2. The giant’s gait

Let’s begin by examining a case involving two investigative practices. We’ll take one as our representative simulation. It involves the use of a computer model to infer the gait of an extinct lineage of dinosaurs. The other is, for our purposes at least, a representative experiment. It is a dissection study which probes the relationship between gait and morphology in vertebrates.

The sauropod lineage boasted the largest terrestrial animals ever. The recently discovered Dreadnoughtus schrani, for instance, managed lengths of 26 meters and weights upwards of 60 ton (see Lacovara et al. Reference Lacovara, Lamanna, Ibiricu, Poole, Schroeter, Ullmann, Aaaa and Novas2014). Such animals present many puzzles,Footnote ⁵ one being their gait. The mechanics of scale say that as animal size increases, some activities become exponentially more difficult.Footnote ⁶ How sauropods managed to shift their bulk, then, is a good question. And a difficult one: paleobiologists are working with limited remains and lack appropriate extant analogues.

Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) respond to this problem by, in brief, simulating a sauropod and teaching it to walk. The strategy is to ‘… construct a computer simulation of sufficient biofidelity to capture the necessary mechanics of the system and to use this to test specific locomotor hypotheses’ (2). Theirs is a sophisticated piece of science, and I only summarize the relevant parts here.Footnote ⁷

Simulation building begins with the digital capture of a reconstruction of the sauropod skeletal system, in this case Argentinosaurus huinculensis. This skeletal anatomy is then represented digitally (see Figure 1). The skeleton is divided into segments which are treated as rigid, modular parts (think of action figures with adjustable limbs, see Figure 2). Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) go on to estimate the distribution of mass, and model both muscle and joints. Significant inference and idealization is involved. Rather than representing an accurate picture of sauropod muscular anatomy, they aim for functional equivalence:

Finally, they estimate muscle mass. This matters because power and force are related to mass, and thus can be inferred from it (see Note 6). In determining muscle mass, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) need to understand the relationship between gait, morphology and musculature for large cursors (quadrupeds build for running). With an obvious lack of living sauropods available, they instead draw on living mammals. We’ll take this study as a putative experiment.

Figure 1. The digitized Argentinosaurus skeleton (from Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013), 3, creative commons).

Figure 2. Simulated Argentinosaur legs, with segments, muscle and joints (from Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013), 4, creative commons).

To estimate muscle mass, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) survey a group of extant cursors: reindeer, hare and greyhound. The data was collected by a technique which is relevantly experimental for our purposes. Dead specimens are examined, dissected, and measured in some detail in order to determine the relationship between the animal’s size, facts about its lifeways, and its muscle mass and distribution. Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) find that ‘there is a relatively consistent pattern even for quadrupeds of different sizes and locomotor specialisations’ (8). On this basis they infer various muscular properties for their simulant.

With the simulation prepared, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) see if their simulant can walk. They run a series of simulations targeting various optima, using results to scaffold further simulations. In brief, the simulants are given an optimum target, such as maximal forward motion over a fixed time period. Various morphs, differing in their muscle activation patterns, are ‘bred’ and those which best achieve the target are used as the basis for the next generation.

Their results are robust. The simulant walks in a largely elephant-like way, however it could only do so ‘… by allowing the wrist joint to lock at a position of maximum flexion and producing a gait somewhat reminiscent of a chimpanzee knuckle walking’ (13). A sauropod walking as an elephant does would catastrophically snap its forelimbs. By locking the wrist-joint, strain is distributed amongst stronger muscles. Thus, their simulation produces a unique gait, unseen in extant animals.

Importantly, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) also generate the trackway patterns such a gait would produce. At medium paces, these are remarkably similar to preserved sauropod trackways. They conclude that although the largest sauropods could happily walk,

Their study, then, makes a prediction: if larger sauropods or other terrestrial animals are discovered, their anatomy will diverge from Argentinosaurus.

To summarize, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) digitize a reconstructed Argentinosaurus; clothe her in muscle; ‘evolve’ gaits by running simulations from various initial conditions. Their results converged on a ‘perfectly plausible’ (1) elephant-like gait, made possible by locking the wrist. The model also produced trackway-patterns which matched remnants, and made predictions about future discoveries. In Section 5 I shall suggest this study is surprising: it generates new, perhaps unintended, knowledge of the target, and opens fruitful avenues of empirical investigation.

Notice two practices involved in the above study. First, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) construct a virtual sauropod – their simulant – and examine its behavior under differing conditions. Second, they investigate the relationship between muscle mass and gait by dissecting a range of vertebrate cursors. The dissection studies are not paradigm experiments – they are more like generic measurements – but for our purposes are suitable. I want to highlight a property these practices share, and a way in which they come apart. Both involve the exertion of control: scientists systematically isolate and manipulate systems to generate results. However, the latter (the experiment) involves interacting with a representative of the class which the scientists are concerned with. The former (the simulation) involves a proxy. Rather than directly examining a specimen of the relevant type, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) investigate something they hope makes for a good representation of that type. In the dissection, we are interested in muscle distribution across vertebrate cursors, and so we examine vertebrate cursors. In the simulation, we are interested in the gait of a long-extinct lineage, and examine a digital representation.

For present purposes we can take the computational study to be an exemplar simulation: Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) conduct a controlled investigation of a proxy, whose behavior is repeatedly observed under varying conditions, and is taken to be informative of their target (Parker, Reference Parker2009). The dissection study will serve as our experiment: Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) conduct a controlled investigation of a set of representative specimens. This is not, of course, a full account of experimentation, nor of simulation. However, as we’ll see, for the purpose of examining surprise, this rough and ready distinction is all that is required.Footnote ⁸

Both of my illustrations have idiosyncrasies, differing from some other experiments and simulations. Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013), for instance, use a phenomenological model: model construction begins from empirical information, rather than from first principles. Moreover, lab based experimental investigation is often very different from dissection studies. And indeed, these differences often make for an epistemic difference (see Currie and Levy Reference Currie and Levyunder review). But not for my purposes here: as we’ll see, the dissection studies have the capacity to surprise in just the way which Morgan intends and – for the purposes of the forthcoming argument – Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation does not.

3. The argument from surprise

Here is a difference between Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation and the dissections which informed their reconstruction. Although the latter are performed under artificial conditions, the investigators are not in complete control of their results.Footnote ⁹ The naturally occurring properties of the dissectees, the hares, say, determine their measurements. The simulation of Argentinosaurus, by contrast, is not like this: although they utilized empirical information, the investigators stipulated, programmed, and constructed the simulation themselves. This difference has prima facie epistemic consequences. It is a tempting thought that, in some sense, simulations don’t give you anything more than what you put in. The argument from surprise relies on just this kind of difference. Although Emily Parke argues that simulations can surprise, she captures the basic thought succinctly:

Mary Morgan (Reference Morgan2005) distinguishes between an investigation’s capacity to ‘surprise’ and ‘confound’. Mere surprise is simply an unexpected result – clearly simulations can provide these. However, a confounding result generates new research by challenging orthodoxy, generating new phenomena, opening new avenues of investigation, and so on. Following the relevant difference, I will call the latter productive surprise.Footnote ¹⁰ Simulations, Morgan argues, may surprise, but cannot do so productively. The incapacity to provide productive surprise underwrites an epistemic distinction between simulations and experiments.

Emily Parke (Reference Parke2014) and Marcel Boumans (Reference Boumans2012) read Morgan’s notion of productive surprise as involving the ‘researcher’s epistemic states regarding results borne out in their research’ (Parke 528), that is, investigators’ knowledge. We can thus distinguish between phenomenal surprise – the sheer feeling of surprise – and surprise in the sense relevant here, an occurrence which is unexpected given particular epistemic or doxastic states.Footnote ¹¹ Naturally, how surprising a study might be in this sense will depend somewhat on the strength of these states. Ceteris paribus, the higher one’s credence that a result will be a certain value, the more surprising it will be when it comes out another.Footnote ¹² Morgan is interested in this epistemic sense of surprise: while experiments can upset our epistemic states in a way which leads to new research and knowledge, simulations (or so the story goes) either cannot do so, or do so badly. This is because we already know what has gone into the simulation’s construction.

In response, both Parke and Boumans point out that scientists are often ignorant of pertinent facts about their simulations. Simulations are usually constructed by multiple researchers, many of whom are in no position to understand the complex layers of code they build on. In virtue of this, simulations often generate epistemically or doxastically unexpected results. Moreover, human scientists are not logically omniscient: we typically do not know all of the consequences which arise from a set of initial conditions, even in the relatively constrained, simple circumstances of computer simulations. Researchers, then, will often have expectations – doxastic and epistemic states – which are foiled by the simulation’s actual behavior.

Moreover, ‘[d]ifferences in researcher’s epistemic states, alone, seem like the wrong grounds for tracking a distinction between experiment and simulation’ (Parke 258). Parke does not deny that some epistemic features are context-sensitive. However, such distinctions shouldn’t be driven only by what researchers know. Presumably it is not our epistemic states which matter, but what the simulation can tell us about the worldly target of our investigation. Parke and Boumans provide putative examples of simulations which apparently are sources of productive surprise. Both responses are similar insofar as they take Morgan’s position to rely on a notion of surprise which is tied to individual epistemic states. As Boumans says,

Both Boumans and Parke argue that as we are ignorant of experiments, so we are similarly ignorant of models, and thus Morgan’s appeal to surprise fails. For all we know, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) lacked epistemic access to their simulation, just as they did to the inner workings of vertebrate muscle mass. In Section 4, I argue this misses the power of Morgan’s position. I develop a notion of productive surprise which doesn’t rely problematically on researcher’s epistemic states. This new notion underwrites a new argument which is not deflected by appeal to ignorance of a simulation’s inner workings.

4. A new argument from surprise

We have seen that Parke and Boumans took the distinction between mere and productive surprise to track scientists’ knowledge of their experiment or simulation alone. In this section I develop a stronger notion of productive surprise. My account is preferable. First, it avoids Parke and Boumans’ criticisms. Second, as we’ll see in Section 5, responding to it provides an explanation of how simulations can surprise. Third, as we’ll see in Section 6, it provides insight into the differences between experiments and simulations. Fourth and most importantly, this notion of surprise is a bone-fide epistemic good, rather than being merely pragmatic or psychological.

In her comparison between experiments and models, Morgan emphasizes experimental freedom: the object’s behaviour is not wholly dictated by experimental design.

Experiments produce results, and results require explanation. Our explanation of experimental behaviour had better not only refer to facts about experimental design. Indeed, I think that explanation is at centre stage:

Here is, I think, the strongest version of Morgan’s argument. If we were to construe what needs explaining narrowly – restricting ourselves to the output of a simulation’s equations, software, and initial values – any result the simulation provides can be explained by appealing to the simulation’s features and generative capacity (this narrow reading will be questioned in Section 5). That is, in principle at least the simulation’s output can be explained in terms of the simulation’s design and implementation. Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation’s behavior is wholly determined by the initial conditions, the design of skeletal arrangements and muscle anatomy, software programming, and the relevant hardware. Facts about the simulation’s construction and programming exhaust explanations of the simulation’s results. By contrast, facts about experimental design do not exhaust what needs explaining about experimental results. For instance, that hare muscle mass distribution follows the same pattern as that of reindeer depends in part on facts about hare, not simply the hare we happen to have dissected. Although both simulations and experiments can surprise us in virtue of generating unexpected results, to explain such results in an experiment requires the re-examination, reassessment and sometimes alteration of ideas pertaining to much more than the experimental context; while in the simulation case only features regarding the computational events are necessary.Footnote ¹³

Let’s get somewhat more precise.

We can distinguish between the immediate objects which scientists interact with in their studies, and their ultimate epistemic aim. Although this distinction is fluid and shifts with scientific goals it is common and useful to draw apart objects of study and targets of enquiry (see Winsberg Reference Winsberg2009; Parke Reference Parke2014). The object is whatever generates an investigation’s data. It is what scientists observe or intervene on. Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulant is their object of study. Another group of objects are the hares which were dissected and measured. An investigation’s target is what the scientists take the data to be revelatory of – it is what we are ultimately interested in. Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) target is sauropod gait. The target of the dissection studies are patterns of muscle distribution across terrestrial vertebrates. A scientist intervenes on or observes an object in order to generate data relevant to the target. Basically, my notion of productive surprise turns on whether an object’s behavior also pertains to the target.

Call the collection of models, theories and narratives pertaining to an object of study or target of enquiry the explanatory resources of that domain. Theories about hare anatomy, or of software functioning, are examples of explanatory resources. These resources can be drawn on to explain an investigation’s results. For instance, our theories of vertebrate muscle-mass are relevant to explaining results of investigations which measure muscle mass in vertebrates; our understanding of computational software and programing are relevant to explaining the behaviour of a computer simulation. A domain’s explanatory resources, then, includes anything relevant to accounting for the results of an investigation in that domain.

Explanatory resources have a range: they apply to a set of subjects. The subjects of a domain include objects and targets. As we saw above, one set of objects are the dissected mammals, another are the computer simulations. Targets we’ve seen thus far have included sauropod gait, and the relationship between cursorial motion and muscle distribution. Theories of hare anatomy most obviously range over (anatomically standard) hares, but may have a wider reach. Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) argue for a theory of muscle distribution that ranges over hare, reindeer and (they hope) sauropods.

From the notion of a domain’s explanatory resources, we can draw a new sense of productive surprise. The crucial idea is that some results challenge our explanatory resources in ways which require alteration or reassessment of ideas and buck our expectations across different ranges. At minimum, investigation is potentially a source of productive surprise when the explanatory resources required to explain the object’s behaviour also range over the target (see Figure 3). What is strikingly different about the hare dissection and Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation is that, in the former case, the explanatory resources (considered narrowly) relevant to the object (a dissected hare) are also relevant to the target (hares); whereas the resources which range over the simulation (how computers operate, etc …) do not range over the target. By this argument, explanations of computer operation have nothing (relevant) to do with sauropod locomotion.

Figure 3. The difference between a potentially productive study, and one which cannot productively surprise.

Results are productively surprising when explaining the results of the investigation give legitimate reason to change, or further investigate, the explanatory resources which range over the target. Discovering that, say, a subset of standard hares have patterned muscle distribution would affect our general theories of hare anatomy. The explanatory resources required to explain the behaviour of Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation appear to lack this character.

An investigation surprises productively when (1) it is an epistemic surprise, that is, the object’s behaviour conflicts with some doxastic or epistemic states pertaining to the object, (2) those states are externally relevant, that is, the same epistemic or doxastic states also pertain to the target (or a wide set of subjects), and thus lead to changes in (or at least challenge) the explanatory resources relevant to those states.Footnote ¹⁴ This is a fairly low bar for productive surprise: it is, for instance, possible to be productive without spurring new research as Morgan discusses. This low bar allows us to distinguish between different types and strengths of productive surprise. In some circumstances, for instance, we might make the following distinction. In one case, surprise occurs only insofar as an investigation’s results challenge the relevant explanatory resources. In another – stronger – case, surprise includes the capacity to spur new research regarding the target. In such cases, it is the need to accommodate the surprising result into our existing knowledge which drives scientific work. This is why productive surprise has two features: upsetting our expectations requires accommodation or updating of those expectations, a wide range means that this accommodation is potentially transformative beyond our knowledge of the object itself. As I take it the former, minimal notion, is necessary for the latter I will discuss them jointly here, only distinguishing them where necessary.

How important is the genuine feeling of surprise to my account? That is, does phenomenal surprise matter?Footnote ¹⁵ Undoubtedly, feeling surprised plays an important role in scientists’ both recognizing and following up on productive, confounding results. And indeed, a fruitful and important line of enquiry would characterize how the feeling of surprise – and its role in generating scientific curiosity, perhaps – motivates and shapes scientific investigation. Here, though, we should take a different tack: the notion of surprise I have developed need not be coupled with a surprised phenomenology. It’s also worth noting that productive surprise needn’t rely on the epistemic status of any particular individual’s beliefs about the investigation at hand. Rather, it tracks the relationship between beliefs about instances and more general ideas about the behaviour of classes and the connections between them. Further, it needn’t be based on the beliefs of individuals themselves: if sense can be made of a community’s beliefs, or of an abstract body of knowledge, either of these could also be transformed in response to productively surprising results. On this account, surprise is a doxastic and epistemic matter, not a phenomenal one. The project of understanding phenomenal surprise in science, and its connection to the sense of surprise I’ve articulated here, is left for another day.

I should add a crucial point to my analysis. I have cashed out ‘productive surprise’ as if it pertains to a specific target. Often, however, scientific targets are ambiguous, vague, under-or-unspecified. This is particularly important for surprise. Surprising results are often unintended: they are important because of some target other than what the scientists had in mind. Moreover, experiments can be used to generate novel phenomena which drive new research (Chalmers Reference Chalmers1999, chapter 13; Franklin Reference Franklin2005). In such cases, productive surprise occurs when the explanatory resources relevant to a surprising result are likely to range far beyond those relevant to the object and controlled by the investigator. A strange result in a computer simulation can be traced back to facts about the computer. An odd experimental result might require resources ranging far beyond facts about the experimental setup. Thus, my appeal to ‘targets’ in the analysis above is merely for convenience. What truly matters for productive surprise is the potential range of the relevant explanatory resources. We can, then, define potential surprise as pertaining to a particular target, as I have above, or as pertaining to a range, like so:

The potential for an investigation to be productively surprising is an epistemic virtue: surprising results generate empirical and theoretical challenges to our knowledge which themselves generate further questions, alterations, and so on. Contrast this with the capacity for confirmation. Where the capacity to generate confirmation turns on the relationship between an observation, a hypothesis, and the background knowledge required to connect the two; the capacity to surprise turns on the relationship between the behaviour of an object, what we need to explain that behaviour, and whether that explanation pertains to further subjects. In the confirmation case, a more-or-less direct connection between object and target is desirable. In the surprise case, a wide range is desirable. Although the two are related, and in some instances overlap, they are distinct epistemic virtues. Further, both of the conditions for an investigation to be surprising in my sense – being an epistemic surprise, and being externally relevant – matter for productivity. The latter condition ensures that results can challenge ideas beyond the narrow scope of the investigation itself. The former condition motivates the challenge to our explanatory resources, and thus the subsequent productivity. Because the result upsets epistemic expectations, it drives us to update those expectations, to re-examine them; further, those changes can then lead to further investigation to bolster previous ideas or explore new ones. A surprise is truly productive when it is both externally relevant and unexpected.

With a notion of productive surprise in hand, we can turn back to the argument from surprise. The central thought is that how Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation behaves is fully explained by the values fed into the machine, the software and hardware of the computer. It does not turn on how sauropods walked.

Compare the data from the dissection studies to the data from Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation. The data produced by the former depends at least in part on naturally occurring features of the dissected animals. The results force us to re-evaluate our theories about them. For instance, I would expect an animal’s means of locomotion to influence its muscle distribution. After all, whether an animal is a cursor, stotter, climber, etc … affects its physiology in relatively regular ways (Davis Reference Davis1964). This initial expectation must be revised in light of the dissection data: after all, the observed collection of animals have similar muscle-distribution despite having different locomotive strategies. The explanatory resources we have about muscle distribution must be altered in light of the evidence. The study produced the data it did because of the actual muscle distribution in hare and reindeer. The simulation results, by contrast, do not appear to have this quality. The data (the resulting gait) is explained by how the computer works, how it was programmed, and so forth. Sauropods having walked differently wouldn’t change that. If the epistemic connection between object and target is ruptured in this way, simulations cannot be productively surprising.

This argument is immune to Parke and Boumans’ objections. First, it does not rely on scientists’ doxastic and epistemic states alone, as it includes the relationship between explanatory resources relevant to target and object. And indeed the notion readily extends to communities or bodies of knowledge. Scientists’ ignorance or otherwise about the mechanics of simulations are largely irrelevant. Second, although Parke and Boumans provide examples of simulations producing tout court epistemic surprise, they have not shown that they surprise in the sense articulated here, nor have they explained how they may do so. Although simulations can upset our epistemic expectations, according to the argument they do not upset expectations which are relevant to contexts outside of the simulation. They cannot, then, produce new phenomena, have unintended consequences, or motivate new research as experiments can. In the next section, I show why this new argument fails, and in so doing, show how simulations successfully surprise.

5. Productively surprising simulations

We have seen that the outputs of simulations can be explained without reference to explanatory resources which range over the investigation’s target. That simulation results can be so explained matters because it purportedly shows that simulations cannot be productive. This argument fails. I’ll argue first that simulations are a potential source of productive surprise, second that in some cases they are indeed productively surprising.

6. Sources of surprise

Does the preceding discussion tell us anything about the differences between experiments and simulations? Recall from the introduction that I’m not in the business of drawing a strict division between two classes of scientific tools or strategies: I’m inclined to think that useful divisions are context sensitive, and so in some contexts we may want to distinguish between practices such as Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulations and the dissection studies which they drew upon, while in others it might be best to lump them together. However, if we ask after the features in virtue of which the former is potentially productively surprising, and in virtue of which the latter is productively surprising, one difference does present itself.

A first guess about the difference turns on the requirements of validity testing: after all, I appealed to this in my argument that simulations can surprise. However, it is not the requirement for external validity which underwrites the difference here. After all, experiments must also be checked for analogous properties. In taking the results of the dissections as relevant to vertebrates generally, Sellers et al. (Reference Sellers, Margetts, Coria and Manning2013) must assume (or empirically test) that the objects in question were relevantly similar to their targets. Similar epistemic issues arise in extrapolating from either kind of object.Footnote ¹⁷ Establishing validity, then, is a necessary condition for both simulations and experiments being productively surprising (as this is required to support external relevance).

Instead, I want to suggest that the difference is due to the source of surprise. Typical experiments – where control is applied to a subset of the class we’re interested in – involve more-or-less confrontation between the world and our theoretical knowledge. As such, the world must be allowed to speak, which is to say, control ought not undermine that confrontation. The construction and running of a typical simulation, by contrast, is at base a way of filling out, making explicit, and probing our theoretical, conceptual and empirical ideas. This is a method of knowledge-generation, but not one which fundamentally involves bringing pre-existing knowledge into contact with new empirical results. Experiment and simulation often look like very similar activities, involving the construction, manipulation and examination of relatively tractable systems. However a distinction may be drawn if we characterize one as generating surprise by bringing our theoretical ideas into contact with the world, and characterize the other as generating surprise by probing, filling out, and expressing pre-existing knowledge. Such a distinction will not, I suspect, neatly track our usual categories of ‘experiment’ or ‘simulation’, and in other epistemic contexts other distinctions may be more appropriate. The dissection study, insofar as it is surprising, is such in virtue of demonstrating that our expectations about the world, of the relationship between muscle distribution and gait, say, is somehow lacking and in need of re-examination. The simulation study, insofar as it is surprising, is such in virtue of our learning where our ideas take us. Prior to Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) investigation, we had no way of realizing that the distinctive knuckle-walk was an open – in fact quite plausible – hypothesis regarding sauropod gait. By combining ideas about evolutionary and morphological constraints on gait, theories about optimization processes, and about sauropod physiology, the possibility hiding within our ideas presented itself. Both experiments and simulations – read in this way – are sources of genuine knowledge, and both can be productively surprising, but the surprise has different sources.

In the case of typical experiments, where our expectations of object and target behaviour are linked, we can generate productive surprise via freedom. As Morgan says,

Insofar as they are interested in productively surprising results, experimenters must ensure that their studies are not too controlled. Simulations, by contrast, do not need freedom to produce surprise. Rather, careful control allows us to bring our ideas and hypotheses together, and it is in these combinations that new knowledge arises. Again, this doesn’t mean that simulations can’t involve control-based surprise, or that experiments must involve it. Rather, my point is that if there is a distinction to be had vis-à-vis surprise, it is in these differing sources.

This has consequences for what successfully productive investigations are like. In some contexts, how much control I exert, and how surprising my results can be, are potentially in conflict (although much more needs to be said regarding the nature of that conflict). As Morgan has pointed out, navigating between the advantages of control and the need to let an experimental object behave freely is crucial to an experiment’s success. In other contexts, surprise does not rely on freedom: indeed, it is somewhat unclear what ‘freedom’ might be for some simulations. Instead, good design is sensitive to the knowledge it represents, brings together, and interacts with. Sellers et al.’s (Reference Sellers, Margetts, Coria and Manning2013) simulation brought together rich knowledge of vertebrate gaits, with specific ideas about sauropods, and a theoretically informed method for inferring gait given a critter’s morphology, mass and muscle distribution. How this information was treated, modelled and integrated in the simulation required careful empirical and theoretical sensitivity on the scientists’ part.

The capacity to surprise productively, as I have understood it, is a scientific epistemic virtue.Footnote ¹⁸ That is, it is a good-making property of scientific investigation. For some investigation to be a potential source of productive surprise, it must not only be the case that the results have the potential to conflict with researchers’ epistemic and doxastic states (be merely surprising). It must also be true that those epistemic states (and the relevant explanatory resources) range over the target of enquiry. This property is virtuous because of the epistemic goods it can produce. Results can create new phenomena, undermine old theories and hypotheses, and push investigation into unknown territory.