Fermat’s Last Theorem–Karl Staubach’s Solution

Updated from from 2018. There are two pages. Click each blue phrase to see each one. Or download each to your device.

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Going To and Fro on the Earth, and Walking Up and Down on It — Looking for Poems


Mount Diablo — 3849 Feet

I Brought Back All the World on My Face

Dear McKowen: I have spent a Sunday up on the mountain of Diablo: Motorcycling up and down, looking at the scenic view . . . I brought back all the world on my face–cheeks set aglow by sunset sky, planes, hawks, people, woods, horses, spring flowers and wind.

Years ago I found those words in a reflection of Lupe, a student of mine, from Puerto Rico, at Diablo Valley College. No wonder I enjoyed my work. Let’s make Lupe’s reflection look more like a poem:


           Dear McKowen

I have spent a Sunday
up on the mountain of Diablo:
Motorcycling up and down,
looking at the scenic view.
I brought back all the worldimages
on my face–cheeks set aglow


by sunset sky, planes, hawks,
people, woods, horses,
spring flowers and wind

How does that look? Any better?

This makes me think of a class I had with some students one morning years ago. I remember putting a poem of William Carlos Williams on the chalkboard one day and pretending–just for fun, but more than that too–that I had written it to my wife and had left it on the refrigerator that morning.

Plums Realms

So I asked the students if they thought Ruth should forgive me. Shouldn’t she be glad I ate the plums? They discussed that back and forth for a while. Some thought it was pretty sneaky.

Then I asked if I could get away with telling Ruth that my note was actually a poem? Maybe she’d go for it? Did they think my note was a poem? Come on!

Well, what if I had typed it up and arranged the words like this:

                                                  THIS IS JUST TO SAY

imagesI have eaten
the plums
that were in
the icebox

and which
you were probably
for breakfast

Forgive me
they were delicious
so sweet
and so cold

I thought she ought be damned glad to have such a swell husband even if he did eat the plums. (I did later  confess that William Carlos Williams was actually the guilty party.)

And along that same line of thought I asked if, say, someone had written a note like that instead of writing a regular reflection, should I forgive him or her? And I played around with that a while: Is he or she “getting it” – getting what the study of our language and its literature is all about? I asked. Isn’t eating a delicious plum, whether school keeps or not, precisely the same thing as reading a delicious poem?


A Delicious Poem

Remember when Piglet asked Pooh, “When you get up in the morning, Pooh, what’s the first thing you think about?” And Pooh says, “What’s for breakfast? And what do you think about, Piglet?” “I wonder what exciting is going to happen today,” says Piglet. Pooh ponders that and then says, “It’s the same thing.”

Pooh and Piglet

It’s the same thing.

Get it?

There are delicious plums right under our noses – wonder moments – lying about on sidewalks and in the dust balls under the bed – everywhere. And as Auntie Mame said to Patrick when things looked dour, “ Remember, my little love, life is a banquet, and some poor bastards are practically starving to death!”


Life is a banquet.

It’s a matter



Teaching in the Realms of Gold

The fog comes

on little cat feet. 4415428193_0e415b884a

It sits looking

over harbor and city

on silent haunches and then moves on.

–Carl Sandburg, 1916

[I read a reflection recently about the role of moments of wonder, joy, and even terror in classrooms, and it fitted so well with this Realms of Gold website that I decided to invite the writer to be my first guest columnist. That there are actually future teachers who want their students’ minds to explode with the pleasure of seeing into the heart of things amazes and delights me.

Dakota Balunis is a sophomore at SUNY Plattsburgh, enrolled in a combined BA/MST program, with the BA degree in biology and the MST degree in education. This reflection was written in response to course work in An Introduction to Adolescence Education, taught by Dr. Mark Beatham. She writes, “We have a nice spread of subjects – English, History, Bio, Math, and one Environmental Science major.”]

Moments of the Divine


Guest Columnist Dakota Balunis

    This week we focused again on enthusiasm and language in the realm of teaching and learning. Right off the bat I would like to say that I really enjoyed watching the excerpts from Louder than a Bomb, even if my main focus isn’t on English or writing.

[“Louder than a Bomb is a film about passion, competition, teamwork, and trust. It’s about the joy of being young, and the pain of growing up. It’s about speaking out, making noise, and finding your voice. It also just happens to be about poetry.” – From a review ]

Visceral-Yet-Ephemeral Awe

     I can appreciate moments when you hear or read a line of poetry, prose, lyrics, etc. and get a little jolt that sets the hair on your arms to standing up. That “Oh damn!” moment doesn’t come frequently and it doesn’t come from the same things every time, but the wonder is worth the search and the wait. It’s the same sense of visceral-yet-ephemeral awe that I personally get when a concept in biology clicks into place inside my brain, when I link the nature of evolution to the almost-impossibly complicated workings of living things; at the risk of waxing poetic and overshooting, it’s as close to religion as I personally will ever get. I look at a cat wandering down the street and start thinking about skeletal muscles and sensory organs and predator-prey relationships, or I drink some water and appreciate how easy the action is to me when in actuality peristalsis and electrolyte balance is amazingly complicated. My brain feels as if it’s a hall of mirrors and the light of a single candle is being reflected all around; everything is clarity, but there’s so much left to see and understand. Some of it will never be understood fully, but the attempt is of itself important. Is that the “moments of the divine” we talked about in class? I think it might be. I kind of hope it is, because anything more revelatory than what I’ve described might be too much for me to handle. I’d like to skirt the absurdist cliff Kierkegaard talked about, not tip over the side into quasi-Lovecraftian madness.

[Danish philosopher Søren Kierkegaard (1813 – 1855)is regarded as perhaps the first existentialist philosopher. He emphasized the priority of concrete human reality over abstract thinking. H.P. Lovecraft (1880 – 1937) is regarded as one of the most significant 20th-century authors of horror fiction.]

State Exams – Not Really the Point at All

     Anyway, back on track. I understand that my students won’t necessarily be as interested in biology as I will be when I’m teaching, and I’m fairly certain there will be a disparity in enthusiasm. That’s a challenge every teacher has to constantly contend with, I think, especially since public schools have a way of taking even the subjects you like and twisting them around until you’re just waiting for the state exam so you don’t have to take any more lessons or do any more practice problems. That’s not really the point of education – that’s actually not the point at all, especially when it encourages load-and-dump methods of cramming information that quickly decays as it’s not applied – and at the risk of sounding somewhat arrogant that’s not what I’d like to spend my life doing. If I have students, I’d like for them to experience those moments of religious-visceral awareness of the nature of life, but then again I have to keep in mind that they might never experience that. If they don’t, that’s not a non-issue, but I can’t force it. You can’t force wonder the same way you can’t force religion. You don’t get to the soul that way, you only get to the meat – or the clay, really, since getting to the meat is arguably the point of biology. I don’t think it’ll be my job to force kids to appreciate things, or even to try to make them curious – axioms about horses and water aside, it’s unfair to students if I try to proselytize. That just perpetuates the system.


The golden apples of the sun, The silver apples of the moon. — Yeats

‘Golden Apples – Moments of Wonder, Joy and Terror

     However, that doesn’t mean I can’t offer them some proverbial apples, right? How do you get people to experience wonder and peel back the shroud of everyday living? (Or, for that matter, how do you do it without the involvement of psychotropics? I’m fairly certain those will still be banned in schools when I’m actually certified.) Do you explain things a certain way? Do you try to link what’s learned to interesting examples, or do you pick everyday moments where the knowledge is relevant? Do you flat-out say to students that they should be experiencing moments of joy and terror as they learn, or do you wait for them to experience it on their own and coach them through it? It’s hard to say. I keep wondering about it and can’t decide either way.

If I feel physically as if the top of my head were taken off,I know that is poetry. –Emily Dickinson

                                         PARTING OF THE SOUL by Roberto Lauro

PARTING OF THE SOUL by Roberto Lauro

Eno’s Adventures in The Realms of Gold

The Spirit’s Body

A “scientific” description of how spirit becomes flesh

I wrote the story of Eno as if it were science fiction, but it is a fairly accurate scientific – as we commonly think of that word – description of how spirit – that’s a metaphor, too, for some kind of life force – generates a physical structure for itself.  .

When we talk about how little babies get started [conception, the physical stages of development – arms, legs, lungs, heart – and mental development – brain, nervous system, mind – we have to understand, reader, that those are words, metaphors, about what’s actually going on. We’re used to this language. But when we penetrate beneath this overlay of language, we discover something mysterious, something magical going on. The raw material of an organism becomes a human being through a genetic code system, more like the binary zeros and ones that lie behind the internet than the biological metaphors we commonly use.

So if you have any interest at all about who that person in the mirror is, you have to go down to and beyond the genetic code.

[A man pauses from shaving one morning and looks thoughtfully at the face in the mirror and asks, “Who are you?” The image replies, “Who wants to know?”]

If you are very quiet and open, you may get a feel for who wants to know and even come fact-to-face with this great and marvelous mystery.

Trailing Clouds of Glory

                       Trailing clouds of glory do we come --Wordsworth

                      Trailing clouds of glory do we come

Our birth is but a sleep and a forgetting;
The Soul that rises with us, our life’s Star,
Hath had elsewhere its setting
And cometh from afar;
Not in entire forgetfulness,
And not in utter nakedness,
But trailing clouds of glory do we come






Eno could see himself in no mirror, however brightly polished; no words could define him, however cunningly shaped and arranged. Though he knew that a reflection referred to something that was Eno, it was also not him at all. Whatever he said he was, he was, and yet he wasn’t at all. What, who, when was he? Was it really he who asked these questions? Was there even a question to ask? Propelled forward as he was, was there time to ask a question? WHAT WAS GOING ON?


Suddenly he emerged on a strange, totally unfamiliar planet, an Energy and Atom Recycler through Temporal Holography (“Earth”), knowing neither who he was nor how he got there. Had some angry god banished him to this chaos? Had he been selected as a special intelligence agent to probe this alien soil light-years from home, to somehow master it and return with his cache to the data banks of a nonphysical world he could not at present even remember? Nothing made sense. Sense itself did not make sense. Sense had something to do with stimuli and his responses, and, out of awareness, he grasped that he was equipped with nerve endings that were nothing more than tools he was using to collect stimuli and figure out this puzzle. He knew that nerve endings themselves were not Eno. And yet, perhaps . . . If he had been sent to probe this world, to study and to understand it truly, then naturally he could not “know” it merely by observing. His intelligence was not specialized to observe in the first place. If there were beings in this planet, he would have to adapt his intelligence to something approximating the tools they presumably possessed. To understand them, he would have to be one of them—completely; he must not even know that he was a spy. Possibly those who sent him might monitor the process, perhaps tag him somehow so that they could retrieve him at the optimum moment. But tagging would not really be necessary because he would always be obvious to his own kind in their own structuring system.


I am not I.
                 I am this one
walking beside me whom I do not see
–Juan Ramón Jiménez

Possibly, then, Eno’s identity was out in the open, but neither the target race nor he himself was capable of sensing it, as though they were tuned to a radio frequency that couldn’t pick him up even though his waves were all about them. He thus might penetrate the target race, taking on more and more of their characteristics until the crucial moment when he would be yanked home for analysis. But that was only one of the limitless possibilities of the riddle of his essence.Eno 1 13

Eno was dimensionless. He did not belong to a place. He did not belong to a time. He had no length, no breadth, no thickness. Any form he achieved might seem to alter, but Eno himself always had been and always would be. He had entered this world through a crack in the time shield. One moment he was nowhere and the next he was physical, as though someone had twisted a kaleidoscope and Eno was the image produced.

imagesIt was not so much a matter of travel as it was a matter of coming into focus or of being translated to another radio frequency. Suddenly, so it seemed, there was a new bias toward form and structure with a thrust toward definition, toward becoming finite. This urgency to define necessitated senses. He began specializing his nerve endings and developed a complete sensorium. Through its agency he became, or seemed to become, concrete. Senses were a means of differentiating, of separating, of setting up distinctions, billions of them, every particle separated from every other by a sensing structure whose nature it was to see isolates. This planet existed through differentiation (“this is different from that”), through the emergence of things, the separating of one thing from another—and putting them together as well! Eno was an emergencee, emerging from the galactic “mother” through the uterus of what his senses identified as the “human” form.

IMG_0006Immediately, he began his research. Because he did not even know he was a spy, he investigated automatically, to begin with. He sharpened his Early Yield External Sensors (“eyes”). Out of the gray blur, he forced entities to emerge, identifiable separations from the vast general jumble. From a few trifling particulars, he deduced general laws. Falling was dangerous.imagesEating was desirable. These were nerve-ending “concepts” felt but not intellectually known. He identified a nippled nutrient sack and grew himself flesh and bones, perfect camouflage for a dimensionless fellow. He became one with time and space. Every planet day new floods of data poured into his Master Integrator of Nervous Data (“mind”), where he automatically began to create a time-space first approximation of his surroundings, his own Boundary Of Dimensional Yin-yang (“body”) being part of the structure. And each dis … covery hid him from himself more and more completely! Nonentity had merged with entity. The investigation had begun, and no one suspected a thing. Birth was so ordinary, just another emergencee.

In the Realm of the Senses

For Eno the validity of the parts of the sensorium (nose, taste buds, fingertips) was unquestioned. That which worked was true. If one thing failed, he tried another and didn’t think about how real or “true” it was. Only that which promoted his own toehold on the planet was important. Out of the sensorium grew a knowledge of the Synthesis of the Entire Life Force (“self”). He had to be totally “self”ish or become overwhelmed by the great wash of “things” pressing against the flimsy dikes of his new flesh. Eno was not conscious of the dangers. His flesh took charge, touched, and assimilated. He did not know this knowledge, this “nourishment,” was his lifeline. His body did the work, and for him it was child’s play! Literally.IMG_0003 He laughed. He fondled, tasted,smelled, played constantly with sounds he could make with his tongue, air, oral cavities. He developed depth perception. He sensed warmth and burning, coolness and the pain of ice. Locomotion became vital. He grew himself “muscles” and forced himself to master Articulated Regulators of Manipulatory Skill (“arms”) and Locomotor Extensions against Gravitational Supremacy (“legs”). He had become some thing, an entity, but his mind did not know it.


If there were watchers, they would have known the immensity of the experiment. The spy Eno was embarked on frighteningly dangerous reconnaissance in complete ignorance. He was hypnotized by the reality of appearance. Each planet day it appeared that he brushed aside another veil and disclosed more and more facets of this shimmering planet. It was all a matter of interstices, of course, intersections of electromagnetic force fields, but within the perception centers of this alien structure (his body) appearance was the only reality. Finally, in the third year of his new time sense, Eno made one of the most startling of his discoveries: his own identity. He had been busy dis … covering things out there; he now dis … covered his self. “I am!” he thought. This discovery launched him toward the next leg of his journey.

During the first stage of his planetary probe, when his senses automatically fondled the world so that he “knew” it on his nerve endings, Eno’s experiments with sound had paid off in a magical assortment of talismans, Wave Ordinates Revealing Dharma Signs (“words”) and “concepts” capable of giving him balance on this slippery sensate flow, a surfboard for riding out the waves. He could shape air and call nourishment to his lips for energy replenishment. He began to capture the world in this symbolic network. He mastered the linguistic code nearest at hand. The power it gave him over his perceived world was amazing. He spent most of his waking hours playing with and perfecting this new instrument. One network of intersecting concepts he identified as his self That bundle of ideas had been given the code name Robert, but of course that referred only to the space-time mask Eno wore. Robert referred to the energy system of bones and kidneys, nose and fingernails. To be was to be physical. Was that the solution to his identity? Was Eno really physical? When he became defined, when he became Robert, did he cease to be Eno? Did nonentity cease when entity emerged? Were being and nonbeing one thing?

His parts were at once instruments for knowing reality and reality itself. For one could not be without the other. This new magical “language” was a probe for exploring, but it created that which was explored as well. The tool shaped the craftsman. Just as his new “eyes” had filtered the continuum of color and presented his mind a “reality” of only one sector of the spectrum, what he perceived through the language tool was limited by the tool. Language pinpointed the intersection of things, showed where the connections were, but it also determined what would be considered to intersect. It was a structure system that gave him a handhold on the planet, but was it the planet, or were there many planets superimposed on each other? If Eno had entered the planet as a tree, it would have been tree “reality” he would have experienced: different sensors, different filtering, different planet. What was really going on?


This entire displacement stage, the “What if .. . . ?” stage, exactly paralled that in which his senses and muscles had identified and shaped a world for him. His mental”senses” now probed this world. He formed relationships and the relationships were his reality. For him, all that he noticed was all that there was. Though he used these processes well, they were as automatic as those of his earlier stages. The eye could not see itself. The planetary searcher had done his job perhaps too well, for he had entered into the life of the planet and assumed its characteristics completely. But was he air and water, emotions, sentiment, intersections of force fields? At this stage the questions did not occur. And without the question he could not discover his self, the Eno, and would continue imagining himself to be merely the surface being Robert. As long as he stayed within the psychophysical structure system he had defined, the combined mind-body package, the question could not occur to him. He felt he had completed his search. He was mistaken, of course, in fact about as far from the answer as he could get; and if he stopped there, the probe would have failed. But he did not know this. He felt he had finished, and he grew listless and depressed. Without something firing his mind and body, he felt pointless. Was he to sit out his remaining planet years working crossword puzzles and drinking beer? The planet, the lustrous jewel that had so fascinated him, now seemed more and more tarnished and drab. There was nothing to do, nothing to integrate. The fires burned low; the energy construct Eno began to decompose into nothingness. Still he lingered, pointlessly.

Finally, the probe almost burned out, reduced to reruns and insomnia, Eno found himself thurst toward a new genesis and discovered that the end was only a second approximation.IMG_0007 Boredom and chance (mere accidents or part of a calculated design?) hurled him into a totally foreign region of the planet. He went on an adventure. Does it matter how it came about, where he went, with whom, or why? Such “accidents” do happen, and for some planetary explorers a new birth occurs. Throbbing through his body-mind came the old question: WHAT WAS GOING ON? His entire being responded.

Nerve endings tingled with new data: His mind lurched into gear. In this far region of the globe he walked among beings of his own “human” class who appeared to experience a different reality! Does it matter whether they were aborigines or university professors? They did not see as Eno saw or as the others of his party saw. The beings among whom they now found themselves selected other things to notice, and they summed them up strangely. One way for Eno to cope with this peculiar world was to translate it into terms of his old reality and force it to fit into his old construct. That was the common way out of the dilemma. Several of those in his party chose to do that. But as someone has said, translations are like the back side of a tapestry, and Eno preferred the front. If their reality was fixed up to fit his, it was no longer their reality. Later he would even have to question this preference. Why wasn’t everyone sparked by the same drive to penetrate this new construct? Why did some cling to the old pictures.

At the moment, however, something more important occupied his thoughts: Everything he “understood” had been assimilated outside of his conscious awareness. That was a shock. He had had his “eyes” open, his “mind” open, but within a closed-off system!— his group’s private, isolated world.IMG_0008 How did he know that any of it was true? This brush with a foreign reality forced the likelihood that his reality was no more accurate than theirs. Wherever the truth might be, it would have to encompass all realities. That meant eight billion human realities, tree realities, whale realities, rock realities, galaxy realities. Following the method he had used for his first two approximations of reality, he began with himself, with his own picture of reality. He began probing his own self-construct. He had constructed reality twice, through his sensors and symbolically; now he must go over the same ground again. What was going on? His picture, his awareness, was based on his sense perceptions, sentience, the capacity to sense. But these were specialized devices for filtering out very restricted kinds and amounts of information. ‘Visions of infrared and ultraviolet, fourth and fifth dimensions, base 2 and base 12 in the numbering systems, came now to shake the basis of his world. Now the entire perception network, the senses, and the mind itself must be questioned. He set out without a map along an unknown road.

Down an unknown road, but perhaps not without a map. For Eno’s investigation of his own sensors, of what had been called sentience, opened the possibility that his search was not so random after all. There now seemed to be some pattern to his behavior coming from deep within. He was not driftwood but a homing device. The gathering of data by the senses was not random but controlled, purposeful, intelligent. The body did not merely collect data as though it were a grain elevator or a museum. He saw that he put things together, that he integrated, organized them into a framework, a system, that information was mere raw material. Even the smallest Fixing And Cross-referencing Trace (“fact”) could exist only by interrelating with all other “Facts.” The framework was already operating in his own mind. That particular framework functioned well in human entities but would not suit a cat or a tree. They experienced their own realities.

It appeared, then, that a deep structure directed his movements toward a physical fulfillment of its potential. Even the narrowest “fact” (2 + 2) was a general concept. The slightest bit of information was the result of a bunching process. There had to be within him already a blueprint for quantities before 2 + 2 could trigger his mind toward the general idea of 4. The process seemed to work like a hologram, the three-dimensional laser picture—any part of which could trigger the whole. Tape a laser picture, cut off any part of it, project it, and the whole image would appear. Likewise, the tiny fact of 2 + 2 was impossible to contemplate as an isolate, for it was embedded in a complete interrelated system. When Eno encountered such a “fact,” he had to step back far enough and toy with it enough so that the system in which 2 + 2 was possible came into focus—very much the way he had come into focus at the beginning of his planet probe. And the numbering system itself was not isolated from the rest of the picture either, for by examining the situation in which 2 + 2 was possible, he could begin to grasp the entire sentient process, the whole process of differentiating and integrating, of noticing differences and of putting things together. Just as a point entered reality through the intersecting of lines, any bit of data gained its existence through the intersecting of concepts. Thus, an accumulation of bits resulted in the concept of 1, and that 1 could only exist as a part of a picture of reality, as part of a complete system.

So Eno began to turn his investigation away from the nerve endings inward toward the blueprint. Sensing was evidence that something inside was going on. It seemed that the instant the kaleidoscope turned and he entered into matter, became flesh, the impulse to generate a “human” nature was already there, and with adequate nourishment he would flesh out and fulfill that nature.IMG_0009

Now he began to guess an answer to one of his major questions. He had discovered that his senses were inaccurate and extremely weak. He could not see an atom; his temperature range was very narrow. How could his senses ever yield a true version of reality? When he apprehended (see prehensile) that the picture he was looking for was inside him, already there, sensing and perceiving took on new meaning. Sensors did not have to be absolutely accurate, for, if they triggered the right “nodes,” Eno within himself would make up for any flaws and would activate his “nature” himself internally. He now saw nerve endings as catalysts. He knew that the operation did not take place out there. For this
surgeon to know where to operate, crude indicators were sufficient; mere traces would suffice.

IMG_0010When Eno’s research took this turn, he found himself in trouble with other “humans.” That they were standing on a planet and that they were made up of atoms that were made up of space seemed irrelevant. “I’m sitting here on what I think is a chair, and that’s enough. I don’t have to go delving into the source of such ideas.” To Eno, when one looked at himself so narrowly, he behaved narrowly and felt narrow. Because he did not see the world in its larger framework, such a person would always feel isolated and alone, would always be mis … taking his situation. For Eno, though the pain of experience was no less severe, indeed was even more intense, the large frame gave the struggle character. It was not wantonly absurd. As a Cosmos Held In Limited Dimension (“child”) he had felt that the world he perceived did not exist for other people and had felt isolated and frustrated. It was only by following through till he could connect his perception to a total world, an inner world, that he could fulfill himself. The limited concept would likely have culminated in disaster, a grain wasting away in barren soil.

To say that he was sitting in a chair was the most incredible leap of faith that anyone could imagine. One was isolated within a limited and faulty sensing system; every thing was composed of fictional qualities. IMG_0011One knew nothing. Yet one “sat in a chair,” a miracle of synthesis. That should have convinced the others. They had leaped to such conclusions countless times. But they seemed blind to their own sleight of hand.

In Eno’s investigation there had been paintings, myths, mandalas, figures of speech, the whole structure of language—all pointing to what? He looked out and said, “That a bush, and that’s Eno, and that’s God.” It appeared that in this fashion he was classifying and organizing the world, but that was not the case at all. What he was doing was illuminating his own self. When Eno “became,” there was a thrust within him; the pattern was already there. It was like the genetic code, but it was a nonphysical thing. It seemed to be saying to him, “Eno, you’re a kind of creature composed of categories and patterns, and what you have to do is fill them in, to realize them.” Thus, his fingers might crudely sense and report some shape. That signal, coupled with his mind, would yield “desk.” It didn’t matter that the signal was crude. All he needed was something to activate what was already there, to bring patterns into focus. For it was an internal world he was illuminating. It was the intuitive leaps his mind took that engaged and excited him; he would use anything he could get, however crude. He was a thrust toward lucidity and that thrust could be triggered by dreams or . . . anything. Those leaps were not based on physical phenomena; it was the other way around. One did not have to experience every single particle of the physical world.

But that led to another question. If traces were sufficient, what need was there for sharpening or tuning his senses? He knew the answer: For triggering to occur, experience had to be sharp, intense. Though the catalyst could be rough, it had to penetrate. Even though the senses were not the answer in themselves, he did have to send out sharply in order to receive sharply. It had to be a vigorous thrust. If he was not intensely fooling around, the insights, the leaps of lucidity would not happen.
And language was part of (or the same as) all the things he had been thinking of. Language (metaphor) could not be less vigorous or less honed than the physical network. Sharpening up metaphors was like sharpening up the senses. (Were not the senses metaphors themselves?) Sharpening up one’s use of language was like finding a way to trigger reality

South Shore Path




How to Talk With a Rock — The Barrier of Species

What They Don’t Teach in Schools (Continued)

Puddle Heart

                 Puddle?     Heart Art?     Realms of Gold?

 Knowing and Knowing About

     Lots of the posts on this site are about how we come to know something, not the kind of “knowing” picked up in books or from people like teachers or politicians or parents and so on, but the deep knowing, like knowing how to beat our hearts or breathe, what’s in our bones – that kind. Anything else, of course, is window dressing, useful for Trivial Pursuits and not much else. But you already know that.  In a couple of earlier posts I referred to  the barrier of species (7/1/13, 8/2 13).  This one takes it deeper and more broadly.

A Way of Knowing

     The usefulness of the phrase barrier of the species  occurred to me a while back during an interview  with pet resort owner  in southwestern Pennsylvania when she told me her resort was designed by a dog, that they had such complete communication that it was like having a conversation, not in English of course, but directly, the way Sandra Artrip and Rosie communicated (3/16 and 5/4/14 posts); Sandra “felt” Rosie’s messages and Rosie “felt” hers. It was the same with the pet resort owner. When I asked her how she was able to do that, she said, “You have to take away the barrier of species.” 

The Crack Between the Worlds.

     This post is about how anyone who wants to can pull that off, how you and I can take away the barrier of species, not just with, say, dogs, but with anything at all, even a piece of granite. You’ll see why thinking of that phrase in a very general sense can guide us in removing the barrier between us and anything we’re looking at, even school subjects.  It’s also connected with the crack  between the worlds that Buddhists talk of and, of course, with the realms of gold you and I glimpse sometimes on our morning walks and while doing the laundry.

The Barrier of Species

Mt. Shasta Serpentine

     The story Carol, the pet-resort owner, told me was similar to Sandra Artrip’s. It was a story of breaking through the barrier of species, and that’s a story we can put to use no matter what we’re trying to do, no matter what we’re looking at, the backyard maple or some piece of serpentine brought back from a camping trip to Mt. Shasta – or any school subject.



The barrier between me and what I’m looking at is a barrier I created.  If I’m stuck on the word ‘iris” when I look at a flower in my hand, that’s what Neil Postman called definition tyranny.

A very compelling illusion.

A very compelling illusion.

I’m not free to let it be, to let it be lots and lots of things, maybe even a message from the cosmos.  That can never happen if it’s fixed in my mind as “iris”.




Definition Tyranny

     Definitions, like questions and metaphors, are instruments for thinking. Their authority rests entirely on their usefulness, not their correctness. We use definitions in order to delineate problems we wish to investigate, or to further interests we wish to promote. In other words, we invent definitions and discard them as suits our purposes. And yet, one gets the impression that… God has provided us with definitions from which we depart at the risk of losing our immortal souls. This is the belief that I have elsewhere called “definition tyranny,” which may be defined… as the process of accepting without criticism someone else’s definition of a word or a problem or a situation.

Teaching as a Subversive Activity (1969);  “Language Education in a Knowledge Context,”  ETC (1980)

    Much like Sandra and Jane Goodall (1/21/13 post), Carol had spent her childhood and youth immersed in the natural world and had collected a menagerie of pets, from a series of dogs to a crow that lived to be over 20, to an alligator, a box turtle, chickens – all sorts of creatures – and had spent hours watching ants and insects of all sorts – without the use of English. Though still an observer from the outside, she was well-attuned to the ‘thinking’ of the natural world; and she felt most at home in nature. But like Jane Goodall and Sandra Artrip, once, with one animal, she crossed over into the now of interspecies communication.

A Sort of Completion

     Carol had assisted the birth of eleven pups one long night when she was about thirty years old, and when the second pup came through the birth canal, she recalled that she had felt suddenly as if she herself had been reborn. She vividly remembered how warm the pup was, warm, wet, all encompassing, and for her, like a sort of completion. In the next nine hours nine more pups arrived, but only this one made such a powerful impact on her feelings.

     Even before his eyes opened, this was the pup that gravitated to Carol’s lap. Vets will tell you, when picking out a pup from a litter, choose the one that gravitates to you. That’s the one to keep. They were together constantly till his death fifteen years later. Through all their experiences together he had taught her how her pet resort should be designed – the swimming pool, the walking paths, the suites of rooms. Mozart, as she called him, taught her body language, touching, massage, health care. Even in his death, she said, he taught her compassion and empathy.

  The Deep Grammar

   Here’s the significant point of this post: As with Sandra Artrip and Rosie, words were unnecessary. She could look at this dog, she told me, and he knew what she was thinking. Because of Mozart, she saw animals in new, deeper and richer way. Though no other dog since Mozart ever made that special crossover that bridges species, her relationship with all animals changed profoundly. She was able to connect personally with every pet at the resort and to provide for each one’s special personality. “I could look deep into their eyes,” she said, “and feel their presence in ways I could never imagine. Mozart was the real turning point in my realization that animals are living beings emotionally similar to us, able to think, and fear, and communicate — all  because of that species crossover with this one dog.”

     I asked her if she could describe how she came to realize that they were communicating in such a special way.

     “Mozart was the first dog in my life that actually breathed my air – both spiritually and physically. We went everywhere together, did everything together. When we slept at night his face is next to mine. I would breath his air. He would breath my air. He would be touching me. I started to listen and watch as Mozart was growing up, the way that he communicated with me. We always communicated. We always communicated until the day he died.

     “If it weren’t for Mozart,” she went on, “there probably wouldn’t have been this pet resort.”

    I said that it sounded as though what  stood out that was different with Mozart was the time she spent with him and the physical closeness. It sounded like information flowed between them effortlessly.

     “Just take away the barrier of species,” she said. “Become one and stop thinking, ‘I’m a human and you’re a dog, we don’t communicate’. You take all of that away. Now to me that dog is a living being.”

    “Take away the barrier of species”? Would that work perhaps with plants and other animals, too, anything in the physical world?

     “Yes, just take away the barrier of species.” she answered

Learning How to Learn

Muad’Dib learned rapidly because his first training was in how to learn. And the first lesson of all was the basic trust that he could learn. ― Frank Herbert, Dune.

   So here’s something useful to take away from this little story:  Do I want to  know something, really know it?  Realizing  there’s no barrier between what’s inside my skin and what’s outside will open the way.  It’s all in how I look at it.

Human with Mentor

Human with Mentor

If I stop putting labels on that serpentine rock on my desk, and pay attention, it will reveal itself.  Break the barrier with just one thing, a dog, a chimpanzee, a parrot, and suddenly you begin to have a conversation with everything along the way.

 On Reflection

    Of course, ‘barrier of species’ could be applied to relationships among humans, too. I / thou – there isn’t such a thing in nature, and thinking there is makes all sorts of messes.

There are dogs loping through parks

and sitting by backyard doors

all over the world

plenty smart enough to amaze us.

It’s a matter of the time spent on one’s rose.

What we see depends

on the soul lying down in the grass

where ‘the hare has lain,’

that field of pulsating frequencies

spinning out infinitely varied content.

Natural Learning: The Role of Telepathy

In Your Bones

I’ve been writing in a number of posts on this website about the Mess-Around Theory of how to learn.  That’s the name I made up for a theory I invented,  and I’m laying odds it will pretty much work for anything you want to do or get good at or know. Since that’s the way little babies and other creatures learn anyway, I could have called it Natural Learning, but you probably wouldn’t have bothered reading that. But ask yourself  How did I learn the billions and billions of things I know in my bones? Yes, in your bones.

                                                                Yes, In your bones

Yes, In your bones

Here’s the remarkable thing: When natural learning really gets rolling, it’s hard to separate it from what people call Telepathy, as you’ll see in the continuing story of Sandra Artrip and Rosie, the genius boxer,  out in Modesto:

Beyond Skin-Deep

Sandra told me lots of stories about telepathy – or whatever you’d like to call it — between the two of them. I’m telling you this, because we all do have this capacity, and we can turn it on whenever we want, whenever we’d like to  really get past the skin of anything in our lives.

I’ll pass on to you some ideas about how that might work and, more important – this is the good part – how we can “read the mind” of a piece of granite – or how we can let a theory of relativity tell us all about itself, or get into “Ode to Joy.” That would certainly come in handy in dispatching a challenging school subject like calculus or getting a good look at a Rembrandt, wouldn’t it?

While I was writing about Rosie,  I got an email from Sandra about a pan of carrots that almost boiled dry.

Sandra and Rosie

Why, who makes much of a miracle? — Whitman

I was in another room and couldn’t see Rosie.  All of a sudden I felt her tell me to come look for her.  She was waiting impatiently.  As soon as I put my eyes on her, she ran and took me right to the stove and started jumping up in the air. The water was almost gone in the pan. Somehow she knew, even though she’d been in another room – her hearing was bad – and there wasn’t a burned smell.

Even more remarkable, when it appeared that Rosie had indeed lost all her hearing, Sandra got an earache.

Four weeks ago, Rosie totally lost her hearing.  I thought it was because she was getting older.  About that time I started getting earaches myself, but the doctor couldn’t find anything wrong. But it started getting really bad.  I couldn’t touch the side of my face. I went back to the doctor, and she still couldn’t find anything.  That night I was using a heating pad on my ear and I noticed Rosie’s ears were way down on the side of her head, not a normal position.  Rubbing her ears I realized she had an earache.  First thing in the morning I ran her to the vet.  She had two seriously bad internal ear infections and a ruptured ear drum.  They flushed her ears and repaired her ear drum.  My earache disappeared.  Maybe we have this link because Rosie and I are closer than most people are to each other. I do know that when I’m sick, she responds as if she is sick also.

The Poem of Creation


     A matter of making connections

Getting into each other’s heads should not be surprising. But before I  connect Rosie and tips on schoolwork or brushing our teeth, let me back off a bit and give a fairly respectable “scientific” explanation about why we don’t get telepathic messages all the time. We’ve become comfortable, for example, with the idea that our living rooms are chock full of round-the-clock radio and television broadcasts – programs that can be picked up anywhere on the planet, even out in the solar system, if our receivers are tuned to the right frequency. Ah, but, as Thoreau observed, “few are the ears to hear.’

Recently a radio was created at the University of California that is 10 nanometers thick and several hundred nanometers long.  (A human hair is 50,000 to 100,000 nanometers thick.) It works by vibrating thousands to millions of times a second in tune with AM and FM signals.



Telepathy and the Way We Learn


Brains are transceivers that may be set vibrating to frequencies of kindred transceivers.


If there was a clear channel between Rosie and Sandra, as indeed there was, then of course they  got each other’s  messages.  Not getting them would be the strange thing.

These messages are not in English, of course. When Sandra speaks of  Rosie telling her things, she says “I felt she was telling me,” “I’d wake up feeling her talking to me.”

How to learn physics

These messages are in the language of nature, of which human language is a pale abstraction.


In fact, interspecies communication involves a different kind of packaging altogether, a way of looking out at the world as if you were the other entity.  A kind of letting go takes over.

Teaching a dog English is about as possible as teaching English to a rock.  The dog simply doesn’t have a receiver that can decode linguistic structures. [And, gee, what a surprise: If a teacher and a student aren’t tuned to the same frequency, guess how much communication can take place.]

Here’s the good part: Messages don’t have to be encoded and decoded in human language  patterns.  In fact, human languages are an infinitesimal speck in the scheme of things. And the job gets done all the same. Any English sentence comes encapsulated in a field of information that’s washes over  all entities – such as us humans –  within earshot (and beyond, not doubt). The “lesson” of any school class involves all that, not just the physical sound coming out of mouths.  The message for us all?  Aw, Marshall McLuhan, you were SO right.  The medium is indeed the message.


The Need to Let Go

When you think about how most humans spend their days – even though it’s as natural as can be to pick up transmissions – it may not be so strange, after all, that we miss out on the messages enveloping us.  How often do we let go of intention, lie down in the grass, and let the world speak to us?

Soul in grass

Soul lying down in grass

Ah, yes, telepathy is not so mysterious when we recognize that most of us don’t pay a lot of attention.  Our growing dependence over the past several centuries on the abstracted world of linguistic structures has estranged us from the world of our noses and hearts  and the intelligence they download.  Rosie and Sandra used them both.

And you can, too, reader.  So, how do I use ‘telepathy’ to learn, understand, know, anything?  I allow myself to fall into the medium –  in a physics class, in the new-car showroom, embarked on a new date.  I let it wash over my senses.  I let it massage my nervous system. (Thanks,  Marshall.) The doors of perception open.  But the message is never in the words. Words are merely the vehicle.  Whitman asked, Why, who makes much of a miracle? Good question.



An A student

Natural Learning on Purpose

The way to make use of our natural learning ability is to make sure the our senses and our nervous systems are ‘turned on’ and then to let nature do the rest.   Years ago, a first-grade teacher wrote on  my dear little daughter’s homework, “Try harder, Kathy.”  No, no, no! Try easy!  Your Self knows just what to do.  Let it.

The Heart – The Missing Factor in Most Classrooms

Learning by Heart

Mark Rothko

–Mark Rothko painting

How can you get so good at something that it seems like magic?  If you’ve ever watched a tech work on your computer, you’ve seem her zip through dozens of steps in seconds – without even seeming to have to think about it.  Well, the fact is, she doesn’t have to think about it, and thinking would actually slow her down.   How the hell do people  get so damned good at stuff like this?

Contrary to what lots of teachers commonly say, it’s not by working hard at it.

It’s because they fell in love.

If you want to get good at something, fall in love.  If you don’t love it to start with, fiddle around till you find a door to it’s heart. Then let your own heart connect with its heart.   When you do, you may find yourself spending hours with it, but just like when you’re in love,  you will not even notice.  And no hard work is involved.

My fossil in rock

To get to know plum blossoms,
Both one’s own nose
And one’s own heart.
                                                  — Basho

How it works.

Where did my older brother study French when he was in Europe in WWII?  In bed, of course. You can learn paleontology that way, too, or linguistics, or . . .  you name it. And the heart is the secret ingredient, not logic, not the mind, not sweaty thinking.

We learn with our hearts.

When you fall in love, all the conditions for absorbing the “other” are there.  You fall into the pulsing ruby heart of the matter and become one with it. It’s the same with everything you ever truly absorbed into your nervous system. You’ve been doing it all your life.  If you buy into this metaphor, you can let yourself fall in love on purpose with anything, anything at all, a school subject, a maple leaf, Jupiter, a fly speck.  Take a moment an let that sink in.

If you want to get good at anything, let yourself fall in love with it.

“Get” that principle of learning and you won’t have to worry about getting to know anything ever again. If I’m wrong, sue me.  If I’m right, pat yourself on the back – and send me a check.

To Learn Is to Love

Here’s a little love story about how a dog and a human I met, Rosie and Sandra,  learned/loved each other so thoroughly that their communication seemed like – as it may well have been – telepathy.  It’s a fairly detailed story but too long for one posting, so I’ll give you just some highlights here.  There’s a key in this story to a way of learning for anyone, maybe for  you.  Watch for it.

The Time You Spend

“Muad’Dib learned rapidly because his first training was in how to learn. And the first lesson of all was the basic trust that he could learn.”Dune, Frank Herbert


AP student getting an intense vision of the facts.

In the midst of exploring interspecies communication for a book I was working on, how it is that humans and other creatures – parrots, horses, chimpanzees, dogs – are able to get into each others’ heads — what the mechanism of that is, the biology of it, the physics of it, I got an email from our daughter Kate,  who was gathering data for  a government study in the Modesto area out in the San Joaquin Valley.


I’ve just met an eleven-year-old boxer named Rosie who can do all sorts of things – square root, spelling, getting the remote for the tv – really wild!  Her owner, Sandra Artrip, asked me what my name was.  I said ‘Kate.’ She asked Rosie how many letters were in ‘Kate.’  Rosie tapped 4 times and then cocked her head –“Is that right?”

 Well, that sounded like an unusual dog indeed, so I emailed Sandra and got this reply:


Rosie’s the smartest animal I have ever had in my life, and I have owned many, many animals. Just a quick view of what Rosie can do: Rosie can add, subtract, multiply and divide. She knows her ABCs by sign language. She knows squares and square roots to 144. She knows how many letters in each of  all the primary colors, she knows the states, and about 250 words. She is also a certified service dog.  She turns lights off and on, gets five flavors of soda out of the refrigerator.  She gets towels, washcloths, paper towels and toilet paper and shuts doors.

Also, she does typical dog tricks like high fives and  low fives, and lies down, rolls over, plays dead, speaks, sits pretty, and says the words mom, I love you, go bye bye, no, damn, I’m hungry, playtime.  That probably sounds crazy to you, but I can hear the words plain as day.

I have had vets tell me dogs do not have the ability to do what she does, but I know for a fact she can do it, and after my vet saw it, he could not believe what he saw.

As Smart as You Need to Be

A very, very smart dog?  It may be that lots of dogs don’t learn what their human companions want them to because they don’t feel like it or are too aloof to learn stupid circus tricks for the amusement of humans.  Another boxer I know, Lucy,  seems able to pick up any behavior her human wants – if she feels like it.  Sandra teaches Rosie with food rewards.  Her brother never uses treats with his English bulldog.  His bulldog  thinks  playing dead, doing high fives, rolling over, and performing all sorts of tricks  is marvelous fun.  He does these things not so much to please his human, it seems,  as to participate in the game. Our wire-haired terrier Geordie was the worst student in his obedience class.  I figured on being humiliated when it came time for graduation.  But when our turn came, Geordie trotted at my side out to the middle of the floor, sat down nice as pie, and received his diploma in front of the whole class with dignity and aplomb.  Training – what a colossal bore.  It was more fun trying to bite the Doberman.


“More input! More input!”

Whose Poem Is This, Anyway?

Maybe we’re all, humans as well as dogs,  as ‘smart’ as we need to be. (And maybe school teachers need to think about this.  Who’s business is your education anyway, yours or some “teacher’s”?)  The great news is that  if we can find out how it works, maybe we can get smart on purpose — whenever we feel like it, of course.  That would come in handy, wouldn’t it, when you need to figure out why you  can’t get your cell phone to pair with the device in your  new car or you have to take some required college course you couldn’t care less about. It ain’t gonna happen unless you yourself want it to.

“It’s gotta come from the heart if you want it to work.”

Here’s the chorus from Kathy Mattea’s “Comes from the Heart”  In my college skills classes — and often in other courses, too — I used to play Guy Clark singing that tune.

You got to sing like you don’t need the money
Love like you’ll never get hurt
You got to dance like nobody’s watchin’
It’s gotta come from the heart if you want it to work

If you have the time, you should stop right now and listen to the whole song; it’s great: http://www.cowboylyrics.com/lyrics/clark-guy/come-from-the-heart-32.html


What circumstances might have influenced Rosie’s ‘intelligence’?  I arranged to go out to the valley for an interview.  There were four assorted dogs in the chain-link fenced front yard when I pulled up, but Rosie, almost twelve by then, was inside, where it was more peaceful.  She was a brindle boxer with a gray muzzle, stiff joints and advancing hearing loss who accepted a couple of Trader Joe peanut-butter flavored treats from me. Then we all three  sat down on the couch – Rosie in the middle with her paw on Sandra’s lap  ‒  and we got straight to the interview.

Time Spent on Your Rose

I knew Rosie had been taken from her mother a little over two weeks after birth.  She had been  infected with coccidia – a parasite of the intestine that can destroy young animals –  and had been about to be put to sleep.  Sandra took her home.  Most puppies are placed with humans after they’ve been weaned – at about eight weeks – so Sandra had to take over the mother dog’s job of nursing, which involved bottle-feeding Rosie every two hours twenty-four hours a day until she weaned herself about three weeks later.  It took seven months of treatment before the coccidia were completely eliminated.  During that time Rosie and Sandra were together almost constantly, as they have continued to be ever since.  Aha, it’s the time spent on your rose!

It’s the Time You Waste on Your Rose.

To get into each other’s heads – or some prehistoric fossil –  we have to waste a lot of time on each other. (If you waste enough time on it, even a bit of old bone will begin to sparkle.)

I asked Sandra if she thought the way Rosie started out in life, the mother role being played by a human rather than a dog, might account for much of her phenomenal responsiveness to Sandra’s teaching.   That seemed likely, Sandra said, since she  hadn’t done doggie things with the puppy.  She hadn’t wrestled with Rosie or held her down when she needed discipline  the way her natural mother would have.  Rosie had had to pay close attention to cues from the only mother she knew and had developed a unique psychic and physical bonding  with a human.  Getting into each other’s heads may be no more complicated than that.

Sandra had had lots of dogs and Rosie did far more human things than any of the others. Of them all, only two came close to being as smart as Rosie, and like her, they had been taken from their mothers at a little over two weeks of age and hand fed by Sandra.  If they had had round the clock teaching the way that Rosie had had, might they not also have become ‘smarter’?

Unique in all the world

Saint-Exupéry’s Little Prince had his own flower, a rose  he had tended every day and thought was unique in all the world. But in his travels he discovers there are millions of roses and is saddened to think that his rose is not so special after all.  Not so, the fox informs him,  “It is the time you have wasted  on your rose that makes your rose so important.”

The Time Wasted on Rosie

To get Rosie to  flip the light switch on or off, Sandra would hold Rosie’s paw over the switch, click it with the paw, say ‘light’ and give her a treat.  She did this  every twenty minutes or so, two or three times each, but not more than that so that Rosie  wouldn’t get bored.  The lessons were spaced out with only a few repetitions at a time.  Once she caught on to the process, Rosie got faster and faster at learning all the things Sandra had listed in her email. (Recently Sandra had to get a dog-proof refrigerator.  Her other dogs had watched Rosie and were getting into the old one any time they felt like it.)


Mark Bittner wasted tons of time on these guys.

What’s striking about Rosie and Sandra getting ‘inside each other’s heads’ is that the process is identical with the way one gets to ‘know’ anything, an ipod, crab apple blossoms, the  world inside an atom, a cherry-headed wild parrot, an autistic person, The Philadelphia Philharmonic Orchestra, or a peach pie.

Sandra had had an absorbing interest in animals of any sort – she had even had a petting zoo at one time.  Getting to know something  starts out, usually, as a playful curiosity and becomes so absorbing that one forgets lunch and dinner.  That’s always the key, an involuntary relinquishing of objectivity; you can’t help yourself.  The situation opens to you and you fall in.  When the wall between the worlds dissolves, the skateboard and the skater become one.

The Wall Between Worlds

                                                                          The Heart of the Matter

The Heart of the Matter

Sandra had taken on the role of surrogate mother – with no strings attached.  There had been no barrier between the two mammals – tiny puppy and human – and there was physical contact during the feeding.  Information flowed back and forth between the two organisms, altering the wetware in each other’s skulls, absorbing each other’s sensory data.  They were quite literally inside each other’s skulls and on each other’s senses (and deeper still, in those pulsating subatomic frequencies sheathing the ‘physical’ world).  The puppy’s brain absorbed Sandra’s world and reconfigured itself.  The human brain absorbed the world of the creature in her arms.  No wonder Rosie turned out to be so smart.

This is always how the curtain between worlds is drawn aside.  Richard Feynman walks around inside the atom.  David Greybeard, a wild chimpanzee, touches Jane Goodall’s hand on a river  bank in an African jungle. Interest, attention, absorption.

Once you fall into each other, you have each other’s ‘number,’ and you can ‘call up’ each other.

Once you fall into each other, you have each other’s ‘number,’ and you can ‘call up’ each other.

In the midst of exploring the atom, say,  you get absorbed into it; meanwhile, the atom has got inside your head and heart.  It keeps on chatting with you, revealing itself even when you’re out sailing or watching ant trails across the kitchen floor.  This is how one can ‘talk’ with a rock.



And then there’s telepathy – which goes to the heart of the matter.  In fact, until that breakthrough into telepathic communication – where it is not necessary to translate – the process is not complete. Telepathy between Sandra and Rosie goes on all the time.  Rupert Sheldrake’s Dogs That Know When Their Owner’s Are Coming Home is full of anecdotes of telepathy between animals and humans and between and among humans, too. “If I think of going to the refrigerator, Rosie is there waiting for me as if she heard me say it.  If I think of leaving the house, she will go to the gate.   I’ll wake up from a dead sleep with this feeling that she’s telling  me she needs to go out or that her water bowl is empty.”

There’s more to this story, but I’ll save it for another posting.

Doing Hard Things

No Hard School Subjects

Contact Artist at Work

Calculus Student at Work

x(t) = a0     + a1 cos (wot + q1) + a2 cos (2wot + q2)
+ … + aN cos (Nwot + qN)



In my December 8, 2013, post  I said,

You can do anything you really want to do.

Here are three ideas from that post:

  • No one taught you how to learn; you were born with that ability.
  • You have a brain that solves problems for you.
  • You don’t solve problems with your conscious mind.

No More Difficult Than a Banana

For far too long I used to think there are some really tough realms out there –  walking the Appalachian trail, understanding particle physics, chemistry – all sorts of things I thought were way beyond my reach.  Then one day it came upon me that those “difficulties” were not out there at all.  “Difficulty” was an idea in my head, not an aspect of whatever it was I was looking at. What I was looking at didn’t come with a label reading Very Difficult Stuff. What a great insight that was.

Come to think about it, you shouldn’t get out of bed without knowing there’s nothing outside your head that’s hard or not hard.  “Difficult” is an idea you have about something.  That “something” is totally indifferent to whatever labels you throw at it.    All those strange squiggles in a calculus book or a chemistry book? They’re  just there.  They’re no more “difficult” than a banana. They don’t bite. “Difficulty” is something you decided.   (Do you really think card sharps, pickpockets, magicians started out that way?)

I’ll get back shortly to how you can get the upper hand on any school subject – no matter how “tough” you may have decided it is – or anything else in your life – once you know that it’s you who decide.

A Pink Rubber Ball

Contact juggler Richard Hartnell, Photo by Mike Kepka, The SF Chronicle

Photo by Mike Kepka, The SF Chronicle

Here’s just one anecdote from among a drawer-full  I’ve collected over the years of “impossible” things people have mastered.  I read in the San Francisco Chronicle (9/16/13) about a contact juggler named Richard Hartnell who does such magical things with a pink rubber ball that people toss folding money at his feet just because he’s so wonderful – which turns out to be plenty to pay his rent and food bills. [See for yourself:  Richard Hartnell Contact Juggling in London – You Tube]

When he was three, Hartnell saw something he thought was wonderful, a scene in Jim Henson’s Labyrinth in which David Bowie appears to magically manipulate a small crystal ball with the tips of his fingers.  The magician was actually Michael Moschen hidden behind Bowie and doing the juggling “blind.”  Moschen’s juggling, Henson said,  was the closest thing to real magic he had ever seen.  That bit of magic so impressed Hartnell that later as a teenager he bought a pink rubber ball and tried to pull off what Moschen had done.  Well, reader, you know what’s coming, don’t you?

I messed around and I did everything wrong,” Hartnell told the Chronicle reporter Mike Kepka.  “It got so hard I stopped.”  I’ve know thousands of students – and myself, too, when I was younger – who bumped up against something too hard . . .  and stopped.  But, then, here’s the great thing Hartnell learned, and it applies to just about anything:

The technique was called contact juggling and,  looking back, Hartnell called learning that technique “a really bad learning curve. It’s not like regular juggling, where you can learn to juggle three balls in, like, a weekend.  Contact juggling sucks for a long time.  It’s like the violin of juggling.” So he stopped, but later on he witnessed some amazing fire juggling and decided to give contact juggling another try, and after some relentless practice, he developed the ability to do the basic moves.

Practice Is Magic

Here’s what Hartnell said about that stage of learning a “hard” thing, and it’s something every learner needs to know and accept:

“You just have to be really open to being terrible at something. Generally, if you can think about it and practice hard enough, you’re going to get it.”


Balancing the ball on the outside of his bent elbow, he told Kepka, “That took me six months to learn.”  What he added was such a profound insight that I’m putting it in bold type: “I think practice is magic.”

The Role of Feeling in Problem Solving


It’s a feedback loop.


How you can get the upper hand on any school subject:

Once you begin to catch on to something, you want to do it more.  You can feel the rush of pleasure – I got it! – and you want to keep going.  Moving a 90mm ball around his fingertips, Hartnell went on to say, “This is what I want to do and get better at.  It’s a feedback loop. The more you do it the better you get at it, and the better you get at it, the more you want to do it.”

The Mess-Around Theory of Learning Re-visited


                                                            How to study

How to Study

Differential calculus: Take a little pail and a little shovel, open your textbook and  start messing around just the way you used to at the beach. When you were three, playing in the sand was not something you had to do.  And even though you may never have been there before, you did not think of it as hard.  Well, differential calculus is a sandy beach.  Play around in that sand and pretty soon, you’ll start to notice little things, and after a while you’ll begin to get curious. Go ahead.  Do everything wrong.  Sooner or later you’ll do something right. Hmm.  Before  you know it,  you’re making a castle.  While you’ve been messing around your non-conscious mind was busy sorting things out, piecing together a pattern, telling your conscious mind what tools you need.  You know exactly how this works.  You’ve been here many times.

JOY in Chinese Letters


There are no hard subjects.

Taking Hard Subjects — The Golden Apples of the Sun

There are no hard subjects

Though I am old with wandering

Contact juggler Richard Hartnell, Photo by Mike Kepka, The SF Chronicle

Why, who makes much of a miracle? —      Walt Whitman

Through hollow lands and hilly lands,
I will find out where she has gone,

And kiss her lips and take her hands;

And walk among long dappled grass,

And  pluck till time and times are done

The silver apples of the moon,

The golden apples of the sun.”

— from “The Song of Wondering Aengus,” W. B. Yeats



The Easy Way to Do Hard Things

Long ago, I gave a little ten-minute talk as faculty speaker at a graduation ceremony at at my college.  I called it, “Things We Forgot to Tell You.”  The gist was that everyone is lots lots smarter than they realize.  When you think of what all you’ve  learned from the instant that sperm hit that egg, never mind what all the sperm and the egg brought to the party,  it would be incredible if it weren’t such an everyday event. Here’s just one infinitesimal thing you deliberately learned when you were a tiny little kid:  You learned to pick up a pencil.  If you look at a little baby at McDonalds  amusing herself with a bunch of her mommy’s keys, you see how you did that.  You were educating your fingers, you were educating your eyes, you were educating your taste buds (you were always putting things in your mouth) — and your parents didn’t even notice.  You did that on your own.

No one taught you how to learn; you were born with that ability.

Contact Juggler at Work

Contact Juggler at Work


The mere process of learning to pick up a pencil involves innumerable bits of data collected into a pattern of knowledge stored in your brain and in all the stuff that makes up a human organism.  And you know what?  It was child’s play.




Your Own Very Personal Computer

If all my students — and all readers of this site — understood this one thing about how they learn, what really happens when they solve a problem or when they learn how to do something, I’d be even happier than I am now. You have to get over the idea that you solve problems with your conscious mind.  You never do. It’s always done elsewhere, out of conscious awareness, in your non-conscious mind.

Prove this to yourself by watching how your mind works as you go about figuring something out.  Have you noticed?  You can actually watch yourself thinking.   Give it a shot. You’ll see

                       You have a brain that solves problems for you.

I didn’t know this about myself till in the late 70s when I was pushing 50 and bought my first personal computer.   It cost a lot of money, and I didn’t have anybody to hold my hand while I tried to figure out how to make the damned thing work.  All I really wanted it for was word processing.  I was sick of having to re-write manuscripts, re-number the pages over an over again as I plowed through even tiny revisions.  So here I was with this thing that should have made composing and editing easier, and I was sweating and having lots of self-doubt.  Even the simplest word processing — bold print, italics,  all sorts of things, spelling errors, commas — required special instructions to the computer. It was hard, and I was not happy about it. Then I left the computer at home and went up to Flathead Lake for the summer and never thought about it  — or anything academic — all summer long.  Now here is the good part, and this is the part you have to  “get” totally, so pay close attention:  When I got home and fired up the computer, everything that had seemed so  hard made all sorts of sense and was effortless!  Wow!  It was the first time in my life — geez, what a slow learner — that I sensed a powerful brain solving a problem for me without my consciously lifting a finger.


Man’s Best Friend


Then I reflected on how I had actually “learned”  things in my life that had seemed hard and then weren’t hard at all.  How much better and surer I was driving home from getting my driver’s license than I had been on the way to the test, learning to read, to ride a bike — all that stuff we all know how to do but once didn’t.

Since that day, I’ve used this awareness time and time again.  No matter what strange country I visit — from  wiring up a three-way switch, to teaching myself Spanish, to matting  and framing paintings, to designing this website, to learning some HTML coding —  I know I have a pal inside my head who loves to figure things out.  That’s how I came to develop the Mess-Around Method For Every Occasion that I explain elsewhere on this website.

So here it is, reader.  What I learned to do on purpose is this:

Mess around till it’s clear what needs to be done. Sometimes that’s the big question:  What the hell is it I want to happen here?  What do I want to be able to do?  What do I want to understand?  If you can mess around and boil it down to a clear question, I can guarantee you your brain will get to work on that and will send you the answer — if you’re listening, of course.

When you’re in the mess-around phase, you’ll be amassing bits and pieces of unconnected junk.  You’ll be noticing things here and there, some of it even making sense.  Meanwhile your non-conscious mind will be piecing all that together, making a pattern, making it all add up.  Yes, it will.  This I guarantee.

Before you decide I’m totally nuts, try it out.  Watch your brain go into gear.  See how it works.  Once you see what and extraordinary thing you have up there in your head and see how to use it, you’re on your way to a full and joyful life.





“Always the beautiful answer the more beautiful question.”





Don’t waste your time taking notes. 

Don’t let your school work interfere with your education.  – Mark Twain.




The Universe posing as students taking notes

If you write down everything that happens, you may as well be a stenographer.  Stenographers are paid to do transcripts, not to understand what a lecture boils down to.  That’s what you’ll want to know, and you can’t be actively looking for the big idea and writing down stuff at the same time.  Yes, I know people are always advising you to take notes.  It sounds terrific. These  same advisers, like Polonius,  will tell you to be good, work hard, always say thank you, and use your napkin.

If you get to class a bit early, though, you can get your mind in gear but thinking about what happened last time and what’s likely to come up.  That’s called formatting, and what it does is set up a little web in your mind, a little skeleton,  so you’ll have someplace to lodge big ideas that come sailing by.

Your Own Invented Shorthand

Native Speaker

Expert Note-taker

During class, as a sharp observer, you will have jotted down – while the lecturer was clearing her throat – maybe half a dozen words or phrases in your own invented shorthand mixed with abbreviations and texting-type stuff.  You’ll have put those key ideas into your own words,  words that will jog your memory later on when you want to recall what that lecture boiled down to.  This is the sort of thing a self-respecting human being who values his or her time here on Earth, obliged to play the school game, would be doing.  You’re in charge.  You call the shots about how you deal with lectures. Speakers has there purposes; you, I would hope, have yours.

Your job is to watch for the main point. 

There will be only one.  You could be asking yourself, “What’s she getting at?”  If you figure that out, then you’ll want to know how she justifies that point.  She’ll probably have two or three sub-points.

Finally, while everyone else is escaping by the nearest exit, you will look over those bare-minimum notes you took.  You’ll be thinking, “OK, which of these is the big idea?”  You’ll mark that with a star or you’ll underline it or highlight it or put a big Roman numeral I beside it.  Then you’ll decide which are the key sup-points and mark them 1, 2, and 3 or A, B, and C.  And just to clean it all up, you’ll add any reminders that seem suitable.

Finally, finally, while your still sitting there, write down in your own words, the fewest  possible, the gist of the lecture.  If you skip this step, within a few minutes you’ll forget 80% of what you just sat through .  That’s just the way short-term memory works. This step reinforces what you just culled from the lecture and moves it into your long-term memory, which is where it needs to be.


Words are the source of misunderstanding. — The Little Prince



Then you’ll go relax and see what’s happening in your neighborhood.






[You can Google Jennis Jerz’s Web article: Taking Notes: 5 College Success Tips/ Jerz’s Literacy Weblog for some more good ideas.]