Spark Of Genius

Book: Sparks of Genius: The Thirteen Thinking Tools of the World’s Most Creative People
Author: Michele Root-Bernstein, Robert Root-Bernstein

Rethinking thinking

• intuitive grasp of an unknown entity already possessed but not yet intelligible
• the words of the language, as they are written or spoken, do not seem to play any role in my mechanism of thought
• Einstein suggested “a certain connection” between “the psychical entities which seems to serve as elements in thought” and “relevant logical concepts”
• Mathematician Stanislaw Ulam made the argument even more strongly. He experienced abstract mathematical notions in visual terms, so the idea of “an infinity of spheres or an infinity of sets” became “a picture with such almost real objects, getting smaller, vanishing on some horizon.”
• Such thinking is “not in terms of words or syllogism or signs” but in terms of some visual algorithm” having a “sort of meta- or super-logic with its own rules.”
• gut feelings and intuitions, an “essential feature in productive thoughts”, as Einstein put it, occur well before their meaning can be expressed in words or numbers. In his own work, mathematics and formal-logic were secondary steps
• “No scientist thinks in formulae” - “mathematics is the form in which we express our understanding of nature; but it is not the content of that understanding”
• Richard Feynman, “In certain problems that I have done, it was necessary to continue the development of the picture as the method, before the mathematics could really be done.”
  • i invented a graphical method to solve a problem in physics before, it was an interesting feeling as the solution just makes sense as I invented it
• our feelings - our intuition - are not impediments to rational thinking, they fom its origin and bases.
• desire to understand that leds to imaginative insight requires sensual + emotional feelings + intellect
• why math? translates these internal feelings into an external language other people can experience!
  • so, if i see a math i should start asking, “what is the internal feelings behind this language?”
• Science and Method by Henri Poincare, “It is by logic that we prove, but by intuition that we discover, … Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end.”
• a need for “tools of thinking” :
• … the worst scientist is he who is not an artist
• every great scientist has experienced a moment when the artist in him saved the scientist
• Insight is born of emotions and images of many sorts conjured within the imagination. Feeling as thinking must, therefore, become part of the educational curriculum.

Schooling the imagination

• illusions failed to connect with reality
  • same disconnection between academic knowledge and physical experience continue to plague education today
  • a need to learn “how to know what you knew”
• learning how to imagine what it felt like to be inside a physical system
• what eventually separates successful scientists and engineers from the rest of the students in their classses is the ability to feel or see what the equations mean.
  • ability to feel or see what the equations mean, how do you train for this??
• only a few can translate back and forth between their mathematical and their physical understanding
  • having learned mathematics as a language of communication without also learning what mathematics communicates means being half-educated.
• keep some distracting interests: art, music, travel!
• The problem with divorcing what and how in education is that knowing about things is not the same as understanding them.
• experimentation keeps imagination from going astray
• “the door is not just a piece of wood hung on hinges; it is also an example of torque and of masses”
  • this is eye-opener: to look at things/object as a source of some physical phenomena or concept
• Productive thought occurs when internal imagination and external experience coincide
• thinking tools:
  • observing
  • imaging
  • abstracting
  • recognizing patterns
  • forming patterns
  • analogizing
  • body thinking
  • emphathizing
  • dimensional thinking
  • modeling
  • playing
  • transforming
  • synthesizing
• 6 important points about these 13 thinking tools
  1. this is based on creative individuals describing their own thinking
  2. its not the first notes on some of these imaginative tools
  3. these tools for thinking promise to bridge the gap between illusions and reality to create synthetic undestanding
  4. these are just tools, it doesn’t replace other cognitive skills
  5. mastery of tools for thinking does not guarantee innovation in science, art, or any other endeavor
  6. our educational system is the embodiment of our cognitive and creative understanding of ourselves. Knowledge is fragmenting at ever-increasing speed; understanding becomes ever more rare.

Observing

• all knowledge begins in observation
• observing in any field: “is almost entirely an acquired skill” - an aptitude for concentrated attention (the patience of yogi)
• the eye have to be trained, both in observation and in notation
  • the patience to look and look again
  • having learned to observe one thing, he had learned the keys to observing and describing everything
  • just as Picasso keep drawing the pigeon’s foot,
    • what is you pigeon’s foot?
• the secret to observation, the bedrock of the sciences, lies in time and patience
  • be a patient observer, look at a speciment over and over until inobvious facts becomes obvious
  • I think the same goes to mathematical or technical knowledge, keep “looking” at the subject/object over and over again until it becomes obvious
  • “I discovered that miracolous worlds may reveal themselves to a patient observer where the casual passer-by sees nothing at all” ~ Kondrad Lorentz
• Part of seeing, is knowing what to look at or for : “seeing order in a random background”
• the keenest observers make use of every kind of sensory information. In fact, the greatest insights often come to individuals who are able to appreciate the “sublimity of the mundane”, the deeply surprising and meaningful beauty in everyday things.
  • even awkward gestures have a beauty of expression begging to be discovered and exploited.
• Think most about what you tend to think about least.
  • think about what you see!
  • mind’s preconception can alter our perceptual sensation
• “Discovery consists of seeing what everybody has seen and thinking what nobody has thought” - Szent Gyorgyi
• explicit observational exercises, to develop sensory acuity
  • listening to television without looking at it
  • watching with the sound off
  • collecting things - serious collectors learns to make finer and finer distinctions in variation and quality
  • Collect all your attention : noting the sublimity of the mundane
• Select an object, notice its form, its lines, its color, its sounds, its tactile characteristics, its smell, perhaps even its taste. Then remove the object and recall one by one as many details as possible. Write about what you pereceived or draw it. Go back and observe it again.
  • “Such an effort causes you to observe the object more closely, more effectively, in order to appreciate it and define its qualities” ~ Stanislavsky
• Observe and describe the same object again and again, over a period of days, weeks, even months, refining your vision through practice.
  • Can I do this to equations? (think of equations or mathematical expressions as object, to be exact mathematical objects)
  • Can I do this approach to physical laws or theories?
  • Will this provide a better understanding different from all other interpretation?

Imaging

• Francois Jacob (Nobel laureate) began each day by mentally recreating his room, then his house, then his neighborhood, and eventually the entire world while lying in his bed with his eyes shut.
• Sir James Black (Nobel Prize winner), says that the focus of his thinking “is an imaginative sense, entirely open-ended and entirely pictorial. That is a vital part of life. I daydream like mad … you can have all these [chemical] structures in your head, turning and tumbling and moving.”
• visualization of various combinations
  • can this be applied to combination of different equations?
• Margaret Geller, “I think that not all scientists have to have a visual image, but I do. I can’t do a problem unless I have a visual image. That’s how I solve problems.”
  • I have to have a visual model or a geometric model or else I can’t do it. Problems that don’t lend themselves to that I don’t do.”
• Physicist Peter Carruthers, makes a broad distinction between those who are “pictorial” and those who are “mathematical”.
  • Physicist who are more mathematical don’t share what Carruthers calls his “physical intuition” or his visualizing tendencies.
  • visualizing in QM is actually discouraged by leading practitioners
• Freeman Dyson:
  • the strictly symbolic approach in this field is compared to attaining fluency in a new, formal language; one undestands QM when one doesn’t try to translate it into some other perceptual form or “tongue”, but comprehends it directly,, mathematically, the way musicians “hear” the meaning of written notes without the aid of an orchestra.
• visualizing is an important thinking tool
• Richard Feynman purposefully converted algebraic problems into geometric ones, asking himself, “Is there a way to see it?”
• consider the advantages of learning a visual subject without seeing its symbols : on learning math by ear training rather than eye training, it forces you to do mathematics in your head and to think of languages as they are spoken rather than as mere exercises in writing
  • listening to some mathematics lecture
  • If necessary, written and oral instructions and physical and mental drawing can be alternated, improving the connections among them.
• Working on your imaging abilities:
  1. recognize your own use of visual, aural, and other images.
  2. indulge yourself. Image on purpose and to your heart’s content. If you like to visualize, reimagine scenes from your favorite movie; better yet rewrite and “resee” the movie so that it is perfect and perfectly your own. Try your hand on visual puzzles. If you like to think in images of sound, try to remember and hear in your mind not just the melody but the harmonies of your favorite song or concerto.
  3. take up an art. But don’t just learn about music or dance or painting or cooking. Learn to make drawings, songs, poems, or gourmet dishes. In many of these activities imaging is part of the process of doing.
  4. Make up excuses to use your inner eye, your inner ear, your inner nose, your inner sense of touch and body.
     • have someone pose math and science problems verbally for your
     • practice hearing different voices and seeing different physiognomies when you read a play
     • pay attention to what you feel and imagine as you listen to music - imaging becomes stronger and quicker with consistent and persistent practice

Abstracting

• abstraction: to bare stripped into essentials for simplicity
• Physicist Werner Heisenberg defined abstracting as “the possibility of considering an object or group of objects under one viewpoint while disregarding all other properties of the object. The essence of abstraction consists in singling out one feature, which, in constrast to other properties, is considered to be particularly important.”
• Although all abstractions are simplifications, the best abstractions are like 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.
• Mathematics is the tool specially suited for dealing with abstract concepts or any kind.
  • e.g. “nothing” itself is an abstraction, zero representing that which does not exist and yet holding the place of everything that could
• One must learn to see past the obvious reality that we observe through our senses to perceive them with the “eye of the mind”.
• It is easy to forget that although we learn to use these abstraction, few of us could invent a new mathematics, discover a new law of nature, devise a new way of portraying perceptions, develop a new gestural language, or describe a fundamental truth about human feelings.
  • such triumphs are rare and difficult to achieve
• the essence of abstraction is that we say to ourselvs, My kid could do that
• Mitchell Wilson: “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 the 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.
  • from fundamental simplicities springs basic theories
• abstracting, by simplifying, yields the common links, the nexuses, in the fabric of perception and nature.
• Werner Heisenberg, “The step toward greater generality is always itself a step into abstraction – or more precisely, into the next highest level of abstraction; for the more general unites the wealth of diverse individual things.
• Richard Feynman: “Phenomena complex – laws simple… know what to leave out.”
• Learning how to find the simple concepts hiding among complex expressions.
• Picasso : “To arrive at abstraction, it is always necessary to being with a concrete reality. There’s no danger then, anyway, because the idea of the object will have left an indelible mark. It is what started the artist off, excited his ideas, and stirred his emotions.”
  • Just as two artists may find very different ways to represent bulls, so there may be many ways of abstracting any object or idea that will reveal different fundamental aspects of it.
• Abstracting: discovering the simplest relationship between form and color in things you observe
• One might even say that reality is the sum of all possible abstractions and that in coming to know these possibilities, we understand reality better. $\sum_i{(\mathrm{abstractions})_i}=\mathrm{reality}$
• Experimentation: a formalized process for discovering important abstractions
• Learning how to abstract in one discipline provides the key to understanding the abstractions of all disciplines - this process is universal
• repetition, patience and mastery:
  • Ramon y Cajal explained that he would spend the morning preparing and observing dozens of sections of the brain or the spinal cord. Then, after lunch, he would draw what he remembered. Then he would compare his drawings to his preparations. He would analyze the differences, then draw again, repeating this process over and over and over. Only when the drawings he made from memory captured the essence of what he saw in an enture series of preparations would he consider them finished.
• Abstracting is a process beginning with reality and using some tool to pare away the excess to reveal a critical, often suprising, essence.
• Abstraction sequences:
  1. choose your subject and your abstracting tool
  2. think about them realistically
  3. play around with their various properties or characteristics
  4. get at what might be most essential
  5. consider and reconsider your results from a distance of time or space
• Practice with simple experiments or mathematical concepts

Recognizing Patterns

• there are so many ways of looking at the same object or idea, yet most of us see only one way.
• Half of mastering mathematics is simply recognizing the type of problem-solving pattern that applies to each problem.
  • To some extent the whole object of mathematics is to create order where previously chaos seemed to reign, to extract structure and invariance from the midst of disarray and turmoil.
• Sometimes all it takes to make a discovery is to recognize the patterns in front of our eyes.
  • "What is the pattern that I'm missing here?"
• maps hold clues that people have seen and not understood
• Nobel laureates Chen Ning Yang: “pieces of jigsaw puzzle”
  • Scientists must assemble the pieces to make sense of the big picture, which unfortunately is seldom available even in outline
    • literature review
  • The most important things is not any one particular piece, but finding enough pieces and enough connections between them to recognize the whole picture.
  • The critical part of research is not getting the data, but making sense of it.
• Yang: “This constant searching for new associations, subconsciously or consciously, is one important element of scientific research. You don’t constantly attack one problem. If you have a lot of small linkages, you try to make them fit, and then once in a while you find one piece which can put five together. That joy is indescribable.
  • When enough data and concepts cohere, and conceptual puzzles becomes conceptual patterns or “pictures”, scientists call them theories or natural laws.
• Knowing what you don’t know, knowing the pattern of your ignorance, can be as valuable as knowing what you do know.
• A scientific researcher must be attracted to these [blank] spots on the map of human knowledge, and if need be, be willing to give his life for filling them in.
  • I’m attracted to unsolved problems!
• The key is to build up, by means of predictions or even vague intuitions, a sufficient sense of what should be present in a particular situation so that absence becomes anomalous and therefore strikingly interesting.
• Determine:
  • when a pattern is absent because it doesn’t exist, or when it is present but can’t be perceived.
• a theory is a pattern of data vs a theory as a pattern
• The problem is that we can’t use what we don’t know
  • enters pattern recognizing ability
  • pattern-recognizing ability benefits from practice with these different versions of space

Forming Patterns

• focus: how original and inovative patterns are formed
• forming patterns is really nothing more than combining two or more structural elements and/or functional operations
  • structural elements
  • functional operations
• as [they] invent new patterns, they often find that those patterns already exist but have previously been overlooked. To understand order it is often necessary to learn how to create it.
• the mathematical description: Fourier transform made of simpler elements
• writers obviously work their magic by combining a relatively small number of words into sentences, paragraphs, poems, stories, and boooks.
  • (less obvious) they structure their works by forming patterns out of diverse experience
• the striking thing about pattern forming is not the complexity of the elements that are combined, but the cleverness and unexpectedness with which the combinations are made.
• creative scientists, like artists, often take different paths and reach different solutions.
  • ~7 different evolutionary trees that are consistent
  • ~450 valid representations of the periodic table of elements (most of which are not tabular at all)
• the specific patterns we invent to embody our understanding of things have different limitations and different strenghts - no single pattern is ever the end all or be all of a subject.
• The nature of the objects or concepts combined alters the outcome.
• learning to create patterns is therefore 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 very limited number of words and exploring all the possible ways to making sense with them.
    • i do this alot during my note taking
• invention is the process of putting together these components in a new way – that is, devising a novel pattern from them.
• makinig patterns for oneself is a lot more fun than memorizing – and a lot more valuable.
  • Teasing apart one pattern and composing another requires real understanding of the basic elements of phenomena and processes.
  • it opens up whole new worlds of knowledge
• 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.

Analogizing

• Physicist: connection between an element’s energy spectrum and its structure, but what?
• how can we learn about or explain anything that we can’t directly, physically sense?
• How is it possible to apply knowlege learned in one context to another very different one?
• How do we realize that musical resonance has some application to atoms, or atomic resonance to medicine?
• it is critical to this process that analogies not be confused with similarities
  • analogies recognize a correspondence of inner relationship or of function between two (or more) different phenomena or complex sets of phenomena.
• The critical part of interesting analogies is that they reveal not mere resemblances but inapparent relationships between abstract functions, one of which is understood, the other not.
• Analogies, as imperfect correspondences presumed in spite of difference, help us make the leap from existing knowledge to new worlds of understanding that no other mental tool allows
  • MD is ? as MC is QM
• No wonder analogizing is one of the imaginative tools of people in all walks of life.
• many scientists rate analogizing as one of their most important mental skills
• Stanislaw Ulam: a good mathematician is one who finds analogies between things; a great mathematician is one who finds analogies between analogies
• “the pleasure the mind derives from the perception of similitude in dissimilitude”
• diverse interests are a frequent source of fruitful analogies for innovators
• training in making analogy:
  • start with what you know or what the person you are teaching already knows, then find the functional analogy that bridges this known thing with the unknown one that needs to be understood.
  • e.g. Leonardo’s notebooks are littered with analogies rendered in words and visual images
  • Siler: we compare the mind with a garden and explore metaphoric figures of speech, imagine stories, form hypotheses, search for puns, following up every image, feeling and association these provoke.
  • this approach can be used with any set of materials to open worlds as unexpected and otherwise unknowable
  • So try a bit of “metaphorming” yourself
    • finding analogies between their analogies – by metaphorming – reveals deeper meanings
• When we seek out and find hidden identities of function and purpose “degree by degree” we “surround” our perception of world and self with meaning. And then, suddenly, we understand.
  • “find hidden identities of function and purpose

Dimensional Thinking

Modeling

• Picasso: “To model an object is to possess it”
  • Johann Wolfgang von Goethe: “so as to make them really my own”
• in science, modeling is inextricably bound to the generation of new ideas, the development of theories, and their experimental verification or falsification.
  • Linus Pauling: modeling is a unique way of thinking
  • “The greatest value of models is their contribution to the process of originating new ideas.”
  • “I would say that models constitute a language”
• Precise models represent precise thinking.
• The role of scientific models can be compared to that of the scaffolds and cranes erected around large buildings as they are being built. There is no way to construct the building without these scaffolds and cranes, but once the building is completed, they need to be removed.
• Models help us gain mastery of concepts, Feynman went on to say, but should not be confused with the concept themselves.
• To achieve conceptually pure models, many scientists have turned to mathematics
  • the notion that every equation or mathematical concept can be represented physically or visually and that every such representation can be expressed as an equation came much later.
  • mathematical concept -> picture
  • visual/physical representation -> mathematical equation
• One reason that graphic models are not as good as physical ones is that abstract “maps” do not always correspond to real “terrain”.
• If we are to understad the world around us, we need to create useful, often multiple, models.
  • for out of modeling come understanding and control
• Visual thinking can also be improved by modeling, because there is a direct connection between the kinesthetic sense and vision
  • develop spatial skills by modeling your school, house, or neighborhood
  • learn engineering and design skills by making structural models e.g. architectural forms

Playing

Transforming

• transformational thinking:
  • use of multiple imaginative tools in such a way that one (set of) tool(s) acts upon another (set)
  • one person may feel and think her or his way through a problem with various imaginative tools
• what had begun as a vague idea had passed through various stages of analogizing, visualizing, modeling, playing, abstracting

Synthesizing

• synthetic understanding, in which sensory impressions, feelings, knowledge, and memories come together in a multimodal, unified way
• Vladimir Nabokov: “cosmic synchronization”
  • a communion between self and universe
  • “the scientist sees everything that happens in one point of space, the poet feels everything that happens in one point of time.”
  • All sensations, all perceptions became all knowing, and the synthesis of sensing, feeling, and knowing become the wellspring of his imaginative achievements.
• to know is passive, to understand is to be able to act on one’s knowledge.
• knowledge = intelletct $\cap$ senses
• synthetic knowing: a combining of sensation, feeling, memory, and rational thought
  • all creative work is based upon this.
  • the union of different form of knowledge
• 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” equivalent melding sensual and intellectual concerns.
• “become what you study … “
• The only real schooling, he believed, trains the mind, the body, and the spirit to strive for synthesis.
  • challenge of modern life and education still remains to reintegrate poetry and physics, art, and chemistry, music and biology, dance and sociology, and every other possible combination of aesthetic and analytical knowledge, to foster people who feel that they want to know and know that they want to feel.
• The future will therefore depend upon our ability to create synthetic understanding by integrating all ways of knowing.

Synthesizing Education

A synthetic education requires only that we change how we teach, bearing 8 basic goals in mind.

1. we must emphasize the teaching of universal processes of invention in addition to the acquisition of disciplinary product of knowledge
   • its focus should be the active process of learning and creating rather the passive acquisition of facts
   • it is possible to know about principle of literature or physics without being able to use them
   • don’t just analyze, copy and imitate to learn the sensual and synosic processes of their inventions
2. we must teach the intuitive and imaginative skills necessary to inventive processes.
   • creative thinking in every filed begins in nonlogical, nonverbal forms
   • to think is to feel and to feel is to think
   • everyone should learn to abstract, analogize, and emphasize; to transform one to the other; and to translate intuitive forms of knowing into words, numbers, plastic images, movement, sound
3. we must implement a multidisciplinary education that places the arts on an equal footing with the sciences,
   • arts + sciences + mathematics + humanities
4. we must integrate the curriculum by using a common descriptive language for innovation
   • education must focus on the truck of the tree of knowledge, revealing the ways in which the branches, twigs, and leaves all emerge from a common core
   • tools for thinking stem from this core, providing a common language with which practitioners in different fields may share their experience of the process of innovation and discover links between their creative activities
   • using “abstracting” one start to think beyond disciplinary boundaries
   • one sees how to transform one’s thoughts from one mode of conception and expression to another
   • linking the disciplines comes naturally when the terms and tools are presented as part of a universal imagination
5. we must emphasize the transdiciplinary lessons of disciplinary learning
   • the object is to help everyone think simultaneously as artist and scientist, musician and mathematician, dancer, and engineer.
   • An education that trains the mind to imagine creatively in one field prepares the mind for creative application in any other, for thinking tools as well as flexible knowledge are transferable.
6. we must use the experiences of people who have successfully bridged disciples as examplars of creative activity within our curricula
   • the best way to learn is to watch others and then model their techniques, insights, and processes
   • until we see the human face of the creative process that underlies the disembodied products of their world, we cannot realize that we, too, may participate in creating their own vision of the future
7. to reach the widest range of minds, ideas in every discipline should be presented in many forms
   • different thinking tools: intuitive, logical, analytical, algebraic, geometric, visual, kinesthetic, emphatic
   • the more ways that one can imagine an idea, the better their chances of insight
8. we must forge a pioneering education, whose purpose is to produce the imaginative generalists who can take us into the uncharted
   • every novel idea takes us into new territory, and creative people are, by necessity, pioneers
   • “different studies gave me practice in ‘abstract’ thinking, in learning to penetrate into fundamental questions.”
   • on mathematics
   • it is the science that demands the utmost imagination
   • it is impossible to be a mathematician without also being a poet in spirit
   • these where whole people, not specialists
   • they made contributions to particular disciples because of, not inspite of, their broad interests. - they were pioneers, generalists, who bridged areas of expertise and pulled together disparate areas of knowledge - “you learn how to use your mind in the act of handling parts and working” - “…mastery of the creative process