- Communicate in person often, one on one, one on few, spontaneously (even if you have prepared for hours).
- Write papers and books that you are inspired to write … if you stick to true inspiration, there might not be that many papers and books, but what there is will be very good.
- Write ideas compulsively, write, write, write … but do not feel the necessity of publishing most of it, even if you make most or all of it available as notes, online.
- See publication, or even posting online, less as carving something into stone and more as an invitation for others to join in your explorations.
- Never let the writing replace thinking — take the time to think (and plenty of it).
- Don’t be afraid of mistakes and don’t edit as you write — edit by iteration, by revision.
- Polish your writing guided by one simple rule — to make your thoughts clearly visible to your readers. Forget all the other rules for proper writing, for how to write.
- Creativity is heightened by simple playfulness. Cultivate it.
- Share generously. Spread your inspiration and passion around. Make your environment rich!
- Sustain your inspiration by a commitment to freedom (with kindness) + connection (with generosity).
Some use faith to connect with finite, comfortable places, perhaps in response to fears of one kind or another. Little boldness is required. Others courageously connect to the ragged edge, but without the calm quietness that warns of errors, omissions or even danger. Yet others refuse to acknowledge the fundamental, critical role of faith, making the mistake of identifying this primitive human faculty with something that implies a belief in God.
Faith is fundamentally neutral, having nothing to do with belief in dogma or God. “True faith” (or “false faith”) is therefore nonsensical: the words cannot sensibly be used together. Faith is simply the human faculty to connect and it is by that connection that know, we experience, we see beyond. The great other, the great wholeness that dwarfs the tiny sliver of the universe that we believe we understand, can be opened by that connection we call faith.
In their abdication to a narrow vision of science and philosophy, many have surrendered an openness to paradox and a truly rich spiritual-mental-physical universe. Respectability tempts and seduces, but enslavement follows.
There is a radical faith not shying away from paradox, connecting us with a rich, bold and yet brilliantly simple vision. This faith draws us into a vibrant, living environment, for it is an explicit connection with Infinite Life.
In the patient, illuminated stillness flowing from connection, mystery and paradox, rather than being indicators of fuzzy or wishful thinking, become marks of clear vision. Quietly insisting on both horns of a dilemma, we are driven deeper until we find the transforming resolution opening us to new wavelengths of light, new worlds of thought and action.
Moving on from second hand knowledge of God to the vision through the torn veil, we find the connection that heals and illuminates.
Metrics — measures of performance or value — drive what we do at every scale, from the small, individual scale to the massive global scales. When those metrics are founded on misconceptions of reality, they contort behavior in such a way as to appear to support those misconceptions. To get back to the natural order of things, away from the artificial reality created by those false beliefs, we must start by reseting our metrics.
I was reminded of this as I perused the Harvard Business Review (HBR) I had purchased for the purpose of inspiring thoughts and reactions. I do not peruse the Review very often, but when I do, I am usually turned off by a large amount of what I find. The price of 16.95$ reeks of self-importance. And the articles overflow with much that I find distasteful in academia and in the broader, elitist culture — the same culture that is currently driving the world to the brink of destruction. But the metrics and implied metrics in the articles got me thinking about the influence of bad metrics, about the models of reality that implicitly encode inequality. Those models are everywhere.
Take the current focus in the news and social media on racism.
The real problem is that racism is an epiphenomena. Looking more deeply, we find the pervasive illusion of organic superiority/inferiority and the (negatively) powerful habits of ranking in all areas of life. These survive only because people can’t tell the difference between (1) powerful (negative) beliefs that become self-fulfilling prophecies and (2) fundamental truths. (While behavior does follow those unhealthy ideas, I am talking about potential here, not the reality created by those self-fulfilling prophecies.)
But to confront the fact that our brains are all pretty much equal, and what really matters is environment and opportunity, we have to face man’s inhumanity to man and our own moral degradation and greed.
And facing that fact is painful and difficult.
Once we begin to understand the effects of trauma of all sorts, of the massive power of emotions — actually, of our entire environment, we begin to understand the observed behavioral data differently. We begin to see that our beliefs in inequality combined with our inhuman treatment of others actually generate inequality. We begin to see that any solution to inequality that does not begin with the understanding that people are, actually, truly born equal is bound to fail.
Because we cannot fix inequality and believe in inequality at the same time.
Though it is a fact that there are organic differences, that there are a relatively small number of (very) basic groups of talents people are born into, any solution to inequality cannot succeed if it does not start with the understanding that these talents are not rankable, but are equally amenable to (even extreme) development.
When this position is taken, we see that inequality is pervasive, that the roots to racism are found in how we treat each other in every environment, including very white environments. In fact, if you were to restrict yourself to purely White Anglo-Saxon Protestant environments (though finding such environments is getting harder), one would find the fundamental disease that becomes racism in other environments.
When we begin building metrics based on the facts of equality, we begin to stand a chance of making a difference.
This brings me back to the HBR articles and their usual conformity to a traditional interpretation of behavioral data.
Of course the mistake the intelligent people who populate academia and the elitist cultures make, is the mistake that scientists often make, of not taking into account the effects of multiple time/context scales in their studies. It is sort of like the Chinese story of the man who lost his horse ( 塞翁失馬 — Sāi Wēng Shī Mǎ) in which what appears to be a good thing or bad thing depends on context that keeps expanding. Not taking all the different temporal/spatial/contextual scales into account, often leads to incorrect conclusions.
To many such observers, the data appears to confirm that (1) unfettered competition and greed are natural and probably good and (2) inequality is organically based. (Note: I am not saying that all competition is bad, only that the current vision for competition is deeply unbalanced and actually unfair to many smaller entities that want to compete.) Of course, the more sophisticated the person, the more polished and palatable their presentation of these ideas. But, as I observed above, the process by which we can see differently is uncomfortable for everyone and painful for most.
So instead, we pretend that the results of greed and inequality are some sort of natural law that we have no power over. And we end up missing the principle that enables us to find richness almost anywhere.
We do not realize that enough is a feast.
I am far from the first to observe that enough is a feast, that aiming for more than enough is wasteful, and that piling up great piles of wealth of all kinds (not just financial) and locking it away literally or figuratively is an obscene crime against humanity. It is just that even though it has been said before, by many others, it seems to be one of those things we need very frequent reminders of.
What I am interested in is a world in which taking time to think has priority over the rush of the over-achiever, where what my family and my dog thinks of me is more important than what my department or academia in general or the National Academy of Sciences thinks of me, where being a fundamentally independent thinker is more valued than status as a “thought leader”, where quiet generosity takes precedence over noisy philanthropy, and success is measured by whether or not I and those around me have enough, not if I have enough money or prestige to supply a small country.
In such a world, where “enough” becomes integral to our metrics, there is enough for everyone. And when this happens the enormous human potential that we have been obscenely wasting is unleashed.
When, as Bryan Stevenson makes a case for in Just Mercy, we understand that healing begins in seeing our own brokenness, we begin to understand why we strayed from “enough” in the first place. We then understand that everything good begins with healing, that, from the humility we gain in that process of healing, every other good thing flows. Then we understand that humility is not so much the opposite of arrogance and the drive for status, as it is the opposite of spiritual blindness.
For blindness was the problem all along. What we needed, what we really wanted, was always at our fingertips. Only our inability to see the true order of things stood in our way.
Accepting this, we are set free to find healing and a rich abundance that has nothing to do with impoverishing others in any way.
This last semester, I ran a fun, informal master class in problem solving. Actually, a graduate student of mine — Yunfeng Hu — who is an expert problem solver, produced all the problems from the immense library he built up over his undergraduate career in China.
I believe that the art and culture of problem solving is not as widely valued in the USA as it ought to be. Of course there are those that do pursue this obsession and we end up with people with high scores on the Olympiad and Putnam competitions. But many (most?) do not having develop this skill to any great degree. While one can certainly argue that too much emphasis on problem solving along the lines of these well known competitions does not help very much in making real progress in current research, I would argue that many have fallen off the other side of the horse — many are sometimes hampered by their lack of experience in solving these simpler problems.
Here is a problem that arose in our Wednesday night session:
for all , that is continuous and differentiable, and that . Prove that everywhere.
Perhaps you want to fiddle with this problem before looking at some solutions. If so, wait to read further.
Here are three solutions: in these first three solutions we are dealing with and so we will denote by .
(Solution 1) Consider all the solutions to and . These are all curves in of the form and We note that if is any function that satisfies equation (1), then everywhere its graph intersects a graph of a curve of the form for some , the graph of must cross the graph of if we are moving form left to right the graph of moves from above to below the graph of . Likewise, crosses any from below to above, when moving from left to right in . Now, supposing that at some . Then simply choose the curves and as fences that cannot be crossed by (one for and the other for to conclude that can never equal zero. (Exercise: Verify that this last statement is correct. Also note that assuming is enough since, if instead then also satisfies (1) and is positive at )
(Solution 2) This next solution is a sort of barehanded version of the first solution. We note that equation (1) is equivalent to
and if we assume that on , then this of course turns into
Assume that and divide by to get Integrating this, we have or
Now assume that . Define and Note that implies that and implies that Use equation (4) together with or , to get a contradiction if either or
(Solution 3) In this approach, we use the mean value theorem to get what we want. Suppose that . We will prove that on the interval .
(exercise) Prove that this shows that . (Of course, all this assumes Equation (1) is true.)
Assume that . Then the mean value theorem says that
for some . But using equation (1) and the fact that , this turns into By the same reasoning, we get that for some , and we can conclude that . Repeating this argument, we have
for some , for any positive integer . Because is continuous, we know that there is an such that . Using this fact together with Equation (6), we get
which of course implies that
Now we could stop there, with three different solutions to the problem, but there is more we can find from where are now.
Notice that one way of looking at the result we have shown is that if
(1) is differentiable,
(3) for some , we have that when and ,
Note also that if we define
we find that
Let denote the continuously differentiable functions from If we define we find that not only is not all of , we also have functions satisfying whose . So we will restrict the class of functions a bit more. The space of continuously differentiable functions from to , , where (compact!), is closer to what we want. Now, contains only those functions which have a root in .
We will call the functions in functions with maximal growth rate . This is a natural moduli for functions when we are studying stuff whose (maximal) grow rate depends linearly on the current amount of stuff. Of course populations of living things fall in the class of things for which this is true. from the proofs above, we know that if , then it’s graph lives in the cone defined by exponentials. More precisely
If then for , and for we have
(Exercise) Prove this. Hint: use the first proof where instead of you use and let .
(Remark) Notice that Equation (10) and implies that scaling a function in by any non-zero scalar yields another function in As a result, we might choose to consider only
In both cases we end up with subsets that generate when we take all multiples of those functions by nonzero real numbers.
(Exercise) If we move to high dimensional domains, how wild can the compact set be and still get these results? It must clearly be connected, so in we are already completely general with our above.
Moving back to Equation (1), we can look for generalizations: for example, will this result hold when How about when maps from one Banach space to another? How about the case in which is merely Lipschitz?
Lets begin with
In this case, the appropriate version of Equation (1) is
where denotes the operator norm of the derivative and is the euclidean norm of in
where is an dimensional row vector and is an dimensional matrix. (Thus the gradient vector is the transpose of the resulting dimensional row vector.) Now we can use this to get the result.
Let be the arclength parameterized line segment that starts at and ends at the The above equation tells us that
Thus, we can conclude that
which implies that
and we can proceed as we did in the second proof of the problem in the case that We end up with the following result
If and , then
(Exercise) Show that this result implies that if f(x) = 0 anywhere, it equals 0 everywhere.
(Exercise) Show that this is implies the one dimensional result we proved above (the first theorem we proved above).
(Exercise) Our proof of the result for the case can be carried over to the case of where are Banach Spaces — carry out those steps!
We come now to the question of what we can say when we are less restrictive with the constraints on differentiability. We consider the case in which is Lipschitz. The complication here is that while we know that is differentiable almost everywhere, it might not be differentiable anywhere on the line segment from to .
Consider a cylinder , with radius and axis equal to the segment from Let . Since is differentiable almost everywhere, we have that . Therefore almost every segment generated by the intersection of a line parallel to the cylinder axis and the cylinder, intersects in a set of length . We can therefore choose a sequence of such segments converging to
Since exists almost everywhere on the segments and is continuous everywhere, we can integrate the derivatives to get:
And because is continuous we get that
so that we end up with the same result that we had for differentiable functions.
There are other directions to take this.
From the perspective of geometric objects, the ratio is a bit funky — for example, if volume of a set , where can be thought of as the center of the set, we have that will be a vectorfield times restricted to the . Thus, will be an -dimensional quantity and a -dimensional quantity. We would usually expect there to be exponents, as in the case of the Poincare ineqaulity, making the ratio non-dimensional.
On the other hand, one can see this ratio as a sort of measure of reciprocal length of the objects we are dealing with. From the perspective, this result seems to say that no matter what you do, you cannot get to objects with no volume from objects with non-zero volume without getting small (i.e. without the reciprocal length diverging). This is not profound. On the other hand, that ratio is precisely what is important for certain physical/biolgical processes. So this quantity being bounded has consequences in those contexts.
This does not lead to a new theorem: as long as the set evolution is smooth, the and are just a special case where and even though actually computing everything from the geometric perspective can be interesting, the result stays the same.
in order to move into truly new territory, we need to consider alternative definitions, other measures of change, other types of spaces. An example might be the following:
Suppose that is a metric space and . Suppose that is continuous and is a geodesic in the sense that for any three points in , , we have that
(1) for any two points in the metric space there is a gamma containing both points and
(2) for all such , is differentiable
then, we have that
And, again we get the same type of result for this case as we got in the Euclidean cases above.
(Exercise) Prove Equation (14).
(Remark) We start with any metric space and consider curves for which
We call such curves rectifiable. We can always reparameterize such curves by arclength, so that and . We will assume that all curves have been reparameterized by arclength. Now define a new metric
You can check that this will not change the length of any curve. Define an upper gradient of be any non-negative function such that .
Now, if , we again get the same sort of bounds that we got in equation (14) if we replace with . To read more about upper gradients, see Juha Heinonen’s book Lectures on Analysis in Metric Spaces.
While there are other directions we could push, what we have looked at so far demonstrates that productive exploration can start from almost anywhere. While we encounter no big surprises in this exploration, the exercise illuminates exactly why the result is what it is and this solidifies that understanding in our minds.
Generalization is not an empty exercise — it allows us to probe the exact meaning of a result. And that insight facilitates a more robust, more useful grasp of the result. While some get lost in their explorations and would benefit from touching down to the earth more often, it seems to me that in this day and age of no time to think, we most often suffer from the opposite problem of never taking the time to explore and observe and see where something can take us.
Rereading parts of Glynne Robinson Betts’ 1981 book, Writers in Residence, recalled simpler, deeper times, when finding places of quietness and taking time to think was part of the routine many people used in order to hear themselves and others. In fact, reading this again prompted me to expand the time I spend without Internet interruptions. Steps as simple as ignoring email for extended periods or as comprehensive as turning the computer off for the entire weekend, are emerging as a necessary part of reclaiming quietness and time to think.
There is nothing profound in these decisions to disconnect — whatever is profound happens as a result of taking that time to see and listen and think.
When I do slow down, every pause, every quietness, every moment taken to see, to listen, to think, rewards with a rich, living connectedness and depth that cannot be exhausted. The fabrics of the past and future join with the present, without seams, without a sense that I am working to recall, to see, to feel. Time opens up, I enter, to travel my own path, to sit or stand or walk … stopping time, finding passage to places beyond space and time.
To the strictly modern intellect, what I have just said probably seems like non-sense. Reason, based on easily observable facts, will find little irrefutable evidence that a skeptic would find compelling.
I therefore offer no argument to convince the skeptic. Instead I say, “Come and see”.
When we begin to let go of dogma, the regard of peers, and the comfort of the in-group, room for discovery is created. Launching into quiet spaces, where fear is replaced by stillness, a boundless infinity surprises. We find flow. In this personal place without limits, I find an overflowing garden, teeming with life. On the living path, everything is illuminated.
Yet this is something I cannot really transmit. It is only something I can hint at in what I write, faintly, incompletely. The experience of discovery, of knowing, of traveling to those places that are here and beyond at the same time, cannot be captured in words.
To see, you must see though your own eyes. To see, you must choose to slow down, find quietness, and dwell there.
I believe that most – possibly all – human beings have, at one time or another, experienced immersion in flow and a connection to the place without limits. There is a resonance emerging from any such experience, no matter how brief, that enables those with that experience to hear each other. But life often seems to conspire to crush those memories, to remove our ability to hear and see. In the quiet, we can be moved to remember, to see, to hear. In the quiet we remember the place without limits.
In writing something of what I see and hear, there is a chance that faint recollections will be stirred in those that read, in the way Writers in Residence stirred my memories, my recollections of a time when quietness and time to think was plentiful.
The thought of this possibility brings a subtle sense of connection, of silent conversation, with those as yet undiscovered friends. Lingering in rediscovered quietness, we move against the flow of noise and commotion and modern distraction, encouraging all those in our circle of influence to rediscover for themselves their own place without limits.
I have come to question a significant portion of the culture in academia, even while I have developed a deeper connection with other parts of that same culture or at least the culture that we could have. While I am deeply committed to mathematics as a creative occupation, and to teaching and mentoring in mathematics, my experience in academia after re-entering it seven years ago has strengthened my rejection of the many parts of that culture because they hinder the best research and teaching.
There are many aspects I could discuss, but here I am singling out four: the question of what makes a mathematical result or paper worthy of recognition together with the place of exposition in mathematics, the value of awards and recognitions in mathematics, and the effects of federal funding on mathematics and academia.
As opposed to trying to do some sort of statistical study — a study which would only be meaningful if there were sufficient numbers of people following the ideas I propose, and there is not! — I will invoke common sense and intuitions that are commonly agreed on, but usually discarded as a guide for actions because of the economic realities of higher education; the institutions that pay us expect and reward the defective model and very few actively step outside those bounds.
We start with a relatively innocuous idea that papers that answer questions completely, are best.
What comes from the idea that results are best if they are definitive? Frankly speaking, I believe this idea is part of a cluster of ideas that impoverishes mathematics and mathematical culture.
I first thought about this when reading Bill Thurston’s 1994 article On Proof and Progress in Mathematics. In this article he contrasted how he approached his first work on foliations (resolve all questions, definitively!) versus his later work in geometry and the huge difference a more generous approach made in creating a rich, open, inspiring environment that many others got involved in, rather than the pinnacle of achievement that was admired from a distance.
Instead of maintaining a museum of monuments, we should propagate a countryside filled with rich, diverse gardens of ideas and a zoo of people tending and changing and expanding and creating new gardens. While the first model leaves a trail of impressive facts, fit for admiration and worship, the second model is defined by engagement and inspiration for widespread creativity.
When Henry Helson visited Poland after the war, he was struck by the purity and simplicity of the mathematical culture that was also very generous. As he relates in his 1997 Notices article, Mathematics in Poland after the War, he was struck by the combination of generosity and fun that pervaded a culture that was serious about mathematics, but happy to publish things that did not aim to grab and own whole swaths of mathematical territory. Rather they published relatively short papers, each of which presented one new idea very clearly.
That exposition has been neglected, in spite of all the lip service to the contrary, can be seen in the response to the astrobites.org site, which has gained a lot of attention in the astrophysics community because of the large contrast between the high quality exposition that astrobites.org offers and the usual difficulty that non-experts have in reading scholarly papers.
I am now convinced that the high art of exposition should be valued as highly as the construction of brand new theorems, that publishing in such a way as to leave much to others is better than cleaning up an area and creating a monument: that what gets considered valuable mathematics ought to be greatly broadened. If anyone finds value — maybe because of explanations that require original thought, maybe because it brings the ideas to new audiences, maybe because it helps students see something clearly, maybe because it brings the understanding to the general public, and yes, possibly because it is completely original and surprising in construction — then it is valuable mathematics, worthy of the deepest respect. In this new model, the quality of the writing becomes very important. (I suspect that some will take issue with that statement saying that this is not a new model, but I will disagree and point to the enormous quantity of poorly written articles and books, some of which are also very valuable, even though they are not written very well. Of course, there are papers and books that are very, very well written. But it seems that this is considered a cherry on top, rather than something that should always, before anything else, be there.)
I am not urging that there be an effort to police exposition, but rather that this be given a great deal more attention at every level of education and practice. If we must have awards, let them go to those that have explained things well, have written things well. Better yet, train students to pursue the intrinsic rewards of doing anything well, from explaining derivatives to a confused calculus student to proving some new, highly technical theorem.
To encourage such changes, we would need to revisit how we reward and support the mathematical enterprise. This brings us to the consideration of the last two cultural components I said I was going to discuss: awards and federal funding.
Why do mathematics? For me, it is another form of art and at the same time, an exploration of the universe we live in. Knowing and understanding and explaining and inspiring others to do the same, exercises deep creativity and generosity; this is an occupation worthy of human beings that value themselves and others. Of course, there are an enormous number of occupations that can beneficially occupy the human mind and spirit. And each one can be as satisfying and beautiful and useful in its pursuit. By useful, I mean useful as an occupation, not useful as a tool to bend the world to my will. It is the occupation itself that is valuable. What happens to us and those we teach and share with, when we occupy ourselves (in a healthy environment!) is the greatest justification for any occupation.
From this position it becomes clear that awards and honors that many aspire to are actually a distraction. The reward is in the occupation itself. There are of course honors that have more to do with real appreciation rather than ranking and fame, and for such honors there is a place in a healthy culture. But the greed that masquerades in all of us as something more beautiful, seeks fame and fortune as a substitute for love and respect, whose lack actually gives room to that greed in the first place.
When the American Mathematical Society proposed the status of Fellow of the society, the negative side effects of such a program were pointed out rather eloquently by multiple individuals. In particular, I remember that Frank Morgan’s argument against the establishment of the program, and Neal Koblitz’ refusal of the offer of the status of Fellow. Of course, there is also the curious case of Perelman who refused the Fields Medal, the mathematical equivalent of the Nobel prize, whose recipients are given a demi-god status. For an interesting telling of the story and more, see Sylvia Nasar and David Gruber’s article Manifold Destiny in the August 28, 2006 issue of the New Yorker. (In the story, they quote Gromov, another prominent mathematician. Even though I very much doubt Gromov’s explanation of Perelmans refusal as a result of some great purity on Perelmans part, it is a story worth reading and thinking about.)
The influence of federal funding in mathematics, while it has enabled a great expansion of the enterprise, has led to a degradation of the culture, and not only in mathematics. It is well known that federal funding has turned academia into a serious addict, willing to do anything for the next fix of federal funds. That, combined with, spurred on by, the neglect of higher education in the public sector, has led to the very bad state of affairs in which grant money reigns supreme, fame (which can be turned into money!) comes second and teaching, for all the lip service it is given, occupies the lowest realms of academia. Proof of this diagnosis is not needed by anyone in academia (other than administrators who profit from illusions proposing some other reality), but if proof is needed, one need not look any further than the way adjuncts and instructors, who do a great deal of the teaching, are treated. Both in terms of the dismal pay and the insecurity of their jobs, we are saying that teaching is not what a university is really about — it is just what we have to do to keep up the charade.
But this is also where the tragedy lies; it lies in the immense impoverishment that results when teaching is not given top priority. It is a law of nature that real greatness, true stature, is proportional to the service to others that an entity or person actually provides. You may prefer to see this as my definition of greatness and stature. Either way, assuming this to be true, we have traded real nobility for a meager, greedy existence when we accept the perverted system of values that we currently have at research universities — and even, in some ways at teaching universities.
While small liberal arts college do in fact value teaching, they still take advantage of the situation generated by research universities and often pay their adjuncts obscenely low wages. It is tragic and funny at the same time that such colleges are usually full of people who think that businesses ought to raise the minimum wage, provide health care and longer paid vacations, and all sorts of other good ideas, but when it comes to the situation they have power over, they turn a curiously blind eye. But there is also this idolization of research universities, of elite institutions and this admiration pulls in some of the poison that they could otherwise easily avoid.
But, as I wrote in the previous post in this blog, Learning to Think and to Act, research is a critical piece in education. It inspires and illuminates and brings a freshness and vitality that should be insisted on. On the other hand, research without teaching becomes selfish and elitist and aimed at goals that can at times be silly and irrelevant in their isolation.
What then, can we do? If the system is so far astray, what can be done?
In my opinion, the most powerful thing you can do is inspire change in your own sphere of influence by a focus on the place of freedom you actually have. Having your principles and philosophy aligned with life and love, and consistently acting in accordance with them, has always been the most powerful thing anyone could do.
Creative exploration and teaching, with a deep sensitivity for those that struggle; the pursuit of both pure and applied research, with generosity, and an acute sense for which applications are morally admirable; a discipline of simplicity, eliminating the pursuit of rank or awards or status or recognition — these are still the fundamental components of a culture worth immersing myself in, worth spreading to others. Taken together, they create a deeply rewarding occupation, an occupation that quietly, powerfully, moves us forward, and higher.
I found William Deresiewicz’ book in a roundabout way. After reading an article in The Nation he had written, I read The Disadvantages of an Elite Education also by Deresiewicz and this led me to his book Excellent Sheep: The Miseducation of the American Elite and the Way to a Meaningful Life.
The book is written empathetically, with a soul in plain sight. Whether you are applauding or arguing, you are engaged. During this personal conversation with the book, that turned into an email back and forth with the author, I decided to write something in response.
I also decided that I will now have all my students read this book. You might wonder why. After all Washington State University is not an elite university. Though we do have students who are brilliant and professors that are as creative and as interesting as those at any university, our university is not top ranked and is unlikely to be so anytime soon. It is true that those dedicated to innovative research and a deep, thorough education, can find agreeable environments here and there at this university. But that is by no means an across-the-board phenomena.
So why should I require my students to read William’s book? After all, it is aimed at students at, or thinking about being at, the most exclusive universities in the world.
The reason is very simple.
The elite universities that Excellent Sheep takes apart have a hold over the imaginations of just about everybody involved in higher education. Why? Because, even if you are not at one of these universities, you are strongly inclined to using those universities as a standard, a measuring stick. As a result, the elite universities end up infecting everybody else.
Tragically, the infection has been chosen by those lower ranked schools … it is a self-inflicted ailment, inflicted because of a lack of imagination and courage.
The freedom and breathing room that the lower ranked schools have — nobody is fighting them for their lower status — could be used to innovate and set a new standard of excellence. There are so many defects with what is considered elite that a faculty with imagination and vision and a disregard for status and tradition, could create something that would actually out-rank the elites by any natural, organic measure focused on real quality.
A Vivid Diagnosis
Excellent Sheep begins with 4 chapters in which the problems with elite education are outlined with frankness and clarity. The mad rush for students to become super-students, driven by parents that believe the Ivy League hype and encouraged by universities that have sold their souls to money, status and the illusion of greatness, has created a class of elite students that are maxed out, stressed out, with little capacity for truly independent thought and little moral fiber. The vast majority of them have no real idea of who they are or what their own passions are. They console themselves with high paying jobs which in the end have little capacity for supplying them with purpose and the satisfaction that comes with following your own muse.
And they make terrible leaders: visionless, risk averse, conceited, and entitled. They are ill equipped to the jobs to which they aspire, that the world hands to them because they are “the best and the brightest”, a term that the author reminds us was invented to describe the technocrats who led us into the quagmire in Viet Nam.
After his rousing diagnosis and illumination of the multitude of problems with the elite schools, he transitions to his vision of what college should do for you and how he sees the humanities playing a big role in the re-imagination, the re-vitalization of education. These 6 chapters in parts 2 and 3 provoked the most thought on my part.
One part of his prescription for education centers around the idea that the humanities, taught correctly, teach students how to think, how to be skeptical and doubt the ideas and opinions they have accepted without critique. He explains how great books, with greatness defined organically and broadly, prompt thought and discovery and exploration leading to deeper self-discovery. While he is not in any way claiming that this is new, his message that this is not happening at the Ivy league schools is something that is not well known.
It is here that I occasionally diverge, but not because I disagree with the general outlines of what he is saying. Rather it is in a few of the details and the extent to which he caries things. He simply does not go far enough sometimes. (Though I dare say that he goes further than almost anyone seems willing to take things.)
The Heart of the Matter
As will become clear in my own story, told later on, I believe in God.
Of course, exactly what that means is a long discussion. In fact it seems that saying you believe in God or don’t believe in God is almost a statement without information, at least if you think about what you believe.
Where this becomes important to this essay is in Deresiewicz’s acceptance of Gould’s idea that the arts and humanities on the one hand, and the sciences on the other, are separate magisteria. I believe this is wrong, that in fact the spiritual realm ties everything together and a God that creates is the beginning of wisdom in the search for an explanation of the ultimate unity of everything.
Of course enormous damage has been done to the conversation that should happen here, both by the believers and the unbelievers. In fact, it is hard to overstate the extent of this damage.
But if one can find quiet spaces in which to discuss and examine these questions, the questions can begin to be seen as an attempt to draw out an understanding that allows both the believer in a God that creates, and a believer in a universe without God, to benefit from each other’s insights.
The quietness and respect and time to think and observe that this enterprise takes, is founded on emotional health. This is where the real problems often lay. Because of the enormous damage that dogmatic ideologies and religions have done or threaten to do to us, we often find it very hard or even impossible to enter discussions with the patience and quietness necessary for such conversations to deepen and enlighten.
But where those conversations can happen, the effect is very powerful.
And it is precisely this environment that we should find in college — an environment where true diversity is respected and encouraged and challenged and supported. Free and thoughtful discussions that illuminate the mind and soul do not need, and in fact are damaged by, the force of dogma, ridicule, combative attitudes and the inability to listen because you have found the truth. Trusting this and boldly engaging in such an enterprise enables us to learn from each other, not just shout at each other. The blunt instrument that science and scholarship devolves into in an adversarial environment, would show itself to be a subtle revealer of mysteries in the environment characterized by love and respect. For love is the only thing that truly moves us to a place of progress.
Love does not imply agreement — our experiences in our families can teach us this. And it is not something that gets in the way of freedom, though twisted conceptions of love could tempt you to believe otherwise.
The freedom that such an environment gives and inspires, begs to be filled up with a rich curriculum covering thought and action in a broad way. In addition to classes and seminars, there would be maker spaces in every subject, jobs for students that range over a widest possible directions and a culture that made working and serving, alongside rather than from above, the norm.
Making and maker spaces, though they are in vogue in some corners of many universities, predominately in engineering departments, have yet to become truly integral anywhere, and that includes engineering departments. Yet, turning thought into tangible action is very valuable for students, if for no other reason than the intellectual and spiritual benefits of the manual crafts, as pointed out in Matthew Crawford’s book Shop Class as Soul Craft.
There are many reasons for teaching all students both academic expertise and a manual trade. To begin with, their way in the world would be much more sustainable, much less fraught with economic peril. Yet even this immediate effect would give them a sense of freedom in their academic pursuit since they would never need to compromise with a job that was nominally aligned with their expertise while actually being a betrayal of their muse or their morals or both.
Yet there are deeper reasons for pursuing manual training in parallel with the more apparently intellectual pursuits. Exercising a creative manual skill is the perfect counterpoint to intellectual pursuits even if only for the rest and deep satisfaction of producing tangible, visible results that are also useful. Yet there is more. The exercise of the faculties used to do practical work also broadens the mind and strengthens key abilities which in turn give us a much more robust approach to problem solving in the more overtly intellectual arenas. In my own experience, that I cover in a bit more detail below, building and tinkering played a significant in teaching me how to solve problems that cross disciplinary boundaries, as most real problems do.
Of course, the variety of things that one can do along the lines of skilled trades is very large and certainly not confined to things one does in a shop. But all of them give you an ability to be less dependent on others for your economic security, both in terms of what you can do for money and what you can do without so much money. If this is combined with a choice to live simply, on less rather than more, to avoid student loans (or in the very least refuse loans that cannot be nullified with a bankruptcy), students gain even more freedom. In not surrendering their own freedom, they are equipped to encourage others to live an equally simple, inspired life.
Along the lines of simplicity and inspiration, there is the matter of having and taking the time to think, as well as the related issue of the overloads that colleges encourage.
I consistently advise my early doctoral students to take at most two classes per semester and fill the rest of the required hours with research credits which are designed to deepen the studies in the classes they are taking. I do that because I can do that. But undergraduates often take 4-6 courses of which 3-4 might each be worthy of their full attention during the semester, and there is little I can do about that. Needless to say, they skim the surface and do not begin to master the subject. Of course, sometimes a whirlwind tour is sufficient, but whenever real thought and effort are merited, the overload takes it toll and mastery or even a touch of depth eludes them.
If this were to be addressed in a meaningful way, in parallel with real efforts to help the students find their muse, we would need to reduce the number of courses significantly and deepen the courses they did take by a significant amount. The result would be revolutionary.
If we moved away from grades to evaluations and portfolios, so that someone wanting to know something about a student would have to look at the students work, not just some set of grades or even worse, a single measurement like the GPA, we would encourage real depth and mastery. There would be real incentives to think about what they were doing and act on the inspiration that followed.
An example of the kind of problem we are up against can be illustrated by the case of the elementary undergraduate linear algebra course at WSU. The course is a 2 hour course because the engineers did not want to waste precious credit hours, precious thanks to the accreditation requirements to which they are beholden. But the organic reality is that for anybody doing anything computational, linear algebra is arguably the most important mathematics class they will take. To do it justice, in line with what advantage mastery of the subject will give them, they should be taking a 6 to 8 hour course. Almost every applied calculation ends up requiring some linear algebra, with many problems requiring a lot of linear algebra. Yet politics between mathematics and engineering combined with the shackles imposed by accreditation generated a 2 hour class. And as a result, most of the students that have taken linear algebra have little to no mastery of what may be the most important mathematics they take.
This is not unusual. Instead of doing what makes sense, we do what some set of people have decided is important, even though they are far from the facts and realities.
Of course, some of this is simply in the air — it is the spirit of the age to give yourself no time to think, to fill all your space with sound and action and tweets and email and messaging with facebook or instagram. Because of the way this swallows up personal, quiet spaces, it should be the first task in college to teach the students to repossess their own minds and souls. They have to take back time to think and see, and hear what the quiet has to say to them. If their could be one thing that you would ask your students to give up, it would probably be their mobile devices. As unrealistic as this might seem, an honest assessment of the situation would make it clear that these devices are robbing many students of the ability to think and focus deeply.
What I have described above boils down to a gentle, bare-handed exploration of ourselves and the universe, unmediated by electronic devices, unnarrated by our culture, unaccompanied by music through our earbuds, in an environment rich in quietness and time to think, broadened and deepened by experience with skilled trades and frequent, face to face interactions with other human beings who know how to listen. Such an environment would produce educational results of a very different nature than the ones we currently see.
If colleges understood research and teaching to be something that is far broader than is now imagined and practiced, then it would be discovered that research and teaching are not at odds, that each can enrich the other and that the stranglehold federal funds have on academia need not continue.
Currently what is valued is papers and external funding and if you had to choose one on which to bank your hopes of getting tenure, it would be external funding. At schools where teaching is the focus, this is not the case. But those schools usually look to research universities with admiration, so that to the extent there is change at those schools, the small steps here and there that can be seen reflect this misplaced admiration.
What would a balanced, sustainable attitude towards teaching and research be like?
To begin with, exposition of well known results and new research results would be highly valued. Ideally, every result would be accompanied by three expositions. There would be one which was a careful, well written record that other researchers could read and understand. Then there would be something that advanced undergraduates and graduate students could read and gain most or all of the picture from. Finally there would be something that was designed for the complete non-expert who is nonetheless inquisitive and motivated to know something about the area.
Right now we often have only the most inaccessible of the three expositions, the research paper. And that is often poorly written and primarily intended stake out territory and give the authors credit for having written a paper. Another goal is to have others cite the paper, to give the authors work “impact”. Supposedly the impact that everyone wants is about dissemination and scholarly, or even societal, benefit.
Yet, if real dissemination and wide benefit were the goal, careful, highly accessible expositions would be considered critical.
Some would argue that talks at conferences serve the purpose of part or all of the exposition I am advocating. But anyone acquainted with conferences and conference talks would know that these talks rarely transmit knowledge to anyone that doesn’t already know almost everything in the talk!
An example of the power of taking the time to explain can be seen in the blog, started by graduate students in astrophysics, focused on explaining the papers that appear in the astrophysics section of the archive at Cornell, arXiv.org. The blog, astrobites.org is a beautiful example that deserves to be imitated in all areas of scholarship.
It is widely understood that research in the widest sense (forget now about publishing or impact) is part of what makes a teacher a truly inspiring teacher. The attitude that explores, that innovates and creates playfully, that asks questions and tries to answer them is critical for the best teaching. Valuing this broader definition of exploration and research would go a long way towards bringing truly high quality teaching and research together.
Some professors are very good at mentoring whole crowds of students, others are very good at explaining very subtle, advanced ideas in classes, yet others are good at running hands on explorations of known and new ideas and environments. And there are many other ways in which professors contribute deep value, if value is measured in a natural, common sense fashion. But the current reward system rewards very little diversity, instead trying to force everything into narrowly defined research or teaching boxes. The result is that the system we have is biased against teaching and towards an insular, largely irrelevant, industry of research. And when it is not irrelevant, it is often beholden to some corporate or defense funded interest.
The low status that teaching has at many schools can also be seen in the way adjuncts are treated. The pay is criminally low, with little to no job security. As many others have noted, this reality makes a mockery of the claim that teaching is a top priority.
Approaching the integrated teaching and research mission more imaginatively, we might consider a system in which all of the teaching staff were tenured faculty, but where the roles they played were as varied as the individuals that made up the faculty. This would be easier with an administrative structure that was grass roots and not top down, but that would be an advantage and not a drawback. If adminstration were tasked with support, and not supervision, this would go a long ways towards eliminating the unhealthy feedback that has strengthened the current damaging definitions of research and teaching. Such a reconfigured support system could easily be directed by an inspired faculty to support a rich, new vision for integrated research and teaching.
And that would be something to get excited about.
Courage to Innovate
And, coming back to the pernicious influence of the elite schools on everybody else, if schools cared little for reputation or accreditation or status that depended on them bowing down and abdicating their own ability to innovate and imagine an effective path to education, we would have a huge diversity and richness in choice when deciding how and where to pursue the education that fits us. For every style of thinking and learning and doing, there would be a place where we could go to learn to think and act, a place where we could become more rather than less.
When I returned to a university setting full time after ten years at a national lab, I was surprised to find how little imagination many professors were willing to exercise to improve their situation and the situation of their students. I also found professors that actively promoted the idea that their university was inferior and that good students should go elsewhere.
I now realize that much of this is the result of a fatalistic acceptance of an environment in which innovation and common sense changes that are within reach, are obstructed by completely visionless, top-down administrative structures. Such systems are presided over by administrators that get to where they are not through the exercise of vision, but through risk aversion accompanied by a conservative point of view that stifles creativity and innovation.
(Are there administrators who do not fit this unflattering characterization? Of course. But they are a very small minority and are effectively neutralized by the effect of the rest of the system.)
As mentioned above, I think a part of the solution is a complete revision of the role of administration, from supervision and direction, to simple support with no supervision. The faculty, thus empowered could innovate and make the changes needed to reward the naturally occurring diversity that would keep things thoroughly inspiring and alive.
One could imagine a structure that was lean enough in non-teaching, non-research expenses that a tuition of 15-20K$ per year, if supplemented with donations that simply supported the infrastructure and equipment, would be sufficient to fund the operation of the school. Such a school would depend on the community for housing and small industries to capitalize in students learning trades, as well as student labor to keep the college running.To keep things focused on the right priorities, federal funds would not be allowed and students would not be allowed to use loans whose repayment was immune to bankruptcy. Instead, private donations for infrastructure and equipment and supplies would be sought, and innovative strategies for student funding would be pursued and supported. Choosing the moral high ground, some avenues of research would be avoided, but the freedom that this brought would be worth the price. (Such a funding model would also eliminate some of the mostly costly areas of research. This would be an acceptable price, especially since much of the most costly research is of questionable societal value anyway.)
By reducing the number of classes the students took, deepening the ones that remained and offering a rich profusion of enrichment experiences giving students exposure to ideas and activities outside their areas, students would experience depth and breadth in healthy balance. The enrichment activities could range from talks by visiting scholars and faculty to hands on activities that brought students into intimate contact with skilled trades. Using graduate students to help teach and mentor, one could have an environment that encouraged teaching and research that were integral, even inseparable.
Of course, the idea that one could operate a college with a much smaller overhead than is usually the case depends on greatly reduced services that have little or nothing to do with education. While there would be no reason why physical activities would need to curtailed, traditional sports would be absent. The legal structure of the school might be one of a cooperative that was supervised by the faculty and supported by a very small set of support staff and a larger contingent of students. But there would be many other options for the organization.
Graduate students, given free tuition and a small stipend to live on, would be expected to be full participants in the integrated teaching and research mission of the university. The suggested undergraduate tuition levels above would support two to four graduate student positions per professor which would be about right in that, this would translate into about one graduate student graduating every year or two for every professor, assuming an average time to graduate of 4 years.
A truly novel feature would be the presence of students in the skilled trades who would be full members of the community, along with those that were teaching those crafts. This would lead to opportunities and advantages that would enrich the university in many ways.
Where would the faculty to staff such a place come from? How would those who had been trained by such a dysfunctional system be able to guide and power such a unconventional approach to education? While it is true that many professors have let themselves be stunted by the system and robbed of their vision and idealism, most have small sparks that could be nurtured back into the enthusiasm that once motivated them. And there are always professors in the system who have never surrendered their vision, who would welcome the chance to be a part of something creatively alive and imaginative. Even if there are only 1% of the professors that are out there that would opt to be a part of something like this, that would be more than enough to get a movement going. If you count the graduates who have left academia because they cannot abide the state of academia, you have many more qualified candidates for something new and different.
Likewise, how would we find students interested in committing to a small, unconventional university? Where would you find these individuals that did not care about accreditation or reputation or status, who had the maturity to recognize that those concerns are separate, and often diametrically opposed to, real excellence and depth? I believe the answer is the same; There would be a large absolute number of students willing to make the commitment even though the relative proportion of all students might be very small.
This minimalistic description gives an idea of the kind of thing that could be created if there were a small group of people that shared the vision. Of course how it all worked out would be a function of exactly who the founders were, but letting go of the dysfunctional form that academia has evolved into and embracing a revitalized, integrated vision for teaching and research, it is certain that the students and faculty of the resulting organization would not lack a sense of purpose and accomplishment. Happiness would follow, as it always does when basic human needs for face-to-face connection and creative productivity are met.
Ready For College?
If everyone took 2-3 years to work and travel after high school, doing work that was useful to someone and travel that taught them independence and benefited others as well, students would arrive at college with a maturity level that enabled them to get a far greater amount out of the experience. This would also go far in counteracting the enormous waste of time and money that happens when students come to college to party and get a job certificate.
When my son graduated from high school we strongly supported his decision to take a break and it is something that I recommend to everyone that will listen.
My experience with returning students is that overall, they are all better off for the break. They return with a sense of purpose and determination to spend their time and money well, to get maximum value from their college experience. They are also much more inclined to heed advice or at least listen carefully before finding their own version of the right thing to do.
Making it personal
My own story is one of extensive meanderings that I now recognize were critical pieces of my education. It began with homeschool and music and parents with very broad interests and experience, combined with the southern New Mexico environment filled with eccentrics, who, contrary to apparent belief today, did not actually encourage me to believe in perpetual motion or the hollow earth theory (both of which were believed by people I knew). Instead, that environment gave me freedom to explore and theorize in my attempts to understand the universe, God and how everything operates. Even though he was a vocal artist and teacher, my father was also able to do almost anything with his hands and because of this my brother and I grew up building and tinkering, which both of us have continued to do in our own substantial shops.
Pausing for a moment on this point, it is important to note that in addition to choosing not to have television, my parents provided all the resources for us to create and invent and fabricate things that we imagined. Eventually we learned trades — I learned piano tuning and my brother learned automotive technology. Though it has been 35 years since I tuned a piano, the habit of working with my hands, of creating things in my shop, has stayed with me to this day. The same goes for my brother who now has other people work on his cars, and instead spends his spare time creating impressive works of art from wood and metal in his shop.
We moved to Eastern Washington to attend Walla Walla University, a high quality parochial school, filled with students and professors that could have been at places with higher reputations. After college, in an attempt to deal with the trauma of losing both parents, there was more wandering that led through graduate schools, divorce, oceanography research, life in a little cabin in the hills above the Santiam River, a research seed farm, construction, consulting, 7th and 8th grade teaching, research in a medical school, remarriage and graduate school in Portland, Oregon. This led to Los Alamos where I started my career as a mathematician, in an environment that was ideally suited to someone with ability and energy who had, so to speak, come out of the woodwork. (This is the biggest tragedy in the decline of the national labs — they were places where good ideas and ability got you somewhere independently of where you were from. They were also places with an almost unique ability to nurture very high quality, inter-disciplinary work.)
Between the wandering and the graduate school in Portland, there was a conversation with a cousin. I had just remarried and was running a small research lab in the medical school in Portland. We visited his small farm in Oregon and he noticed that I was emotionally out of sorts, not peaceful about something. He remarked that when I had lived down in his area (that little cabin above the river) he had noticed that every time I went on walkabouts in the hills and mountains, I could leave in a state of anxiety or under some emotional cloud, but I would return with peace and clarity. He said, “You should do this every day!”
I took his advice to heart and upon returning to Portland started taking long walks in the woods and forests where I lived. On those walks I discovered who I was and what my passion was. I had found my muse. In conversations with God (my atheist friends have alternate, though sympathetic descriptions for what I experienced), I began to see things in a different light, finding that there was a living path into whatever you wanted to do, one that was as different from the usual career trajectory as a rich, living garden was from a herbarium with its dried and described plants.
I returned to graduate school with an entirely new perspective (and a new baby son).
Since then there has been evolution in thought and perspectives, but the experience in the woods and forests remains pivotal. I believe that the experience explains why I have often approached situations with a different viewpoint, believing that there are many ways to solve problems, that there is usually something good to be preserved and yet that is no reason to insist on keeping the bathwater with the baby.
The experience is also the reason that I view my job as a professor and mentor very broadly. i see it as my duty to encourage students to find their own muse, to listen to talks like David Levy’s No Time to Think, to read books like David Shenk’s The Genius in all of us and Buscaglia’s Love, to get some of their news from places like Truthdig and the Real News Network, to publish open access papers and think carefully before giving up copyright and think deeply about what it implies before you accept money from places like the defense industry or the security industry. In addition to teaching geometric measure theory and nonlinear analysis and other fascinating subjects, in addition to guiding dissertations and projects and interactions with industry, it is my duty to prompt them to think, to live examined lives and settle for nothing less than wholeness and emotional health. In that way, and only in that way, will I have helped set them free to travel and thrive on a sustainable, living path.
The conclusions they arrive at may be very different from mine, but then, thinking in unison is never a good goal. What I do know is that they will have the tools, not only to adapt and thrive, but also to correct and restore and recover from the mistakes that they will inevitably make.
Inspired and Provocative
I found a variety of reviews of Excellent Sheep when I was reading the book and not surprisingly, some people loved the book, other hated it. One that I enjoyed quite a bit was James McWilliams’ review, Why Did ‘Excellent Sheep’ Alienate So Many Readers?, which appeared in the October 2014 Pacific Standard. Like James, I believe that it is probable that those who disliked the book are those for whom the book hits too close to home. Though a thoughtful reading of the book will often inspire vigorous discussion, it seems to me that such a reading will also recognize that the book is long overdue, that the author has the experience to make the book worth reading and that attacks on the book reveal more about the attackers than the book.
But even those attacks on the book are useful, for they remind us that the emotions, acknowledged or not, can easily overwhelm everything else, irregardless of how much sophistication and skill one uses to try to disguise the fear or pain that drives our responses. And if we read those other reviews sympathetically, they will remind us that we are all susceptible to these reactions and complicit in a society that lets fear rob us of deeper insight and deeper lives.
To rob fear of its prey, to turn around the slide into the illusions of our modern age, we must first understand the guiding delusions and then direct our energies towards inspired, counteracting goals. As an antidote to the current delusions and an inspiration for change in higher education, I know of no better book to begin with than this book by William Deresiewicz.