifles an early and natural association of perceptions. “Synesthetic perception is the rule” says the French philosopher Maurice Merleau-Ponty.
If thinking is naturally synesthetic, it should be possible to maintain and develop associational synesthetic with practice. Philosopher Steve Odin points to Japan where artists and philosophers have long considered synesthesia to be the highest form of aesthetic experience and where it is explicitly cultivated. The green tea represents the living things of nature and drinking it infuses the celebrant with the aroma, taste, color and feel of this nature. Every sensation is orchestrated to produce a oneness. “ True practice of tea brings all senses to function simultaneously and in accord.
Poet-artist e.e. Cummings made copious notes on analogies between arts , translating many “ an image of one of the sense in terms of another of the sense.” As he did in the last lines of
“Somewhere I have never travelled” ,
“ the voice of your eyes is deeper than all roses
Nobody not even the rain, has such small hands”
Synosia is the natural and necessary result of imaging, analogizing, modeling, playing and transforming. Creative people have always combined many ways of feeling and knowing simultaneously, often describing in detail personal “tea ceremony’, equivalents melding, sensual and intellectual concerns.
Artist Otto Piene felt strongly that “mind, which is really body and body which really exists in the mind, do not wish to allow us to treat them as separate entities… The man who uses his body to enclose his mind and his mind to lift up his body lives this timeless moment, this heavenly reality, in order to stride free through space, this man has paradise within him.”
George Bellows agreed, “The ideal artist is he who knows everything, feels everything, experiences everything and retains his experience in a spirit of wonder and feeds upon it with creative lust… he uses every possible power, spirit, emotion, conscious or unconscious, to arrive at his ends.”
Aaron Copland felt, an individual must be aware of simultaneously on three planes. “(1) the sensuous plane, (2) the expressive plane (emotional) plane.
The need for a synesthetic and synosic education is best summarized by the simple image of printed circuit board (PCB), one of the most telling ‘cosmic synchronizations” of modern times. The image of PCB is a piece of art, although it looks like one. Or rather it is a piece of art, but only unintentionally. It is a pattern, a series of visually designed logical relationship, mathematical calculations. That it has the form of art work, not by chance. Electronic chips made by a process derived from the technique of etching and silk-screen printing and adapted to coating silicon components with copper and gold. Chips are literally designed as patterns on huge piece of paper, photographically reduced and made into the masks used to etch or to plate material onto silicon wafers.
This is where the course of civilization taken us. Logic is an image that must be printed, just like an art print. The purpose and materials may be different, but the links between art and science and technology are as strong today as they were in Renaissance. To comprehend the advances of this century, one must be able to perceive the connections between mathematical calculations, logical constructions, patterns, visual images and the technical process of manipulating artistic media to produce electronic inventions or to make similarly unexpected concatenations of thinking tools. Only those who became excited by such inspirations will have the desire to create the next synthesis.
The future will therefore depend upon our ability to create synthetic understanding by integrating all ways of knowing. In Buckminster Fuller’s essay, “Emergent Humanity” he warned that in evolution “overspecialization leads to extinction. We need the philosopher-scientist-artist-the comprehensivist, not merely more deluxe quality technician mechanics.
With so many eminent people in so many different disciplines proclaiming the same need, it is incumbent that we listen. Synosia is not an ideal or a dream; it is a necessity.
Chapter 16 – Synthesizing Education.
A synthetic education requires that we change how we teach , bearing eight basic goals in mind.
We must emphasize the teaching of universal process of invention in addition to the acquisition of disciplinary products of knowledge. The purpose of education should be understanding rather than simply knowing. It follows that we must teach the intuitive and imaginative skills necessary to inventive process. As shown, creative thinking in every field begins in nonlogical, nonverbal forms. To think, is to feel and to feel, is to think.
We must implement a multidisciplinary education that places the arts on an equal footing with the science. Arts and science constantly interact in very fruitful ways that are often overlooked.
We must integrate the curriculum by using a common descriptive language for innovation. There is no point in teaching a liberal arts and sciences curriculum that continues to fragment knowledge and creates specialists who cannot communicate across disciplinary lines.
We must emphasize the trans-disciplinary lessons of disciplinary learning. An education that trains the mind to imagine creativity in one filed prepares the mind for creative application in any other, for thinking tools as well as flexible knowledge are transferable.
We must use the experiences of people who have successfully bridged disciplines as exemplars of creative activity within our curricula. The best way to learn is to watch others and then model their technique, insights and process.
To reach the widest range of minds, ideas in every discipline should be presented in many forms. There is no one single imaginative skill or creative technique that is adequate for all thinking people. We must forge a pioneering education, whose purpose is to produce the imaginative generalities who can take us into the uncharted future. Every novel idea takes us into new territory and creative people are, by necessity pioneers.
We need polymaths (Greek word means ‘to know much or very knowing’) and pioneers who know that imagination thrives when sensual experience joins with reasons, when illusions link to reality, when intuition couples with intellect, when the passions of the heart unite with those of the mind, when knowledge gained in one discipline opens the doors to all the rest.
“Everything in your life ends up in your act”, says Aaron Freeman.
The wider your range of knowledge and feeling, the greater your range of imaginative possibilities and the more synthetic and important your work will be.