Whatever is my right as a man is also the right of another; and it becomes my duty to guarantee as well as to possess.

With this posting, I am putting an end to this blog. I do not want to do this, but I feel I am being forced to. In addition, I do not feel that I am at liberty to go into the nature of the pressure being placed on me to stop. Nonetheless, I am being clearly pressured, if not threatened. When you call your wife to talk to her about an event and her response is fear bordering on terror, it gets your attention. I don’t want to hear that ever again. That is enough to get you to say, “fuck this shit”.

At a minimum this is a hiatus, but it is likely the terminal point of this part of my journey. For those of you who enjoyed reading, thank you, your views and comments helped make this more worthwhile. Frankly having readers was not the reason I did this. The reasons are varied and largely personal. First and foremost, the blog was a way to practice writing as a habit. Writing is a core professional and personal activity. A focus on writing is key area of personal and professional development. It is difficult and often exposes one to intense and personal criticism. A blog meant that the work would be published and read by others. That has a way of focusing the mind, and you take things more seriously. When you write only for yourself, the level of care and attention is not nearly so acute. Occasionally a blog post would resonate and get a lot of viewers, which is a nice feeling. More often I would get a handful of viewers, but the post had already achieved its intended purpose.

The topics of the blog posts were varied as well. Many blog posts were simply highly technical discussions of the many topics I’m interested in. In other cases, I am giving a talk and it helps to write about the narrative arc of the presentation in advance just to get my thoughts in order. Other blog posts were commentary on our scientific programsat a National level. The level of intellectual discourse around our programs is dismal, I’m lending my thoughts to the vacuum of ideas. Other blog pasts were pointed at dealing with the management of science. To say that science is managed poorly today is an understatement of some magnitude. It is getting worse. Finally, a handful of posts were completely out of character, and simply existed to maintain the writing habit and speak to something I really believe in. This won’t be the end of my writing, but it will happen in a different forum probably anonymously. I may experiment with different forms of writing too, fiction, poetry, …

I can easily guess what type of blog post generated the pressure to stop. Let’s just say that it’s not likely the technical blog posts. In addition, the blog was a wonderful relief valve for frustrations that my workplace has low tolerance for. Apparently, they also have a low tolerance for freedom of speech too, or any intellectual discourse for that matter. It is amazing that a place that talks about defending the Nation has such low regard for its core principles!

I’ve noted the parallels between the modern work environment and our increasingly toxic and appalling societal culture. I believe that the treatment here is utterly consistently with today’s prevailing culture. To put it plainly, Donald Trump is the most obvious symptom of the disease and his rise was enabled by the sort of toxic behavior I see here. He did not happen in a vacuum; he has a legion of enablers even among those who didn’t vote for him. Whoever set the gears in motion to end this blog is absolutely 100% a Trump-enabler. They might be a supporter of the President, or more ironically an opponent.

I can say that there was a very clear and unambiguous message to “shut the fuck up”. I heard it and I’m making a reluctant, but rational choice. So, I am shutting the fuck up.

Goodbye. It has been a wonderful experience. Thank you for coming with me.

An idea that is not dangerous is unworthy of being called an idea at all.

― Oscar Wilde

Uncertainty quantification (UQ) is a truly dangerous activity for modeling and simulation. This might seem to be a rather odd thing to say with all the focus and interest on research in UQ. The problem with uncertainty is its seeming contradistinction with precision. Computers are seen as a tool to provide precise well-determined solutions with some degree of repeatability. Examining the uncertainty of the solutions and the models run counter to the seeming spirit of the field. More deeply the computer-based solution of the models is treated with a degree of suspicion by many. The purveyors of these solutions seek to blunt these suspicions with a degree of confidence about their legitimacy. The notion of uncertainty runs counter to the intent of providing confidence in solutions. As such uncertainty is frequently downplayed and poorly executed to buoy confidence. This mentality is a genuine threat to the scientific credibility of modeling and simulation.

One of the prevailing uncomfortable aspects of computed solutions to models is their intrinsically approximate nature. We don’t have the sense of security that analytical solutions provide someone (even if this is largely an illusion). Numerical practitioners are both arrogant and slipshod in their approach. They show too much arrogance in providing solutions without necessary caveats and appropriate care for the correctness of solutions. The slipshod and scientifically careless approach of proof by overwhelming power and colorful graphics is easy to fall back on. Moreover, these terrible practices are effective. The approximate solution of the models of nature is an intricate and highly technical nature of the expertise. There are numerous ways to completely screw it up. Too many users of numerical model solution are either oblivious to the intricacies or willfully ignore concerns.

One of the major issues with modeling and simulation is the lack of negative feedback for egregious practices. Either willfully or implicitly major sources of uncertainty are ignored usually to the benefit or modeling and simulation. If modelers were truthful and accurate about uncertainty there is a perception that the results might be treated with less confidence. This might indeed be true, but the lack of disclosure and honestly in this practice is genuinely dangerous. By failing to address the uncertainty of computational models directly we are harming progress in distinct ways. We are failing to use the knowledge of what we don’t know to guide our research. Uncertainty is the study of how well know or don’t know something. In other cases, there is a limit to how much we can know, in some cases there is a core uncertainty that is irreducible. We need to know this and act accordingly.

All of this discussion is a subtext to the observation that we allow ourselves to default to uncertainty estimates of zero. In other words when we know nothing at all we chose a default uncertainty estimate of zero, which is the smallest value possible. In other words, we demonstrate a complete lack of knowledge with an estimate that implies exact and complete knowledge. This is patently and utterly absurd. We only get away with this utterly untenable situation because of the exotic and esoteric nature of computational modeling. It is viewed as the purview of experts and deeply technical and complex.

When the depth of a technical field is used to shield the associated work from scrutiny, it is deplorable. For UQ this is the standard way of operating. The modeling associated with typical simulations is quite complex on a number of different levels. The most esoteric and technical aspects of the entire field are the models themselves usually based on differential equations, which must be solved by complicated mathematically complex numerical methods. Physical reality is then represented by a mesh along with modeling choices to make the overall simulation tractable. Each of these areas is only well understood by highly specialized scientists invariably having PhD’s who are actively working on research. The complexity only diminishes slightly in the voyage down to the computing hardware. In each of these areas there are incredibly detailed technical fields that are inaccessible to all but the most educated and specialized scientists. The result is an intricate interlinked set of activities that all must be executed at a high level to produce competent modeling and simulation. Looking into UQ is then another complex specialty added into an immensely complex system.

One of the most difficult issues about UQ is its focus on the most technical part of the simulation pipeline. UQ is heavily focused on physics, engineering and mathematics often blended together intricately. UQ is demanding in terms of computation, but far more demanding in terms of intellectual labor and the overall flow of work. The hardest aspect of the field is dealing with all the things unknown or barely known. There are swaths of knowledge and information we have no grasp on. With UQ we combine the deeply esoteric along with the unknown into a stew of impenetrable complexity. It can also produce the effect of being a great place of people to obfuscate. Being part of a generally esoteric activity, poor and shoddy work can easily pass as high quality, especially with gee-whiz graphics and movies to provide panache to information. Somebody who is engaged in this sort of marketing-based approach to work will likely want to under-estimate the uncertainty to provide a false sense of better precision than is justifiable.

Here we get to the crux of the problem with uncertainty. Large uncertainty is almost invariably judged as a problem. With a complex and esoteric subject like modeling and simulation the ability to either pass poor work off as good, or outright lie and bullshit about quality is great. Increasingly the management and customers for the work are incompetent at judging its quality. As such they are prone to reward work that provides low uncertainty even if the nature of the work is poor. What we have is the perfect storm for promulgating bad work, complex multi-disciplinary work judged by technically inferior management and customers. It is the perfect storm for skipping large portions of the quality work needed for excellent work. In addition, high quality work is expensive, time consuming and difficult. Why do this when the customer will accept a shoddy cheap product? Why do it when the customer cannot tell the difference?

In this view the failure to address conduct UQ rather completely reduces our ability to determine where progress can most impactfully be made. Uncertainty can be used to guide investments in the wide array of disciplines needed to conduct modeling and simulation. It shows the source of lack of knowledge in clear terms, which should dictate effort toward progress. In places where the uncertainty cannot be removed because it is intrinsic, we can accommodate the uncertainty and look to progress elsewhere. In either case, the UQ is needed to provide meaningful direction. For example, our current emphasis on providing and using massive computers is not grounded on any necessity based in uncertainty. If you look at the program only the barest lip service is paid to UQ or its parent activities of verification and validation. For the most part the justification in focus on computing hardware is based entirely on superficial and naïve arguments divorced from evidence.

We can use the knowledge for bad or good. If we are good we can push ourselves to demand excellence by identifying and either computing, estimating or bounding all the uncertainty. On the other hand, knowing that good work is not rewarded and often not payed for, we can promote bad work. We have managers and customers who don’t know the difference anyway, so why do the extra work? This would seem to be the spirit of today, why do good work when bad work is just as acceptable?

Everything you’ve learned in school as “obvious” becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There’s not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines.

― R. Buckminster Fuller

Suddenly summoned to witness something great and horrendous, we keep fighting not to reduce it to our own smallness.

― John Updike

Much of my thinking goes into figuring out what the hell is going on these days. I’m distinctly unhappy with how work has evolved over the course of my career. On the one hand I feel like I’ve become that guy who pines for the “good ole days”. At the same time, I crave progress and a better world. I don’t want tomorrow to be like yesterday at all. The progress and World I desire didn’t exist in the past, but we were moving far faster toward it then. The good times of the past were defined by progress and purpose of work. It is the sense of progress, the meaning of work and sense of purpose that has been drained from my day. I realize that my expectations of work resolve around the spirit of progress toward something with importance and meaning. Work should have a clear purpose beyond simply delivering a paycheck. Work should be life affirming beyond its mere conduct.

I feel I’m living in parentheses

― Steven Wilson

I sat down recently with one of my managers to make an admission that felt rather profound. My expectations of work are rather far beyond anything my employer can deliver on. This conclusion is rather intensely sad. Rather than lift me up and encourage me to greater heights, the demands of my job are smaller than me. I will have to lower myself to meet them. I don’t think this is uncommon, but rather a sad testament to today. I think this sentiment is broadly applicable and the strain between survival and a life of meaning has grown acute society-wide. More and more we aren’t dreaming or grasping for something bigger than ourselves. Day in and day out life is merely about survival and a host of petty concerns. The lack of meaning and purpose is a reflection of society as a whole. Most people are struggling even if the economy is humming. Our Nation is about reacting to fear, distrust and hatreds than aspiring to progress, hope and betterment. Work sadly reflects this time with cruel parallels.  \

Smallness is subversive, because smallness can creep into smaller places and wreak transformation at the most vulnerable, cellular level. In a time when largeness is threatening to topple us, I wish to remember and praise the beauty of smallness, in order to banish the Goliath of loneliness.

― Sarah Ruhl

I told my manager, “I think you’re all basically good people, you can’t meet my needs in the current system.” I continued, “the system isn’t going to change to meet my expectations, so my expectations need to change.” It was an earnest and deep realization about the nature of work today. It is easier said than done. To make this happen, I need to let go of my deepest principles, hopes and dreams about work. I never wanted to be that guy who just went to work for a paycheck and spent time daydreaming about living a different life. I never wanted to be that guy who couldn’t wait to leave each day to really live, and found the weekends were never long enough to make up for the time lost. Yet here I am, being all those things because work has become so entirely empty of importance, meaning and value. It does not have to be like this, and ultimately this state serves no one, not even those who seemingly benefit.

In order to escape accountability for his crimes, the perpetrator does everything in his power to promote forgetting. If secrecy fails, the perpetrator attacks the credibility of his victim. If he cannot silence her absolutely, he tries to make sure no one listens.

― Judith Lewis Herman

It is instructional to examine some of the concrete aspects of work that could step into this abyss and form some purpose and meaning. For example, we have a national program to reclaim the supercomputing throne again. It is an exemplar of what is wrong with today’s World in many ways. It is what masquerades as a big idea today. Instead, it is a very small idea. Supercomputing has ridden the coattails of Moore’s law for fifty years and that time is coming to an end. For a while we could advance in computing without any strategy or effort, just an expenditure of money. Those days are over, but the tiny thoughts surrounding it are still present. Rather than react to this reality we are simply repackaging the same old stale ideas we have used for the past 25 years. The use of modeling and simulation is an essential modern scientific tool. Among the things that need to be done to enable effective modeling and simulation the supercomputing hardware is the least important thing. It is the furthest away from reality and its impact is diluted by a host of steps that all must be done correctly for the hardware to have meaning. This current program is shorn of effort in all of the most important things in modeling and simulation. The greatest gap is the sense of meaning that this program has in the real world is simply a marketing ploy. It has no reality or substance at all.

Beyond scientific progress, we need social and societal progress in many fronts. Science has often been at the vanguard of change either providing new truths to confront or energizing change through technology. We should all be trying to make a better World for all our citizens. Today’s world is trying to resist the truth and changes at every turn. We have huge swaths of society resisting the clearly defined risk of climate change through desperate ignorance. Technological change with information technology has become incredibly destabilizing both socially and politically. It is driving subtle social changes with how we form community, how we communicate and inform each other. It is having also been harnessed by the forces against progress to energize fear, and anger. This has emboldened hatred, bigotry and conflict that acts to solidify the hold of the powerful over society. We are headed for a massive conflict that will shape our future. The current situation is not sustainable in any way.

At the core of the conflict is the clash between the old and the new, the forces of progress against stagnation. In the United States this looks like a poorly educated shrinking white majority joined with a hyper-wealthy ruling class pitted against an array of minorities along with the highly educated. The status quo forces on the right want two things: putting these minorities back in their ghettos and closets, and a continuation of the pillaging of the Nation and stockpiling of wealth. They are using fear and authoritarian tendencies along with anti-democratic means to fight against progress. Right now, they are winning. Many of the people most harmed by the hyper-wealthy ruling class are supporting their political agenda. This support comes directly from the agenda of hate, violence and bigotry arising from their misplaced blame for their woes.

Part of the problem is that the forces of progress are not unified about anything, and this lack of solidarity as a movement is exploited by the right. If the forces on the left cannot find common ground all of them will be ground up under the jack boot of the right. Progress is preyed upon by fear and mistrust at every corner. The forces on the right behave with utter contempt of history, science and decency at every turn. They are hypocrites in every act, yet they still win. Their actions produce an increasingly desperate economic situation for their poorly educated, but hateful supporters without consequence. Without this critical feedback loop, we are in a dangerous spiral toward fascism, which the authoritarian rabble would welcome.

Perhaps one of the greatest issues we have is a deep and pervasive lack of trust. We don’t trust anyone with anything today. The cost of this lack of trust is massive and paralyzing. It is very clear that my employer doesn’t trust me at all. It is clear that the government doesn’t trust my employer either. People don’t trust the government, and everything is getting worse. We now have a President who pours gasoline on the lack trust by attacking our most trusted institutions. He is in the midst of turning the conservative movement against our most hallowed law enforcement agencies. The very rule of law is being challenged. All of this will drive wedges into our social order that will end up killing people. Long before people die the social chaos and damage will unfold. We will see problems already present due to low trust to magnify. The challenges already existed, and the current situation is only amplifying an already dangerous situation. A host of difficult economic concerns that already limit any benefit that normal people receive from economic growth will only get more strained.

Micromanagement is the destroyer of momentum.

― Miles Anthony Smith

I can see the lack of trust daily at work. We are micromanaged in everything we do and watched like hawks. Everything we do is treated with suspicion. The micromanagement at attitude toward the work we do is a leading cause of smallness of thinking. With little trust in evidence in the work place we cut our work into tiny increments that are devoid of risk taking. The overwhelming lack of trust leads to the definition of work that takes minuscule risks since failure is unacceptable. Increasingly, our expertise is unwelcome either in informing the government, or even internally. There used to be a time where the experts, the institutions and the government worked together to solve big problems and craft solutions to vexing issues. Now everything is so small that nothing big can even be attempted.

Authority—when abused through micromanagement, intimidation, or verbal or nonverbal threats—makes people shut down & productivity ceases.

― John Stoker

Vexing problems require risky solutions as well, and with risk off the table we simply avoid hard problems. Today that chain is broken at every level with our leadership being increasingly devoid of intellectual depth. Our experts are ignored, the institutions just want money and the government controls the money. Expertise is unwelcome because it only complicates the process and gets in the way of the money. This problem is one of the core issues with any strive for excellence and utility of peer review. Our institutions increasingly don’t care what they do as long as its paid for. The government has no interest in the work or its quality. All of this is a horrible downward spiral. In its wake value, meaning and quality are sacrificed. At the core of this maelstrom is an awful lack of trust and honesty that sprawls across society. If we can’t trust each other, we can’t work together and doing anything great is completely out of reach.

We are incredibly fear driven as a society. This fear makes us small, timid and undermines any chance for greatness. The lack of progress, fear driven beliefs and trust deficit only benefits the powerful and rich at the top of society. It only benefits these people in the short term. in the long term their power and wealth are diminished by the lack of growth overall. They only gain a relative degree of power, wealth and standing in comparison to the common man. We are living in a period where overwhelming fear is being used as a tool of the powerful. In the wake of 9/11 we saw irrational fears used to justify vast authoritarian overreach that continues to this day. We see huge defense budgets to be pillaged by the wealthy. The post 9/11 World has taken the United States directly toward a being a police state. People don’t even bat an eyelash at our massive level of imprisonment. It is a deeply unhealthy characteristic of our Nation, and most people are oblivious. At the same time the fear produces a compliant populace hungering for the safety of strong man rule. We see this playing out across the West as Democracy recedes in response. As Democracy recedes war will surely follow.

People care much more for how things look than how things are.

― Donna Lynn Hope

Today, work just seems small, a tidal wave of the small and insignificant drowns purpose and meaning. The tide of micromanagement underlies a lack of trust combined with a broad core of structural dishonesty. Almost everyone is drowning in this sea of minutia that cripples our ability to focus on anything big. All of us are simply buried in mountains of useless bullshit too deep to allow us to concentrate on anything important. Meanwhile we are being taken over by authoritarian forces pushing us headlong into a police state. Many Americans are welcoming the imposition of rule by a strong man ruler. The loss of fundamental principles of our democracy are accepted and even welcomed. We are headed headlong toward some sort of modern version of civil war. Conflict is almost inevitable, it is just a matter of time until society fractures. Maybe work is small because more important things are happening. It is time to pay attention.

Distrust is like a vicious fire that keeps going and going, even put out, it will reignite itself, devouring the good with the bad, and still feeding on empty.

― Anthony Liccione

Everything must be made as simple as possible. But not simpler.

― Albert Einstein

A few weeks ago, I wrote about the variety of partial differential equations with their hyperbolic, parabolic and elliptic character. The point of the essay was noting that parabolic and elliptic equations have some intrinsically unphysical aspects. While this is true to an extent, I failed to note the linearity of these concepts. Some of my wise readers called me on this oversight in particular with respect to nonlinear parabolic equations that exhibit clear wave like behavior. Where linear parabolic equations produce infinite speeds that are clearly unphysical, the nonlinearity of the diffusion produces finite wave speeds and fronts usually associated with compressible flows. The nonlinear diffusion equations are used to model porous media and radiative transfer. The higher the degree of nonlinearity, the sharper and more shock-like the fronts behave. Furthermore, this sort of diffusion can be extremely useful for numerically stabilizing the solution of hyperbolic PDEs. My failure to note this texture was a significant oversight on my part.

One of the points of looking at linear equations is related to the nature of our knowledge of analytical solutions. Our ability to solve problems where the equations are linear is far greater than for nonlinear equations. The most general approach to understanding equations uses the technique of linearization to help understand the nature of solutions. For nonlinear hyperbolic equations this approach has been quite powerful for providing some systematic explanations of the basic character of solutions. As the nonlinearity of the equations grows, the limitations of this common approach grow. Eventually the linearized equations are of little use for practical understanding. Nonlinear diffusion is a powerful example of this. Eventually compressible fluid dynamics also departs from any strong connection to the linear analysis. In particular the nature of turbulence is definitely nonlinear and poorly understood. Moreover, the nonlinearity that produces turbulence is only quadratic, yet eludes any real deep understanding analytically. One can only imagine the mysteries that surround greater nonlinearity.

Other aspects of modeling with PDEs are problematic. One issue that comes up frequently with hyperbolic heat conduction is relativity. Generally, models are not Lorenz invariant. Almost every equation can be recast in a relativistic form to fix this issue. For many cases this has no significant influence on the solutions to the model. In hyperbolic heat conduction the changes return the equations to satisfying the second law of thermodynamics. The speeds in the equations are generally not relativistic, which makes this an extremely curious result. In greater depth, the entire notion that grounds the second law is equilibrium thermodynamics, and the processes in hyperbolic heat conduction are out of equilibrium. We need to carefully apply principles and assumptions when their foundations are being shaken.

Simplicity is a great virtue but it requires hard work to achieve it and education to appreciate it. And to make matters worse: complexity sells better.

― Edsger W. Dijkstra

What’s measured improves

― Peter F. Drucker

What gets measured gets managed.

– Peter Drucker

The United States appears to have a white-hot economy, or at least the stock marketseems to indicate this. At the same time the vast majority of people are not benefiting. Life is genuinely hard for most people and getting harder. People have generally had jobs, but the jobs don’t lead to a good life with people stretched paycheck to paycheck, and health care ravaging any chance of having extra money. Simultaneously the rich are just getting richer. At the core of this disparity in outcomes from a seemingly robust business climate is the fundamental philosophy of our businesses, the maximization of stockholder value as the preeminent goal of business. This philosophy does not benefit business, customers, employees or society, it benefits shareholders who are the very rich. We now have moved to the point where the idea and the wealth it created at the top of the food chain has bred graft and corruption. The laws of the Nation have been altered to serve their wealth and away from serving the people. We are moving headlong toward catastrophe ushered in by the resulting imbalance.

So the question is, do corporate executives, provided they stay within the law, have responsibilities in their business activities other than to make as much money for their stockholders as possible? And my answer to that is, no they do not.

– Milton Friedman

The situation gets worse when one looks at government. Increasingly the government looks to business practices to effectively deliver results from their programs. The business practices that the government looks to are drawn from the prevailing philosophy, maximized shareholder value. Government programs don’t have shareholders, but the influence is strong. We see money as driving everything in our work. Technical excellence, service, employee engagement, social impacts and long-term health of programs are all scarified to this philosophy. In business the maximize shareholder value leads to short-term thinking (driven by quarterly statements, profits), and these breeds short-term thinking in government programs. As a result, we have produced terrible government, and terrible results. Increasingly, the result of government being ineffective and awful is a self-fulfilling prophesy. Government can be effective, but only if we manage using principles that focus on effectiveness. In a sense the right philosophy for government needs to be different because the profit motive is not present. In the place of profit we simply see an acute focus on money and cheapness replacing service and excellence.

On the face of it, shareholder value is the dumbest idea in the world.

– Jack Welch

Shareholder value is a result, not a strategy…your main constituencies are your employees, your customers and your products.

– Jack Welch

Maximizing shareholder value is not the only business principle we might focus on. Given the ability for the rich to buy government, it is no surprise its power has grown. Moreover, the rich only get richer as a result of this singular focus. Instead we might choose a business principle that balances profit and shareholders with the long-term health of the business (research & development, capital investment), employee benefits, developments, concerns and engagement, customer-orientation and social responsibility. All of these other priorities are conspicuously missing from our business climate, and our government program execution. In business we have happy rich stockholders, and in government programs no one is happy. The government exists to serve the people of the Nation and increasingly we are utterly inept. Government is not a bad idea, the bad idea is how we are managing it.

A change in focus in both business and government would benefit everyone except the very rich. We could have happier and better businesses in the long run, happier and better employees and customers. Business would act with social responsibility and benefit their respective communities beyond simply giving citizens jobs. They would act like good stewards of their community instead of trying to undermine all manner of laws and regulations that might undermine pure profit. The same attribute would be transformative for government programs. We would see long-term interests replace short-term approaches, employees would be served along with the taxpayers, and social responsibility would be served. We would see the idiotic and destructive idea that government-based work has any customers other than the Nation and its citizens.

These basic philosophies have major influence on how our society functions. In a sense we have chosen an approach that leads to rather predictable outcomes in vast wealth inequality and growing social deficits for everyone else. In adopting this principle mindlessly, we have helped create ineffective government. Let’s face it, the choice to make business principles the basis of government execution has produced terrible results. Perhaps it is not this basic principle, but the choice of the business principle to use. This choice was largely an article of faith. The leaders of business on like maximizing shareholder value because they are shareholders. It benefits them financially. In every other resect his philosophy is terrible for the businesses themselves, hurts employees, harms customers and allows abdication of social responsibility. We see businesses that are absolutely eager to harm the Nation, its citizens, the environment, and break the law all in the name of short-term profit.

Free enterprise cannot be justified as being good for business. It can be justified only as being good for society.

–Peter Drucker

Each of these is a pretty good description of how wrong everything is wrong with the United States at large. The bosses are doing great. The higher the boss is in the company or government function, the better they doing. Executive compensation is soaring while everyone else falls behind. The nation has become utterly short-term focused in its thinking. We can barely focus on anything for more than a day these days. The employees are struggling mightily. People are hurting, and these people are the employees. We can’t expect people to be good employees, parents, citizens if their lives are hanging by a thread. Almost no one exercises any social responsibility with both government and businesses showing total disregard for the citizens of their nation and community. All of these ills are the direct result of embracing greed as the core principle for business and government. The outcomes should surprise no one. Fixing this would mean a wholesale change in the emphasis of the ruling class away from self-enrichment to broader leadership with responsibility for others.

Management is doing things right; leadership is doing the right things.

– Peter Drucker

The eye sees only what the mind is prepared to comprehend.

― Robertson Davies

In the classical view of uncertainty, we see nicely distributed errors often associated with the Gaussian probability distribution. In this view of uncertainty, it is symmetric, and it is smoothly distributed. In most real cases our lack of knowledge is hardly like this at all. In most cases we have significant bias in what we don’t know. In addition, we have systems that are calibrated so that models (simulations) have sufficient congruence with measurements to yield comfort to those who use them. In particular when we have a calibrated result, the bias in uncertainty is utterly essential to represent if we hope to predict with any justifiable confidence. For most cases where calibration is utilized, the bias is inherent in that process, and should be reflected in the uncertainty. If we are engaged in genuine prediction with the uncertainty, these biases can have rather profound impacts away from where we have data and where we are actually predicting results.

In many modeling exercises it is quite difficult to separate the act of calibrating models from validating those models. In the simplest setting we see models calibrated using some sort of regression technique, most often a form of least squares. The use of these techniques only serves to amplify the kneejerk view of uncertainty as the errors between the data and the best fit are Gaussian in least square regression. Once we merge these models with a more complex nonlinear system model we begin to systematically diverge from this idealized circumstance.

For very many systems the model is needs to represent a careful balance between large nonlinear terms. In this sense we have many important problems where the core of the scientific or engineering problem is very close to an equilibrium state. Our weather and climate are epitomes of this principle. In these systems the answer is determined by small deviations away from the equilibrium state. Another wonderful example of this principle is a Type II Supernova where it teeters on the edge of this equilibrium and complex processes determine whether the star explodes or collapses into a black hole. A well represented equilibrium is more important to modeling than numerical or physical accuracy of the individual terms. In these cases the numerical error can be sufficient to upset the equilibrium rendering the simulation functionally useless. A calibration of a poorly understood model is used to compensate for the numerical error and place the system back into equilibrium. This common circumstance presents a distinct challenge for uncertainty estimation.

Quite often in these systems, the numerical error in the model is rather substantial even with today’s massive computers. Moreover, the numerical error will remain important for any foreseeable future, we cannot simply build computers powerful enough to erase this issue. So that we can continue to conduct useful modeling and achieve appropriate dynamic balances (where large terms almost equal and opposite are modeled), we must calibrate the model and compensate for the numerical error. In a vast number of cases this calibration is thrown into the broad category of turbulence effects, justified by the general lack of understanding that turbulence engenders. In this light any view of numerical error as an unbiased error is harmful. The standard view of the V&V community (Roache, Oberkampf & Roy, AIAA, ASME, DoE,…) views numerical error this way. In my opinion this unbiased view renders the numerical uncertainty almost useless for many applied cases. Well-behaved and controlled numerical error is invariably a strong bias error as we model in a mesh converged manner. We see results approach the “mesh independent” solution (by the way I hate that term because it lets people off the hook for doing verification/error estimation). If a solution is approached in a manner that is consistent with convergence, the error is almost always a bias. Presenting it as such serves the purpose of improving simulations directly.

The path forward for useful uncertainty quantification for the systems must acknowledge the generally biased nature of the numerical error, and the anti-bias that the calibration often takes on. These two effects cancel each other out where the calibration data exists, but when we get into an extrapolation of results into a predictive scenario we can expect these uncertainties to grow. This can be seen in the standard view of uncertainty for regression where any uncertainty grows quite large when data is no longer tethering the calibration. Therefore we might expect numerical errors to remain similar in the extrapolated region, but the compensation modeling uncertainty would grow away from calibration data. This could have profound consequences for many of the simulations of near equilibrium systems that dominate high consequence investigations. To get a reasonable and defensible uncertainty for these predictions the bias is absolutely essential. Without bias in the uncertainty and the effects of the cancellation in calibrated results, the uncertainty will be poorly and inaccurately represented. If the bias is not included in the assessment we can expect the predicted uncertainty to be wildly out of character with the reality of modeled prediction.

We all see only that which we are trained to see.

― Robert Anton Wilson

Oberkampf, William L., and Christopher J. Roy. Verification and validation in scientific computing. Cambridge University Press, 2010.

Roache, Patrick J. Verification and validation in computational science and engineering. Vol. 895. Albuquerque, NM: Hermosa, 1998.

V&V, ASME ASME. “V&V 10-2006: guide for verification and validation in computational solid mechanics.” New York: American Society of Mechanical Engineers (ASME) (2006).