…fuck?
WTF has become the catchphrase for today’s world. “What the fuck” moments fill our days and nothing is more WTF than Donald Trump. We will be examining the viability of the reality show star, and general douchebag celebrity-rich guy as a viable presidential candidate for decades to come. Some view his success as a candidate apocalyptically, or characterize it as an “extinction level event” politically. In the current light it would seem to be a stunning indictment of our modern society. How could this happen? How could we have come to this moment as a nation where it is even a possibility for such a completely insane outcome to be a reasonably high probability outcome of our political process? What else does it say about us as a people? WTF? What in the actual fuck!
The phrase “what the fuck” came into the popular lexicon along with Tom Cruz in the movie, “Risky Business” back in 1983. There the lead character played by Tom Cruz exclaims, “sometimes you gotta say, what the fuck” It was a mantra for just going for broke and trying stuff without obvious regard for the consequences. Given our general lack of an appetite for risk and failure, the other side of the coin took the phrase over. Over time the phrase has morphed into a general commentary about things that are generally unbelievable. Accordingly the acronym WTF came into being by 1985. I hope that 2016 is peak-what the fuck, cause things can’t get much more what the fuck without everything turning into a complete shitshow. Going to a deeper view of things the real story behind where we are is the victory of bullshit as a narrative element in society. In a sense the transfer of WTF from a mantra for risk taking has transmogrified into a mantra for the breadth of impact of not taking risks!
Indeed if one looks to the real core of the Donald Trump phenomena it is the victory of bullshit over logic, facts and rational thought. He simply spouts off a bunch of stuff that our generally uneducated, bigoted, and irrationally biased public wants to hear, and the rubes vote for him in droves. It does not matter that almost everything he says is complete and utter bullshit. A deeper question is how the populace has become so conditioned to accept a candidate who regularly lies to them. Instead of uttering difficult truths and dealing with problems in a rational and pragmatic manner (i.e., actual leadership) we are regularly electing people who simply tell us something we want to hear. Today’s world has real, difficult and painful problems to solve, and irrational solutions will only make them worse. With our political discourse so completely broken, none of the problems will be addressed much less solved. Our nation will literally drown in the bullshit we are being fed.
It is the general victory of showmanship and entertainment. The superficial and bombastic rule the day. I think that Trump is committing one of the greatest frauds of all time. He is completely and utterly unfit for office, yet has a reasonable (or perhaps unreasonable) chance to win the election. The fraud is being committed in plain sight and the fact that he speaks falsehoods at a marvelously high rate without any of the normative ill effects. Trump’s victory is testimony to how gullible the public is to complete bullshit. This gullibility reflects the lack of will on the part of the public to address real issues. With the sort of “leadership” that Trump represents, the ability to address real problems will further erode. The big irony is that Trump’s mantra of “Make America Great Again” is the direct opposite impact of his message. Trump’s sort of leadership destroys the capacity of the Nation to solve the sort of problems that lead to actual greatness. He is hastening the decline of the United States by choking our will to act in a tidal wave of bullshit.
There is a lot more bullshit in society than just Trump; he is just the most obvious example right now. Those who master bullshit win the day today, and it drives the depth of the WTF moments. Fundamentally there are forces in society today that are driving us toward the sorts of outcomes that cause us to think, “WTF?” For example we are prioritizing a high degree of micromanagement over achievement due to the risks associated with giving people freedom. Freedom encourages achievement, but also carries the risk of scandal when people abuse their freedom. Without the risks you cannot have the achievements. Today the priority is no scandal and accomplishment simply isn’t important enough to empower anyone. We are developing systems of management that serve to disempower people so that they don’t do anything unpredictable (like achieve something!).
The effect of all of this is an increasing disconnect from achievement and the concept of accountability. The end point is that the transition of achievement into bullshit is driven by the needs to market results, and marketed results being impossible to distinguish from actual results by most people. This is the sort of path that leads to our broken political discourse. When bullshit becomes identical to facts, the value and power of facts are absolutely destroyed. We are left with a situation where falsehoods are viewed as having equal footing with truth. Things like science, and the general concept of leadership by the elites in society becomes something to be reviled. We get Donald Trump as a viable candidate for President.
I wonder deeply about the extent to which things like the Internet play into this dynamic. Does the Internet allow bullshit to be presented with equality to bona fide facts? Does the Internet and computers allow a degree of micromanagement that strangles achievement? Does the Internet produce new patterns in society that we don’t understand much less have the capacity to manage? What is the value of information if it can’t be managed or understood in any way that is beyond superficial? The real danger is that people will gravitate toward what they want to view as facts instead of confronting issues that are unpleasant. The danger seems to be playing out in the political events in the United States and beyond.
Like any technology the Internet is not either good or bad by definition. It is a tool that may be used for either the benefit or the detriment of society. One way to look at the Internet is as an accelerator for what would happen societally. Information and change is 
happening faster and it is lubricating changes to take effect at a high pace. On the one hand we have an incredible ability to communicate with people that is beyond the capacity to even imagine a generation ago. The same communication mechanisms produces a deluge of information we are drowning and input to a degree that is choking people’s capacity to process what they are being fed. What good is the information, if the people receiving it are unable to comprehend it sufficiently to take action? or if people are unable to distinguish the proper actionable information from the complete garbage?
A force that adds to entire mix is a system that increasingly only values the capacity to monetize things. This has destroyed the ability of the media to act as a referee in society. Facts and lies are now a free for all. Scandal and fiction sell far better than facts and truth. As a result we scandalize everything. As a result small probability events are drummed up to drive better ratings (the monetization of the news), and scare the public. The scared public then acts to try to control these false risks and fears through accountability, and the downward spiral of bullshit begins. Society today is driven by fear and the desire to avoid being afraid. Risk is avoided and failure is punished. Today failure is a scandal and our ability to accomplish anything of substance is sacrificed to avoid the potential of scandal.
All of these forces are increasingly driving the elites in society (and increasingly the elites are simply those who have a modicum of education) to look at events and say “WTF?” I mean what the actual fuck is going on? The movie Idiocracy was set 500 years in the future, and yet we seem to be moving toward that vision of the future at an accelerated path that makes anyone educated enough to see what is happening tremble with fear. The sort of complete societal shitshow in the movie seems to be unfolding in front of our very eyes today. The mind-numbing effects of reality show television and pervasive low-brow entertainment is spreading like a plague. Donald Trump is the most obvious evidence of how bad things have gotten.
The sort of terrible outcomes we see obviously through our broken political discourse are happening across society. The scientific world I work in is no different. The low-brow and superficial are dominating the dialog. Our programs are dominated by strangling micromanagement that operates in the name of accountability, but really speaks volumes about the lack of trust. Furthermore the low-brow dialog simply reflects the societal desire to eliminate the technical elites from the process. This also connects back to the micromanagement because the elites can’t be trusted either. It’s become better to speak to the uneducated common man who you can “have a beer with” than trust the gibberish coming from an elite. As a result the rise of complete bullshit as technical achievements has occurred. When the people in charge can’t distinguish between Nobel Prize winning work and complete pseudo-science, the low-bar wins out. Those of us who know better are left with nothing to do but say What the Fuck? Over and over again.
The bottom line is that the Donald Trump phenomenon isn’t a localized event; it is the result of a deeply broken society. These type of WTF events are all around us every day albeit in lesser forms. Our workplaces are teaming with WFT moments. We take WTF training for WTF problems. We have WTF micromanagement that serves no purpose except to provide people with a false sense of security that nothing scandalous is going on. The WTF moment is that the micromanagement is scandalous in and of itself. All the while our economic health stands at the abyss of calamity because most business systems are devised to be wealth-transfer mechanisms rather than value creation or customer satisfaction mechanisms.
We live in a world where complete stupidity such as anti-vaxxers, climate change denial, creationists,… all seem to be taken as seriously as the science stacked against them. WTF? When real scientists are ignored in comparison to celebrities and politicians as the oracles of truth, we are lost. We waste immense amounts of time, energy, money and karma preventing things that will never happen, yet doing these things is a priority. WTF? What the fuck! Indeed! All of this is corrosive in the extreme to the very fabric of our society. The corrosion is visible in the most repugnant canary every seen in our collective coalmine, the Donald. He is a magnificent WTF indictment of our entire society.
Effectively we are creating an ecosystem where the apex predators are missing, and this isn’t a good thing. The models we use in science are the key to everything. They are the translation of our understanding into mathematics that we can solve and manipulate to explore our collective reality. Computers allow us to solve much more elaborate models than otherwise possible, but little else. The core of the value in scientific computing are the capacity of the models to explain and examine the physical World we live in. They are the “apex predators” in the scientific computing system, and taking this analogy further our models are becoming virtual dinosaurs where evolution has ceased to take place. The models in our codes are becoming a set of fossilized skeletons and not at all alive, evolving and growing.
People do not seem to understand that faulty models render the entirety of the computing exercise moot. Yes, the computational results may be rendered into exciting and eye-catching pictures suitable for entertaining and enchanting various non-experts including congressmen, generals, business leaders and the general public. These eye-catching pictures are getting better all the time and now form the basis of a lot of the special effects in the movies. All of this does nothing for how well the models capture reality. The deepest truth is that no amount of computer power, numerical accuracy, mesh refinement, or computational speed can rescue a model that is incorrect. The entire process of validation against observations made in reality must be applied to determine if models are correct. HPC does little to solve this problem. If the validation provides evidence that the model is wrong and a more complex model is needed then HPC can provide a tool to solve it.
seamlessly to produce incredible things. We have immensely complex machines that produce important outcomes in the real world through a set of interweaved systems that translate electrical signals into instructions understood by the computer and humans, into discrete equations, solved by mathematical procedures that describe the real world and ultimately compared with measured quantities in systems we care about. If we look at our focus today, the complexity of focus is the part of the technology that connects very elaborate complex computers to the instructions understood both by computers and people. This is electrical engineering and computer science. The focus begins to dampen in the part of the system where the mathematics, physics and reality comes in. These activities form the bond between the computer and reality. These activities are not a priority, and conspicuously diminished significantly by today’s HPC.
HPC today is structured in a manner to eviscerate fields that have been essential to the success of scientific computing. A good example is our applied mathematics programs. In many cases applied mathematics has become little more than scientific programming and code development. Far too little actual mathematics is happening today, and far too much focus is seen in productizing mathematics in software. Many people with training in applied mathematics only do software development today and spend little or no effort in doing analysis and development away from their keyboards. It isn’t that software development isn’t important, the issue is the lack of balance in the overall ratio of mathematics to software. The power and beauty of applied mathematics must be harnessed to achieve success in modeling and simulation. Today we are simply bypassing 
this essential part of the problem to focus on delivering software products.
To avoid the sort of implicit assumption of ZERO uncertainty one can use (expert) judgment to fill in the information gap. This can be accomplished in a distinctly principled fashion and always works better with a basis in evidence. The key is the recognition that we base our uncertainty on a model (a model that is associated with error too). The models are fairly standard and need a certain minimum amount of information to be solvable, and we are always better off with too much information making it effectively over-determined. Here we look at several forms of models that lead to uncertainty estimation including discretization error, and statistical models applicable to epistemic or experimental uncertainty.
where 
is the mesh converged solution, 
is the solution on the 
mesh and 
is the mesh length scale, 
is the (observed) rate of convergence, and 
is a proportionality constant. We have three unknowns so we need at least
meshes to solve the error model exactly or more if we solve it in some sort of optimal manner. We recently had a method published that discusses how to include expert judgment in the determination of numerical error and uncertainty using models of this type. This model can be solved along with data using minimization techniques including the expert judgment as constraints on the solution for the unknowns. For both the over- or the under-determined cases different minimizations one can get multiple solutions to the model and robust statistical techniques may be used to find the “best” answers. This means that one needs to resort to more than simple curve fitting, and least squares procedures; one needs to solve a nonlinear problem associated with minimizing the fitting error (i.e., residuals) with respect to other error representations.
ables can be completely eliminated by simply choosing the solution based on expert judgment. For numerical error an obvious example is assuming that calculations are converging at an expert-defined rate. Of course the rate assumed needs an adequate justification based on a combination of information associated with the nature of the numerical method and the solution to the problem. A key assumption that often does not hold up is the achievement of the method’s theoretical rate of convergence for realistic problems. In many cases a high-order method will perform at a lower rate of convergence because the problem has a structure with less regularity than necessary for the high-order accuracy. Problems with shocks or other forms of discontinuities will not usually support high-order results and a good operating assumption is a first-order convergence rate.
To make things concrete let’s tackle a couple of examples of how all of this might work. In the paper published recently we looked at solution verification when people use two meshes instead of the three needed to fully determine the error model. This seems kind of extreme, but in this post the example is the cases where people only use a single mesh. Seemingly we can do nothing at all to estimate uncertainty, but as I explained last week, this is the time to bear down and include an uncertainty because it is the most uncertain situation, and the most important time to assess it. Instead people throw up their hands and do nothing at all, which is the worst thing to do. So we have a single solution 
at 
and need to add information to allow the solution of our error model, 
, which then can be used to provide an uncertainty estimate, 
|A – 
multiplied by an appropriate safety factor 
.
A lot of this information is probably good to include as part of the analysis when you have enough information too. The right way to think about this information is as constraints on the solution. If the constraints are active they have been triggered by the analysis and help determine the solution. If the constraints have no effect on the solution then they are proven to be correct given the data. In this way the solution can be shown to be consistent with the views of the expertise. If one is in the circumstance where the expert judgment is completely determining the solution, one should be very wary as this is a big red flag.
. The starting assumption is often that these are dominated by discretization error, or tied to the discretization. Evidence in support of these assumptions is generally weak to nonexistent. For round-off errors the modeling is similar, but all of these errors can be magnified in the face of instability. A key is to provide some sort of assessment of their aggregate impact on the results and not explicitly ignore them.
standard modeling assumption is the use of the normal or Gaussian distribution as the starting assumption. This is almost always chosen as a default. A reasonable blog post title would be “The default probability distribution is always Gaussian”. A good thing for a distribution is that we can start to assess it beginning with two data points. A bad and common situation is that we only have a single data point. Thus uncertainty estimation is impossible without adding information from somewhere, and an expert judgment is the obvious place to look. With statistical data and its quality we can apply the standard error estimation using the sample size to scale the additional uncertainty driven by poor sampling, 
where 
is the number of samples.
|A – 
where 
is the data point. In these cases the standard error estimate would be equal to 
where 
. Both of these approaches have the strengths and weaknesses, and include the strong assumption of the normal distribution.
– 
. A question is how representative a single piece of information 
For statistical models eventually one might resort to using a Bayesian method to encode the expert judgment in defining a prior distribution. In general terms this might seem to be an absolutely key approach to structure the expert judgment where statistical modeling is called for. The basic form of Bayes theorem is 
where 
is the probability of 
given 
, 
is the probability of 
I have noticed that we tend to accept a phenomenally common and undeniably unfortunate practice where a failure to assess uncertainty means that the uncertainty reported (acknowledged, accepted) is identically ZERO. In other words if we do nothing at all, no work, no judgment, the work (modeling, simulation, experiment, test) is allowed to provide an uncertainty that is ZERO. This encourages scientists and engineers to continue to do nothing because this wildly optimistic assessment is a seeming benefit. If somebody does work to estimate the uncertainty the degree of uncertainty always gets larger as a result. This practice is desperately harmful to the practice and progress in science and incredibly common.
t shortcomings, a gullible or lazy community readily accepts the incomplete work. Some of the better work has uncertainties associated with it, but almost always varying degrees of incompleteness. Of course one should acknowledge up front that uncertainty estimation is always incomplete, but the degree of incompleteness can be spellbindingly large.
within the expressed taxonomy for uncertainty. I’ll start with numerical uncertainty estimation that is the most commonly completely non-assessed uncertainty. Far too often a single calculation is simply shown and used without any discussion. In slightly better cases, the calculation will be given with some comments on the sensitivity of the results to the mesh and the statement that numerical errors are negligible at the mesh given. Don’t buy it! This is usually complete bullshit! In every case where no quantitative uncertainty is explicitly provided, you should be suspicious. In other cases unless the reasoning is stated as being expertise or experience it should be questioned. If it is stated as being experiential then the basis for this experience and its documentation should be given explicitly along with evidence that it is directly relevant.
estimation. Far too many calculational efforts provide a single calculation without any idea of the requisite uncertainties. In a nutshell, the philosophy in many cases is that the goal is to complete the best single calculation possible and creating a calculation that is capable of being assessed is not a priority. In other words the value proposition for computation is either do the best single calculation without any idea of the uncertainty versus a lower quality simulation with a well-defined assessment of uncertainty. Today the best single calculation is the default approach. This best single calculation then uses the default uncertainty estimate of exactly ZERO because nothing else is done. We need to adopt an attitude that will reject this approach because of the dangers associated with accepting a calculation without any quality assessment.
random uncertainty. This sort of uncertainty is clearly overlooked by our modeling approach in a way that most people fail to appreciate. Our models and governing equations are oriented toward solving the average or mean solution for a given engineering or science problem. This key question is usually muddled together in modeling by adopting an approach that mixes a specific experimental event with a model focused on the average. This results in a model that has an unclear separation of the general and specific. Few experiments or events being simulated are viewed from the context that they are simply a single instantiation of a distribution of possible outcomes. The distribution of possible outcomes is generally completely unknown and not even considered. This leads to an important source of systematic uncertainty that is completely ignored.
value in challenging our theory. Moreover the whole sequence of necessary activities like model development, and analysis, method and algorithm development along with experimental science and engineering are all receiving almost no attention today. These activities are absolutely necessary for modeling and simulation success along with the sort of systematic practices I’ve elaborated on in this post. Without a sea change in the attitude toward how modeling and simulation is practiced and what it depends upon, its promise as a technology will be stillborn and nullified by our collective hubris.
Fluid mechanics at its simplest is something called Stokes flow, basically motion so slow that it is solely governed by viscous forces. This is the asymptotic state where the Reynolds number (the ratio of inertial to viscous forces) is identically zero. It’s a bit oxymoronic as it is never reached, it’s the equations of motion without any motion or where the motion can be ignored. In this limit flows preserve their basic symmetries to a very high degree.
The fundamental asymmetry in physics is the arrow of time, and its close association with entropy. The connection with asymmetry and entropy is quite clear and strong for shock waves where the mathematical theory is well-developed and accepted. The simplest case to examine is Burgers’ equation, 
, or its conservation form ![u_t + 1/2 \left[u^2 \right]_x = 0](https://s0.wp.com/latex.php?latex=u_t+%2B%C2%A01%2F2+%5Cleft%5Bu%5E2+%5Cright%5D_x+%3D+0+&bg=ffffff&fg=000&s=0&c=20201002)
. This equation supports shocks and rarefactions, and their formation is determined by the sign of 
. If one takes the gradient of the governing equation in space, you can see the solution forms a Ricatti equation along characteristics, 
. The solution on characteristics tells one the fate of the solution, 
. The thing to recognize that the denominator will go to zero if 
and the value of the derivative will become unbounded, i.e., form a shock.
. The same basic character is shared by shock waves and incompressible turbulent flows. It implies the presence of a discontinuity in the model of the flow.
On the one hand the form seems to be unavoidable dimensionally, on the other it is a profound result that provides the basis of the Clay prize for turbulence. It gets to the core of my belief that to a very large degree the understanding of turbulence will elude us as long as we use the intrinsically unphysical incompressible approximation. This may seem controversial, but incompressibility is an approximation to reality, not a fundamental relation. As such its utility is dependent upon the application. It is undeniably useful, but has limits, which are shamelessly exposed by turbulence. Without viscosity the equations governing incompressible flows are pathological in the extreme. Deep mathematical analysis has been unable to find singular solutions of the nature needed to explain turbulence in incompressible flows.
where 
is the fluid velocity, and 
is the speed of sound.
. This quantity is dominantly and asymptotically positive (i.e., convex), but may be negative. For ideal gases 
. For convex equations of state shocks then always form given enough time if the velocity gradient is negative just like Burgers’ equation.
. Once the shock forms, the dissipation rate is proportional to the cube of the jump across the shock. In addition this limit is actually most appropriate in the zero Mach number limit (i.e., the same limit as incompressible flow!).
. The subscript 
means longitudinal where the differences are taken in the direction the velocity is moving over a distance 
. This relation implies a distinct asymmetry in the equations that means negative gradients are intrinsically sharper than positive gradients. This is exactly what happens in compressible flows. Kolmogorov derived this relation from the incompressible flow equations and it has been strongly confirmed by observations. The whole issue associated with the (in)famous Clay prize is the explanation of this law in the mathematical admissible solutions of the incompressible equations. This law suggests that the incompressible flow equations must support singularities that are in essence like a shock. My point is that the compressible equations support exactly the phenomena we seek in the right limits for turbulence. The compressible equations have none of the pathologies of the incompressible equations and have a far greater physical basis and remove the unphysical aspects of the physical-mathematical description.
simulation is build the next generation of computers. The proposition is so shallow on the face of it as to be utterly laughable. Except no one is laughing, the programs are predicated on it. The whole mentality is damaging because it intrinsically limits our thinking about how to balance the various elements needed for progress. We see a lack of the sort of approach that can lead to progress with experimental work starved of funding and focus without the needed mathematical modeling effort necessary for utility. Actual applied mathematics has become a veritable endangered species only seen rarely in the wild.
structures and models for average behavior. One of the key things to really straighten out is the nature of the question we are asking the model to answer. If the question isn’t clearly articulated, the model will provide deceptive answers that will send scientists and engineers in the wrong direction. Getting this model to question dynamic sorted out is far more important to the success of modeling and simulation than any advance in computing power. It is also completely and utterly off the radar of the modern research agenda. I worry that the present focus will produce damage to the forces of progress that may take decades to undue.
If there is any place where singularities are dealt with systematically and properly it is fluid mechanics. Even in fluid mechanics there is a frighteningly large amount of missing territory most acutely in turbulence. The place where things really work is shock waves and we have some very bright people to thank for the order. We can calculate an immense amount of physical phenomena where shock waves are important while ignoring a tremendous amount of detail. All that matter is for the calculation to provide the appropriate integral content of dissipation from the shock wave, and the calculation is wonderfully stable and physical. It is almost never necessary and almost certainly wasteful to compute the full gory details of a shock wave.
y to progress. I believe the issue is the nature of the governing equations and a need to change this model away from incompressibility, which is a useful and unphysical approximation, not a fundamental physical law. In spite of all the problems, the state of affairs in turbulence is remarkably good compared with solid mechanics.
An example of lower mathematical maturity can be seen in the field of solid mechanics. In solids, the mathematical theory is stunted by comparison to fluids. A clear part of the issue is the approach taken by the fathers of the field in not providing a clear path for combined analytical-numerical analysis as fluids had. The result of this is a numerical background that is completely left adrift of the analytical structure of the equations. In essence the only option is to fully resolve everything in the governing equations. No structural and systematic explanation exists for the key singularities in material, which is absolutely vital for computational utility. In a nutshell the notion of the regularized singularity so powerful in fluid mechanics is foreign. This has a dramatically negative impact on the capacity of modeling and simulation to have a maximal impact.
Being thrust into a leadership position at work has been an eye-opening experience to say the least. It makes crystal clear a whole host of issues that need to be solved. Being a problem-solver at heart, I’m searching for a root cause for all the problems that I see. One can see the symptoms all around, poor understanding, poor coordination, lack of communication, hidden agendas, ineffective vision, and intellectually vacuous goals… I’ve come more and more to the view that all of these things, evident as the day is long are simply symptomatic of a core problem. The core problem is a lack of trust so broad and deep that it rots everything it touches.
on the whole of society leeches. They claim to be helping society even while they damage our future to feed their hunger. The deeper physic wound is the feeling that everyone is so motivated leading to the broad-based lack of trust of your fellow man.
In the overall execution of work another aspect of the current environment can be characterized as the proprietary attitude. Information hiding and lack of communication seem to be a growing problem even as the capacity for transmitting information grows. Various legal, or political concerns seem to outweigh the needs for efficiency, progress and transparency. Today people seem to know much less than they used to instead of more. People are narrower and more tactical in their work rather than broader and strategic. We are encouraged to simply mind our own business rather than seek a broader attitude. The thing that really suffers in all of this is the opportunity to make progress for a better future.
The simplest thing to do is value the truth, value excellence and cease rewarding the sort of trust-busting actions enumerated above. Instead of allowing slip-shod work to be reported as excellence we need to make strong value judgments about the quality of work, reward excellence, and punish incompetence. The truth and fact needs to be valued above lies and spin. Bad information needs to be identified as such and eradicated without mercy. Many greedy self-interested parties are strongly inclined to seed doubt and push lies and spin. The battle is for the nature of society. Do we want to live in a World of distrust and cynicism or one of truth and faith in one another? The balance today is firmly stuck at distrust and cynicism. The issue of excellence is rather pregnant. Today everyone is an expert, and no one is an expert with the general notion of expertise being highly suspected. The impact of such a milieu is absolutely damaging to the structure of society and the prospects for progress. We need to seed, reward and nurture excellence across society instead of doubting and demonizing it.
Ultimately we need to conscientiously drive for trust as a virtue in how we approach each other. A big part of trust is the need for truth in our communication. The sort of lying, spinning and bullshit in communication does nothing but undermine trust, and empower low quality work. We need to empower excellence through our actions rather than simply declare things to be excellent by definition and fiat. Failure is a necessary element in achievement and expertise. It must be encouraged. We should promote progress and quality as a necessary outcome across the broadest spectrum of work. Everything discussed above needs to be based in a definitive reality and have actual basis in facts instead of simply bullshitting about it, or it only having “truthiness”. Not being able to see the evidence of reality in claims of excellence and quality simply amplifies the problems with trust, and risks devolving into a viscous cycle dragging us down instead of a virtuous cycle that lifts us up.
I chose the name the “Regularized Singularity” because it’s so important to the conduct of computational simulations of significance. For real world computations, the nonlinearity of the models dictates that the formation of a singularity is almost a foregone conclusion. To remain well behaved and physical, the singularity must be regularized, which means the singular behavior is moderated into something computable. This almost always accomplished with the application of a dissipative mechanism and effectively imposes the second law of thermodynamics on the solution.
One of the really big ideas to grapple with is the utter futility of using computers to simply crush problems into submission. For most problems of any practical significance this will not be happening, ever. In terms of the physics of the problems, this is often the coward’s way out of the issue. In my view, if nature were going to be submitting to our mastery via computational power, it would have already happened. The next generation of computing won’t be doing the trick either. Progress depends on actually thinking about modeling. A more likely outcome will be the diversion of resources away from the sort of thinking that will allow progress to be made. Most systems do not depend on the intricate details of the problem anyway. The small-scale dynamics are universal and driven by large scales. The trick to modeling these systems is to unveil the essence and core of the large-scale dynamics leading to what we observe.
. If we apply a Fourier transform 
to the operator we can see how simple viscosity works, 
(just substitute the Fourier description for the function into the operator). The viscosity grows in magnitude with the square of the wave number 
. The dissipation now kicks in faster (
) with the wavenumber allowing the simulation to be stabilized at comparatively coarser resolution than the corresponding simulation only stabilized by a second-order viscous operator. As a result the simulation can attack more dynamic and energetic flows with the hyperviscosity. One detail is that the sign of the operator changes with each step up the ladder, a sixth order operator will have a negative sign, and attack the spectrum of the solution even faster, 
, and so on.
. Here 
. It provides what linear hyperviscosity cannot, stability and robustness, making flows that would be 
computed with pervasive instability and making them stable and practically useful. It provides the fundamental foundation for shock capturing and the ability to compute discontinuous flows on grids. In many respects the entire CFD field is grounded upon this method. The notable aspect of the method is the dependence of the dissipation on the product of the coefficient 
and the absolute value of the gradient of the solution.
This isn’t generally considered important for viscosity, but in the content of more complex systems of equations may have importance. One of the keys to bringing this up is that generally speaking linear hyperviscosity will not have this property, but we can build nonlinear hyperviscosity that will preserve this property. At some level this probably explains the utility of nonlinear hyperviscosity for shock capturing. In nonlinear hyperviscosity we have immense freedom in designing the viscosity as long as we keep it positive. We then have a positive viscosity multiplying a positive definite operator, and this provides a deep form of stability we want along with a connection that guarantees of physically relevant solutions.
. If one wanted better high-frequency damping a different form would work like 
. To finish the generalization of the idea consider that you have eighth-order method, now a ninth- or tenth-order viscosity would work, for example, 
. The point is that one can exercise immense flexibility in deriving a useful method.
. This system of equations will have characteristic speeds, 
determined by the eigen-analysis of the flux Jacobian, 
. A reasonable way to think about hyperviscosity would be to write the nonlinear version as 
, where 
is the number of derivatives to take. A second approach that would work with Godunov-type methods would compute the absolute value jump at cell interfaces in the characteristic speeds where the Riemann problem is solved to set the magnitude of the viscous coefficient. This jump is the order of the approximation, and would multiply the cell-centered jump in the variables, 
. This would guarantee proper entropy production through the hyperviscous flux that would augment the flux computed via the Riemann solver. The hyperviscosity would not impact the formal accuracy of the method.
Sometimes the blog is just an open version of a personal journal. I feel myself torn between wanting to write about some thoroughly nerdy topic that holds my intellectual interest (like hyperviscosity for example), but end up ranting about some aspect of my professional life (like last week). I genuinely felt like the rant from last week would be followed this week by a technical post because things would be better. Was I ever wrong! This week is even more appalling! I’m getting to see the rollout of the new national program reaching for Exascale computers. As deeply problematic as the current NNSA program might be, it is a paragon of technical virtue compared with the broader DOE program. Its as if we already had a President Trump in the White House to lead our Nation over the brink toward chaos, stupidity and making everything an episode in the World’s scariest reality show. Electing Trump would just make the stupidity obvious, make no mistake, we are already stupid.
I think there are parallels that are worth discussing in depth. Something big is happening and right now it looks like a great unraveling. People are choosing sides and the outcome will determine the future course of our World. On one side we have the forces of conservatism, which want to preserve the status quo through the application of fear to control the populace. This allows control, lack of initiative, deprivation and a herd mentality. The prime directive for the forces on the right is the maintenance of the existing structures of power in society. The forces of liberalization and progress are arrayed on the other side wanting freedom, personal meaning, individuality, diversity, and new societal structure. These forces are colliding on many fronts and the outcome is starting to be violent. The outcome still hangs in the balance.
The Internet is a great liberalizing force, but it also provides a huge amplifier for ignorance, propaganda and the instigation of violence. It is simply a technology and it is not intrinsically good or bad. On the one hand the Internet allows people to connect in ways that were unimaginable mere years ago. It allows access to incredible levels of information. The same thing creates immense fear in society because new social structures are emerging. Some of these structures are criminal or terrorists, some of these are dissidents against the establishment, and some of these are viewed as immoral. The information availability for the general public becomes an overload. This works in favor of the establishment, which benefits from propaganda and ignorance. The result is a distinct tension between knowledge and ignorance, freedom and tyranny hinging upon fear and security. I can’t see who is winning, but signs are not good.
The core of the issue is an unhealthy relationship to risk, fear and failure. Our management is focused upon controlling risk, fear of bad things, and outright avoidance of failure. The result is an implemented culture of caution and compliance manifesting itself as a gulf of leadership. The management becomes about budgets and money while losing complete sight of purpose and direction. The focus on leading ourselves in new directions gets lost completely. The ability take risks get destroyed because of fears and outright fear of failure. People are so completely wrapped up in trying to avoid ever fucking up that all the energy behind doing progressive things moving forward are completely sapped. We are so tied to compliance that plans must be followed even when they make no sense at all.
ry small degree. Our managers are human and limited in capacity for complexity and time available to provide focus. If all of the focus is applied to management nothing is left for leadership. The impact is clear, the system is full of management assurance, compliance and surety, yet virtually absent of vision and inspiration. We are bereft of aspirational perspectives with clear goals looking forward. The management focus breeds an incremental approach that too concretely grounds future vision completely on what is possible today. All of this is brewing in a sea of risk aversion and intolerance for failure.
that I work for. It has resulted in the wholesale divestiture of quality because quality no longer matters to success. It is creating a thoroughly awful and untenable situation where truth and reality are completely detached from how we operate. Every time that something of low quality is allowed to be characterized as being high quality, we undermine our culture. Capability to make real progress is completely undermined because progress is extremely difficult and prone to failure and setbacks. It is much easier to simply incrementally move along doing what we are already doing. We know that will work and frankly those managing us don’t know the difference anyway. Doing what we are already doing is simply the status quo and orthogonal to progress.
micromanagement. Each step in micromanagement produces another tax on the time and energy of every one impacted by the system and diminishes the good that can be done. In essence we are draining our system of energy for creating positive outcomes. The management system is unremittingly negative in its focus, trying to stop stuff from happening rather than enable stuff. It is ultimately a losing battle, which is gutting our ability to produce great things.
management work shouldn’t be done in the abstract. Almost all of the management stuff are a good ideas and “good”. They are bad in the sense of what they displace from the sorts of efforts we have the time and energy to engage in. We all have limits in terms of what we can reasonably achieve. If we spend our energy on good, but low value activities, we do not have the energy to focus on difficult high value activities. A lot of these management activities are good, easy, and time consuming and directly displace lots of hard high value work. The core of our problems is the inability to focus sufficient energy on hard things. Without focus the hard things simply don’t get done. This is where we are today, consumed by easy low value things, and lacking the energy and focus to do anything truly great.
s a general ambiguity regarding the purpose of our Labs, the goals of our science and the importance of the work. None of this is clear. It is the generic implication of the lack of leadership within the specific context of our Labs, or federally supported science. It is probably a direct result of a broader and deeper vacuum of leadership nationally infecting all areas of endeavor. We have no visionary or aspirational goals as a society either.
