Jacob Lavallee's Somewhere in Between
dances gently through to the place
without limits.
Quietness sings
Music, simply and quietly, moving me to stillness.
Quietness in musical form.
The quietness moves through easily.
The heart opens to simple beauty.
Light falls gently.
This moment becomes home
The Inner Quietness of Snow (IV)
a silence falling, filled with light
crisp
sharply fresh
sunlight, dancing its way through the clouds
flowing stillness
quiet singing
the white light of tiny crystals singing together
quiet poetry
moving light
the poetry of sunlight, falling gently down
---
the inner quietness of snow illuminates everything
Sadness Sings Quietness
underneath anxiety, there is only sadness
slowing down to feel, anxiety dissolves into sadness,
into memories of loss
quietness invites those deeper notes of memory ... memories
waiting the release of healing
sadness sings
sadness becomes stillness
stillness, Infinite Life
Infinite Life, songs of healing
________
sadness sings quietness,
Quietness gently singing healing into being
Fragments
in the space between
silence sings
and light shines through the broken places
inspiration comes quietly
The Inner Quietness of Snow (III)
music from silence
the white light of tiny crystals singing together
poetry from sunlight, gently falling
the inner quietness of snow illuminates everything
The Inner Quietness of Snow (II)
silence, singing
the white light of tiny crystals singing together
quiet poetry
moving light
flowing stillness
the poetry of sunlight gently falling
_____________________________________
the inner quietness of snow illuminates everything
Waiting for the Music
I am working on a post focused on eight (by one method of counting) intertwining mathematical threads. At the present moment, a significant part of my attention is centered on exposing the simplicity and beauty and connection that become obvious when you are immersed in the experience of the mathematical poetry these threads illuminate.
The eight pieces are (order not significant) the area formula, the Gauss map, curvature measures, Gaussian curvature, degree theory, Gauss-Bonnet theorem, mean curvature, and the tube formulas.
I suppose the key feature of this quest for the somewhat elusive music I hear when immersed, is the persistent conviction that there is some way to share this experience using (relatively) simple language and tools. This belief is founded in the experience (over and over) of the deeper, core essence of something that might at first look complicated, being simple, easily graspable and possible to explain to non-experts.
Coming back to the eight threads, the three core components are (a) the derivative as a linear approximation and the difference between the derivative and its determinant, (b) how sets and measures transform under maps with derivatives, and (c) three technical tools/ideas – Sard’s Theorem, regular level sets, degree theory – that enable us to get where we want to go, and illuminate how we get there. Central to this weaving together of the threads are the derivatives of two different maps – the normal flow generated by a surface with positive reach and the Gauss map of a co-dimension 1 submanifold of \(\Bbb{R}^n\) .
And as I am writing this, it seems to me that a significant part of the beauty is the way in which non-trivial conclusions emerge from the arrangement and collaboration of (a)-(c). Another piece is surely the sense of vital flow pervading the geometric, dynamic experience of seeing and feeling the mathematical realities formally exposed in the various theorems and lemmas. As I have written elsewhere, there is a language that cannot be spoken that is being evoked, triggered in the minds eye, in the heart that can hear those things.
While this might seem much too fuzzy and imprecise to some who read it, I suspect that there are quite a number of mathematical travelers that will resonate with those sentiments.
I believe that the best I can do in opening to others what I see and hear is to write as simply as possible, to not obscure the connections that contain the flow I refer to above, and to explicitly invite the reader to consider that what they are to get from what is written is much more than is written and is only visible when what is written has been internalized, converted to that language that cannot be spoken.
And so, what is written, at its best, becomes a trigger for an experience much greater that what is on the page, for a living, bare-handed exploration engaging the whole person. This is the goal to work towards.
Comment on “In the Company of Bees”
Of the previous five posts, two — “In the company of Bees (Again)” and “In the Company of Bees (and Again)” — were edits of the fifth post, “In the Company of Bees”.
I decided that instead of simply editing the original post, I would edit in full view. So I left versions 1 and 2 so that version 3 could be compared with them.
In general, I think too much polished product and too little process is visible in creative output, whether in mathematics papers, in poetry, in music, in film, etc. etc. While it is starting to be possible to get a look behind the scenes of large budget items like movies, and it is true that Youtuber DIYers sometimes post the full history of a project, it is still the case that creative output very often seems almost magical and not subject to struggle. This is true even if, in some rational, abstract way, we know a great deal of work and struggle was involved. Because we don’t feel the struggle, we can’t grasp the reality of the struggle.
So I thought I would experiment with having all three versions up there. Rubin’s book “The Creative Act: A Way of Being” played some sort of influence here. In particular, just before doing these two edits I read and felt “The Abundant Mindset”, “The Experimenter and the Finisher”, and “Temporary Rules”. I recommend Rubin’s book very highly.
In the Company of Bees (and Again)
A bee at work
Warmed by the sun, surrounded by bees focused on tiny flowers, the artificial, the disconnected, the un-grounded, fades away.
Occasionally, bees sit on my finger as they work. The smell of herbs, the sound of bees, the warm, quiet light, fill my attention. I enter an illuminated world outside the modern flow of time.
The bees and I commune, holding quietness together, inside and outside of time.
In the Company of Bees (Again)
A bee at work
Sitting quietly, surrounded by bees focused on tiny flowers, the artificial, the disconnected, the un-grounded fades away.
The sun’s warmth encompasses me.
Occasionally, bees sit on my finger as they work. The smell of the herbs, the sound of the bees, the undisturbed quietness, the light and warmth, combine to fill my attention, to become an illuminated world outside of a modern flow of time.
The bees and I commune, holding quietness together, inside and outside of time.
The Inner Quietness of Snow
a silence falling, filled with light
crisp
sharply fresh
sunlight, dancing its way through the clouds
a flowing stillness
the white light of tiny crystals singing together
quiet poetry
moving light
the poetry of sunlight falling gently down
the inner quietness of snow
illuminates everything
The Stillness We Inhabit
stillness and words,
music from stillness
time stops, listening
stillness overflows
---
the Stillness we inhabit
sings to us
words creating life
speaking the language that cannot be spoken
In the Company of Bees
A bee at work in our herb garden
Sitting quietly, surrounded by bees of many different varieties, all focused on the flowering herbs, I forget the artificial, disconnected, un-grounded world that large swaths of academia and the other industrial institutions of our modern society have evolved into.
The sun and warmth encompass us.
Occasionally, the bees sit on my finger as they work on a blossom. The smell of the herbs, and sound of the bees, quietness undisturbed, joins the light and warmth to fill my attention, to become an illuminated world outside of a modern flow of time.
The bees and I commune, holding the quietness and light and warmth together, inside and outside of time.
Sacrament and Offering
sacrament
____________
quietness
stillness outside of time
illuminating everything
words
flowing by
silently
stillness
guarding the heart, illuminating
waiting
waiting for living words
words that speak
in the words
flowing by
silently
offering
___________
letting go of words
what remains, speaks
illuminating
in and out of time
Holding Space, Singing
holding space
breathing time into music
music into space
space into time
filling my soul
spilling over
into this place without limits
a quietness sings
space filled with time and music
listening
time singing
music holding space without limit
into the place without limits,
music sings space into time,
breaths time into music,
expanding,
spilling over,
singing
time stops to listen,
holding space,
filling space with music
i quietly pause,
time sings to me
holding space
singing
Listening to “On Proof and Progress in Mathematics”
I first read the article by Thurston titled On Proof and Progress in Mathematics sometime before the summer of 2011 when I used that article as inspiration to teach three undergraduates some analysis through the vehicle of derivatives. This in turn eventually motivated me to write an undergraduate analysis text, In and Around Geometric Analysis – An Invitation. Here is an excerpt from the preface of that text …
I decided to write this text after teaching parts of the contents of this
text to three undergraduates during the summer of 2011. We met 2-3
hours a day, 2 days a week. The next year I expanded it a bit and
taught it to about 10 students – I believe it was 8 graduate students
and 2 undergraduate students. I did not assume a course in analysis
as a prerequisite, though students with and without that background
took the course.
[…]
Part of the inspiration for the course is Bill Thurston’s 1994 Bulletin
article, where he shows a few entries from a list of the different
ways in which the derivative can be understood. He made the state-
ment that “The list continues; there is no reason for it ever to stop”.
That stuck with me. The course notes that inspired this book were
based on the idea that derivatives can lead you (almost) anywhere in
analysis. And to prove it, I did just that, throwing in integration and
high dimensional geometry as needed.
Since then I have regularly assigned Bill Thurston’s article to both graduate and undergraduate students as either extra credit or required reading. I believe this article, with its informal authenticity and even vulnerability here and there, is a good example of the kind of writing that becomes influential because it penetrates more deeply than mere technical discussion. This is not unrelated to the fact that very often, the things we say and do that positively impact others often seem minor to us, certainly not big or even worth remembering. It is directly related to the fact that while Fred Almgren wrote his monster paper of about 1700 mimeographed pages (and is respected for the fact that in this paper there were three truly new ideas — from a conversation I had with Bill Allard), it was his expository papers that were widely read and very influential in many mathematician’s paths of exploration. An example is his wonderful Questions and Answers about Area Minimizing Surfaces and Geometric Measure Theory.
In On Proof and Progress in Mathematics, Bill Thurston describes and contrasts his experiences, first, in his essentially solo work on foliations (for which he won the Fields Medal), and then in his later work on the geometry of 3-manifolds, where he instead created a large community of mathematicians working together, with him concentrating on explaining his ideas and supporting the efforts of others to get involved, to understand the problems. While this entire paper is very much worth reading, it is the last section with the personal stories that is, to me, the most memorable. For stories integrate and ground everything. Reading that story again renews my determination to focus on helping students gain the wisdom necessary to find and maintain the right balance between getting results and explaining things deeply, generously.
Coming back to that course I taught those three undergraduates in the summer of 2011, the piece of the paper that inspired me was a minor point, almost a footnote, in an article focused on what it means to make progress in mathematics, to prove things, to contribute to the advancement of mathematical knowledge (however you define that).
Regarding minor things, former students and acquaintances have sometimes told me how some small thing I have said or done had a significant impact on them. Discussing this with others, I find this is fairly common. Things we might not even remember, that are simply part of who we are or what we do, are often what others find most helpful. Small, comparatively insignificant things, inspire larger significant things. Dwelling a little bit more on this experience, I arrive at a new, embodied sense for significance. Measuring significance (as I now do) by the impact something has on the happiness, the creativity, the ability to thrive for the other human beings in my smallest circles, and then aiming my intentions and attentions at maximizing this kind of significance, the usual measures of significance simply fade away.
The focus on those that you can literally reach out and touch, who need and can use your attention, feeds back into a sense of something accomplished, even when what is being accomplished is slow to emerge. The very act of directing attention, of exercising faith in those around you, in shedding the light that you have collected in their direction, carries in it its own reward.
Planting seeds is a very small part of creating and maintaining a thriving garden. And good gardeners never worry about exactly which seeds grow … they plant the right seeds and then focus on keeping the soil right, supplying water, keeping the weeds out … in other words, they focus on getting and keeping the environment (i.e. the culture) right.
As we inhabit light filled gardens of small (and big) living things, we learn to embody principles making us collaborators in the creation of environments tuned for significance.
Moving back to cultures for, and optimal experiences in, mathematics, when we direct an embodied awareness towards learning to create and helping others create with us, we gain a deeper awareness of how everything we do effects culture. And it is this living culture, created by our actions, that inspires (or inhibits) the rich, creative productivity (mathematical) humans need to thrive.
Set free, the human being integrates the mathematical universe.
Against Awards and Honors, For Appreciation and Gratitude
The reality of work, for so many, is so often so far from the ideal, it seems tone deaf or insensitive to say, “The work, itself, should be its own reward”.
But it must be said for two reasons.
The first reason is that creators of work, business owners, leaders — those that set standards and measure value — so often put profits of one sort or another, ahead of people, culture and sustainable human thriving. As a result of this, many people have accepted the idea that work is not something you do for enjoyment. Some of these employers and leaders then give a tiny fraction of what they accumulate back in the form of awards, prizes, and recognition. This practice is as deceptive as it is stingy, supporting the false idea that excellence and talent is rare, scarce, a thing for elites we should all look up to. In this dysfunctional system of work and workers, work as its own reward becomes just one of many abandoned, betrayed truths.
The second reason is the acceptance by the majority of workers of this state of affairs — the acceptance of the idea that it is OK for work to be drudgery, to lack meaning, instead of the willingness to stand up for themselves in small (and sometimes big) ways, to use their imagination and creativity to change how they work, where they work, how they use their time.
Both sets of people in these two reasons have some responsibility.
But there is a third set of people with responsibility. And it is this group I focus on here.
This third group with responsibility are those in a unique position to help those implicated in the first two reasons see and pursue the cultural healing implied by the vision of work as its own reward.
This third group have work they would do anyway, even if they were rich enough to not work. They understand the power of doing what they were created to do, of having work rich with meaning and intrinsic rewards. Some are well off financially, some are not, but everyone in this group is (some version of) an independent thinker and knows their own muse. And they are all well equipped for the work the next three steps entail.
The first step is the rejection of the idea that awards and honors are a good idea for the simple reason that these awards and honors presuppose a false model of human potential and give life to a morally bankrupt, spiritually blind philosophical system.
The second step is a dedication to helping others see how they can choose a life of independent thought and action, in community with like-minded folk, aimed at spreading the power of this creativity and independence as far and wide as possible.
The third step (really a inseparable companion to the second) is the discipline of following their own muse, of not betraying who they are for the sake of more money, for external awards and honor … to model the power of living on a path full of meaning and creative expression.
(Honors and awards can come completely unbidden, unsought. A life organized without regard for recognition can, nonetheless, garner recognition. The real test for those who have chosen to take step one and are recognized anyway, is how this affects their outlook, their behavior, their interaction with others, their devotion to the three steps.)
Regarding the first task. That awards and honors presuppose a false model of human potential, is a proposition most humans disagree with because of their belief in that defective model and because of the self-fulfilling nature of that belief system which creates an experience validating the broken model.
Awards and honors are a crucial part of why most people look up to other humans, devalue and abandon their own (brilliant) potential, and end up believing they are intrinsically inferior and incapable of truly deep development, deep wisdom.
Awards and honors lead to violations of the command “… have no other gods before me” because the sure effect of giving prestigious awards and honors is humans, looking up to other humans, in a way not fundamentally inspiring or healing, but is instead, deeply limiting, even a sort of enslavement. For all false gods debase, degrade, and enslave.
While it is true there are vast disparities between humans in development, in accomplishment and in productivity, these are not due to corresponding disparities in abilities and potentials, but rather to differences in support, opportunity, emotional and physical health, environments favorable or unfavorable to development, and the fact that many do not know their own muse, their own path of inspiration .
Another contributor to disparity is the lack of hard work, perhaps because of reasons in the previous paragraph, perhaps because of some unwillingness to commit, perhaps because what needs to be done for mastery is not understood, but usually because the path of inspiration has not yet been encountered or some undealt with trauma interferes.
Because hard work is the only thing humans truly have control over, it is the only thing that could conceivably deserve an award. But this is never the reason for awards and honors that give the recipients fame and recognition, awards like Nobel Prizes, Fields Medals, membership in exclusive societies like the US National Academy of Sciences, Olympic Champion, World Champion of <whatever>, etc.
A very deep concern awards and honors should evoke is the way in which, because they are looked up to, those honored are assumed to be sources of wisdom and guidance.
This is a deeply misguided assumption. In fact, the very process by which they gain those honors almost always means they have compromised away (or even explicitly sold out) at least some of their integrity, betrayed at least parts of who they are, and abandoned large pieces of the path on which they would find their wisdom. As a result, this looking up to is dangerous and pathetic — dangerous because they rarely have any wisdom and treating them like they do impoverishes everyone under their influence, and pathetic because results are so tragic, though this is often only visible over longer time scales.
Moving towards the second task, if wide human thriving were the goal, instead of a culture celebrating awards and honors, we would have a culture that handed out appreciation and expressed gratitude broadly, frequently, authentically, meaningfully, looking for every chance to encourage more inspiration and healing, the two fundamental ingredients of human thriving.
Honesty about importance would be the natural state of the many diverse pursuits of excellence.
For example, there is almost nothing in modern science and engineering that needs to be discovered or developed to “improve the world”. Improvements aimed at making the world a “better place” almost uniformly make it a worse place, a fact easily seen if all externalized effects (costs) of the “improvements” are taken into account when measuring “betterness”.
This fiction should be abandoned.
The truth — we need things like mathematics and physics and geology and chemistry and engineering and economics in precisely the same way we need art and music and poetry and literature — would change how we operate. If the goals were first and foremost filtered through a stubborn devotion to “first do no harm” and aimed at an all encompassing goal of true human thriving, our vision of work would be transformed by a radical change of values. Our new principles, our new philosophy, would still drive deep discovery and development, but in a way that promotes truly universal human thriving, in harmony with patience and wisdom, and with wide participation.
This is what must drive the second task.
The third task is the task of not betraying yourself and those that depend on you for inspiration. For the acceptance of the current, broken system is indeed a very deep betrayal of yourself and everyone looking up to you, learning from you.
The current system of awards, honors, prestige, and privilege, reward cleverness instead of wisdom, so that the more honored an individual is, the less wisdom they are likely to have, the more in line with the broken, spiritually blind system they will be. The narrow siloed reality that so many accept as the way to efficiency and universal freedom and human thriving, instead ensures higher levels of honor correlate closely with the lack of wisdom and vision.
The pursuit of promotion, honor, awards, and prestige inevitably leads to radical narrowing and very often an impoverishment of the rich creative potential of those in that pursuit … we trade away our own souls in the pursuit.
We become willing collaborators in our own betrayal.
One of the biggest effects of the siloing encouraged by the accepted, broken measures, is a blindness to true costs, because externalized costs are essentially invisible, almost if by design. And in our blindness we throw away the massive potential of all but the privileged class.
Then, we have become willing collaborators in the betrayal of everyone else … all those masses who pay the externalized costs in their own bodies and souls.
The clear, “the emperor has no clothes” style whole-system measurement leaves little doubt that if the externalizations of cost were eliminated, we would shift towards a system of first do no harm and broad human thriving. Honesty about costs then, is a first step in halting and reversing the slide into the betrayal of everything valuable, everything good. The next steps must be driven by a bold courage to act on what we see, to refuse to be complicit in our own betrayal, to boldly refuse to collaborate in the betrayal with those that cannot or do not know enough to fight for themselves.
When we understand the scale of what we are throwing away in ourselves and others, we are given an opportunity for redemption, an opportunity to shift to a completely different orbit where abundance and a rich vision of what is possible drives and sustains us. Opening to this redemption, we are given the chance to be alongside others in their paths of redemption, to be collaborators in opening the “kingdom of heaven” (here and now) to everyone.
Then our work is its own reward. Then we have found our place, and because we have, others find theirs.
In this new, living system, in quiet awareness of what is actually real, the only sensible response to gifts is gratitude … appreciation and gratitude.
The Power of a Pure Heart
Suffer the little children and forbid them not to come unto me, for of such is the kingdom of heaven
Matthew 19:14
While some, perhaps many, would be offended if I were to tell them that they are childlike, I would in fact be giving one of the very highest compliments I can give. I would probably add a little bit more to make the most likely interpretation positive, saying something like “in the best sense of the word, you possess something I strive for — authentic childlikeness”.
For the power of true childlikeness is immense.
Children live in hope, connected to the infinity all around us, consciously experiencing “Him in whom we live and move and have our being”.
So powerful, even irrepressible, yet so vulnerable and fragile.
The music that could be, so rarely is, and even when it is, is often muted or twisted, the casualty of the war between the world and the kingdom of heaven.
And yet, while children, abandoned and neglected, can grow into twisted, damaged traumatized creatures, frequently traumatizing new generations of children, those same children, guided away from the selfish fear permeating the world and towards a trusting, open generosity, show that a pure heart produces beauty and kindness begetting more beauty and kindness, opening to view an immense, inexhaustible hope.
Surrendering to this hope, to this ability to see and feel and hear, we transcend and begin to heal, returning to the place where we began.
We see again with the eyes of a little child. We lay down the burdens we thought we had to carry. We stop trying to control everything. We begin to live by faith.
What our minds could not comprehend, we now simply experience.
Letting go, we find life and peace and love and joy. And in this transformed place, we also begin to understand, to find wisdom, to know as we are known.
Letting go, we remember the place we began, we become children, again
Letting go, we enter the Kingdom of Heaven.
you do not have to fight
set yourself inhabit this stillness breath wait wait in the stillness wait in the starlight wait in the darkness of remembering wait wait in the remembering of light wait for the dawn to sing wait for the light to shine through the broken places wait inhabit the stillness breath
The Tyranny of Righteousness
The past 7 years has permanently cured me of the attachment to the Liberal Tribe as surely as the horror that Israel has visited upon the Palestinians permanently removed me from the Conservative Tribe 30 years ago.
The insanity and self-righteousness of the cancel culture and woke tribes, the unbalanced liberal response to Trump, the shocking abuse of power by the left in suppression of the truths about the covid virus and vaccines, the suppression of so many true things on twitter (along with some false things) in an “end justifies the means” mode (that ugly demonic principle behind all the horrors of the modern age), and the continuing fight against truth tellers like Matt Taibbi, Michael Shellenberger, Glen Greenwald and Chris Hedges (to name just four) have all convinced me that all the tribes are not only not useful, but actually very harmful if you are interested in the truth, in real health, in a thriving human existence.
And all of this has been done with an attitude of superiority, recalling something I first heard from an undergraduate professor in mathematics. We were talking about some aspect of religion or politics and at some appropriate moment in the conversation he said “Seek those who seek the truth, but flee from those who have found it”. I do not know who first said that, but I am sure that statement, in some form, has been around for a very long time.
Industrial agriculture, industrial medicine, industrial education, industrial media and an industrial (social media) culture have all become deeply corrupt and even fraudulent, often acting in direct opposition to their stated goals. Yet so convinced are they of their righteousness, they will use any means — frequently force, coercion, and deception — to further their ends.
The only real antidote to this violent industrial complex is a firm rejection of the industrial and the global, and an embrace of the local and personal and community and love and wisdom. If we take the pledge to first do no harm, we are forced to change our perspectives rather radically.
Because the woke culture has worsened racism through a deep lack of wisdom and a lack of understanding how sustainable, healing change actually happens, through the mistakes in labeling and identification of the problems, and through its embrace of force and violation of others, I believe that the problems we need to solve when we move to a very local, wisdom-based, love-based approach are harder than they would have been.
The unintended consequences of these social media driven movements are deeply negative, even dark. The dis-integration of human beings and human culture allows the demonic nature of social media to hide in plain sight. Integrated, whole, thriving human beings cannot help but (eventually) recognize that evil nature. But the modern afflictions of materialism and rationalism — by which I mean believing that all there is is what you see with your eyes and that truth is arrived at by a purely mental, intellectual exercise — have resulted in a decay of the traditional regard for wisdom, for spiritual insight and vision. Cleverness is mistaken for wisdom, the spiritual is dismissed as either a fantasy or something cooked up by neurons for some evolutionary purpose. The chance that what we see is an infinitesimal piece of what there is, that truly mystical connections to the large universe exist and that science is not somehow the ultimate tool to solve every problem, is dismissed, usually with ridicule, always with an arrogant confidence.
After the apostle Peter pulled out a sword and cut off the High Priest’s guard’s ear in an effort to defend Jesus, Jesus reached out and healed the ear, saying to Peter, ” … put away thy sword Peter — those that live by the sword, die by the sword …”. In this, Jesus was revealing that the tools we use, dictate the plane we live on. This is the first fundamental mistake that those who indulge in “the end justifies the means” approach to solving problems make. Often, they defeat themselves from the beginning through the choice of tools.
I believe this is the clearest rationale for rejecting tribalism, for all the tribes have given into that principle of darkness, that accommodation of devils, that use of what we should abhor in order to obtain that which we adore.
For in the state of imagined righteousness, we delude ourselves that tyranny is actually loving care, that anything we do must by definition be righteous because we are righteous and that if someone gets hurt, it was worth the price.
We have forgotten “first do no harm”, we have forgotten “love thy neighbor” (to say nothing of “love your enemies”!), we have become blind to the tyranny of our righteousness.
But there is hope. Moving to a place alongside others, insisting on real connections to real people in real places and real time, we move back to the local and back to an orientation towards embodied living, integrated lives, and thriving human cultures based on healing and inspiration.
Instead of “righteousness”, we celebrate healing and inspiration. Then we understand that this is what was meant by righteousness all along — that the old wisdom which starts first with “fear not” and “he heals the broken heart and binds up their wounds” and moves on to “love your neighbor” and “love your enemies”, leads to a human thriving which was, in fact, the precise (and only) goal of righteousness.
living words from brokenness
music moving through, stillness, a radiant intensity
feeling and seeing and knowing, words failing for their feeble smallness, words longing for living wholeness, for beginning again at the very beginning, before the ancient, fractured brokenness
feeling and seeing and knowing, broken words failing, only stillness remains
feeling and seeing and knowing, light shines through the brokenness
words fail, brokenness opens, a Word shines through
a word encompasses, is mind, body, and soul, integrates the universe
quietness overflows
brokenness transmuted into light
healing words, born again through brokenness, light shining through brokenness, brokenness singing radiant, living, infinite stillness into being
light shinning through brokenness, Life speaking new words released by brokenness
feeling and seeing and knowing
you become the words, singing again, whole again, speaking life again
you become that perfect language
for in our healing, He redeems the universe
New Book: In and Around Geometric Analysis
I have finished the first version of the analysis book that emerged from my teaching of the undergraduate analysis class the last few years. The e-copy will always be free and available here.
Update: I am updating the version number to 1.0 since I have read through the notes and made quite a few corrections and modifications. I will also print a few copies.
In and Around Geometric Analysis, November 4, 2023 version
If you want to buy a printed copy from me, let me know. The price will be ~60$ (Getting a firm number soon) plus shipping (if you are not in Pullman, WA and you want me to send it to you). The books are printed by Gray Dog Press in Spokane WA.
Of course, the pdfs will always be free and will be updated from time to time.
Dirt, Gems and the Web of Everything
Transcending the impulse to run away from heresy, eccentricity, and other forms of the rejection of tribalism, yet resisting the opposing, unwise impatience ready to disrupt everything all the time, we can begin to explore and see with a clarity open only to those willing to choose the narrow way.
The mistakes of assuming that what is tells us what could be, that what we can see is what there is, and that truth is something that can be comprehended or encompassed by finite ideas and visions, block us from seeing the infinity open to us in and out of time.
These mistakes block us from seeing humanity from the perspective of what could be.
Believing the self-fulfilling prophecies of scarcity and elitism, which in turn support and promote the foundational ecosystem of fear and greed, we cannot see the misconceptions woven into phrases (and the use of phrases) such as “as common as dirt” and “rare genius”.
The only sound approach to seeing through established illusions, is spiritual in nature and therefore incomprehensible to those that reject the fundamentally spiritual nature of the universe. Yet there are clues visible to everyone, independent of their position on these deeper things, clues in the form of people who exhibit transcendent love and a capacity for healing.
Ultimately, it is the life and death of Jesus, God in human form, that settles every question, that heals all problems, that swallows up all death. Unfortunately, the Christian forms in which “the cross” is adored and worshiped are an empty and impoverished shadow of the living reality that defies containment in anything finite in time or space. And it must defy containment, for this resolution, this transcendent singularity, this ending and beginning centermost to the “things the angels desire to look into”, is the key to all the deepest mysteries.
To believe that every human being truly contains a brilliant gem, a talent capable of an intense, unique, inexhaustible contribution is a truly radical belief. It too flows from that singularity, from that life that opened infinity to man.
But to those that actually embrace this, who are “all in” to the vision making sense of this position, it is also part of a resolution of mysteries besetting anyone who observes honestly.
For the world is too full of extreme evil for anything less that a transcendent singularity to resolve. And only in that resolution can the vision for what could be (what is, in the potential sense), be harmonized with what is (in the immediate sense).
Returning to the phrases “as common as dirt” (and the associated phrase “rare gem”), and “rare genius”, closer examination shows that these actually, already nudge us towards a much more fantastic, rather radical vision of what could be.
For example, it is well known that the rarity of (and prices of) diamonds on earth is artificially inflated by the greed of those that have explored and mined them. Off the earth, it is known, for example, that there is a burned out star (a white dwarf) in Centaurus that has crystalized into a diamond 2500 miles in diameter!
Fertile, living dirt is anything but simple and common, in the sense of unremarkable and comprehensible. Instead the complexity and wonder present in a handful of dirt defies complete description, as it is truly the mother of all living things and complex in the extreme. “Rare genius” is of course just a codification of the illusion that extreme talent is rare due to the fact that the greed and fear overwhelming the world also succeeds in squashing all but a tiny fraction of human potential.
Yet, in the present reality, as experienced by the vast majority of people, the chance to follow their intrinsic muse, to develop the potential they hold, seems far-fetched. It might be considered cruel to suggest that things could be different. Yet I am convinced that the simple truth of what is possible is a great gift, having in itself the power to unleash intense power and light. It is an idea that once grasped could change everything.
I believe it was and is at the core of what Jesus taught.
As a result, I no longer find it very interesting to see talent that has been deeply developed as something to admire … at its best, such development is a call to “go and do likewise”. It tells us what can be, in everyone’s lives, in each path of those that find and follow their muse and use it to bless the world.
The world I want to live in is a world where magnificent things are abundant, living components of an infinite garden, constantly spilling over with life and inspiration, not a sculpture garden of static objects aimed at inciting devotion or disengaged admiration.
This world is accessible to everyone, here and now — as Jesus said “the Kingdom of Heaven is at hand” — but to enter it, we have to be willing to diverge from the “blind leading the blind”, to move through death to life. This paradox of life through death, opening an infinity in every sense, is something that cannot be effectively described, only experienced.
“Come and see”, the phrase ancients used to share transcendent illumination, is still the only authentic invitation consistent with freedom and love.
Deciding you are ready to see, willing to venture into that unknown, the way will open. Life will flow, you will find the Infinity that was always there, surrounding, waiting, eager to illuminate and inspire.
One consequence of the viewpoint above is the decision to pursue discovery for the pure joy of discovery and the even deeper privilege of sharing what is discovered, inspiring an overflowing abundance in the experience of others. Through the companion choices of simplicity and “enough is a feast”, we open the door to the infinite, inexhaustible riches that were there all along. In this kingdom of creativity and living exploration, awards and competition make no sense, if for no other reason than the energy they divert from exploration and the task of sharing.
The scope of this vision has no limits — the good news overflows with the rich, fauvistic music of life, defying all constraining description. The opening expanse inspires stillness and wonder.
The broken ones, in that stillness where the healing began, find quietness, inspiration and wonder in abundance.
And the light shines through the broken places.
The Lack of Courage and Clarity in the Rush to Judgement against Andrea Bertozzi.
I was disappointed, but not at all surprised, by the news that the Association for Women in Mathematics (AWM) had recently decided to condemn Andrea Bertozzi, through facts that turn out (after careful, nuanced investigation) to not be facts at all. The evident lack of care is not surprising, but the incidents point to much deeper problems.
I am referring to the articles you can find here.
Now, while I deeply respect the right of the article and letter writers to write what they wrote, the whole spirit of this ongoing saga, with its deeply religious/ideological perspective — one that crosses the line repeatedly to the “the end justifies the means” principle — is something I find very disturbing.
I suppose that if was in favor of policing as it is, thought that racism was not a problem, or believed that the left/progressive side of things has nothing to offer, I would shrug this off as another example of the “idiotic leftest academics” not getting their facts straight.
But I don’t believe those things.
In fact, I have had very deep problems with the way policing is done, with the cultures that are tolerated, with the extreme lack of wisdom with the new fad of machine learning for everything, and the fact that the data we use is extremely problematic.
So why am I not a fan of this edition of the AWM newsletter?
To begin with, the facts, with respect to Andrea Bertozzi, are wrong. She did not come up with the core algorithm developed by PredPol, the paper by Lum and Isaac did not even use the actual PredPol algorithm in daily use by the company (that, again, Andrea did not develop), and, as can be seen by a careful look here, while Andrea’s name was on the list of organizers, she did not even attend the workshop on predictive policing at ICERM, so she could not have actually led the event. As mentioned above, the PredPol algorithm was not developed by Andrea, as evidenced by the fact she is not on the patent underlying the company and the one paper that has her name on it, was a paper to which she contributed only a very small amount, but again, long after the invention of the method (which is based on a model of earthquake aftershocks). Additionally, the Lum and Isaac claim that PrePol attempts to “identify future offenders” cannot be true, since Prepol only uses the distribution in time and space of crimes (including their types) in their prediction calculations, without any personal data or identification of previous criminals being used. And as others have noted, Lum and Isaac apply this to the one type of data the PrePol algorithm is not intended to be used with — drug offender data. The fact that the perpetrator and victim are usually the same person in drug crimes, is very significant. Finally, since the article was clearly intended for the general public, the speculation and hypothetical nature of various assumptions should have been couched in much more careful language. The “scientism” of the general public often leads them (and, actually, too many scientists) to treat hypothesis and conjecture as fact. (It was only clear that they used the algorithm published openly by those associated with PrePol, instead of the proprietary version used in reality, in their 2018 Medium article. Those acquainted with how what is used in practice differs from what is released to the public, in companies like PrePol, understand the significance of this difference. While Lum and Isaac could not be expected to use the proprietary version, the fact they were not, should have been made very, very clear, especially given the certainty of the controversy the paper would generate.)
There is another fact that seems lost on the writers in the AWM newsletter — the study and description of crime (just one of Andrea’s many threads of research) is not the same thing as its use and does not dictate whether that use is positive or negative. That is up to the (non-academic) culture that the activists are correctly wanting to change.
A deeper, more nuanced analysis, looking for the true source of the negative uses of what academics discover, finds it in academic culture itself, in the culture of separation, disconnection and lack of grounding in the barehanded reality of the world we live in. (As a result, everyone in this saga of judgement and protest against judgement is implicated (to some extent) in doing too little to connect and be relevant — and that includes me!) I am convinced that if those academics that study and discover (all sorts of) things were deeply grounded and connected to the nuanced reality we live in, their empathy would kick in and help them craft how they innovate and how the connect so that the uses of what they discover would be positive.
But, with the facts wrong, and nuance jettisoned, there is no way that the freedom I support in terms of what was written in the newsletter will also get my agreement or applause.
What makes this all the more distasteful is the fact that I agree that data science and machine learning are very frequently, deeply unwise and damaging, and that trauma, the true elephant in the room, is screaming at us to be healed, yet is in actual practice, ignored. We would rather give that trauma a pill to silence it, immerse ourselves in struggles against symptoms, with a deep sense of self-righteousness and an invigorating belief that our adoption of “the ends justifies the means” is OK because what we fight for is so clearly, so good.
For what is being aimed at is truly good. And this is clear to anyone with any kindness or love.
Because, those not outraged by the way many young black men are treated by the police are truly calloused and lacking in basic human decency. Anybody not deeply disturbed by the outrage of what is called the justice system in the US clearly needs help, empathetically speaking, and the fact that so many groups of people have been mistreated in systematic ways is depressing when the comprehension begins to grasp the enormity of it all.
I suspect that the difference, for me, originates in the experience of being raised very religiously, leading to a deep acquaintance with a very wide variety of very enthusiastic coreligionists. While eventually I was led to a personal spiritual walk that might be described as primitive Christianity, not attached to any particular denomination, that did not happen before I developed a deep allergy and acute sensitivity to self-righteousness, to good people believing that “the end justifies the means” if the end you are trying to reach is good enough. I suspect that many of the (typically) privileged souls that are driving the kind of thing we see in the AWM newsletter, do not have similar experiences that would have, at least to some extent, inoculated them against self-righteousness and misguided principles.
But there is something even more disturbing — and that is the silence of almost all the leading mathematicians in this matter. On the other hand, this is not surprising. Prestige and advancement in academia (and in society in general) is systemically biased against boldness, against nuance and wisdom and towards cleverness that masquerades as wisdom, and towards attention seeking that masquerades as boldness. The result is “leaders” and “experts” that lack real courage, have little to no wisdom, and no willingness to risk their social capital for the principles that are the actual foundation of the freedom and rich flourishing that make living a joy.
This is a deep shame.
Because the fundamental aims of the activist — stop the killing, remove prejudice, create a human culture in which everyone can truly flourish — are incredibly important and timely. It seems that there are reasons to think that the current chaos could, with wisdom and true empathy, be transformed into real progress.
But the misguided principles in evidence, the lack of courage and wisdom that can be seen from spending the time to think and see and hear and feel all suggest that this opportunity will be missed.
But, let us say for the sake of argument, that Andrea was actually much more involved in predictive policing (which she is not), was actually making money from the technology (which she is not and did not), and was actually somewhat insensitive to the plight of the criminals police are trying to obstruct (which again, she is not). Even under these (false!) hypotheses, a fair and balanced look at her, to determine whether or not she should be uninvited to give talks (as she has been) or that honors should be rescinded (as they have been) would have to look at the rest of what she does.
Because, even though this is an unpopular idea in the current climate of instant, knee-jerk shaming of people not in your tribe, the whole person must be understood to correctly assess any action of that whole person.
Such a look would be deeply revealing.
Those looking would rapidly find a woman who has bent over backwards to help junior mathematicians, both men and women, who has worked hard to create opportunities for students and postdocs. Digging deeper, they would find some of odds stacked against her that she overcame, that helped encourage her to become the encouraging champion of younger people. They would find, at her core, a very warm heart and someone who is fundamentally kind, even though her energy and enthusiasm for progress can make that hard to see at times when she moves fast and makes things happen.
If in fact, those that have a problem with her took the time to sit down with her, they would see this side of her as well, and the more reasonable ones might see the wisdom in starting a debate with her, instead of a war. Because, they would understand whatever mistakes she makes (she is human) are precisely the kind of mistakes they have made themselves!
In a nutshell: such a strategy would not only have a higher chance of effecting change, it would also reveal that the negative things they observe are not a result of any kind of racism, but in fact are much, much more nuanced and complex — in the same way that they themselves are complex and a mixture of light and dark.
Of course, it is rare to find people who are honest and disciplined to this extent, because it moves them out of their comfort zone (which is another of Bryan Stevenson’s principles of change — be willing to move out of your comfort zone!)
In the end though, Andrea is not actively involved in predictive policing, she is not involved in the company PrePol, she did not actually make money from the company, she did not attend, let alone lead, the workshop at ICERM (that her name was on the organizer list is actually a clear indication of her generosity in lending her stature to those that ask for help), and her real interest is in the science of crime — something that is not the same as predictive policing, any more than biochemistry is the same as Purdue Pharma’s deep abuse of the products of biochemistry).
Actually though, this whole saga is no surprise if you believe, as I do, that the trauma almost all humans experience, is the true source of misery in the world. Trauma is experienced by the vast majority of people, but is almost never effectively dealt with. This unhealed trauma leads to a seemingly infinite variety of dysfunctions and disconnections that in turn opens the door for mistreatment and atrophied empathy. I am speaking from experience here: both my brother and I ended up with severe PTSD after watching both parents die from cancer over an 8 year period, starting when we were both preteens. In addition to that, I experienced severe psychological abuse from an (extended) family member that took years to recognize and deal with.
All this has convinced me that the methods themselves dictate the results, that the means has in itself the seeds for the end you actually reach, and that love and healing are at the roots of all means moving us to any truly good end.
So, while I am a general foe of the idea that machine learning can add anything of value to the world, while I believe that the culture of policing must change, and even more radically, that love is the only thing that cannot be defeated in the long run, I cannot align myself with much of what currently claims to be for progress.
In the same way that so much Christianity has too often aligned itself with evil in spite of its truly phenomenal foundation and (I believe) divine origin, social activism that uses impure principles to get ahead is doomed to fail.
Being intent on helping create an increase in human flourishing, means, for me, that I have to use my freedom to protest the methods of those who claim to be for progress, but instead are adopting methods and strategies that auger against their success.
There is one last point that I believe has been lost because of the lack of imagination that seems to have overtaken our current culture. Instead of simply opposing all predictive policing and “mathematics of crime” methods as fundamentally racist, why not attempt to inject corrective ideas and thoughts into what gets produced? This would have the advantage of simultaneously correcting what is done and building defensible trust between the police and the public. It should be clear to careful observer on both sides, that policing would be far, far more effective and humane with an informed, engaged and supportive general public. The data that could be used to help solve the trouble at the roots of the current crisis is actually only going to be available in a society that is characterized by trust. The evidence for this is very, very strong. It is also clear that in a society based on trust, tools like data analysis can be positive. While I am for thick data and grounded, action based on insights like those in Bryan Stevenson’s Just Mercy, and I also believe the knee-jerk “big data” and “machine learning for everything” instincts are dangerously foolish, tools that mathematics gives us can, with wisdom and constraint, be very useful.
With enough imagination and creativity, in an environment rich with thick data, filled with people having widely different experiences and perspectives, in an environment with a dedication to taking the time to think and see and hear and feel, and a real focus on wisdom and groundedness, the tools of mathematics and the hearts of healed humans can help craft a future that anyone would want to be a part of and in which everyone is welcome.
I suspect, that if I were able to sit down with the letter and article writers, in the patient proximity that Bryan Stevenson so effectively argues for, and we were to actually see and hear each other, the power of that proximity and basic human empathy would enable us to see a path forward based on nuanced awareness of the barehanded facts of each other’s lives. I can easily imagine that while we might not agree on everything, we would agree deeply on the supremacy of the goal of human flourishing for everyone.
Quietness and Confidence
In a world obsessed with data, and at a constantly accelerating pace, the idea that to know, we might need to surrender the idea of arriving there through rational means, seems just silly.
Yet this is precisely what I now believe.
The struggle to express the state of being implicit in the opening statement seems similar to me to the struggle I wrote about in Speaking the Language that cannot be Spoken. Yet the fraction of my energy expended at various times in the pursuit of certainty leads me to persist. For I believe imperfect explanations are better than none at all, at least in the case of this subject.
The search has led me to the wisdom literature and so I begin with two quotes:
“In him we live and move and have our being”
St. Paul
“If any man will come after me, let him deny himself, and take up his cross, and follow me. For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it. For what is a man profited, if he shall gain the whole world, and lose his own soul? or what shall a man give in exchange for his soul?”
Jesus
The last quote has admittedly led to huge excesses and is undoubtedly deeply misunderstood because of the stubborness of the human desire to not surrender control. Yet when surrender to the only Power that will not exploit you is finally embraced, you begin to see this last quote as something entirely different, entirely positive — we begin to see it as the beginning of an abundant, thriving life not built on illuision, one not having to hide from pain in order to be characterized by joy, one that reveals the influence of a living water spoken of so long ago to the Samaritan woman at the well.
Yet, in spite of the almost irresistible impulse to identify the above quotes and associated traditions with Christianity (as a religion or whole family of religions), I believe there is very good reason to consider the (subtly different) alternative of seeing them as invitations to a transformed life from those with insights into how the universe actually works.
This will be a distinction lost on those who are certain “spirituality” is some product of natural evolution, an illusion that will pass from the collection of useful things in the future.
But to those who believe there is more than the material world, that the physical is indeed an epiphenomenon of the spiritual, perhaps this slight shift in perspective will enable them to consider the depth and power of the wisdom in those two quotes and the possibility that the ideas, the paths suggested, should be reexamined, separately from the masochistic fetishes which have attached themselves to ideas like those.
Admitting that knowing is never divorced from faith (small f) is the first step to an acknowledgment of the necessity of the “things not seen”, and a step in the direction of acceptance of certainty as something that must be transcendent, beyond the reach of the finite rational process of thinking, yet somehow intimately connected to the mind.
And yet, certainty — confidence, without qualification — is central to the whole fabric of wisdom and the transformed life we are invited to:
“They that wait on the Lord shall renew their quietness and confidence …”
Isaiah
Letting go of the attempts to save ourselves from inner storms that rage when we resist surrender, we find peace and quietness. Certainty finds us, for we rest in Him and His constant stream of life and quietness no longer finds resistance in us. The same virtue that went out from him to heal when He walked among us so long ago, works its miracle in our hearts, bringing stillness and confidence.
Quietness and stillness, then music — the music emerging from a new stillness marks the dawning of a confidence, a certainty we will never mistake for anything but a gift from Him in whom we live and move and have our being.
Freedom is a Delicate Thing – A Manifesto
The violence of the belief that you have found the way all others must conform to, must give in to, is rarely evident before there are concrete collisions between two different groups with this perspective. But those collisions happen frequently enough that the assertion this belief is violent, is not controversial. It also seems most of us become entangled in these type of struggles in some form.
The universal experience with traumas of one sort or another makes us all susceptible to (or even ruled by) fear. As a result, the understanding and practice of freedom and love in their most natural, primitive and sustainable forms, become casualties to our efforts to save ourselves from these fears. Very frequently, the inspiration at the foundation of a religious practice becomes deeply perverted by these efforts, by these arrangements we make for our own salvation. Shared with a group, there is a sense of deeper validation for this violent perspective.
The false notion that science is uniquely free of this bigoted, religious spirit is quite common these days, especially among those that are insufficiently grounded by first hand experience in the diversity of universal religious forms present in religious experience. Thus, those raised in a nominal Christian household or a household that is essentially (traditional) religion free are at a disadvantage because they are less able to recognize religious behavior in its many disguises, including the current bigoted form of science as a religion.
While I am a Christian in a deep organic sense — and I certainly believe things that the materialist and atheistic thinkers will see as deeply deluded — I believe that Jesus did not come to start a religion, even though I believe he was God in human form, and that his life, death and resurrection form the universal singularity through which all life flows.
The true, spiritual inspiration at the foundation of every religious tradition invariably morphs into religious, institutional forms over time scales associated with how inspiration works. Without constant innovation and deep renewal to overthrow the religious, institutional instinct, the original inspiration is captured and perverted.
It is very important to underline the point that I do not consider primitive Christianity — that organic, deeply personal walk with God, intrinsically individual, based on a direct and living connection between the individual and God — as a religion. It is also clearly not possible to institutionalize this path.
There are similar, organic paths in other religions, likewise avoiding the religious, institutionalized paths.
The principle to understand is that the religious instinct is a universal human instinct, powered by the very real need for connection. But the instinct is particularly vulnerable to the corrupting influence of the drive to save ourselves from fear. It is also true that this instinct, in and of itself, has nothing to do with a belief in God or faith in some mystery, and can just as easily emerge in, for example, an atheistic ideology, because those carried away by any ideology are still human.
The deepest crimes against humanity have always been perpetrated by those motivated by a religious zeal. While deeply evil individuals, amoral and without consciences, have often been key players in these deep crimes, these individuals are rare enough that, without the masses gripped by the religious fervor of that moment, they would have been powerless to inflict the catastrophic harm that ends up being inflicted. Nazi Germany is a classic example of this fact.
While I believe the depth of what Jesus taught in its fullest form is absolutely breathtaking and inexhaustible, this would be true, even if you looked at his teachings as insights into everyday wisdom. His thoughts were universal, deep at every scale, to every perspective. But this is lost sight of because he is seen as belonging to one religion.
Turning inspiration into idols, we are enslaved and robbed of life and light.
We have come to a time when underneath the dogma of almost every group lies a bigoted violence ready to rise up and dismember those that disagree and dissent. While the burning at the stake is not yet a literal experience again, the metaphorical experience is not rare when one questions the dogma in a way that is considered threatening by the group in question.
Take, for example, the battle between conservatives and liberals.
Broadly, crudely, conservatives do not mind philosophical dissent as long as it stays completely philosophical, but dissent that costs money or property becomes something to hound out of existence. Liberals go on the attack when the ideas are heretical, because ideas are somehow the the fundamental touchstone, perhaps because they are less obviously driven by financial greed.
But both groups are capable of great violence, if violence is measured organically, intrinsically, and not just by its grossest, most primitive physical forms. The liberal class uses weapons of ridicule and hate, attempting to bludgeon dissenters into submission, while the conservatives use authoritarian control and financial dominance and subjugation. (At the highest levels, the two methods of operation merge — dissent is fought with every tool in the toolbox of the powerful.)
In very similar ways, the conflicts that fill a world divided into warring tribes have moved us closer and closer to a world ready to sacrifice the foundation upon which everything worth living for is built — the foundation of freedom, powered by love.
Watching this process, we learn that freedom is a delicate thing — it is strong, even invincible, only when powered by a deep, transformative love.
The deep, created harmony of all things, disrupted by equally deep violence, presents a puzzle for an incomplete worldview.
I believe the resolution found in the story of creation and a great controversy between between love and freedom on the one hand and fear and slavery on the other, understood in its deepest, most profound form, passes Occam’s test — it is the simplest, most elegant path explaining life, the universe and everything.
Last Voyage
Beata’s mother, Lucyna, passed away on Tuesday afternoon.
From the instant she met me, very soon after Beata and I married in 1993, Lucyna — Mom — accepted me completely, in a way that moves and warms me every time I think of it.
Mom was a deeply kind soul, generous to a fault.
She loved quietly.
Remembering, I feel it in those deep places opened by grief.
I will miss her so much.
15 years ago, Beata’s father Jan passed away (at the young age of 63). An enthusiastic explorer, playful in his approach to business and life, I was just beginning to know him. I have very often longed for what I know would have been a deep friendship illuminated by his fine mind and warm, adventurous heart.
26 and 22 years before that, when my brother and I lost our mother and father to long illnesses, we became acutely sensitive to the presence or absence of family, to the very few individuals that have opened in the rarest of ways.
With Lucyna’s passing, our son Levi no longer has a living grandparent.
And a large hole in our world has become even bigger.
I used to believe we have had great misfortune. While, in some ways, this is true, I have come to realize that not so many people have been privileged with the intensity of love and inspiration that has been ours.
For those four grandparents of Levi were each giants in their own way.
Lucyna passed away on Tuesday afternoon.
She who loved quietly, faithfully, now rests in Infinite Love.
I will miss her so much.
Verses and Footnotes
I very recently completed the first version of the short book, Verses and Footnotes.
I have a different perspective on writing and editing, including the fact that I am very, very careful about letting the process of editing remove too much. In fact, I think that the real art is in letting there be just enough of what some would call raw or rough traces in the writing to lend real authenticity to the writing.
I think perhaps a better term would be “idiosyncrasies”, instead of the phrase “raw or rough traces”.
But I know that a trained editor might itch to make those pieces conform to their view of writing. And this is not something I believe is the right thing to do if readers are to see into the writers experience, into what they might experience in a conversation with the writer.
Here is a link to the PDF of version 1.1
Link to PDF of Verses and Footnotes, Versions 1.1
The book is now in print and is available for 15$ a copy. This price includes shipping. Simply email me at vixie@speakeasy.net to arrange payment and shipping. (Of course, the e-copy is, and will remain, free.)
Speaking the Language that cannot be Spoken
Though I have gone further in my mathematical career, my past is also filled with music.
Violin performance in multiple orchestras and chamber groups, together with with several concerto competitions and intense practice this required, had a large impact in my life. There is also the fact that my father was a musician, that our family was immersed in a musical environment.
I recently listened to a concerto while watching the notes scroll by. The complexity of the notes on the page were, somehow, not matched by the experience of music in that innermost place — that place from which you play when you perform. I found this experience very similar to the experience of creating new mathematics and then writing it down to communicate what I see.
Why?
Because I believe musical notes on paper and detailed proofs in a book or published paper are both misleading.
The music and the mathematics are, somehow, much simpler in their pure, newly created form. The complication evident in the written form comes from the unnatural way we have to communicate music and mathematics.
When I slowly recall or relive the creation of a proof, whose written form is non-trivial and may even seem imposing, I find the natural state of the proof in the imagination to be simpler, even minimalistic. Yet when written, expanding to something that looks imposing, it is often hard to read or imagine.
In the natural language of the soul, both mathematical proofs and musical compositions sing and flow. But in the language of things written down, we usually lose this living simplicity and beauty.
When we do harmonize the imagining and the telling, it is through the action of a whole person, in real time, speaking, writing, drawing, adapting, listening, responding … finding the music that, for us, connects the inner and outer universe.
For it is the human being integrates the universe, speaking the language that cannot be spoken.
A Guide to Previous Posts: January 2020
Here is a guide to posts so far: I am writing this for myself and anyone else that does not like the WordPress navigation system for older posts. This makes is easier to quickly browse through past articles. The first is the most recent …
- Yunfeng Hu in Seattle My former student is now in Seattle and I wrote a short note about it.
- A Sort of Synesthesia Thoughts on the difficulty in writing about deeper things.
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Silence and Beauty Inspired by Makoto Fujimura’s paintings seen at the Jundt Museum (at Gonzaga University) and videos the experience led me to.
- Ode to My Father Poetry.
- Soul Vibrations Poetry.
- Goodbye Twitter Thoughts about deleting my twitter account.
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- Finding and Following Your Own Path The title is pretty descriptive — what I wrote is pretty autobiographical, inspired by my finding my own path and the power of words.
- Fun with simple analysis problems I: the rest of the story A continuation of the earlier post with the same title, containing an exploration of an elementary problem in analysis.
- The Colors of Memory and Wisdom Reflection on Zeyn Joukhadar’s novel, The Map of Salt and Stars.
- Cultures of Creativity and Innovation Thoughts on Daniel Coyle’s book, The Culture Code.
- Letting Go Poetry.
- Median Shapes A short invitation to explore the paper, Median Shapes, that I wrote with collaborators.
- A Silence, Rich with Inspiration Something inspired by Glynne Robinson Betts’ 1981 Writers in Residence
- Everything is Illuminated Poetry.
- Dual Tyrannies of Data and Democracy (and what to do about it) Being data driven is almost always assumed to be equivalent to correct or right. But the assumptions or axioms that one must have in place to use data are very often unexamined, without nuance, shallow or in some other way deficient. And since when did the majority have an inside track on the truth?
- Other Planets Poetry
- Animals and Empathy My reflections on why I do not support experimentation on animals, focusing on what happens to us when we allow ourselves to participate in these acts of cruelty.
- Freedom and Writing terse notes on writing
- The Space Between Poetry
- Faith Is Connection Reflections on the nature of faith.
- Obi Requiem for our late dog Obi
- Disrupting Digital Delusions Reflections on David Sax’s book, Revenge of Analog.
- Metrics and Inequality Thoughts on how we mislead ourselves in the practice of being obsessed with metrics and idea that this makes us fair.
- Fun with simple analysis problems I An exploration of where a simple analysis problem can take you if you sit with it and listen to it speak to you.
- Finding Quietness Also inspired by Glynne Robinson Betts’ 1981 Writers in Residence.
- Connection vs Attention A meditation on quietness and inspiration that is unleashed by attention.
- Doing Mathematics What it means to do mathematics, why I do mathematics, how to do this in a way generous to others.
- Learning to think and to act Thoughts inspired by William Deresiewicz’ book Excellent Sheep: The Miseducation of the American Elite and the Way to a Meaningful Life.
- Heresy and Freedom Thoughts inspired by the Epilogue of Albert Schweitzer’s autobiography, Out of My Life and Thoughts, Schweitzer’s autobiography and by Roger Williams’ life.
- Using Photography On my beginning to take photogtaphs and my perspective about photography
- Beginning Again Poetry
- An Invitation to Geometric Measure Theory: Part 1 The beginning of a book on geometric analysis — this piece is about differentiation.
- Thoughts on receiving a negative review Inspired by a rude review of a paper.
- Geometric Measure Theory by the Book A review of 9 books on geometric measure theory, an area I work in.
- Higher Education: the real problem is not the cost Short thoughts on four mistaken assumptions about higher education.
- Connection Poetry.
- The Power of solitude … and Social Connection Meditation on the power of a life tha combines time to think and deep connection with others.
- Rage Poetry.
- Stillness Thoughts on stillness and the power of walkabouts
- Anarchy as Optimal Versatility In this perhaps too provocatively titled article, I talk about the advantages of not tying yourself to an authoritarian system and what the import of the phrase Ye are the salt of the earth means to me.
- By the Light of the Moon in Broad Daylight Review of the movie Moonrise Kingdom.
- Cultures of Disrespect Reaction to commonly used phrases in mathematics that are not helpful.
- Scream Poetry.
- Brilliance and Renaissance My reactions to the the documentary The Philosopher Kings.
- First Post self-explanatory …
Yunfeng Hu in Seattle
View From Yunfeng’s New Office in Seattle
Yunfeng Hu was recently moved from EMSI in Moscow, Idaho to a new research team at Amazon in Seattle. He is understandably very excited. Not only is the pay good, but the work is challenging and interesting and he has an excellent, inspiring team leader, Dennis Craig.
As readers of this blog know, Yunfeng was a PhD Student of mine that graduated in the spring of 2018. His work with myself and Bala (and a couple of other collaborators) is talked about in this post.
Yunfeng deserves this — he worked hard as an undergraduate, becoming an expert problem solver and as a graduate student, becoming an accomplished analyst and programmer as well. His internship and following year and a half at EMSI has prepared him very well for this new challenge.
Congratulations Yunfeng — you deserve this!
A Sort of Synesthesia
Experiences of seeing, hearing, feeling, and knowing, often compel me to try to communicate those experiences in some way. A sort of obsession with the beauty, with the experience of being in the moment, undulating, flowing, singing, vibarting, simultaneously opens all the senses and quiets the mind in a way that, at least for me, makes translation into words extremely hard. Sometimes I find the words to transmit something of value, but very often I find what I have written is unconvincing or even completely mute.
I need a sort of synesthesia, making translations from what I sense to words more natural or perhaps even involuntary.
Talking or writing about the experience directly, as though it were a story or a play is something I cannot do. The full experience is so rich, so overflowing, so infinite in possibilities that direct representation is clearly unattainable. But, like visual subtleties easier to see with your peripheral vision, something of the experience can be captured indirectly, by way of analogies, of shadows and impressionistic portraits, in reflection, after the experience.
This is why some of the most effective, powerful art is abstract or impressionistic. To transmit infinity, direct representational art, creating an expectation of finiteness, must be abandoned. Minimalism in music, moving us into rhythms and flows that slowly shift us to different states, is again, a sort of indirect encompassing, carrying us somewhere, but not directly. Experiences in nature align with this method of illumination, gently soaking in, moving us, so that we gradually become aware of the fact that we have been transformed, our attention has been shifted, profoundly altering what we see and hear and know.
Quietness — rich, vibrating, living, infinite — finds its way from our experiences to the experience of others as they immerse themselves in our art.
We have, together, attained a sort synesthesia.
Silence and Beauty
Silence and Beauty – Makoto Fujimura (Jundt Museum)
Immersing myself in the light and color and feeling of Mako Fujimura’s paintings, I listened over and over to Bach’s “Erbarme dich, mein Gott”, as though somehow this experience could open my eyes to the words communicating what I was feeling and seeing.
immersing, drawn into deep stillness, the quietness sings. time stops to listen, to know color and feeling light shines through the brokenness
Words feel clumsy, infinitely poor in comparison to the visual experience. But words can tell my own story of brokenness opening me to light, to color and feeling, to quietness that sings.
It becomes clear. The deep drive to express, to illuminate the experience, can only be satisfied by taking others by the hand and leading them to their own experience of listening, of seeing, of feeling. I can invite others to “come and see”, to know why their brokenness is the beginning and not the end.
For there was One broken for them and that One is ready to shine His light through their brokenness, to pour Himself into their darkness and trauma, to heal them with his Quietness and Beauty.
come and see the quietness and beauty in brokenness
Ode to My Father
Listen to the softly flowing wind creating gentle thoughts,
soft with sunlight
Strong with deep music,
feeling time only by how it sings
Misunderstood by the deaf multitude,
the blind, the dead
Though you sleep,
you live
I am your son
Soul Vibrations
prose surrenders, waiting
poetry, unafraid, waits for words
listening to soul vibrations
colors, moving my soul
soaring
paint the skies in all my visions
infinity pauses, stops to listen
breathing
everything is one
encompassed in the light
singing
poetry is singing
Goodbye Twitter
I really did not have a lot going on in my twitter account. With 27 tweets over a few months, 20 followers and a collection 87 I followed, I was certainly not making any waves. But I spent a fair bit of time collecting those 87 threads to follow and found immersion in twitter threads to be oppressive and distracting, though this sense was more of an aftertaste than an in-the-moment realization. I also found that Twitter did not encourage habits of thought, attention and focus.
I had read Hamlet’s Blackberry by William Powers and Deep Work by Cal Newport, and had rifled through things written by Jaron Lanier (Jaron and I were both hanging around NMSU at about the same time back in the 1970’s, he in computer science, I in the music world, though I do not remember meeting him, if I ever did). Even before this, I had read The Shallows by Nicholas Carr and listened to (and had many students listen to) the Google Tech Talk, No Time To Think, given by David Levy at Google in 2008.
These books and Levy’s talk had in fact inspired habits of taking breaks from the internet and email, something that came naturally for me because I grew up keeping a pretty strict Sabbath one day a week.
Given the experiences with Twitter and the fact that I was now reading Shoshana Zuboff’s book, The Age of Surveillance Capitalism, I began having an internal debate as to whether or not I should just get off Twitter. What argued for getting off twitter was the state of mind I seemed to always edge towards (or even run towards) when focusing on twitter — a restless, distracted state that was very far from quiet. What argued against exiting Twitter was the fact that it seemed that every once in awhile, interesting people would announce something using Twitter. You could discover cool things by browsing Twitter.
Action came as a result of a combination of the internal debate, slowly moving to a Quit Twitter stance, and the part of Shoshana’s book about Pentland’s Lab at MIT. (I was acquainted with Pentland and his lab — in fact, some of my early scientific work was connected to his, in the ares of face recognition.) The description of the Lab and his funders and his position in the minds of many that access his expertise, somehow, pushed me across the decision boundary.
And so, a few days ago, I deactivated my Twitter account. I believe it will be deleted in 30 days.
I would like to have something like Twitter, only slower, deeper, and much easier to tune or customize. But it also seems to me that if I succeeded in getting what I wanted from Twitter, I would be operating in an asymmetric fashion, one that expected others to behave in a way that I would not agree to act.
For the time being I have decided to focus on internet enabled tools and activities naturally co-existing with quietness, with taking time to think, with slowness-of-response enabling time to think. And of course whatever gets my attention and repeated use must be surveillance-capitalism free.
For now, this set of places and activities will be this blog, my arts blog (http://viksekrarts.com), my website (http://geometricanalysis.org), email (several accounts) and things like github and Google Scholar and LinkedIn (for contacts — I never read the LinkedIn posts).
A requiem for quietness can be seen and heard and felt beneath the noise of the mobile device generation. Yet, like the Requiem of requiems, it is also a door to renewal.
Slowing down to be embraced by that requiem, our own responding stillness opens new paths to explore. Dwelling there, listening to the music of quietness and stillness, alternatives to a slide into a shallow, subhuman future emerge.
Finding Depth, Seeing Clearly
The frequent presence of a serious thread of self-righteousness in the opinions and speeches and exhortations to save the earth, to stop hating, to become accepting, to love everyone, to be inclusive, to stop being a racist, to take responsibility, to work hard — you know, to be righteous — corrupts the conversations we need to have, blinding us to where we actually are and what we need to do.
Little that I hear that strikes me as coming from a simple, humble spirit of deeply honest, good will. Perhaps this is because most who have that authentic goodness — that simple approach to making the world a better place — do little talking and no preaching.
Instead, in the opinions and speeches and exhortations (and tweets and posts) there is often a clear dose of hypocrisy or arrogance or self-righteousness (or all three). Sometimes they are muted. Sometimes it is difficult to see anything but these three. The intensity with which this is impressed on me can be overwhelming, perhaps because I am myself particularly vulnerable to the temptation to self-righteousness.
Take, for example, the ongoing circus in Washington DC.
I am deeply opposed to almost all that Trump is doing. From a distance he seems to be a deeply narcissistic bully, to be into precisely one thing: himself. Yet the rhetoric of Trump’s many enemies is almost always very distasteful because of the self-righteousness, the hypocrisy, and sometimes even hatefulness.
This phenomena is not new with Trump – politics has always had these elements.
But in the era of Trump, it is out of control. While Trump has descended to a level that was unimaginable by most before he became president, his opponents have unwittingly become the flip side of the same debased coin they so despise, though this can only be seen in the nuance and the subtle details of the fantasy that is unfolding in Washington DC. This ugly show began as soon as Trump became a threat to the elites who were used to running things. Starting with the mistakes they made in thinking it was impossible for him to win, they quickly settled into the role of full out attack, with little attention to depth and nuance and detail and fairness. (It is not without merit to wonder what would have been if Trump’s enemies had not opposed him with such contempt and hatred, for does this not feed his worst instincts?)
This dearth of nuance, patience and depth is pervasive, extending far outside of the DC fantasy. The shallowness of TED talks, thought leaders and talking-head experts lulling elites into a self-satisfied state of cozy superiority is rarely interrupted by wisdom, deep thought or fearless attention to detail.
Stories in the news, podcast/televised interviews and broadcast discussions all suffer, sometimes to a great degree, from a lack of details and nuance that would put events in a very different light. This is intentional at some level — if there were a real will to produce deep reporting, the money aimed at truly thorough reporting would not be so microscopic. In the battle between thick data and big data, between clever TED talks and deep wisdom, between “faster, better, cheaper” and and taking the time to think, it seems that the big data, the TED talks, and the “faster, better, cheaper” is winning.
One hot topic suffering deeply from the lack of nuanced, detailed, deep examinations is the nature and uses of big data, machine learning and AI. I know that some would claim that O’Neil’s Weapons of Math Destruction, or Broussard’s Artificial Unintelligence: How Computers Misunderstand the World, or Lanier’s Ten Arguments for Deleting Your Social Media Accounts Right Now, and others like them fill that gap. While these admittedly are a small start, these books neither plumb the depths nor exhaust the subject. In fact, they are rather unsatisfying as an answer to the threat that these hitherto undisciplined forces represent.
More generally, non-fiction literature is now dominated by book-length expansions of TED talk or Atlantic articles. There is an idea or two, inflated into a book, often with haste, with little attention to nuance. The time to think and the discipline of patient observation leading to a mastery of the art of waiting, to finding a “feeling for the organism”, is not often evident.
Every once in awhile though, you run across someone who has taken the time to really think, and feel, and see, and then write from a place of true depth and intense focus. While I have not finished the book, I am convinced the new book by Shoshana Zuboff, The Age of Surveillance Capitalism: the fight for a human future at the new frontier of power, is one such book. There is a depth and a passion flowing from the immersive focus that created the book. This intensity in combination with the focus on the threat to the very soul of civilization posed by surveillance capitalism is unique.
I first heard of this book when I listened to Shoshana being interviewed on the NPR show, On Point. I was very impressed. But a much deeper impression was made when I started reading the book.
I quickly came to the realization that I was dealing with the results of deep, focused thoughts I was accustomed to seeing in mathematics (for example, Federer’s Geometric Measure Theory) or in philosophy (for example, Josef Pieper’s Leisure – the basis of culture). An example from Shoshana’s book: though I had thought about the parallels between the ruin brought on the natural world by industrialization and the ruin the information age promises to bring on the human mind and spirit, Shoshana’s book is the first time I have seen someone else put these thoughts on paper. And it was not only the fact that these observations were there, it was the way in which they appeared and the care with which she examined and stated things. Yet is is not a dead, scholastic work, though it is very deeply researched.
Somehow, it is also alive.
While I have not yet finished the book, the parts I have read so far only confirm the initial impressions of depth and thoroughness and even wisdom.While I am sure that there will be things I quibble with, I am certain they will not be because she is being hasty, careless or thoughtless in some way. I am convinced enough of its value to have chosen this to be the next book my own graduate students have to read, the next book for the book discussion group I lead, and the next book that I buy multiple copies of to give away.
In order for us to do something, we have to see things correctly and deeply — that is the thesis behind Shoshana’s book. If we are to do this in the political arena, we must first recognize that things were extremely corrupt, even completely bankrupt at the deeper levels long before Trump came along.
While Obama put a good face on things, he was not getting in the way of the massive transfer of wealth from the poor to the super-rich, nor was he into the truth, if that truth cost him power. Witness how he dealt with Ed Snowden. (Those that think the Democrats are somehow more righteous than the Republicans are dangerously deluded. It is not an accident that “House of Cards” has the psychopathic president in the democratic party.) Listening, for example, to Jame Risen (at http://theintercept.com), you begin to understand that both Bush and Obama were doing deeply disturbing things, that they were precursors to Trump in very important, often ignored ways.
What allows almost all of the elite-bubble inhabitants to miss these facts is the haste with which they seek to know and the elitism that blinds them. Their devotion to the big, fast, crowd and the unwillingness to spend the time to think and see and feel, to wait patiently for wisdom, doom them to a darkness they think is light.
The humility that comes from realizing how all of us are actually susceptible to these errors opens us to the pursuit of depth, to investment in thick data, and, above all else, to a fundamental reorientation towards wisdom. When we prioritize the time to think and attention to the patient search, we begin to understand the intense power of quietness. Slowing down, our eyes are opened to a rich, living path in and through everything. We begin to avoid labels. We abandon the naming so detrimental to our ability to see and to the desire to search more deeply. Where we are and what we see becomes rich with information and nuance.
In this place of deeper awareness, armed with clearer pictures of the complexities and grounded truth, we begin to have a chance of making progress on real problems.
Returning to the work of Shoshana Zuboff, it is this universal lesson that comes as a corollary to a careful reading of her work. Though it seems obvious — that for real solutions, time to see, to feel, to think, to know, must be invested, the fact that books like Shoshana’s are not the norm tells us that the lesson needs much more emphasis.
In fact, I believe it is this deeper universal message that can have the biggest impact on thoughtful readers of the book. And this, in turn, compels me to do my part to make the number of such readers larger.
The stakes could not be higher.
Finding and Following Your Own Path
When my brother succeeded in persuading me to join an Alanon group in 1995 or 1996 I had little understanding of the healing for mind and spirit I would find among those gentle, powerful souls. They opened the door to healing simply by listening to me and speaking of their own paths in a way that made it clear I could take what I found healing and leave the rest.
I did know I was deeply afraid of others trying to tell me how to think, how to live, or even who to be. But I did not know the boundary violations I had experienced when I was young had created some very large traumas that were only increased by living through the slow deaths of both of our parents when my brother and I were teenagers.
Healing and a deep inspiration flowed from a combination of those illuminated spaces for listening and the walkabouts in the forests and mountains, first in Oregon, and then in New Mexico. In those experiences I found an understanding that no one had the answer for me, no one had the right to tell me what I should do, that only by that personal walk with God in those places of quietness and stillness could I hear and see and feel and find my own muse, my own path, my own unique way of creating and connecting.
I began to experience the power of the right words, at the right time.
I am still learning to understand the enormous power of words and the extent to which the misuse of words has created large swaths of humanity and society with seriously reduced capacity for sensing reality, for understanding the negative power of words and images thrown around carelessly or even maliciously.
So much of what we say to each other is either powerless, without inspiration or filled with power to damage and limit those who accept the words. This comes either as a result of ignorance (the most common case) or intentional malevolence. I have been guilty of using words in ways that were not respectful of the need for others to find their own way. Phrases like “you should do …” are rarely helpful or useful and are often damaging. I would now argue that they never belong in print because, when they are appropriate, it is always very situation dependent. When they do appear with well intentioned people, I believe it is most often due to enthusiasm for discovered insights that have worked well for them.
We discover something that works for us and we immediately evangelize others, certain we know the way, that we have the answer for them as well. This is most pronounced in those that have an undeveloped gift for teaching, but it seems to effect everyone who has made discoveries they think others might need. So often we speak these words and add force of our own, lest those listening (or who are forced to listen) not get the importance of what we are saying.
Yet this betrays a misunderstanding of the power of truth and inspiration. It shows we are not sufficiently aware of how others find their muse, their path of creativity and connection.
It is arrogance, blind as it always is, that leads us to think we can find the path for others. Sometimes that arrogance is a subtle, cultural type of arrogance. Other times it is overt and obnoxious.
When we begin to see clearly and deeply, the humility that must accompany this leads us to get out of the way of others in their quest to discover who they are, where they can go and what they are privileged to create. We discover that the path of the creative teacher and mentor, collaborating alongside those involved in the joy of finding and following their own paths, is an experience full of living energy and fresh discovery.
Balanced, wholistic truth contains in itself all the power needed to take root and grow. In growing, it adapts to the soil it finds, encouraging the uniqueness it finds, illuminating the creativity that results. The creativity that results in turn illuminates new and original facets of the truth.
A narrative containing a truth, told simply, without force, transmits the truth in a way most likely to be accepted, though sometimes lying, like seeds in the ground, awaiting just the right conditions to take hold and grow.
A telling of parts of our stories, encouraging listeners to find, explore, hear the stillness themselves, to become adventurers and participants in that deepest conversation with their Teacher — this becomes the most powerful thing we can do for others.
In their seeing what we have learned, what we have found, what is part of our story, they are inspired to begin their own journey, to find their own muse.
Fun with simple analysis problems I: the rest of the story
In an earlier post with the same title (and without the subtitle) I introduced some thoughts that were triggered by this simple problem:
Suppose that
for all 
Prove that 
In that post (which you can find here Fun with simple analysis problems I ), I started by presenting three solutions and then generalized and explored further.
What I did not reveal in that post, was that writing it, gave me an idea for a more advanced problem. Not too long afterwards, Laramie Paxton joined my group and I gave him this problem to work on for his dissertation. We collaborated in solving the problem, since that is how I mentor all my students — their dissertations are collaborations with me. This resulted in a paper we wrote together: A Singular Integral Measure for 
Laramie Paxton arrived at WSU quite naive with respect to analysis, having completed an online masters in mathematics that did not give him a good foundation in analysis. But he very quickly he adopted habits that led to rapid progress. He started by studying intensely the summer before arriving and passing the qualifying exam on his first try. Then he took my challenging undergraduate analysis course (I used Fleming’s Functions of Several Variables), pushed through courses in advanced analysis, and geometric measure theory, and worked on applications in image analysis (generating papers he actually led) and finished his dissertation, all in the space of two years. After a year of postdoc, he landed the job he is about to start, at Marian University in Wisconsin. I believe that both the University and Laramie are lucky to have each other.
In general, I believe that small universities are good places to be nowadays, but from everything I hear, this place is better than good — it is perfect for Laramie’s talents and skills. (In addition to his impressively growing mathematical skills, he was already phenomenally skilled in logistics and organization which can be seen in his highly effective help in making the events listed here, from April 2017 to July 2018, a reality.)
A major point of both the original post on the problem and this present post, is that the paper with Laramie, as well as the results in the first post, flowed from taking time to think about a simple analysis problem that would usually be viewed as a not-too-hard exercise, not worthy of more thought than it takes to find one solution.
While I am sure that there are other undiscovered aspects of the problem that launched these two posts and Laramie’s dissertation problem, I believe that what has been explored illustrates why it makes sense to treat simple problems as invitations to playful exploration and creativity.
The Colors of Memory and Wisdom
Reading Zeyn Joukhadar’s novel, The Map of Salt and Stars, has taught me once again that fiction can be more truthful than non-fiction. And even though the vast majority of fiction is to reading what junk food is to eating, there are novels that inspire even the pickiest of readers, with the highest (or most peculiar) standards for what is inspiring or illuminating.
What we know is a such a minuscule particle in a vast infinite universe of what could be known, that the skeptical inquirer is doomed to a rather poorly illuminated reflection of tiny bits of what is known. But skepticism is not the only option. Those willing to use all the tools at the disposal of an aware, enlightened human being, can embark on a voyage filled with light and a rich, ever-unfolding life.
In the living experience and fable woven together in Zeyn’s novel, the human spirit and the Infinite meet in an explosion of life and color and light and dark, moving us to a place where we can see and feel far beyond the narrow confines of overly rigorous, reductionistic thinking and experience. The deeper truths in the stories, sometimes stated very plainly, other times only seen in the wholistic experience of the story, are profound, demanding a stillness and quietness before they open to our view.
The overwhelming energy moving through the story, illuminating my response, was one of light and color and memory and feeling, reinforced by the synesthesia of Nour, the little girl through which we see the story. While a few might consider Nour’s synesthesia to be an unnecessary device, I found it completely natural, even essential. For me it was a door anyone can enter if they will but take the time to listen to the music and feel the color in the stillness and quietness, to see the light shining through the broken places, to experience the infinity between the ticks and tocs of a clock.
When I taught 7th and 8th grade science during graduate school, I used to take my students out into nature with notebooks in hand and ask them to see and feel and hear, and then write. Most had a very difficult time finding the stillness necessary to do this. I know they had a hard time connecting with my descriptions of what happened on my walkabouts, when I moved into that living path mode of seeing and hearing. It was also my first time trying to describe this mode and inspire others to try it for themselves. After those experiences I often simply shared the insights I found in that state, realizing that it is a very hard thing to actually move somebody into that mode of being.
Nevertheless, over the years, I remained as hopeful as I was when I tried guiding the students, that this mode of seeing and hearing and feeling is open to anyone willing to listen to stillness.
Lately, though, I had started losing hope in the power of words to actually enlighten or inspire or even prompt others to begin a journey. I could find lots of examples that supported my growing doubt. But when I finished this book I was struck by the strong sense that I was wrong. Some written words are still very powerful, inspiring and healing, opening readers to that infinity I began to experience so many years ago in my walkabouts in the desert and later in the forests. Immersing myself in this story, I find again, in yet another form, that stillness containing infinity.
I was also reminded that when you have passed through extreme crisis, you learn what is important and what is not, you learn to choose the simple life and connections with those that love you and those that can benefit from your simple help. You remember that so many things in our surroundings, considered so important, cannot compare with the song of an insect, or connection with a friend, or peace of encompassing sunshine. You realize there is nothing to prove, that simple things contain everything you need because they are doors to infinity. You see helping those who struggle, easing the path of those who have very little and seek simply to live in peace, is an integral part of finding and sharing the depth and beauty we are wired to seek, to explore. One cannot truly have depth and beauty without the healing and compassion.
What remains for me, as I write these words in the afterglow of the story, is a sense of living stillness and remembering and color, and the deep peace when we remember the intense richness of knowing what is important.
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