Elephant and ant: The social and cognitive organization of computer simulation

Representation vs. imitation

I would like to point out that a particular tension between imitation and representation characterizes simulation in a quite general sense. Küppers et al. (2006) elaborated on this tension as structural versus functional accounts:

Alan Turing (1912–1954) situated the validation of a simulation in the setting of an ‘imitation game’ (Turing 1950). An interrogator had to pose questions via telex and received responses from a human and a computer. Could he discriminate which set of answers was given by the machine and which by the human? A computer whose answers are indiscernible would imitate the answers of a human being and thus pass the ‘Turing Test.’ To date, no computer has succeeded! Hence the imitation game that constitutes the Turing Test afforded a sophisticated arrangement to filter the functional equivalence out of the plenitude of theoretical possibilities. A computer has to behave like a human to pass the test, but the potential success has to be independent of the mechanisms that are employed to simulate. Turing, therefore, adhered strongly to a functionalist perspective. … This standpoint has been challenged by a position that can be called ‘structural’ and that maintains that a valid simulation has to be structurally valid, that is, has to be based on a simulation model that represents [emphasis added] the structure of the system under investigation. This problem has been taken up in J. Searle’s (1980) famous and controversial ‘Chinese room’ argument that boils down to the point that imitation [emphasis added] of intelligent behavior is not itself intelligent behavior. … Should [a test for artificial intelligence] provide a functional or structural imitation of cognition? (2006: 14–15)

This lengthy quote describes an instance with general significance. Where simulation is used as an instrument, the tension between representation and imitation (or between a structural and a functional account) is present. If you remind yourself of Terry Shinn’s characterization of research instruments, like genericity, and disembedding – re-embedding, it does not come as a surprise that the instrument does not work on the basis of representation alone. The versatility of imitating several dynamics of interest, contrary to representing one particular dynamic, correlates with the facility of being embedded in new contexts, contrary to being tied to one particular context.

Feedback loop in modeling

A look at the methodology of simulation modeling shows why imitating phenomena is a persistent principle of simulation that sustains the tension between imitation and representation.

There are certain classes of simulation models, like artificial neural networks, which aim at imitation from the outset. Their point is exactly to connect input and output in a highly implicit way that is based on extensive parameter adjustments – ‘learning algorithms’ – instead of explicit mathematical equations. If such models are successful in simulating a phenomenon, it is because their behavior can be adapted to the desired input–output patterns, not because the models would represent the essential structure of the phenomena of interest. The role of imitation therefore is straightforward. The more difficult case for my argument is when the researchers start from a theory in the form of mathematical equations, like thermodynamics for example. ² The role of adaptation should be smaller since the models are based on a strong theoretical structure. In the remainder of this subsection, I want to concentrate on this case where a certain quantity of interest, say x, is represented in a theoretical model by x^mod.

Models of thermodynamics, to keep this example, are older than the computer. So what is the point of simulation? With simulation methods, researchers can build and handle complex models in a flexible way. At the same time, the modeling process becomes broader and more sprawling. Addressing problems by simulation connects three important issues: setting up the theoretical model (suitably based on the theory of thermodynamics), implementing and executing it on computers and analyzing the results. ³ Obviously, the discrete modeling and implementation steps are particular to simulation. They transform the theoretical model with its continuous equations into that sort of discrete object computers can handle. This transformation includes specifying algorithms for solving the (now discrete, i.e. step-wise) equations, coding in a particular programming language, and compiling on a given constellation of soft- and hardware.

The analysis and evaluation of the theoretical model via comparison to the target system is still the standard rationale. In general, the quality of a model depends on two aspects that counteract each other. It depends both on adequacy of representation, else the model would not yield results revealing anything about the target system, and tractability, which is prerequisite for obtaining any result at all. Here is where computers have changed the picture. They can handle very long and convoluted iterative algorithms that would be intractable for human beings and, hence, make models tractable which otherwise would be useless.

Although the modeling process is enlarged, it makes complexity more manageable than it has been on the basis of theoretical (formal, mathematical) models alone. The key is a feedback loop that renders models adaptable to an extraordinary degree. Making use of adaptability, in turn, affects how simulation is socially organized. First let me explain how the feedback loop operates. Consider researchers are interested in a quantity x^real of some target system. The quantity of interest could be the elasticity of a mixture of certain substances. Chemical engineers will use thermodynamics theory to specify a model based on so-called equations of state that determine the desired quantity, i.e. x^mod, the model-counterpart to the target quantity x. Typically, it is too difficult to directly calculate x^mod because the equations are too complex to solve. Researchers hence resort to simulation and build a model that approximates the theoretical model so that the computer can retrieve numbers for the corresponding quantity x^sim of the simulation model, see Figure 1 for a schematic display.

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Figure 1.

Scheme showing relations between the real world, modeling, simulation and experiments.

Up to this point, simulation helps to determine quantities, but these quantities are merely modeled versions x^sim of the quantity x^mod that itself has been modeled. Now the feedback loop displayed in Figure 1 comes into play. Scientists can vary the model input or parameters of the model and ‘observe’ how x^sim changes. This is an experimental activity, but one that does not deal with nature or some material system in the laboratory, but rather with the simulation model.

Consider the elasticity example. The researchers are interested in properties like elasticity of the mixture of two substances. Of course, large data banks of substance properties are available, but they cannot possibly specify properties of all mixtures: since these properties change with mixing ratios, the possible entries are too numerous for data banks to ever be exhaustive. Typically, data about elasticity of the mixture of interest exist, but are sparse.

Moreover, no theoretical model will be able to match the measured data perfectly, because any particular mixture of particular substances will present a special case not fully covered by general theory. Adapting parameters at the right places of the model, however, allows matching the simulated values with the measured ones. If the theoretical model is good enough and if the parameters are adequately chosen, matching the available data will give confidence for predicting new data, designing processes, etc. Even if the theoretical knowledge has important gaps, and even if the software is imperfect, iterative adaptation does not care and might still provide a pragmatic solution. Thus flexibility, rather than sheer computational power, is the crucial property!

While models with adjustable parameters have been around much longer than computers, practical hurdles had limited their use in the past. The easy availability of computers and optimization software has tremendously lowered these hurdles. It has become much easier to utilize the adaptability of models, ⁴ and therefore much more tempting to succumb to the lure of making models fit by adjusting enough parameters. In terms of the tension described above: adjustment targets imitation rather than representation.

This general description of methodology suggests a certain organization of simulation. Adaptation creates a networked structure. The theoretical model is a shared object of a wider community. A generic simulation model adds discretization and parameterization, but leaves parameter values still unassigned. It is shared by a smaller group of researchers. Moreover, this group can use several of these models. This model still is a not-yet complete entity that is ready to be specified by a research team or working group. Facets of specification include particular implementations, choice of parameterization, tricks to speed up computation and formulating a mixing rule (in our example). Additionally, the measured data to which a model gets adapted exert a strong influence. Different teams of researchers might prefer to work with different sets of reference data. One reason is what data collaborating experimental groups can produce. Depending on reference data, specifications of simulation models will be different.

Simulation thus shows a peculiar embedding and dis-embedding pattern: the theoretical core of the simulation model remains invariant between different teams of scientists, but other specifications do not. Thermodynamic simulation models, for instance, differ greatly in performance depending on parameter assignments. The instrument undergoes a more significant transformation than suggested by ‘embedding’. It is apt, therefore, to remember that simulation has been characterized as an ‘instrument of instruments’, indicating an additional layer of freedom. This is a philosophical –and admittedly a bit abstract– argument showing the plausibility of my claim about how the methodology and organization of simulation are intertwined. Now, I return to empirical evidence.

Quantum chemistry: mirroring the first and second turns of simulation

Here is a fast-forward history of quantum chemistry. In the early 20th century, chemistry was firmly established as a discipline with a strong experimental culture, considered to be profoundly different from the rational–theoretical branch of physics. The difference was put into question when the new quantum theory was formulated in the 1920s. It describes the electronic structure of atoms and molecules, which in turn determines their chemical properties, like bond energies. Hence quantum theory seemed to establish a bridge between theoretical physics and chemistry. At least such a bridge started to look like a real possibility. The Schrödinger equation (1926) seems to provide a useful formulation of the problem, because this equation contains all information about the electronic structure of molecules. Shouldn’t one be able to compute chemical properties by solving the Schrödinger equation?

This question was answered in the positive very quickly. The 1927 joint paper by the German physicists Walter Heitler and Fritz London is widely acknowledged as the first seminal work in quantum chemistry. There they treated the simplest case, the hydrogen molecule, and argued that homopolar bonding could be understood as a quantum phenomenon. The argument was of mathematical nature: from the Schrödinger equation it follows that two electrons with antiparallel spin (a quantum concept) that aggregate between two hydrogen protons reduce the total energy, i.e. create a stable configuration.

It soon became clear, however, that moving beyond the simplest cases leads into terrain utterly intractable for reasons of computational complexity. Basically, the Schrödinger equation expresses the energy via a wavefunction Ψ(1,2,…,N) that has as variables all N electrons of an atom, molecule or bunch of molecules. The electrons interact and hence Ψ has 3N degrees of freedom (three dimensions of space, leaving spin aside), a number of discouraging cardinality in many circumstances. Practically, to solve Ψ is extremely difficult and computationally demanding – it can be seen as a paradigm of computational complexity. Quantum chemistry did not die out, but progressed in a ‘quasi-empirical’ mode where measured values replaced those quantities in theoretical models that were too complicated to compute. There exist comprehensive historical accounts of the history of quantum chemistry of which I would like to mention the chapter in Mary Joe Nye (1993) and, in particular, the recent book by Kostas Gavroglu and Ana Simões (2012).

These accounts portray how the pathway of quantum chemistry meandered between physics and chemistry and also between theoretical and experimental means. The historians agree that quantum chemistry has been established as a sub-discipline of chemistry due to the electronic computer. With computational and simulation methods one could tackle models that had been out of reach previously. In a sense, one elephant (quantum theory in the form of the Schrödinger equation) had got stuck, but when the second elephant (the computer) arrived, they together were successful. Numerical methods were developed that aimed at solving the Schrödinger equation ab initio, i.e. without recurring to measured values. The timeline coincides with the first turn to simulation. The historical accounts agree that the computer changed the game and superseded the quasi-empirical approaches (around 1970). After that the written histories of quantum chemistry fade out.

DFT: stunning success

There is more to discover, however, namely a turn that elevated quantum chemistry to one of the most visited spots in all of science. Though there is not yet a commonly accepted terminology, it is apt to call this turn the turn toward computational quantum chemistry. ⁶

All those readers who trust my line of argument will expect that this turn happened around 1990 and is related to simulation instrumentation and how it is organized. The remaining part of this section will convince you this expectation is correct.

One theory plays a particular role here, namely DFT. There are a couple of theories undergoing similar developments, but DFT arguably deserves the most attention. Among quantum chemists, to begin with, there is widespread agreement on the special role that DFT plays among a couple of ab initio methods: ‘The truly spectacular development in this new quantum chemical era is density functional theory (DFT)’ (Barden and Schaefer, 2000: 1415)

Let me first make evident that the development of DFT is in fact spectacular. After that, I will argue why and how this development is related to simulation as an instrument. As I mentioned, so-called ab initio methods flourished in quantum chemistry from the 1970s onward. All these methods made heavy use of the computer and numerical approximations. Two prominent examples of ab initio methods are Hartree-Fock and coupled cluster. DFT has its origins, in the 1960s, in condensed matter physics and was an influential theory in physics since then, but marginalized in chemistry. The ISI Web of Science database consistently counts only around 30 papers per year that were published on DFT ⁷ in all of chemistry (according to the disciplinary assignment of ISI) throughout the 1970s and up to the late 1980s. However, around 1990 a tide change happened. Figure 4 displays this development vividly and makes it evident that DFT underwent a serious phase transition in the 1990s. Between 1990 and 2005, the number of scientific papers on DFT grew exponentially from around 30 to a level of more than 4,000 per year. Moreover, the fast growth has continued since then. Today, more than 15,000 papers on DFT appear each year in the sciences.

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Figure 4.

Number of papers with ‘density functional theory’ in title or abstract per year in the ISI Web of Science database.

I would even dare to claim the staggering growth of DFT has made it the dominant scientific theory of present times. In addition to the number of papers published, I want to add another piece of quantitative evidence. Consider the journal Physical Review, a flagship journal in physics and chemistry. What are the most highly cited papers that appeared ever in this journal? As you might expect, the paper by Einstein et al. (1935) is high on this list. The same is true for the one by Bardeen et al. (1957) on superconductivity, or the one by Binning et al. (1986) on the scanning tunnel microscope. These are well-known ‘elephants’ with high impact not only in science, i.e. physics in this case, but also in history and philosophy of science.

The breaking news is that among the top ten most highly cited papers more than two thirds are about DFT. ⁸ Yet, DFT does not play a role in either history or philosophy of science. Given the kind of evidence presented, the missing attention from the side of science studies seems bewildering. In my opinion, this is an instance where the ants escaped notice though they actually outweigh the elephants. Counting citations is a bit like weighing ants and the question is how significant such quantities are. A critical reader might ask whether and how the turn of DFT and its recent success is related to simulation instrumentation in a systematic way.

A closer look on DFT

Answering this question requires a closer look at DFT. What is DFT about? Quantum chemistry deals with the electronic structure of atoms and molecules. The Schrödinger equation expresses this structure as a wave equation of frustratingly high complexity. Much of quantum chemistry was and still is occupied with finding suitable numerical approximations of what this equation implies about certain values of chemical interest.

In a nutshell, DFT is a theory of the very same electronic structure that circumvents the problem of solving the Schrödinger equation. DFT expresses the energy in a different way, namely in terms of the (joint) electron density – roughly the more likely it is that electrons visit a certain location in space, the higher the electron density. The density hence is an object in space and has only three degrees of freedom. On the face of it, this formulation reduces complexity starkly.

The computational advantages of such a reduction of complexity brought this approach into heuristic use in engineering fields, even before the theory was formulated. The theoretical condensed matter physicist Walter Kohn played a major part in advancing this approach to the level of theory. He and his colleague Pierre Hohenberg contributed the two founding theorems (Hohenberg and Kohn, 1964). They established that the corresponding electron density indeed uniquely determines the ground state energy, that is, the energy is a function only of the electron density and thus can be calculated without reference to the Schrödinger equation, at least in principle. However, the promise is one in principle, whereas in practice one gets from the frying pan into the fire.

Note that the reported 1964 results did prove that there exists a function f that gives the energy and that is dependent only on the electron density. ⁹ While the energy entirely depends on the exact form of this function, the theorem does not give any clue as to how that function looks or how it can be determined. The space of mathematical functions is extremely large, definitely larger than a haystack, hence, to actually determine one particular function might be very difficult. As long as the function is unknown the advantage of reduced complexity does not pay out. Kohn was aware of this shortcoming and in the following year he introduced, together with his co-worker Liu Sham, a practical computational scheme (Kohn and Sham 1965) for approximating the desired functional. This scheme (counterfactually) postulates an idealized situation that makes the approximation of the unknown functional computationally feasible.

The mentioned 1964 and 1965 publications were – and still are – very influential papers. One can read this from bibliometrical evidence. Indeed, they lead the list of most highly cited papers in Physical Review. Eventually, in 1998, Kohn received the Nobel prize ‘for his development of density functional theory’. The reader might wonder how this story about theoretical physics in the 1960s can possibly throw light upon the 1990s turning point of simulation.

Well, I want to ask for only a little more patience. The next step is the observation that the Kohn–Sham scheme for density functionals is attractive because it is computationally relatively ‘cheap’, but it does not provide results of high accuracy. This is sufficient when the objects of interest are regular structures like in crystallography, but most of the interesting questions in chemistry require higher accuracy. DFT therefore was of little use in chemistry, which resonates with the observation made previously that only few papers in chemistry dealt with DFT. The situation is reflected in the following statement by chemists:

However, the correct functional of the energy is unknown and has to be constructed by heuristic approximation. Initial functionals, based principally on behavior of the electron gas … [the Kohn–Sham scheme], were lacking in the accuracy required for chemical applications. Breakthroughs over the past two decades … have led to the development of functionals capable of remarkable accuracy and breadth of applicability …. (Friesner and Berne, 2005, 6649) ¹⁰

Simulation re-organization

What brought the breakthrough in accuracy around 1990 that opened the doors to chemistry for DFT? The answer makes use of the results obtained in the section [Computer simulation as instrument’ above, where the feedback loop in modeling was highlighted as a crucial element in simulation modeling. Some feedback loop always plays a role in modeling, since hardly any model will be entirely correct from the beginning and hence needs to be modified over the process of model building. It is a different thing, however, if modelers deliberately leave their model unspecified and open to adaptation.

In the case of quantum chemistry, ab initio modeling was targeted at numerically solving the Schrödinger equation, The success of DFT came with a new strategy that hybridized ab initio and semi-empirical modeling. Researchers started with a plausible functional (the theoretical, ab initio part) that included multiple parameters open for assignment so that the behavior of the functional could be made to match known data (the semi-empirical part).

The new accomplishments around 1990 have been multi-parameter functionals. They do not stand for a breakthrough in theory, but rather for a breakthrough in the potential of adaptation. Researchers could use such functionals for following a strategy that thrives on the feedback loop of modeling. The strategy was new in that the starting point was not any longer the best available model, but a highly adaptable one. This strategy could become an integral part of the simulation instrument only around 1990. Exploratory modeling of this kind requires iterating modifications of the model (especially its parameters) for sounding out model behavior. This in turn requires cheap and easy access to computing technology – a condition that was in place when desktop computers, workstations and other microcomputers quickly spread around 1990.

If this point is valid, it would suggest that DFT does not thrive by developing functionals ever closer to the correct one. Instead, DFT-based approaches should splinter and develop a variety of functionals, each one being capable of adapting to different types of substances and chemical and physical conditions. This is indeed what happens: there is a flurry of functionals implemented in more than hundred software packages. Manuals even advise researchers not to trust single functionals, to try out several and to combine them into so-called hybrid functionals. Since there is no known reason why one particular functional should work best, researchers have to explore by experimentally fitting various functionals to their data. Typically, working groups and laboratories have a laundry list of which functionals are promising candidates for adapting them to certain types of substances and materials.

Thus, the astounding upswing of DFT since around 1990 is happening on the basis of a theory already developed in the mid-1960s. DFT thrives on the plurality of functionals and a large variety of adaptation practices. Together, they combine accuracy with feasibility in a way that makes DFT so attractive. In other words, the 1990s turn is not based on a general theoretical breakthrough, rather on very many particular achievements. At this point, simulation methodology and organization are intertwined. In a sense, DFT-researchers are organized like a colony.

One institution that is especially ill equipped to account for ant colonies is the Nobel committee. Of course, the overwhelming success of DFT in chemistry and related fields could not be overlooked. Hence Walter Kohn received the Nobel prize in 1998 for DFT, although he was a theoretical physicist and got the price – to his own surprise – for chemistry. Kohn shared the prize with John Pople, a mathematically minded chemist who had a leading role in promoting computational modeling in quantum chemistry. Pople was rewarded ‘for his development of computational methods in quantum chemistry’. ¹¹ Pople was one of the pioneers in the 1970s who realized early that software would be key for fostering quantum chemistry. He and his colleagues did much for standardizing procedures and compiling the software package ‘Gaussian’, which is still the market leader today. However, Gaussian did not include DFT methods (up to the 1990s) because of their lack of accuracy in chemical problems.

What makes DFT researchers look like an organized colony? Ant colonies quickly spread out and explore new territory on very many pathways. At the same time, sustaining this undertaking requires keeping the colony connected. DFT shows a similar pattern of organization. A great number of small teams of researchers locally adapt a number of simulation models to their particular environment. These teams typically operate in a sort of niche, i.e. are interested in particular properties of particular materials under particular conditions. In the easiest case, such groups are successful adjusting and re-combining existing simulation models. On today’s networked computers, a great number of models is easily available and it is a straightforward task to take a number of them and test which one fits best to the situation of interest. Notably, this kind of activity calls more for computational scientists of a general stripe than experts in quantum theory. Arguably, the number of users of DFT is much higher than the number of quantum theoreticians.

Another case is when a small team or individual person develops a new parameterization, for instance a new multi-parameter functional. This functional then easily can be made available to other local teams that might want to include this functional among their candidate models, even if they only want to use it for showing the relative superiority of their own favorite model. Another factor is the networked infrastructure on which models and data can quickly travel; more than hundred software packages are available that contain DFT methods. Different groups develop very specialized types of functionals for particular materials. On the existing networked infrastructure functionals from different working groups can quickly be exchanged via software plug-ins and even re-combined as hybrids, which then create new functionals. One can see this process as a variant of dis-embedding and re-embedding, in the terminology of Joerges and Shinn (2001).

Simulation is an instrument that crosses the boundaries of local research teams as easily as that of scientific disciplines. Again DFT is a telling example. For decades, it was firmly rooted in condensed matter physics, but since the 1990s turning point chemistry has the largest share, weighed by the disciplinary assignment that the ISI database gives to articles written on DFT. Though chemistry has the largest share, there is a multitude of other disciplines, from engineering to materials science, that also have significant shares. If a scientific discipline is indicated by a color, DFT has become a multicolored object.

Overall, DFT is an important instance of simulation in recent science. It shows a remarkable success that starts in the 1990s, exemplifying a general and significant turn for simulation. The somewhat lengthy chain of argument has established that explaining the 1990s turn and the following success of simulation depends on how simulation is organized as an instrument.