# The End of the Regularized Singularity

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.
― Thomas Paine

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

# We can’t do big things; We are swamped by small things

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

# We are drowning in bad laws

Errors do not cease to be errors simply because they’re ratified into law.

― E.A. Bucchianeri

Today I’ll stick my nose into some of the appallingly destructive laws we have to live under. We are about to see a new one enacted to all of our detriments. We are a Nation that depends on laws for order and the common good. When the laws are simply veiled attempts to push other agendas that harm innocents, all law is undermined. In other cases, the law is simply incompetent and ill-suited to provide the intended good. The worst case are laws that are both veiled agendas and incompetent.  These laws threaten the future, order and the tolerance of people. They do genuine harm to all of us. Unfortunately, we have far too much legislation that follows these characteristics. Many of these laws are marketed as something they are not so that they can serve the agendas of the powerful, often oppressing the weak and vulnerable as a side-effect.

Most people are not aware of what is happening to the Internet right now. The congress is in the process of passing a censorship of free speech associated with sexuality. These laws are packaged as efforts to stop sex trafficking, a horrendous crime and genuine problem. The bills are quite frankly Trojan horses for a whole bunch of other stuff and will actually harm the people it is marketed to help (https://en.wikipedia.org/wiki/Stop_Enabling_Sex_Traffickers_Act,  https://www.engadget.com/2018/03/30/congress-just-legalized-sex-censorship-what-to-know/). It is the latest in a long line of laws that are marketed as one thing but have a different effect. This law will help solidify the hold of the corporate giants for online services and attack online expression of sexuality. We’re already seen Craigslist shut down their personal ads in response. An important avenue for conceptual sex has disappeared along with driving sex work underground where it is more prone to be preyed upon by criminal elements. In total this is destructive legislation that actively harms the people it is purported to help and amplifies existing problems in society rather than alleviate them. We already live in an obsessively shame driven culture with a sex negativity that harms many especially women. The way to combat human trafficking is to make sex work legal and allow it to proceed in the full light of day. It will happen and when it is underground it will attract criminals.

Let’s look at some concrete examples of current laws. At my work we have to abide by export control laws. Calling this law idiotic is an insult to idiots. It combines terrifying penalties for violations with sketchy and piecemeal guidance. It rules by fear and incompetence blended into a toxic stew. For what I do the technical guidance needed for export control is intricate, and the law provides none. At the same time the legal jeopardy is extreme and exceeding that for classified data associated with nuclear weapons. The result is chaos and non-uniformity. The parallels to FOSTA/SESTA are stunning and terrifying. The new legislation is defined by the threat of massive legal jeopardy. These legal hammers are bludgeoning people like Craigslist to take steps to insulate themselves as a result.

Another set of stupid laws are related to drugs and the war on drugs. These laws have produced vast carnage on the population, particularly minorities. In a sense they have worked exactly as their authors intended, the war on drugs was an invitation to massive racial discrimination and a systematic of minority populations. The American prison system is a testament to its success in this horrible regard. The war on drugs has been a failure in every other respect. Americans are just as addicted and commonly using drugs as ever. Drug money flows into the coffers of organized crime and powers murders south of the border. We failed to learn from the failure of prohibition where the illegal booze provided the financial basis and leverage for the mafia. Today we are creating the new mafias with drug money, and FOSTA/SESTA is handing them a lucrative new source of money, the sex trade.

The illegality of cannabis is outrageous, an impediment to full utilization of a drug which helps produce the serenity and insight, sensitivity and fellowship so desperately needed in this increasingly mad and dangerous world.

― Carl Sagan

Marijuana is illegal without regard for its level of risk. It has genuine medical benefits that the law does not acknowledge, and its hard is far less than alcohol by virtually every reasonable standard. Rather than be a gateway to harder drugs, it is an alternative that reduces abuse of opioids. It is only illegal because it was the drug of choice by minority groups and an invitation for systematic targeting by police. Again, the parallels with FOSTA/SESTA are uncanny. We see legislation that sounds like it is a public good and instead is a targeting a vulnerable population. It make sex more illegal and drive it underground where it will help provide money to organized crime. Superficially the legislation sounds good, enacted and in practice it will hurt people and our society.

We cannot expect people to have respect for law and order until we teach respect to those we have entrusted to enforce those laws.

― Hunter S. Thompson

# Nonlinear equations defy simple categorization

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

# Let’s Choose a Better Business Model

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

– 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

# Bias in Uncertainty is Essential

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).

# People are really weird

A perfectly normal person is rare in our civilization.

― Karen Horney

Looking out into the wide world one can easily conclude that people are really weird. There are lots of odd ones who engage in all sorts of irrational and odd behavior. I’m certain that I’m weird too. At the base of all this weirdness is a general lack of honesty and openness. No matter how much I might want to be honest and open, it is generically impossible. Generally speaking, if people could be more honest their behavior would make much more sense. Such honesty is breathtakingly hard to accomplish. In many cases honesty is punished brutally. To be honest is to risk judgement, confrontation, and ridicule from many quarters. Many of those engaging in these reactions themselves hide major portions of themselves for the same reasons. As a result of all this, people are weird, and their actions are not rationally explicable.

The differences in people add to the weirdness because I react to things far differently than others. I’m sure that many others are put off by my wiliness to directly confront issues is weird. In other ways I might dress or act weirdly. This could be a direct result of different tastes, lack of attention or reasoning that is completely hidden by secrecy. For other people who I’m judging as weird, the reasons could be exactly the same. Sometimes the secrecy is driven by shame, or a desire for privacy, or difficulty in managing any meaningful communication. For example, people are highly motivated by sex, but society is extremely sex negative. The combination is shame. People want things with passion yet are pushed to disavow these wants from any public face. We live in an increasingly hostile and judgmental world and many things that might engender these reactions are kept private. Some people simply can’t be bothered to communicate effectively. They simply don’t try. In other cases, if I communicated to you exactly what motivated me, the actions would be entirely sensible. The result is the appearance of unbridled weirdness.

Pushing all of these things out of society and organizations would be worthy progress toward a better World. Shame does nothing for anyone but drive natural behaviors and desires underground. Everyone would be better without its negative force on society. It only works as an engine for projecting someone else’s moral code onto an unwilling person. It creates a host of horrible side-effects that harm people. Desires for privacy are similar. We want things to be private because they are shameful. Some things are worthy of privacy like financial information because of potential for criminal conduct. Some things like a personal pain simply are not the subject of broad interest. In other cases, one wishes to only have certain things shared with a person whom they are intimate. All of this ultimately revolves back to communication. Our communication is the most important and essential aspect of our humanity. Without communication we are just animals. With it we are a society. A focus on doing it well is worth the effort.

The only people we can think of as normal are those we don’t yet know very well.

― Alain de Botton

# We preach diversity and inclusion. We practice exclusion. We need better leadership.

White privilege is an absence of the consequences of racism. An absence of structural discrimination, an absence of your race being viewed as a problem first and foremost.

― Reni Eddo-Lodge

Every Monday I stare at a blank page and write. Sometimes it is obvious with work demands driving my thoughts in a very focused direction. I’d love to be there right now.  Work is pissing me off, and providing no such inspiration, only anger. It’s especially unfortunate because I ought to have something to say on differential equations. Last week’s post was interesting, and the feedback has provided wonderful topics to pick up. One comment focused on other constraints and invariants for modeling that equations commonly violate. A wonderful manager I had from Los Alamos argued with me about nonlinearity, and integral laws with respect to hyperbolic PDEs and causality. Both of these topics are worthy of deep exploration, but my head isn’t there. The issue of societal inclusivity and the maintenance of power structures looms in my thinking. The acceptance of individuality and personal differences within our social structures is another theme that resonates. So, I take a pause from technical to ponder the ability of our modern World to honor and harness the life work and experience from others especially those who are different. The gulf between our leader’s rhetoric and actions is vast leading to poor results, and maintenance of traditional power.

Why am I concerned?

It does strange things to you to realize that the conservative establishment is forcing you to be a progressive liberal fighter for universal rights.

― Brandon Sanderson

This whole topic might seem to be odd coming from me. I am a middle aged white manwho is a member of the intellectual elite. I’m not a racial minority, a foreigner or part of the LBGTQ community although I have a child who is. Of course, my (true) identity is far more complex than that. For example, my personality an outlier at work. It makes many of my co-workers extremely uncomfortable. I’m an atheist and this makes people of faith uncomfortable. Other aspects of my life remain hidden too, maybe they aren’t germane; maybe they simply would make people uncomfortable; maybe they would result in implicit shunning and rejection. All of this runs against the theme of inclusion and diversity, which society as a whole and our institutions play lip service to. In the backdrop of this lip service are entrenched behaviors, practices and power that undermines inclusion at every turn. Many forms of diversity have no protection at all, and the power structures attack them without relief. The talk is all about diversity and inclusion, the actions are all about exclusivity. Without genuine leadership and commitment diversity and inclusion fail. Worse yet, a great deal of our leadership has moved to explicit attacks on diversity as a social ill.

A great democracy has got to be progressive or it will soon cease to be great or a democracy.

― Theodore Roosevelt

Let’s pull this thread a bit with respect to the obvious diversity that we see highlighted societally, race, gender, or sexual identity. These groups are protected legally and the focus of most of our diversity efforts. The discrimination against these groups of people has been pervasive and chronic. Moreover, there are broad swaths of our society that seek to push back progress and reinstitute outright discrimination. The efforts resisting diversity are active and vigorous. In lieu of the explicit and obvious discrimination we have plenty of implicit institutional discrimination and oppression. The most obvious societal form that implicitly targets minorities is the drug war and the plague of mass incarceration. It is a way of instituting “Jim Crow” laws within a modern society. Any examination of the prisons in the United States shows massive racial inequity. Police enforce laws in a selective fashion letting whites go, while imprisoning blacks and Hispanics for the same offenses. Prison sentences are also harsher toward minorities. Other minority groups have been targeted and selected for similar treatments. In these cases, everyone is claimed to be under the same legal system, but the execution of the law lacks uniformity. At work we have policies and practices often revolving around hiring that have the same effect. They work to implicitly exclude people and undermine the actual impact of diversity.

Equality before the law is probably forever unattainable. It is a noble ideal, but it can never be realized, for what men value in this world is not rights but privileges.

― H.L. Mencken

Other practices hurt women in an implicit manner. These practices are relabeled as “traditional values” and are reflected through health care and sexual harassment. The implicit message is that women should be barefoot and pregnant, second class citizens whose role in society is child rearing and home making. Young women are also there to provide sexual outlets to men, although those that do are sluts. They are not worthy of enjoying the same sexual pleasure the men are free to pursue. The whole of the behavior is focused on propping up men and the center of society, work and power. None of their needs or contributions in the realm where men traditionally rule is welcome. Our health care coverage and laws completely reflect this polarity where women’s needs are controversial. Men’s needs are standard. Nothing says this more than the attitudes toward reproductive and sexual health. Men are cared for; women are denied. The United States is a nexus of backwards thought with labor laws that penalize women in the name of the almighty dollar using religious freedom as an excuse.

If we cannot end now our differences, at least we can help make the world safe for diversity.

― John F. Kennedy

In the past decades we have seen huge strides for the LBGTQ community. The greatest victory is marriage equality. Discrimination is still something many people in society would love to practice. At an implicit level they do. Everywhere that discrimination can be gotten away with, it happens. Many people remain in the closet and do not feel free letting people know who they really are. Of course, this is a bigger issue for transgender people for whom hiding is almost impossible. At the same time the level of discrimination is still largely approved by society. Most of the discrimination is the result of people’s innate discomfort with LBGTQ sexuality and opening themselves to even considering being somewhere on any non-standard spectrum of sexuality. It becomes an issue and a thought they would just as soon submerge. This discomfort extends to other forms of non-standard expressions of sexuality that invariably leak out into people’s everyday lives. This sort of discomfort is greater in the United States where sexuality is heavily suppressed and viewed as morally inferior. Our sexuality is an important part of our self-identity. For many people it is an aspect of self that must be hidden lest they suffer reprisals.

This is a global issue

Hate and oppression are rising Worldwide. This hate is a reaction to many changes in society. Ethnic changes, migrations, displacement and demographics are undermining traditional majorities. Global economics and broad information technology/telecommunication are also stressing traditional structures at every turn. Disparate people and communities can now form through the power of this medium. At the same time disinformation, propaganda and wholesale manipulation are empowering the masses to both good and evil. Some of these online communities are wonderful such as LGBTQ people who can form greater bonds, and outreach to similar people. It also allows hate to flourish and bond in the same way. The technology isn’t bad or good, and its impacts are similarly divided. It is immensely destabilizing. Traditional culture and society is also rising up to push back. The change makes people uncomfortable. Exclusion and casting the different out is a way for them to push back. They respond with a defense of traditional values and judgements grounded in exclusion of those who don’t fit in. As with most bigotry and exclusion, it is fear based. Fear is something promoted across the globe by the enemies of inclusion and progress. The same fear is being harnessed by the traditional powers to solidify their hold over their hegemony. This fear is particularly acute with the older part of the population who also tend to be more politically active. These two things form the most active implicit threat to achieving diversity.

In many cases this whole issue is framed in terms of religion. Many traditional religious views are really excuses and justification for exclusion and bigotry. The aspects of the religious traditions focused on love, compassion and inclusion are diminished or ignored. This sort of perversion of religious views is a common practice by authoritarian regimes who harness the fear-based aspects of faith to enhance their power and sway over the masses. This is true for Christians, Jews, Muslims, Hindus, … virtually every major faith. It is manifesting itself in the movement to authoritarian rule in the United States. The forces of hate are cloaked in faith to immunize themselves from critical views. Hatred, discrimination and bigotry are justified in their faith and freed from much critical feedback. They also complain about being repressed by society even when they are the majority and ruling social order. This is a common response when the forces of inclusion complain about their institutionalized bigotry. In the United States the minority that is truly oppressed are atheists. An atheist can’t generally get elected to office and in many places needs to hide this identity lest be subject to persecution. It is among the personal identities that I need to hide. At the same time Christians can be utterly open and brazen in self-expression of their faith.

In virtually every case the forces against inclusion are fear-driven. Many people are not comfortable with people who are different because of how it reflects on them. For example, many of the greatest homophobes actually harbor homosexual feelings of their own they are trying to squash. Openly accepted homosexuality is something that they resist because it seems to implicitly encourage them to act on their own feelings. In response to these fears they engage in bigotry. Generally, gender and sexual identities will bring these attitudes out because of the discomfort with possibilities the identities offer people. These sorts of dynamics are present with religious minorities too. Rather than question their faith, gender or sexuality, the different people are driven into their respective closets and out of view.

Getting at Subtle Exclusion

‘Controversial’ as we all know, is often a euphemism for ‘interesting and intelligent’.

― Kevin Smith

I’m writing this essay on diversity as a white middle-aged male who is seemingly a member of the ruling class, what gives? I represent a different diversity in many respects than the obvious forms we focus on. Being discriminated against happen without consequence. I’m outgoing and extroverted in a career and work environment dominated by introverts who are uncomfortable with emotion and human contact. I’m opinionated, outspoken and brave enough to be controversial in a sea of committed conformists. Both of these traits are punished with advice to blunt my natural tendencies. You are expected to toe the line and conform. The powers that be are not welcoming to any challenge or debate, the mantra of the day is “sit down, shut up, and do as you’re told” and “you’re lucky to be here”. The message is clear, you aren’t here as an equal, you need to be a compliant cog who plays your role. Individual contributions, opinions and talent are not important or welcome unless they fit neatly into the master’s plan. Increasingly in corporate America, you are either part of the ruling class or simply a disempowered serf whose personal value is completely dismissed. In this sense any diversity is discouraged and squashed by our overlords.

If one trait defines the vast number of people today, it is disempowerment. Your personal value and potential are meaningless to our management. Do you job; do what you are told to do; comply with their requirements. Whatever you do don’t make waves or question the powers. I’ve done this, and the reaction is to punish people through marginalization and lack of access. Retribution is implicit and subtle. In the end you don’t know how much you were punished through opportunity and information denial. The key is that the powers that be are in control of you and if you don’t play ball with them, you are an outsider. A way of not getting into trouble is being a compliant, boring and utterly vanilla worker bee. If you tow the party line you simply get the benefit of employment “success”. Eventually if you play your cards right you can join the power structure as one of them. In this way diversity of any sort is punished. They see diversity as a threat and work to drive it out.

You could jump so much higher when you had somewhere safe to fall.

― Liane Moriarty

Given that the treatment of relatively benign diversity is met with implicit resistance, one might reasonably ask how edgier forms of diversity will be welcomed? Granted, one’s personality can have a distinct work-related impact, and behavior is certainly work appropriate, but what are the bounds on how that is managed? My experience that the workplace goes too far in moderating people’s innate tendencies. My particular work has promoted the aspirational view toward diversity of bringing your true and best self to work. In all honesty, it is an aspiration that they fail at to a spectacular degree. When relatively common and universal aspects of our humanity are not accepted, how would more controversial aspects be accepted? A fair reaction is the conclusion that they wouldn’t be accepted at all. To add to the mix is a broader governance that is getting less accepting of differences than more. As a result, people whose lives are outside the conservatively defined norms are prone to hide major aspects of their identity. The accepted majority and accepted identity is white, male, Christian, heterosexual, and monogamous. We still accept political differences, but to varying degrees we expect people to fall into only a few narrow bins.

It is time for parents to teach young people early on that in diversity there is beauty and there is strength.

― Maya Angelou

What happens when someone falls outside these identities? If one is female and/or non-white there are protections and discrimination and bias is purely implicit. What about being an atheist? What about being gay, or transsexual? The legal protections begin to be weaker, and major societal elements seek to remove these protections. What if you’re non-monogamous, or committed to some other divergent sexual identity? What if you’re a communist or fascist? Then you are likely to be actively persecuted and discriminated against. Where is the line where this should happen? What life choices are so completely outside the norm of societal acceptance that they should be subject to effective banishment. If you have made one of these life choices, your choice is often hidden and secret. You are in the closet. This is a very real issue especially when large parts of society want you in the closet or put you back there. Moreover, this part of society is emboldened to try and put gays, women and people of color back in their traditional closets, kitchens and ghettos.

We are in a time where progress in diversity has stopped, and elements of society are moving backwards. Progress in expanding diversity and acceptance has stopped, and we are making America Great Again by enhancing the power of whites hiding people of color, closeting gays, and making women subservient. All of this is done in service of those in power both to maintain their power, wealth and control. Any sort of commitment to diversity is viewed as an assault on the power and wealth of the ruling class. As a result, we see a continued concentration of wealth and power in the hands of the few. General social mobility has been diminished so that people keep their place in society. For the rank and file, we see disempowerment and meager rewards for slavish conformity. Step out of line and draw attention to yourself and expect punishment and shunning. The slavishly conformant masses provide the peer pressure and bulk of the enforcement, but all of it serves those in power.

Instead of creating a society and system that gets the best out of people and maximizes human potential, we have pure maintenance of power by the ruling class. We let people act out through their basest fears to squash people and ideas that are uncomfortable. We are not leading people to be better, we are encouraging them to be worse. Rather than act out of love, we are emboldening hate. Rather than accept people and allow them flourish using their distinct individuality and achieve satisfying lives, we choose conformity and order. The conformity and order that is imposed serves only those in power and limits any aspirational dreams of the masses. The masses are controlled by fear that naturally arises with those who are different. Humans are naturally fearful of other humans that are different. Rather than encourage people to accept these differences (i.e., accept and promote diversity), we encourage them to discriminate against them by promoting fear of the other. This fear is the tool of rich and powerful to create systems that maintain their grip on society.

We are in need of leadership that blazes a trail to being courageous and better. Without leadership and bravery, the progress we have achieved will turn back and be lost. There is so much more to do to get the best out of people, which cannot happen when our leaders allow and even encourage the worst in people to serve their own selfish needs. We have a choice and it is past time to choose excellence and progress through inclusion and diversity.

Here’s to the crazy ones. The misfits. The rebels. The troublemakers. The round pegs in the square holes. The ones who see things differently. They’re not fond of rules. And they have no respect for the status quo. You can quote them, disagree with them, glorify or vilify them. About the only thing you can’t do is ignore them. Because they change things. They push the human race forward. And while some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world, are the ones who do.

― Rob Siltanen

# The Primal Nature of Hyperbolic Conservation Laws

Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won’t come in.

― Isaac Asimov

In conducting science, the importance of models is central to practice. Modeling is paired with observation as Man’s abstraction for understanding the World around us. Models need to be descriptive and tractable for examining nature.  These two aspects can be in direct conflict with each other. Observation under natural or controlled circumstances provides the core of scientific knowledge. Observation becomes science when we provide a systematic explanation for what we see. More often than not this explanation has a mathematical character as the mechanism we use. Among our mathematical devices differential equations are among our most powerful tools. In the most basic form these equations are rate of change laws for some observable in the World. Most crudely these rate equations can be empirical vehicles for taking observations into a form useful for prediction, design and optimization. A more basic form is partial differential equations (PDEs) that describe the basic physics in a more expansive form. It is important to consider the consequences of the model forms we use. Several important categories of models are intrinsically unphysical in aspects thus highlighting the George Box aphorism that “essentially, all models are wrong”!

Assumptions are the most damaging enemies of our mind’s equilibrium…An assumption is an imaginary truth.

― A.A. Alebraheem

Partial differential equations come in three basic flavors, hyperbolic, parabolic and elliptic. These flavors describe some of the basic character of the equations and have fundamental differences in how they are solved, understood as objects and more importantly physical context. The core of this essay is going to be physical in nature and to the point only hyperbolic equations are primal in physics. This is to say that at the basic level everything that we might describe as a physics law is hyperbolic in character. This is for a simple and very good reason, the principle of causality. Cause and effect, the flow of time and the presence of a cosmic speed limit. If we adhere to these maxims, the conclusion is utterly obvious. Other forms of PDEs produce instantaneous global effects that violate this principle. This in no way implies that parabolic or elliptic models are not incredibly useful, they are. Their utility and other properties exceed the issues with causality violations.

More on that point soon, but first a bit of digression on the other forms of PDEs. The classical elliptic equations is Laplace’s equation, $\partial_{xx} u + \partial_{yy} = 0$. Elliptic equations are the simplest form and often describe physics where spatial terms are in equilibrium and there is no temporal, rate terms. Elliptic equations can include time terms, but usually implying something so deeply unphysical as to be utterly outlawed. If time is elliptic, the past is determined by the future, and since we know that time flows in one direction, this is deeply and fundamentally unphysical. In other uses, the elliptic PDEs are found through ignoring temporal terms. This is a philosophical violation of the second law of thermodynamics, which can be used to establish the arrow of time. In this sense we find that elliptic equations are an asymptotic simplification of more fundamental laws. Another implication of ellipticity of PDEs is infinite speed of information, or more correctly an absence of time. If elliptic equations are found within a set of equations, we can be absolutely sure that some physics has been chosen to be ignored. In many cases these ignored physics are not important and some benefit is achieved through the simplification. On the other hand, we shouldn’t lose sight of what has been done and its potential for mischief. At some point this mischief will become relevant and disqualifying.

Assumptions aren’t facts; they’re opportunities for research and testing.

― Laurie Buchanan

Next along the way we have parabolic equations and we can repeat the above discussion. Most classically the equation of heat transfer is parabolic (along with other diffusion processes). The classical form is the heat equations, $\partial_{t} u - \partial_{xx} u$. We often learn that these diffusion processes are fundamental, leading to the second law of thermodynamics. This comes with a deep problem that we should acknowledge. The parabolic equations imply an infinite propagation speed. Physically the process of diffusion is quite discrete associated with collisionality of the particles that make up materials, or discrete effects of solids (where electrons are particles that move, exchange and interact). This physical effect is utterly bound by finite speeds of propagation.

With elliptic equations the strength of the signal is unabated in time, but with parabolic equations, the signal diminishes in time. As such the sin of causality violation isn’t quite so profound, but it is a sin nonetheless. As before we get parabolic equations by ignoring physics. Usually this is a valid thing to do based on the time and length scales of interest. We need to remember that at some point this ignorance will damage the ability to model. We are making simplifications that are not always justified. This point is lost quite often. People are allowed to think the elliptic or parabolic equations are fundamental when they are not.

We now get to the third category of PDEs, the hyperbolic kind. The simplest form is a wave equation, $\partial_{tt} u + \partial_{xx} u = 0$. This can be written as a system of equations first-order PDEs, $\partial_{t} u + \partial_{x} v = 0$ and $\partial_{t} v - \partial_{x} u = 0$. We can derive the simple wave equation by differentiating the first equation in time and the second in space then substituting to eliminate $v$. The propriety of these steps depends on the variable being continuously differentiable, i.e., smooth. The second, first-order form is the entry point for the beautiful mathematics of hyperbolic conservation laws. As we will show, the elliptic and parabolic equations are simplifications of the hyperbolic equations made upon applying some assumptions.

I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.

― Abraham H. Maslow

One key example of an equation where the presumption of the basic laws of physics is generally wrong are diffusion processes. One might consider Fourier’s law to be a fundamental law of physics as applied to heat condition in a parabolic form, $C \partial_t T = \nabla\cdot q; q = k \nabla T \rightarrow C \partial_t T = \nabla\cdot\nabla T$. Instead this is a simplification of a more broadly valid law where heat flows using a hyperbolic equation. This requires a simple modification of the Fourier law to $\tau \partial_t q+ q = k \nabla T$.  For most applications heat flow can be modeled in the parabolic form as the hyperbolic form is important over very short time and space scales. Still the more fundamental law is the hyperbolic form, and the classical parabolic form is derived by assuming that certain aspects of the dynamics can be ignored. We must always remember that the standard modeling of diffusion processes has an unphysical aspect baked into the equations.

The importance of the hyperbolic character of heat conduction may be more important. It is related to the property of material called second sound. This property is measured and known to be significant under cryogenic conditions where quantum effects are significant. It is also very hard to measure. The leading and rather compelling fact is its relation to the sound speed; the second sound is slower than the sound speed. This would mean that its effective time scale is also longer than the acoustic time. If this aspect is generally true, then the time scale can’t be ignored under many conditions. The deeper question is how all of this plays with thermodynamics. So much of the grounding of thermodynamics is in an equilibrium setting, and this phenomenon adds a natural and potentially important relaxation time scale.

There is an issue with hyperbolic diffusion that we should acknowledge. This form of the equations can violate the second law of thermodynamics, which underpins the macroscopic dynamics of the universe and the arrow of time. By the same token the imposition of the second law through a physical process in continuum physics is invariably tied to diffusion. As such we have formed a veritable technical Mobius strip.  A question is whether a fundamentally different equation can actually violate a less physical law that it is based upon. This might call the violations of the second law by hyperbolic diffusion into question rather directly! In other words, what would change about the second law of thermodynamics; if the diffusion process itself were hyperbolic. Perhaps this is a specific inroad to discussions of non-equilibrium thermodynamics. This may provide a necessary and distinct framing of a deeper discussion. Clearly infinite speeds of propagation for information is unphysical, functionally the second law could be recovered to account for temporal effects.

There is nothing so expensive, really, as a big, well-developed, full-bodied preconception.

― E.B. White

The incompressible Navier-Stokes equations are second primal example where hyperbolic equations are replaced by both parabolic-elliptic equations. A starting point would be the compressible equations that are purely hyperbolic without viscosity. Of course, the viscosity could be replaced with hyperbolic equations to make the compressible flow totally hyperbolic. These equations are the following, $\partial_t {\bf u} + {\bf u} \cdot\nabla{\bf u} +\nabla p = 0;\nabla\cdot {\bf u} = 0$. Previously, we discussed the replacement of hyperbolic diffusion by the parabolic terms. For the incompressibility we remove sound waves analytically. The key to doing this is remove any connection between pressure and density with the divergence free constraint, $\nabla\cdot {\bf u} = 0$. This also turns mass into a passively advected scalar. This is a useful model for low speed flows, but the diffusion and suppressed sound waves both produce infinite speeds of propagation. This violates the principle of causality where there is cause and effect. Instead everywhere is impacted by everything immediately.

As noted repeatedly these infinite speeds are definitely and unabashedly unphysical and signs that the equations are intrinsically limited in modeling scope. These issues are almost routinely ignored by most scientists and engineers. The reason is that the assumptions associated with parabolic or elliptic equations are valid for use. This will not always be true. It should be in the back of their mind. The message is clear, the equations will become invalid under some conditions, some length or time scale will unveil this invalidity. The question is what are these scales, and have we stumbled upon them yet? More generally the use of parabolic or elliptic equations produce these unphysical effects as a matter of course. This implies that the model equation will lose utility at some point under some conditions. We simply need to guard ourselves to this potential and keep this firmly in the back of our mind. The issue in this regard is the lack of capability to solve these non-standard models and make a complete assessment of model validity. By the same token, the non-standard models are harder to solve and may have deleterious side-effects if the full physics is retained.

A very good example of these side effects occurs with compressible flows when the Mach number is small. Solving low-Mach number flows with compressible codes is terribly inefficient and prone to significant approximation errors. This has a great deal to do with the separation of scales. As a result, the solutions often do not adhere to expectations. The consequence is there are many “fixes” to compressible flow solvers to remove the difficulties. The odd thing about this issue is the definitely greater physical reality associated with the compressible flow equations as compared to the incompressible equations. This might imply that the conditioning of the equations is the greatest problem. In addition, modern shock capturing methods have an implied discontinuity with their construction. It would seem that a continuous approximation might alleviate the problems. Conditioning issues with the separation of scales remains.

For modeling and numerical work, the selection of the less physical parabolic and elliptic equations provides better conditioning. The conditioning provides a better numerical and analytical basis for the solutions. The recognition that the equations are less physical is not commonly appreciated. A broader and common appreciation may provide impetus for identifying when these differences are significant. Holding models that are unphysical as sacrosanct is always dangerous. It is important to recognize the limitations of models and allow ourselves to question them regularly. Even models that are fully hyperbolic are wrong themselves, this is the very nature of models. By using hyperbolic models, we remove an obviously unphysical aspect of a given model. Models are abstractions of reality, not the operating system of the universe. We must never lose sight of this.

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

― Albert Einstein

Courant, Richard, and David Hilbert. Methods of mathematical physics [Methoden der mathematischen Physik, engl.] 1. CUP Archive, 1965.

Lax, Peter D. Hyperbolic partial differential equations. Vol. 14. American Mathematical Soc., 2006.

Körner, C., and H. W. Bergmann. “The physical defects of the hyperbolic heat conduction equation.” Applied Physics A 67, no. 4 (1998): 397-401.

Chester, Marvin. “Second sound in solids.” Physical Review131, no. 5 (1963): 2013.

Christov, C. I., and P. M. Jordan. “Heat conduction paradox involving second-sound propagation in moving media.” Physical review letters 94, no. 15 (2005): 154301.

Fefferman, Charles L. “Existence and smoothness of the Navier-Stokes equation.” The millennium prize problems 57 (2006): 67.

Doering, Charles R. “The 3D Navier-Stokes problem.” Annual Review of Fluid Mechanics 41 (2009): 109-128.