If you want a new tomorrow, then make new choices today.

― Tim Fargo

Ultimately the importance of what we compute is determined by how useful the results are. Are the results good at explaining something we see in nature, confirming an idea, providing concrete evidence of how a scenario might unfold, or helping create a better widget? The classical uses of scientific computing are solving initial value problems and large-scale data analysis each of which can play a role in the answering the above questions. How much have we moved bey ond this classical view in the 70 or so years the field has existed?

I think the answer is “not nearly enough,” and computing is failing to deliver on its full potential as a result.

Never attribute to malice that which can be adequately explained by stupidity.

― Robert Hanlon

Scientific computing is still dominated by the same two big uses that existed at the beginning. Recently data analysis has reasserted itself as the big “new” thing. This is mostly the consequence of the deluge of data coming from the Internet, and the impending Internet of things. For mainstream science, the initial value problem still holds sway for a broader set of activities although data is big in astronomy, geophysics and social sciences.

To change ourselves effectively, we first had to change our perceptions.

― Stephen R. Covey

The problem is that bigger, better things are possible if we simply marshal our efforts properly. Computing has the potential to reshape our ability to design through combining our forward simulations with optimization. The same could be done with data analysis to power calibration of models. Another powerful would be a pervasive analysis of uncertainties in our modeling. Almost all of these cases have direct analogs in the World of data analysis. Together this array of untapped potential would contribute greatly to our understanding and mastery of nature.

Engineers like to solve problems. If there are no problems handily available, they will create their own problems.

― Scott Adams

What is holding us back?

Probably the greatest issue holding us back is our absolute intolerance of risk. It is always less risky to incrementally improve what you are already doing. This has become the singular focus of science today. Making small improvements to something that is already deemed a success is a path to avoiding failure, “building on success”. Most progress looks like this, and today almost all progress looks like this. To get more out of computing, we need to risk doing something really new, and with that risk comes the possibility of failure. Without that risk the level of success that may be achieved is also much lower. I believe that this is the main driver behind not taking advantage of computing.

Evolution is more about adaptivity than adaptability.

― Raheel Farooq

This modern pathology also creates a myriad of side effects. One of the engines of innovation is applied mathematics where the act of playing it safe is sapping the vitality from the field. Increasingly the applied math work is focused on ideal model problems, and eschews the difficult work of attacking real problems, or problems where the math is messy. Without a more applied and more daring approach to developing capabilities, the innovative energy will not be unleashed. Part of the innovation means simply trying new things whether or not it is amenable to analysis. Work is guided by importance and utility rather than tractability.

Life’s journey is built of crests and troughs, the movement is always going to be fast only towards the trough and the progress is bound to be slow towards the crest.

― Anuj Somany

A good place to look at where analysis should be applied is to methods that work. The topic of compressed sensing is a great example. By the time compressed sensing was “invented” it had been in use for 30 years as a practical approach in several fields, but lacked theoretical support. When the theoretical support arrived from some of the best mathematicians alive today, the field exploded. New uses for this old methodology are discovered almost every day. It is an example of what a coherent theory can do for a field. Without the theory, the topic was stranded as a “trick” and its applicability was limited. With the theory the applications that could be attempted grew immensely (and continues to grow).

Our culture works hard to prevent change.

― Seth Godin

Another place where we have systematically failed to advance appropriately is the simulation of stochastic or random phenomena. We are still devoted to solving almost everything in terms of a mean field theory. While the mean field view of the World has served us well, today many of our most important applications are driven by statistics. How often will something really good, or really bad happen? How much of a population of devices will fail in a certain may? How likely is a certain event? Today most of our simulation capability is ill suited to answering these questions. In many cases we try to answer these incorrectly by merely examining the uncertainty in the mean field solution (i.e., sampling uncertainty parametrically, which is not the same thing). Almost none of the simulation techniques are suitable for examining the variability of the systems being simulated.

If failure is not an option, then neither is success.

― Seth Godin

The foundation of our limitations is not our intellectual abilities, but rather our taste for risk and change. With change and risk comes the potential for failure or unexpected outcomes. Lately, these sorts of things can’t be tolerated by our society. Without tolerance for bad things, our capacity to experience good things is undermined. Instead we are left to swim in an era of unmitigated mediocrity. It is sad that we’ve come to accept this as our mantra.

Fear does that. We have become afraid of everything, and fearful of things we used to simply overcome.

I must not fear. Fear is the mind-killer. Fear is the little-death that brings total obliteration.

― Frank Herbert, Dune

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

― Abraham Maslow

One of the most insidious and nefarious properties of scientific models is their tendency to take over, and sometimes supplant, reality.

— Erwin Chargaff

In scientific computing the quality of the simulations is slaved to the quality of the models being solved. The simulations cannot be more useful than the models allow. This absolute fact is too often left from the considerations of the utility of computing for science. Models are immensely important for the conduct of science and their testing essential to progress. When a model survives a test it is a confirmation of existing understanding. When a model fails and is overturned, science has the opportunity to leap forward. Both of these events should be cherished as cornerstones of the scientific method. Scientific computing as articulated today does not fully honor this point-of-view.

…all models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind…

— George E.P. Box

The purpose of models is not to fit the data but to sharpen the questions.

— Samuel Karlin

The centrality of the utility of models is defined by the role of models in connecting simulations to reality. When a scientist steps back from the narrow point-of-view associated with computing and looks at science more holistically, the role of models becomes much clearer. Models are approximate, but tractable, visions of reality that have utility in their necessary simplicity. Our models also define in loose terms what we envision about reality. In science our models define well how we understand the World. In engineering our models define how and what we build. If we expand our models, we expand our grasp of reality and our capacity for creation. Models connect the World’s reality to our intellectual grasp of that reality.

Science is not about making predictions or performing experiments. Science is about explaining.

― Bill Gaede

Computing has allowed more complex models to be used because it is freed of the confines of analytical techniques. Despite this freedom, the nature of models has been relatively stagnant with the approach to modeling still tethered to the (monumental) ideas introduced in 17^th, 18^th and 19^th centuries. Despite the ability to solve much more complicated models of reality that should come closer to “truth,” we are still trapped in this older point-of-view. In total too little progress is being made in removing these restrictions in how we think about modeling the World. Ultimately these restrictions are holding us back from a more pervasive understanding and control over the natural World. The costs of this seeming devotion to an antiquated perspective are immense, essentially incalculable. Succinctly put, the potential that computing represents is far, far from being realized today.

It’s not an experiment if you know it’s going to work.

― Jeff Bezos

If science is to be healthy the models of reality should constantly be challenged by experiment. Experiments should be designed to critically challenge or confirm our models. Too often this essential role is missing from computational experiments, and to some extent can only come from reality itself, that is classical experiments. This hasn’t stopped the hubris of some that define computations as replacements for experiments when they conduct direct numerical experiments and declare them to be ab initio.

The world as we have created it is a process of our thinking. It cannot be changed without changing our thinking.

― Albert Einstein

This is very common in turbulence, for example, and this approach should be blamed for helping to stagnate progress in this field. The truly dangerous trend is for real World experiments being replaced by computations, which is happening with frightening regularity. This creates an intellectual disconnect of science’s lifeblood and its modeling by allowing modeling to replace experiments. With models then taking the role of experiment a vicious cycle ensues where faulty models are not displaced by experimental challenges. Instead an incorrect or incomplete model can increase its stranglehold on thought.

The real world is where the monsters are.

― Rick Riordan

Nothing is more damaging to a new truth than an old error.

— Johann Wolfgang von Goethe

Indeed lack of progress in understanding turbulence can largely be traced to the slavish devotion to classical ideas, and the belief that the incompressible Navier-Stokes equations somehow contain the truth. I feel that they do not, and it would be foolish to adopt this belief. That has not stopped the community from fully and completely adopting this belief. Incompressibility is itself an unphysical approximation (albeit a useful one), but woefully unphysical in its implied infinite speed of propagation for sound waves. It is also strains any connections of the flow to the second law of thermodynamics, which almost certainly plays a key role in turbulence. Incompressibility removes thermodynamics from the equations in the most brutish way possible. Computing has only worked to strengthen these old and stale idea’s hold on the field, and perhaps set progress backwards by decades. This need not be the case, but outright intellectual laziness has set in.

It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.

― Richard P. Feynman

Experimental observations are only experience carefully planned in advance, and designed to form a secure basis of new knowledge.

― Sir Ronald Fisher

Classically experiments are conducted to either confirm our understanding, or challenge it. A convincing experiment that challenges our understanding is invaluable to the conduct of science. Experimental work that provides this sort of data is essential to progress. When the data is confirmatory, it provides the basis of validation or calibration of models. Too often the question of whether the models are right or wrong is not considered. As a result the models tend to drift over time out of applicability. The derivation and definition of different models based on the feedback from real data is too infrequent. Explaining data should be a far more important task in the day-in-day-out conduct of science.

Theories might inspire you, but experiments will advance you.

― Amit Kalantri

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

― Henri Poincaré

In computational modeling and simulation this is happening even less. Part of the reason is the lack of active questioning of the models by scientists. Models have been applied for decades without significant challenge to assertion that all we need is a faster, bigger computer for reality to yield to the model’s predictive power. The incapacity of the model to be predictive is rarely even considered as an outcome. Another way of expressing this problem is the lingering and persistent weakness of validation (and it brother in arms, verification). Too often the validation received by models is actually validation disguised as calibration without the correctness of the model even considered. The ultimate correctness of a model should always be front and center in validation, yet this question is rarely asked. Properly done validation would expose models as being wrong, or similarly hamstrung in their ability to model aspects of reality. The consequence is the failure to develop new models and too much faith placed in heavily calibrated old models.

Humans see what they want to see.

― Rick Riordan

 Remember, you see in any situation what you expect to see.

― David J. Schwartz

The current situation is not healthy. Science is based on failures, and failure is not allowed today. The validation outcome that a model is wrong is viewed as a failure. Instead it is an outstanding success that provides the engine for scientific progress so vitally needed. In most computational simulations this outcome is ruled out from the outset. Rather than place the burden of evidence on the model being correct, we tend to do the opposite and place the burden on proving models wrong. This is backwards to the demands of progress. We might consider a different tact. This comes as an affront to the viewpoint that scientific computing is an all-conquering capability that only needs a big enough computer to enslave reality to its power. Nothing can be further from the truth. In the process we are wasting the massive investment in computing rather than harnessing it.

The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.

― Albert Einstein

To succeed scientific computing needs to embrace the scientific method again instead of distancing itself from the engine of progress so distinctly. We need leadership in science that demands a different path be taken. This path needs to embrace risks and allow for failure while defining a well-defined structure that puts experiment and modeling in proper roles and appropriate contexts.

Never in mankind’s history have we so fundamentally changed our means of existence with so little thought.

― James Rozoff

Any fool can write code that a computer can understand. Good programmers write code that humans can understand.

– Martin Fowler

I don’t think software gets the support or respect it deserves particularly in scientific computing. It is simply too important to treat it the way we do. It should be regarded as an essential professional contribution and supported as such. Software shouldn’t be a one-time investment either; it requires upkeep and constant rebuilding to be healthy. Too often we pay for the first version of the code then do everything else on the cheap. The code decays and ultimately is overcome by technical debt. The final danger with code is the loss of the knowledge basis for the code itself. Too much scientific software is “magic” code that no one understands. If no one understands the code, the code is probably dangerous to use.

Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning.

– Rich Cook

Recently I’ve taken to harping on deconstructing the value proposition for scientificcomputing. The connection to work of importance and value is essential to understand, and the lack of such understanding explains why our current trajectory is so problematic. Just to reiterate, the value of computing, or scientific computing is found in the real world. The real world is studied through the use of models in scientific computing that are most often differential equations. Using algorithms or methods we then solve these models. These models as interpreted by their solution methods or algorithms are expressed in computer code, which in turn runs on a computer.

Good code is its own best documentation. As you’re about to add a comment, ask yourself, ‘How can I improve the code so that this comment isn’t needed?’

– Steve McConnell 

Each piece of this stream of activities is necessary and must be competently executed, but they are not equal. For example if the model is poor, no method can make up for this. No computer code can rescue it, and no amount of computer power can solve it in a way that is useful. On the other hand for some models or algorithms, no computer exists that is fast enough to solve the problem. The question is where are the problems today? Do we lack enough computer power to solve the current models? Or are the current models flawed, and the emphasis should be on improving them? In my opinion the key problems are caused by inadequate models first, and inefficient algorithms and methods second. Software, while important is the third most important aspect and the computers themselves are the least important aspect of scientific computing.

With that said we do have significant issues with software, its quality, its engineering and its upkeep. Scientific software simply isn’t developed with nearly enough professionalism. Too much effort is placed on implementing algorithms compared to the effort in keeping the software up to date. Often software is written, but not maintained. Such maintenance is akin to issues with upkeep on roads and bridges. Often the money only exists to patch the existing road rather than redesign and rebuild it to meet current needs. In this way technical debt explodes and often overwhelms the utility of the computer implementation. It simply becomes legacy code. The code is passed down from generation to generation and ported to new computers. Performance suffers, understanding suffers and ultimately quality dies. In many places the entire software enterprise allows the code to be written then only maintained, and ported to generation after generation of computer.

C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do, it blows away your whole leg.

– Bjarne Stroustrup

More importantly software often outlives the people responsible for the intellectual capital represented in it. A real danger is the loss of expertise in what the software is actually doing. There is a specific and real danger in using software that isn’t understood. Many times the software is used as a library and not explicitly understood by the user. The software is treated as a storehouse of ideas, but if those ideas are not fully understood there is danger. It is important that the ideas in software be alive and fully comprehended. 

Perhaps, the biggest problem we have is the insistence that the most important issue is the hardware; our computers simply aren’t fast enough. This is an overly simplistic view of the issues and ultimately saps energy from solving more important issues with software is among these. Unfortunately, it isn’t the weakest part of the chain of value, but it is too weak for the health of the field. In total the present National focus in computing is almost completely opposite to the value of the activities. The least valuable thing gets the most attention, and the most valuable thing gets the least. How things got so far out of whack is another story.

 People who are really serious about software should make their own hardware.

― Alan Kay

In algorithms, as in life, persistence usually pays off.

― Steven S. Skiena

Over the past year I’ve opined that algorithm (method) research is under-supported and under-appreciated as a source of progress in computing. I’m not going to backtrack one single inch on this. We are not putting enough effort into using computers better, and we are too much effort to building bigger, less useful and very hard to use computers. Without the smarts to use these machines wisely this effort will end up being a massive misapplication of resources.

The problem is that the issues with algorithm research are even worse than this. The algorithm research we are supporting is mostly similarly misdirected. It turns out we are focused on algorithm research that does even more to damage our prospects for success. In other words, even within the spectrum of algorithm research there isn’t an equality of impact.

The fundamental law of computer science: As machines become more powerful, the efficiency of algorithms grows more important, not less.

— Nick Trefethen

There are two fundamental flavors of algorithm research with intrinsically different value to the capability of computing. One flavor involves the development of new algorithms with improved properties compared to existing algorithms. The most impactful algorithmic research focuses on solving the unsolved problem. This research is groundbreaking and almost limitless in impact. Whole new fields of work can erupt from these discoveries. Not surprisingly, this sort of research is the most poorly supported. Despite its ability to have enormous and far-reaching impact, this research is quite risky and prone to failure.

If failure is not an option, then neither is success.

― Seth Godin

It is the epitome of the risk-reward dichotomy. If you want a big reward, you need to take a big risk, or really lots of big risks. We as a society completely suck at taking risks. Algorithm research is just one of enumerable examples. Today we don’t do risk and we don’t do long-term. Today we do low-risk and short-term payoff.

Redesigning your application to run multithreaded on a multicore machine is a little like learning to swim by jumping into the deep end.

—Herb Sutter

A second and kindred version of this research is the development of improved solutions. These improvements can provide lower cost of solution through better scaling of operation count, or better accuracy. These innovations can provide new vistas for computing and enable the solution of new problems by virtue of efficiency. This sort of research can be groundbreaking when it enables something to be done that couldn’t be reached due to inefficiency.

This is the form of algorithm research forms a greater boon to efficiency of computing than Moore’s law has provided. A sterling example comes from numerical linear algebra where costly methods have been replaced by methods that made solving billions of equations simultaneously well within reach of existing computers. Another really good example were the breakthroughs in the 1970’s by Jay Boris and Bram Van Leer whose discretization methods allowed an important class of problems to be solved effectively. This powered a massive explosion in the capacity of computational fluid dynamics (CFD) to produce meaningful results. Without their algorithmic advances CFD might still be ineffective for most engineering and science problems.

The third kind of algorithm research is focused on the computational implementation of existing algorithms. Typically these days this involves making an algorithm work on parallel computers. More and more it focuses on GPU implementations. This research certainly adds value and improves efficiency, but its impact pales in comparison to the other kind of research. Not that it isn’t important or useful, it simply doesn’t carry the same “bang for the buck” as the other two.

In the long run, our large-scale computations must inevitably be carried out in parallel.

—Nick Trefethen

Care to guess where we’ve been focusing for the past 25 years?

The last kind of research gets the lion’s share of the attention. One key reason for this focus is the relative low risk nature of implementation research. It needs to be done and generally it succeeds. Progress is almost guaranteed because of the non-conceptual nature of the work. This doesn’t imply that it isn’t hard, or requires less expertise. It just can’t compete with the level of impact as the more fundamental work. The change in computing due to the demise of Moore’s law has brought parallelism, and we need to make stuff work on these computers.

Both are necessary and valuable to conduct, but the proper balance between the two is a necessity. The lack of tolerance for risk is one of the key factors contributing to this entire problem. Low-risk attitudes contribute to the dominance of focus on computing hardware and the appetite for the continued reign of Moore’s law. It also compounds and contributes to the dearth of focus on more fundamental and impactful algorithm research. We are buying massively parallel computers, and our codes need to run on them. Therefore the algorithms that comprise our codes need to work on these computers. QED.

The problem with this point of view is it’s absolute disconnect with the true value of computing. Computing’s true value comes from the ability to solve models of reality. We solve those models with algorithms (or methods). These algorithms are then represented in code for the computer to understand. Then we run them on a computer. The computer is the most distant thing from the value of computing (ironic, but true). The models are the most important thing, followed by how we solve the model using methods and algorithms.

Our current view and the national “exascale” initiative represents a horribly distorted and simplistic view of how scientific value is derived from computing, and as such makes for a poor investment strategy for the future. The computer, the thing the greatest distance from value, is the focus of the program. In fact the emphasis in the national program is focused at the opposite end of the spectrum from the value.

I only hope we get some better leadership before this simple-minded mentality savages our future.

Extraordinary benefits also accrue to the tiny majority with the guts to quit early and refocus their efforts on something new.

― Seth Godin

Conformity is the jailer of freedom and the enemy of growth.

― John F. Kennedy

In watching the ongoing discussions regarding the National Exascale initiative many observations can be made. I happen to think the program is woefully out of balance, and focused on the wrong side of the value proposition for computing. In a nutshell it is stuck in the past.

All the heroes of tomorrow are the heretics of today.

― E.Y. Harburg

The program is obsessively focused on hardware and the software most closely relatedto hardware. As the software gets closer to the application, the focus starts to drift. As the application gets closer and modeling is approached, the focus is non-existent. It is simply assumed that the modeling just needs a really huge computer and the waters will magically part and the path the promised land of predictive simulation will just appear. Science doesn’t work this way, or more correctly well functioning science doesn’t work like this. Science works with a push-pull relationship between theory, experiment and tools. Sometimes theory is pushing experiments to catch up. Sometimes tools are finding new things for theory to answer. Computing is such a tool, but it isn’t be allowed to push theory, or more properly theory should be changing to accommodate what the tools show us.

The opposite of courage in our society is not cowardice, it’s conformity.

― Rollo May

I’ve written a lot about all of these problems.

One of the other observations I haven’t written about is how antiquated this entire point of view is. The supercomputers are run in a manner consistent with the old fashioned “mainframes” that IBM used to produce. Mainframes have faded from prominence, but still exist. They are no longer the central part of computing, and this change has been good for everyone. The overly corporate and centralized computing model associated with mainframes is still in place. It is orthogonal to the nature of computing in most places. The decentralized computing associated with phones, and laptops, and tablets and the cloud all democratized computing. That democratization led the way for everyone using computing, and often not realizing they were. It was one of the keys to value and the explosion of information, data and computing. It is completely opposite of supercomputing.

 The conventional view serves to protect us from the painful job of thinking.

― John Kenneth Galbraith

The question is whether there is some way to learn from everyone else. How can this centralized supercomputing be broken down in a way to help the productivity of the scientist. One of the things that happened when mainframes went away was an explosion of productivity. The centralized computing is quite unproductive and constrained. Computing today is the opposite, unconstrained and completely productive. It is completely integrated into the very fabric of our lives. Work and play are integrated too. Everything happens all the time at the same time. Instead of maintaining the old-fashioned model we should be looking into harvesting the best of modern computing to overthrow the old model.

Mainframes represent the old way and conformity; freedom from them represents the new way and freedom. To succeed at supercomputing freedom is the path to success

Great people have one thing in common: they do not conform.

― P.K. Shaw

No amount of genius can overcome a preoccupation with detail

—Levy’s Eighth Law

I’ve been inundated with thinking about exascale computing this week. Programming models, code, computer languages, libraries, and massively parallel implementations of algorithms. At the end of all the talk about advanced computing, I’m left thinking that something really key is being ignored moving forward. We are already indrowning in data whether we are talking about the Internet in general, the coming “Internet of things” or the scientific use of computing. The future is going to be much worse and we are already overwhelmed. If we try to deal with every single detail, we are destined to fail.

How can we move forward and keep our sanity?

Of course reality is actually much simpler, or at least the part we care about. In almost every decision of any importance, the details fade away and we are left with only an important core of significance. This is a key concept moving forward in computing, sparsity. Not everything matters and the important thing is discovering how to unmask this kernel of essential information. If we can’t the data deluge will drown us.

Fortunately some concepts have emerged recently that hold promise. The whole area of compressed sensing is structured around the capacity to unveil the important signalin all the noise and represent this importance compactly and optimally. This class of ideas will be important in managing the Tsunami of data that awaits us.

The future will give us more data than we can ever wade through, and we need principled ways to manage our view of it. In many cases we won’t even be able to get the data off the computer at all, only a part of it. If our code or calculation crashes we won’t be able to restart from exactly the same state. We are going to have to let go of the details. This should be easier because the reality is that they don’t matter, or more properly the vast majority of the details don’t. The trick is holding on to the details that do matter.

Tradition becomes our security, and when the mind is secure it is in decay.

― Jiddu Krishnamurti

Over the past couple of posts I’ve opined that the essence of value in computing should be best found in the real world. This is true for scientific computing as it is for the broader world. The ability of computers to impact reality more completely has powered an incredible rise in the value of computing and transformed the World. Despite this seemingly obvious proposition, in recent years and with current plans, the scientific community has focused its efforts on the part of computing most distant from reality, the computing hardware. The bridge from the real world to the artificial reality of the simulation are our models of reality.

Tradition is a fragile thing in a culture built entirely on the memories of the elders.

― Alice Albinia

In science these models are often cast in the esoteric form of differential equations tobe solved by exotic methods and algorithms. Ultimately, these methods and algorithms must be expressed as computer code before the computers can be turned loose on their approximate solution. These models are relics. The whole enterprise of describing the real world through these models arose from the efforts of intellectual giants starting with Newton and continuing with Leibnitz, Euler, and a host of brilliant 17^th, 18^th and 19^th Century scientists. Eventually, if not almost immediately, models became virtually impossible to solve via available (analytical) methods except for a handful of special cases.

There is no creation without tradition; the ‘new’ is an inflection on a preceding form; novelty is always a variation on the past.

― Carlos Fuentes

When computing came into use in the middle of the 20^th Century some of these limitations could be lifted. As computing matured fewer and fewer limitations remained, and the models of the past 300 years became accessible to solution albeit through approximate means. The success has been stunning as the combination of intellectual labor on methods and algorithms along with computer code, and massive gains in hardware capability have transformed our view of these models. Along the way new phenomena have been recognized including dynamical systems or chaos opening doors to understanding the World. Despite the progress I believe we have much more to achieve.

What might be holding us back? The models are not evolving and advancing in reaction to the access to solution via computing.

 The difficulty lies not so much in developing new ideas as in escaping from old ones.

― John Maynard Keynes

Today we are largely holding to the models of reality developed prior to the advent of computing as a means of solution. The availability of solution has not yielded the balanced examination of the models themselves. These models are
artifacts of an age where the nature of solution was radically different. One might wonder what sorts of modifications of the existing paradigm would be in order should the means of solution be factored in. For example the notion of deterministic unique solutions to the governing equations is pervasive, yet reality clearly shows this to be wrong. Solutions to reality are always a little bit, to very different even given nearly identical initial conditions.

The assumption of an absolute determinism is the essential foundation of every scientific enquiry.

― Max Planck

Originally the models focused on the average or mean tendency of reality. This is reasonable for much of science and engineering, but as the point-of-view becomes refined other issues begin to crowd this out. These variations in outcome can dominate the utility of these models. For many cases the consequence of reality is driven by the uncommon or unusual outcomes (i.e., the tails of the distributiuon). Most of our current modeling approach and philosophy is utterly incapable of studying this problemeffectively. This gets to the core of studying uncertainty in physical systems. We need to overhaul our approach of reality to really come to grips with this. Computers, code and algorithms are probably at or beyond the point where this can be tackled.

It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset.

― Arthur Stanley Eddington

Here is the problem. Despite the need for this sort of modeling, the efforts in computing are focused at the opposite end of the spectrum. Current funding and focus is aimed at the computing hardware, and code with little effort being applied to algorithms, methods and models. The entire enterprise needs a serious injection of intellectual energy in the proper side of the value proposition.

Cynics are – beneath it all – only idealists with awkwardly high standards.

― Alain de Botton

…Next time you’re faced with a choice, do the right thing. It hurts everyone less in the long run.

As the best practices in scientific computing continue to improve, verification is more frequently being seen in papers and reports. The progress over the past decade has been fantastic to see. Despite this progress there are some underlying problems that are pervasive in the community’s practice, and whose impact will ultimately reduce progress. These poorly executed practices are inhibiting the characterization of methods and their impact (positive or negative) on solutions.

Firstly, code verification is almost always applied to problems that bear little resemblance to the problems that are intended to be solved in the application of a method. Code verification usually only reports order of accuracy for the purposes of matching the theoretical expectations. This is meeting the minimal requirements of code verification as a practice. Often ignored is the capability to report the precise numerical error for the problem being computed. Both the rate of convergence and the error contain important and useful information for the developers and users of a numerical method. Both should be systematically reported rather than just the minimum requirement.

For solution verification the problem is much worse. Even when solution verification is done we are missing important details. The biggest problem is the lack of solution verification for the application of scientific computing to problems. Usually the problem is simply computed and graphs are overlaid, and success is declared. The comparison looks good enough. No sense of whether the solution is accurate is given at least quantitatively. An error estimate for the solution shown, or better yet a convergence study would provide much enhanced faith in the results. In addition to the numerical error, the rate of convergence would also provide information on the tangible expectations for the solution for practical problems. Today such expectations are largely left to be guessed by the reader.

In any moment of decision, the best thing you can do is the right thing. The worst thing you can do is nothing.

I believe on of the deeper issues is the belief that the rate of convergence and numerical error only matter for problems with analytical results. This matters for code verification purposes, but also matters greatly for practical problems. In fact it is probably more important for practical problems, yet it is rarely reported. To get things working better we need to move to a practice where both convergence and error are reported as a matter of course. It would be a great service to the community.

If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them.

― Henry David Thoreau

In all endeavors we desire success, and the best success endures. The endurance of success is predicated on the foundations upon which that success is grounded. If foundations are systematically deprived of the basis, they will crumble and induce a crisis. Another way of saying this is success is dependent on balance. If the short-term success is continually rewarded, the long-term success will be undermined. These principles apply broadly including to the conduct of computational science and scientific computing.

To apply this principle it is important to understand the nature of the foundation, and how the inter-linking areas of focus come together to provide a broad base for success. I see “computing” as a general stream of activities running from an impact in the reality of people’s lives to the method of achieving this on a computer (models with methods and algorithms). These methods and algorithms need to be expressed to the computer in useful form through computer code, and ultimately have a computing platform adequate to the purpose. Every single step in the chain is important, but the relative value and priority of each is different. A lot depends on what the pacing requirements for progress are, but the focus of the value proposition should be an imperitive.

Insanity is doing the same thing, over and over again, but expecting different results

― Narcotics Anonymous

Let’s explore.

I made the argument that the thing that has set apart computers in recent times is the ability to make things matter to our daily lives, in and out of work. Computers can now have a huge impact on every aspect of living. When this happened the value of the entire computing enterprise exploded to a level unimaginable before. Every other aspect the model, algorithm, code and computer needed to be competently executed and adequate, but the connection to reality was the enabler for unprecedented growth.

Observing and understanding are two different things.

― Mary E. Pearson

The secondary fuel for this revolution is the model of interaction and the algorithms to efficiently deliver the value. The actual code and compute needs of this delivery needs to be competently executed, but beyond that offer nothing distinguishing to it. This is a massive lesson right in front of the scientific community, which seems to be not understood these observations as measured by its actions. Today’s computing for science emphasis has completely inverted the value stream revolutionizing computing in the rest of the World.

The computing hardware has taken center stage in scientific computing followed by computer code. The methods and algorithms have greatly diminished importance in charting the path forward. More troublingly the methods and algorithm work is typically focused upon the effective implementation on new exotic computing hardware, not establishing fundamentally new capabilities. It is important to get the most out of expensive computers, but we fail to harness the power of algorithms; the greatest power of algorithms is to transform what is possible to do with a model of reality. They can change what is even conceivable to solve, and open new vistas of fidelity to solution. A prime example is Google’s search, the value is putting the right information is people’s hand, the model is the connectivity of the Internet, and the PageRank algorithm makes it happen well enough. The code and computers putting it together are necessary, but not innovative.

But better to get hurt by the truth than comforted with a lie.
― Khaled Hosseini

The models of reality are important as the interface between reality and algorithms for solution. Without the model all the algorithms work is for naught. Without an algorithm all the beautiful code and powerful computers are useless. Without the model you don’t have a connection to reality. Thus the lack of focus on modeling in scientific computing is perhaps even worse.

Current work almost assumes that modeling available is adequate for the purposes. It is most assuredly not presently adequate, and it will almost as assuredly never be completely adequate. Modeling must always be improving. If we are doing our computing correctly the models we use should continually be coming up short. Instead, the models seem to be completely frozen in time. They aren’t advancing. For example, I believe we should be undoing the chains of determinism in simulation, but even today deterministic simulations are virtually all of the workload.

Instead of seeing a need for improvement of the underlying models, and the way these models are solved, we have a program that tries to solve the same models, with the same algorithms on massive computers only changing the fidelity of the discretization. This assumes that everything in this chain is already at its ultimate state. This implicit assumption should be rejected out of principle.

To acquire knowledge, one must study;
but to acquire wisdom, one must observe.

― Marilyn Vos Savant

These concepts should be almost self-evident, but in practice we continually trade long-term success for short-term gains. We have adopted practices that lower the short-term risk by raising the long-term risk. Ultimately the entire enterprise is lurching toward a crisis in sustainability. The key to this crisis is starving the foundation of value in scientific computing that is found foremost in models and their solution via algorithms and methods. The other aspect that has been systematically shortchanged is the value of the people who provide the ideas that form model, methods and algorithms. Ultimately, the innovation in scientific computing is the intellectual labor of talented individuals.

The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter—for the future. His duty is to lay the foundation for those who are to come, and point the way.

― Nikola Tesla