Creativity and Practical Underdetermination: How Experimental Science Steps into the Epistemic Adjacent Possible

Humans can use artifacts for purposes other than those to which they are conventionally put. This is a banal fact. Colonel Mustard need not be a creative genius to recognize that candlesticks aren’t just for holding candles. But he does need to be minimally creative—at least in the sense of the word that I intend here. The purpose of this article is to offer some insight into this form of creativity and, more importantly, to locate its exercise within experimental practice in science. I claim it is operant in the means by which researchers cope with what philosophers of science have called problems of "practical" (or sometimes "transient") underdetermination.

In contrast with "permanent underdetermination" embodied in the various theses to which philosophers appeal in problematizing realist interpretations of our best scientific theories, practical underdetermination is, according to some, "familiar," "routine," and epistemologically "non-threatening" (Kitcher 2001).^{Footnote 1} Permanent underdetermination implies the threat that, for any scientific theory, there are (now or in the future) empirically equivalent theories that scientists would be as well justified in believing as they are in believing the theories they in fact do. For many philosophers, this raises serious skeptical concerns and hence has been a primary focus of philosophical discussion. On the other hand, some philosophers have argued that practical underdetermination—the mere "routine" fact that in work-a-day science researchers at a given time might have a number of hypotheses between which their evidence cannot adjudicate—warrants at best, short philosophical shrift.

I am certainly not the first to disagree with that assessment (Biddle 2013; Brown 2013; Elliott 2011; Intemann 2005). Longino (1990, 2016), to give a particularly influential example, has argued that practical underdetermination is the primary form with which philosophers ought to be concerned. Permanent underdetermination, she suggests, is overly tied up with purely philosophical concerns about realism and the authority of science. Practical underdetermination, in contrast, represents a "genuine feature of scientific inquiry" that concerns the means by which actual scientists "fix evidential relevance and evaluate the background assumptions that facilitate such fixing" (Longino 2016). A key aspect of her view is that fixing evidential relevance requires taking on board, wittingly or otherwise, potentially value-laden background assumptions that mediate the evidential relations between data and hypotheses. This is how non-epistemic values get smuggled into the context of justification.

Many writings on values in science have followed suit and, with Longino, construe background assumptions as vehicles through which non-epistemic or "contextual" values enter into scientific reasoning and practice (see Biddle 2013 for a summary). Indeed, along with related considerations of "inductive risk," philosophical reflection on how scientists cope with practical underdetermination has led philosophers to identify significant consequences for our understanding of scientific rationality (Douglas 2000). As Holman and Wilholt (2022) state, there is "now a general consensus amongst philosophers ... that values necessarily play a role in core areas of scientific inquiry." So much for practical underdetermination being philosophically uninteresting.

I think such problems are still more interesting beyond the role they have played in enabling us to appreciate the role of values in science. In the analysis of practical underdetermination problems I develop here, I also follow Longino in highlighting the role of background assumptions (or "empirical criteria," as I will call them, following Bollhagen (2021a) in mediating inferences from data to hypotheses. However, rather than focusing on their role as vehicles for values in science, this article seeks to understand them from a point of view concerned with the development of science.^{Footnote 2} More specifically, in the context of my analysis, they represent indices for the operation of a characteristically creative form of human epistemic agency, one that explains how experimental practice in science can develop in genuinely novel or, as Kauffman (2019) would say, "unprestatable" ways.

In developing the analysis, I aim to offer a partial answer to Hasok Chang’s (2022) call to pursue "a more serious understanding of scientists as agents, not as passive receivers of information or algorithmic processors of propositions" (2022, pp. 27–28). I am motivated, in part, by his comment that "there is a tendency in the philosophy of science to present the scientist as a ghostly being that just has degrees of belief in various descriptive statements, which are adjusted according to some rules of rational thinking (e.g. Bayes’ theorem)" (2022, p. 27). Though my priorities in this article do not permit me to argue for the claim at length, I want to suggest, here in this introductory section, that this tendency haunts discussions of practical underdetermination and that the analysis I provide can help us exorcise it.

Brown (2013) points out that it is a general feature of the literature on values in science that standard accounts of the nature of practical underdetermination problems emphasize "evidence" and logical "rules of reasoning" in their explications of such problems. To give a recent example, DiMarco and Khalifa (2019) specify the structure of a practical underdetermination problem in the following way: "There exists some hypothesis h and some time t such that there is some other hypothesis h* that is as well supported as h by all of the epistemic considerations available at t." (2019, p.1018). As they make clear, by "epistemic considerations," they mean "empirical evidence" as well as "rules of reasoning that take evidence and background information as their inputs and probabilities of hypotheses as their outputs." "Rules of reasoning" include the "canons of inductive and deductive inference, plus some prima facie plausible methodological maxims, e.g., ceteris paribus, if h correctly predicts some novel phenomenon e, then P(h/e) > P(h)" (2019, p.1018).

This is an effective strategy. The goal, after all, is to characterize the epistemic thresholds through which non-epistemic values enter into scientific reasoning and practice. ^{Footnote 3} So, it stands to reason that the threshold itself should be characterized in epistemological terms, with the non-epistemic values entering through it only once the threshold itself has been constructed. According to Brown (2013), however, this "lexical prioritization of evidence over values" in formulations of practical underdetermination problems implies a distorted picture in which "values" only enter into scientific reasoning incidentally. As Brown puts the point, "... underdeterminationists insist that values only come into play in filling the gap" (2013, p. 832; my emphasis). Similarly, Brown writes, on standard formulations, a practical underdetermination problem is "a situation where the evidence is fixed and ... values ... play a role in the space that is left over" (2013, p. 834).

I want to suggest that we can amplify Brown’s observation regarding the prioritization of evidence and logic in formulations of practical underdetermination problems by transposing his point into a corresponding picture of the practicing scientist facing such problems. These scientists are, as Chang (2022) might put it, "ghostly beings" indeed. Reflecting the lexical priority of evidence and logic over values, they are represented, if they are explicitly represented at all, as little more than where the "rules of reasoning" to which DiMarco and Khalifa refer are housed, rules into which evidence is input and which output probabilities of hypotheses.^{Footnote 4} These ghostly scientists are ones whose typical practice is not impeded under "normal" non-evidentially underdetermined circumstances. After all, in such circumstances, evidence and logical rules of reasoning alone can do the trick in determining which hypothesis is best supported by the evidence. But, when faced with problems of practical underdetermination—circumstances in which "evidence and logic leave off"—those otherwise ghostly scientists are imbued with human values to facilitate a decision when evidence and logic alone cannot make a determination.

In other words, the human scientists facing practical underdetermination problems, as they are standardly formulated, are, in the first instance, Chang’s "algorithmic processors of propositions." They are merely contingently endowed with the values that enable the sort of genuinely agential capacities that Chang exhorts us to make essential to our conception of the human scientist.^{Footnote 5} My analysis of how scientists cope with practical underdetermination problems attributes to scientists such agential capacities—specifically, a form of creativity—and thus represents a step toward answering Chang’s call. In contrast to the "gap" formulation, what I will call my "experimental dead-space" formulation of practical underdetermination understands the human scientists confronting problems of practical underdetermination as creative epistemic agents. And it does so in a way that makes them out to be more recognizably human than is the rational "ghost" implicit in the epistemic gap formulation.

This is the frame in which I aim to situate the analysis of the case study that represents the main focus of the article and to which I now turn. I borrow the particular problem of practical underdetermination that I discuss from Bollhagen (2021a).^{Footnote 6} In the case, researchers studying the movement of a molecular motor protein called kinesin constructed what I called an "experimental dead-space"—a practically underdetermined space of alternative hypotheses between which they could not adjudicate using the experimental tool that anchored their research. Here, I build on the philosophical apparatus that I introduced in giving my earlier account of the means by which researchers coped with this practical underdetermination problem. To this end, I construe an experimental dead-space as a construct built within a broader unit of analysis, namely, a research platform (Griesemer 2013). Finally, I identify an "experimental dead-space" with an "epistemic adjacent possible." Borrowing the idea of the "adjacent possible" from Kauffman (2019) enables me to characterize the form of creativity I have in mind and to illustrate scientists’ exercise of it in resolving the practical underdetermination problem they confronted in the concrete case I previously analyzed. Overall, the analysis enables us to describe how the exercise of this form of creativity enables experimental practice in science to develop in genuinely novel, "unprestatable" ways.

As I mentioned, I believe that this analysis represents a step toward answering Chang’s (2022) call to develop "a more serious understanding of scientists as agents," not merely "algorithmic processors of propositions" (2022, pp. 27–28). Kauffman’s framework of the adjacent possible is particularly useful in this regard. He develops it in giving an innovative account of the means by which systems in the biosphere evolve—one on which they do so "creatively" in a sense Kauffman contrasts with "algorithmically." By identifying the practical underdetermination problem that researchers in the case confronted with an epistemic adjacent possible, we can likewise offer an account of the means by which the researchers resolved their problem—an account according to which the resolution involved the exercise of a form of "non-algorithmic" creative agency.

The next section provides a brief introduction to Kauffman’s framework of the adjacent possible. I build specifically on Kauffman’s (2019) remarks, according to which biological evolution occurs by creative, "non-algorithmic" means. As we will also see in this section’s discussion of the Duncker Candle Task, there is a clear analogy to this kind of creativity in the sphere of human activity. The section "The 'Inchworm Episode'" walks through my earlier article (Bollhagen 2021a) and introduces the conceptual apparatus I developed to support my philosophical account of the case study. The fourth section, "Embedding Experimental Dead-Spaces in Research Platforms," further develops this apparatus. It highlights how the case study reflects the exercise of the form of creativity I have in mind, and how it enabled researchers to solve their practical underdetermination problem and "step into" their experimental dead-space, that is, the epistemic adjacent possible. The final section concludes by situating my analysis in relation to thoughts on novelty and creativity from Rheinberger (2011, 2012, 2016) and Nersessian (2010) and sharpens the contrast between my "experimental dead-space" analysis and the standard "epistemic gap" analysis of practical underdetermination problems.

Think of chess. As moves in chess are bound by a finite set of well-defined rules, we can specify, or, as Kauffman (2019) puts it, "prestate," for any given board position, a space of alternative possible configurations into which the board can develop, given a single legal move. The given board position represents what Kauffman calls "the actual." The possibility space we "prestated" is its "adjacent possible." According to Kauffman, current "actual" systems in the biosphere also have adjacent possibles. The difference, though, is that on Kauffman’s view, the evolution of such systems is not explicable in terms of a finite set of well-defined rules. So, we cannot prestate their adjacent possibles.^{Footnote 7} But, if not by means amenable to explication in terms of a finite set of well-defined rules, how do systems in the biosphere change? Kauffman’s answer is that they do so "non-algorithmically," "inventively," or, to use the term I favor here, creatively.^{Footnote 8} What does "creatively" mean in this context?

Kauffman illustrates using two examples—exaptations and screwdrivers (Kauffman 2019). An "exaptation" or "Darwinian preadaptation" is a trait that evolves for one function but is later co-opted for a different one. Analogously, a screwdriver can be used to screw in a screw or, if circumstances call for it, open a can of paint. Kauffman uses these examples to motivate a distinction between two different kinds of change. As he puts the point quite pithily, I quote him at length:

Perhaps my favorite Darwinian preadaptation is the swim bladder. Some fish have a bladder that holds air and water ... [and] tunes neutral buoyancy in the water column. Paleontologists think swim bladders evolved from the lungs of lung fish ... With the swim bladder’s emergence, a new function came to exist in the biosphere: neutral buoyancy in the water column. But there is more ... might a worm or bacterium evolve to live only in swim bladders? Yes, of course. So the swim bladder, by existing, opens a new crack in the floor of nature, to borrow from Darwin, and a worm can live in that new crack ... Do you think you could have said ahead of time that the swim bladder ... would emerge? Could you have prestated the swim bladder? Try to prestate all the Darwinian preadaptations in humans for the next 5 million years. You cannot. We’ll see why ... when we discuss screwdrivers ... (2019, pp. 116–117)

I hand you a common screwdriver. Please list for me all the uses of a screwdriver in, say, New York, in 2017. Well, go ahead: screw in a screw, open a can of paint, scrape putty from a window, stab someone, display as an objet d’art, scratch your back, wedge the door open, prop a window open, jam a door closed, tie to a stick and spear a fish, rent the spear out at 5% of the local catch, and so on ... (2019, p. 118).

... is the number of uses of a screwdriver infinite? No, for discretely different things, like the uses of screwdrivers, to mean "infinite," we require a recursion, 0, 1, 2, 3, N, N + 1 as for the integers But if we have N uses of a screwdriver, what is the next, N + 1, use of a screwdriver? Can you enumerate it forever, for all N to infinity? No you cannot ... the number of uses of a screwdriver is indefinite (italics in original) ... The uses of a screwdriver are merely a nominal scale. There is no ordering relation between the different uses of a screwdriver and no fixed intervals ... (2019, p. 119).

I claim two major results: (1) no rule-following procedure, or algorithm, can list all the uses of a screwdriver; and (2) no algorithm can list the next new use of a screwdriver!.. But Darwinian preadaptation, or exaptations, are new uses of screwdrivers (2019, p. 119; italics original).

Again, Kauffman’s discussion is not about exaptations and screwdrivers per se. The point is to distinguish between two different conceptions of change. On the one hand, there is the kind of change that is explicable in terms of a finite set of well-defined rules. There are such conceptions of change in biology. Erwin (2017) discusses Maynard Smith’s conception of how proteins change between functional states due to single-base-pair changes in the genes that code for them. Iteratively applying the rule "change a single base pair" to a gene allows us to "prestate" the possibility space that the corresponding protein can explore. Similar to chess, each "step" in its exploration will represent a kind of change explicable in terms of the application of the rule to the system.^{Footnote 9}

In contrast, according to Kauffman (2019), the kind of change involved in "a new function coming to exist in the biosphere" in the form of an exaptation is not so analyzable. A structure functioning as a lung does not, over the course of evolution, change into one functioning as a swim bladder in such a way that is amenable to the kind of "algorithmic" analysis given to proteins above. If it did, then, in principle, we could exhaustively "pre-state" the possible evolutionary trajectories of the lungfish’s lungs at a time before the swim bladder’s actual evolution by means of iteratively applying a rule to the lungs, as we did to genes in the paragraph above. But, and this is Kauffman’s point, we cannot even prestate the space of the lung’s possible evolutionary futures, much less predict which one of those possibilities—the swim bladder, for instance—the lung’s actual evolution would realize. This is a key premise in Kauffman’s argument that change in the biosphere is not governed by "laws" and therefore that biology constitutes a "world beyond physics." ^{Footnote 10}

At the end of the discussion that I quoted at length above, Kauffman goes on to describe what he calls "jury-rigging"—the creative human activity of "using a set of things or processes for purposes other than those for which they may have been designed." To illustrate, he gives the example of a man who "fixed" a leak in a ceiling by rigging "a funnel attached below the leak, to a tube leading out the front door over a railing, dropping toward the ground, slowly draining. Finding that a lamp in his house was hanging too low, the man also slung the lamp cord over the tube, jury-rigging on jury-rigging" (2019, p. 120). We could not, Kauffman claims, have a deductive theory of jury-rigging. "There is no deductive theory of jury-rigging to solve different problems, but we do it all the time. We are inventive. So is evolution ... And none of us can predict in advance what we might invent and what might be invented from our inventions" (2019, p. 121).

The kind of change involved in an artifact coming to serve, in the hands of a user, a function other than that for which it may have been designed is analogous to that involved in Kauffman’s discussion of exaptations. To repeat Kauffman, "The uses of a screwdriver are merely a nominal scale. There is no ordering relation between the different uses of a screwdriver and no fixed intervals." You might put the point by saying that the screwdriver’s use, opening a can of paint, is not some distance in a metric space from its use as a paper weight. It makes no sense to say, for example, that within the space of possible screwdriver uses, opening a can of paint is twice as far from screwing in a screw as it is from removing gunk from a baseboard. Alternatively, as Kauffman’s allusion to integers suggests, you might say that uses of a screwdriver are not commensurable with each other in the way that integers are. Bollhagen (2021b) explains, "5 is commensurable with 10 insofar as there is some base unit out of which they can both be constructed. Take "5" as our base unit. 5 is made out of one "5" and ten is made out of two "5"s. Or take "1" as our base unit. 5 is made out of five "1"s, and 10 is made out of ten "1"s. The prime-ness of prime numbers consists in the fact that they can only be shown to be commensurable with natural numbers less than themselves by appeal to a base unit of "1." We might say, then, there is no base unit out of which one can construct, for a screwdriver, both to open a can of paint and use as a paperweight.^{Footnote 11}

Whether we put the point in terms of metric spaces or in terms of commensurability, these are, for my purposes, two ways of saying the same thing. And, I take it, two ways of saying the same thing that Kauffman himself puts in terms of "algorithmicity." That is, Kauffman’s way of saying it goes that the change involved in moving from one use of a screwdriver to another is not explicable in terms of a finite set of well-defined rules. By analogy, the kind of change involved in biological structures adopting new functions is likewise not "algorithmic." We can call this form of change "discontinuous."

Although using screwdrivers and jury-rigging with funnels clearly involves human cognitive activity, Kauffman’s point is to illustrate how the evolution of systems in the biosphere works. His ultimate point, in other words, is an ontological one that he uses to characterize "the emergent, creative, unentailed, becoming of the biosphere" (Kauffman 2014). Here, in giving his idea an "epistemic twist," my focus remains on human epistemic agents.^{Footnote 12}

So, keeping the focus on humans, what is cognitively involved in jury-rigging?^{Footnote 13} Psychologists have studied this form of creativity in humans using an experimental paradigm named after its inventor, the Gestalt psychologist, Karl Duncker (Duncker and Lee 1945). In the Duncker Candle Task, subjects are seated at a table next to a wall on which a corkboard is mounted. They are given a wax candle, a box of tacks, and a book of matches and are told to find a way to support the candle above the table such that, when the candle is lit, it does not drip wax onto the table. As psychologists put it, the solution hits subjects as an "insight." The insight is to realize that the box of tacks is not merely a box of tacks but is materially constituted such that it can support an alternative functional deployment, namely, a candle holder. What Kauffman calls "jury-rigging" is essential here. Successful subjects will dump the tacks onto the table, emptying the box, and then use the tacks to pin the empty box to the corkboard. They will then melt the bottom end of the candle, press it into the box, and let it cool so that the candle stands upright. When the match is lit, the empty box serves as a well to catch the dripping wax (Fig. 1).

Psychologists characterize the difficulty involved in succeeding on this task as "functional fixedness"—a tendency to understand artifacts narrowly, that is, in terms of their conventional purpose (German and Defeyter 2000). The insight is a matter of breaking out of this functionally fixed mindset. The term "insight," however, might sound slightly hyperbolic given the banality of jury-rigging. While an artifact’s conventional use may carry some psychological inertia in our interactions with it, we do, in fact, overcome that inertia and break through functional fixedness often enough that the act hardly warrants the epithet "insight." As Kauffman writes, "we jury-rig all the time." It is "routine." Indeed, appropriately so, for my purposes, given that philosophers have characterized scientists’ coping with practical underdetermination in precisely those terms.

As we will see in the next section, researchers in the "Inchworm Episode" modified the conventional use of their research platform to test for features beyond those which prior conventional usage countenanced. The form of change that the research platform underwent as a result is the same as that involved when, for Kauffman, a "new function comes to exist in the biosphere." In fact, as we will also see, this change opened up a new "crack in the floor knowledge," to paraphrase Darwin, for the research platform to develop into that which was not antecedently "prestatable."

Before turning to the case study, I want to note that there is much more to be said about the form of creativity studied in the Duncker Candle Task. Indeed, I believe that further analysis of this form of creativity and how it is exercised in scientific practice has much to contribute in answering Hasok Chang’s call to develop "a more serious understanding of scientists as agents, not as ... algorithmic processors of propositions" (2022, p. 27–28). I discuss this further in my conclusion, where I situate my analysis in relation to Rheinberger (2011, 2012, 2016) and Nersessian (2010). My main point here, however, is simply to point out that the creative means by which Duncker Candle Taskers, jury-riggers, or scientists break through functional fixedness and redeploy an artifact to serve a function other than that with which it is conventionally associated are "non-algorithmic" in just the sense that Kauffman intends.

According to Bollhagen (2021a), from 1989 to 2002, researchers studying the motor protein kinesin produced data supporting the hypothesis that the proper characterization of its stepping pattern along its microtubule "tracks" was "hand-over-hand" as depicted in Fig. 2.

On that recounting, a number of experimental studies using what was then a novel tool, the single-molecule motility assay, supported the claim. The assay took one of two forms. First, in the "bead assay," researchers immobilize microtubules to glass coverslips, attach single kinesin molecules to plastic beads large enough to visualize under a video microscope, and watch the beads move as kinesin carries them like cargo down the immobilized microtubule. A second version, the "gliding assay," flipped the geometry of this design. Here, researchers would immobilize single kinesin molecules "heads up" to a glass coverslip and watch them slide microtubules around (see Fig. 3). In either case, researchers were drawing inferences from data that they could see—moving beads or microtubules—to the phenomenon that they could not, the characteristic stepping pattern of the molecular motor.

How did these "data-to-phenomenon inferences" work (Bogen and Woodward 1988)? According to Bollhagen (2021a), the hand-over-hand hypothesis was operationalized in terms of what he called two empirical criteria: (1) processivity and (2) coordinated head activity. Processivity means that the molecule remains attached to the microtubule at all times during its walk. Co-ordinated head activity means that the behavior of one head is dependent upon or "gated by" the behavior of the other (for example, the trailing head can only release once the leading head has securely bound to the microtubule). Thus, if data using the single-molecule assay indicated that the molecule was processive and coordinated the activity of its heads, it would support the hand-over-hand hypothesis over "stroke-release," an alternative which denied that the molecule was processive and coordinated the activity of its heads.^{Footnote 14} If, for example, researchers using a bead assay saw that the beads moving along immobilized microtubules would intermittently diffuse away from the microtubule, this would indicate that the protein driving the bead’s motion occasionally "jumps"—separates entirely from the microtubule—on its journey. It would indicate that kinesin’s stepping pattern is not processive and that, therefore, "hand-over-hand" is not an accurate characterization of its movement. ^{Footnote 15}

From 1989 to 2002, researchers understood how to deploy the single-molecule motility assay to test for processivity and coordinated head activity. During that time, researchers did substantial experimental work that provided support for the "hand-over-hand" hypothesis. However, a practically underdetermined space of alternative hypotheses—an "experimental dead-space"—remained, which attributed both processivity and coordinated head activity to kinesin’s stepping pattern, but also attributed to it further features beyond those that researchers understood how to functionally deploy their tool to assay (Fig. 3). In other words, they attributed to it features other than those attributed to it by the more general "hand-over-hand" hypothesis which was formulated in terms of empirical criteria.

Notice, briefly, that "inchworm" counts as a species of hand-over-hand as illustrated in Fig. 3. This might be counterintuitive given that, on an inchworm, the rear "hand" never passes "over" the leading "hand." Rather, the same one is in the lead during the entire duration of its walk. Nonetheless, it maintained that the molecule was processive and coordinated the activity of its heads, so it counted as a hand-over-hand hypothesis by the lights of the relevant empirical criteria in terms of which that more general hypothesis was formulated. The problem was that although researchers could, as they put it, "conceptually" distinguish "inchworm" from the other hypotheses in the experimental dead-space, they could not do so "empirically," that is, in terms of empirical criteria. This will be important shortly when we see how researchers formulated a new empirical criterion that changed the overall space of alternative hypotheses in such a way that inchworm was rendered experimentally live.

The experimental dead-space represented in Fig. 4 persisted for as long as coordinated head activity and processivity constituted the empirical criteria in terms of which hand-over-hand kinesin motility was conventionally operationalized within single-molecule research (1989–2002). However, Hua et al. (2002) introduced a new empirical criterion—torque generation—and, around it, built a new space of alternative hypotheses in which the formerly "dead" inchworm hypothesis became experimentally live. Taking cues from a key review article (Howard 1996), these researchers noted that, if the molecule’s two heads move hand-over-hand as they step, this would result in a reversal of the molecule’s orientation with respect to the microtubule axis with each step. This, in turn, would generate torque, which would be communicated to the cargo the molecule is carrying. By using a stiff-necked kinesin derivative to ensure that the torque would not be taken up by the native molecule’s torsionally flexible neck, they reasoned that, if the molecule generates torque, they should observe 180-degree rotations of microtubules in a gliding version of the single-molecule motility assay. If the microtubule rotated, it would confirm hand-over-hand, now formulated in terms of the empirical criterion, torque generation, in addition to processivity and coordinated head-activity. If not, it would confirm inchworm, now an experimentally live hypothesis formulated empirically as a non-torque generating processive and coordinated walk.

Hua et al. (2002) created their stiff-necked kinesin mutant and took to deploying the single-molecule platform to test for torque generation. They did not observe the 180-degree microtubule rotations that they understood and anticipated torque generation to produce visibly, and therefore concluded that inchworm is the correct characterization of kinesin’s stepping pattern. But these observations did not constitute the whole of their argument. As Hua et al. acknowledge, there is a third possibility—"asymmetric hand-over-hand (HoH)," a putative hand-over-hand-style walk in which a structural asymmetry between kinesin’s two globular heads is such that the molecule’s step compensates for the torque that a symmetric hand-over-hand walk would otherwise generate. Since both "inchworm" and "asymmetric HoH" are non-torque-generating walks, and since the relevant empirical criterion in this study was torque generation, this experiment could not empirically distinguish between them. Thus, while their introduction of "torque-generation" as an empirical criterion enabled access to the pre-2002 experimental dead-space by empirically distinguishing "inchworm" from "symmetric hand-over-hand," it also created a new experimental dead-space populated by "inchworm" and "asymmetric hand-over-hand."

In other words, with the introduction of torque generation, "hand-over-hand" split into two versions—symmetric and asymmetric—such that "inchworm" became empirically distinguished from the former but not the latter (Fig. 5). Concomitantly, a new experimental dead-space opened up, occupied by inchworm and asymmetric HoH. Acknowledging that their experiment could not adjudicate between these hypotheses, Hua and colleagues (2002) criticized asymmetric HoH indirectly, arguing a priori that it was implausible to attribute to the molecule the kind of complex and nuanced structure that it would have to have in order for it to perfectly compensate for the torque it would otherwise generate. In other words, though they acknowledge that these hypotheses occupy a newly constructed experimental dead-space, they conclude in favor of inchworm based on both their empirical data and an a priori argument to the effect that the alternative is implausible.

This new experimental dead-space did not persist long, however. In the following two years, researchers published a number of studies in which they introduced yet another new empirical criterion that empirically distinguished between inchworm and asymmetric hand-over-hand, namely, limping. A number of researchers reasoned that if the molecule walks in an asymmetric hand-over-hand manner, a "limp"—a difference between the time one head spends attached to the microtubule versus the other—should be discernible in their data. As Bollhagen (2021a) discusses, a number of key studies discerned the limp such that, by 2005, the consensus among single-molecule researchers was that asymmetric hand-over-hand is the correct characterization of kinesin’s stepping pattern.

Hua et al.’s (2002) introduction of torque generation was characteristically "creative" in the sense illustrated in my discussion of the Duncker Candle Task. As I discuss in more detail in the next section, these researchers realized that the "material conditions" of their research platform were such that they could be functionally deployed to assay for a putative feature of kinesin’s stepping pattern other than those for which it had conventionally been deployed to assay. In other words, like successful Duncker Candle Taskers, these researchers had the "insight" that they could deploy their research platform to test for torque generation, rather than merely processivity and coordinated head activity. Accordingly, the kind of change that characterized the dynamic reorganization of the overall space of alternative hypotheses that was catalyzed by the introduction of torque generation is not a form of change that can be explicated "algorithmically" in the sense I described above. To see this more clearly, I step back now to build upon the philosophical apparatus that I introduced in my previous analysis of the means by which researchers in the Inchworm Episode coped with their practical underdetermination problem.

The single-molecule research platform was anchored in the use of a particular experimental tool to study kinesin stepping—the single-molecule motility assay.^{Footnote 16} A research platform is "a collection of conventions for the use of material circumstances, conditions, or resources to which researchers commit for the sake of regulating and standardizing their work practices and procedures" (Griesemer 2013).^{Footnote 17} This characterization gives philosophers a wide berth in applying it to the analysis of cases. In analyzing the dynamics of a particular research platform, one will differentially emphasize those aspects that Griesemer builds into his characterization depending upon the contingencies of the case and the purpose of the analysis. Depending on one’s interest in analyzing a case, that is, one might emphasize the relevant material circumstances or, perhaps, the financial resources available to practitioners. I would also add, as a nod in the direction of the usefulness of my analysis for discussions of values in science, that an analysis of a research platform may involve identifying the ways in which values, biases, political environment, or other "contextual factors" contribute to its structure at a time.

Accordingly, I emphasize certain aspects of the single-molecule research platform that I take to be key in understanding the creative form of change that characterized its development as presented above.^{Footnote 18} Of particular interest is what I take to be the distinctively epistemic aspect, namely, what Griesemer (2013) calls "conventions." I identify these with the empirical criteria around which researchers organized a space of alternative hypotheses about kinesin’s stepping pattern, constructed experiments to test those hypotheses, and in light of which they interpreted the resulting data. In the Inchworm Episode, then, "processivity" and "coordinated head activity" were the 1989–2002 "conventions" to which researchers committed for the use of their "material circumstances, conditions, or resources" to the end of "regulating and standardizing" the empirical study of kinesin’s stepping pattern.

As empirical criteria are an important category in Bollhagen’s (2021a) prior analysis, I pause here to show how identifying them with Griesemer’s (2013) "conventions" represents a development on the original idea.^{Footnote 19} Bollhagen (2021a) writes, "Empirical criteria individuate [hypotheses about] the phenomenon along lines experimentally tractable from the point of view of a particular experimental tool" (2021a, p. 19). Thus, insofar as alternative hypotheses are formulated in terms of different empirical criteria, they count as "empirically distinct" (2021a, pp. 16, 19). In my prior telling of the Inchworm Episode, "stroke release" was a hypothesis that denied that the molecule was processive and coordinated the activity of its heads and, therefore, was empirically distinct from the hand-over-hand hypothesis. Second, Bollhagen (2021a) uses "empirical criteria" to refer to "certain supposed features of the phenomenon that are understood or expected to give rise to characteristic patterns of data in [a particular experimental tool]" (2021a, p. 20). Researchers take the presence or absence of these features to explain why certain characteristic patterns of data show up on the display side of their tools while others do not. In this way, empirical criteria facilitate data-to-phenomenon inferences (Bogen and Woodward 1988; Woodward 2011).

I build on this by understanding these empirical criteria as conventions characteristic of the single-molecule research platform, which regulated and standardized the deployment of the single-molecule motility assay. Identifying "empirical criteria" with Griesemer’s "conventions" enables me to embed the former category and, in turn, the idea of an "experimental dead-space," into a wider unit of analysis, namely, a "research platform," that includes the other aspects that Griesemer (2013) mentions in his characterization of it. These other aspects are also crucial for providing an account of the creative change that the research platform underwent with the 2002 introduction of torque generation as a new empirical criterion.

First, take Griesemer’s (2013) "material circumstances." I identify these with the technological and biological material constitutive of the single-molecule motility assay, including glass coverslips, video microscopes, ATP, kinesin molecules, microtubules, and so on. Under the 1989–2002 epistemic conventions (empirical criteria), researchers understood the biological and technological material they were working with to be functionally deployable to test for processivity and coordinated head activity in the same way that functionally fixed Duncker Candle Taskers understand the material they are working with to be functionally deployable as a box of tacks. Thus, by embedding my prior philosophical apparatus into Griesemer’s wider one, I can characterize a notion of function on which the function of a research platform at a time is specified by the conventional empirical criteria operative during that time period. Insofar as those empirical criteria do not change, I will say that the research platform remains functionally fixed. Thus, the single-molecule research platform remained functionally fixed from 1989 to 2002 and was thereby unable to access its experimental dead-space.^{Footnote 20}

Finally, I also make use of Griesemer’s (2013) "researchers," which I encourage readers to identify with Chang’s (2022) "epistemic agents." In the model of the Inchworm Episode I am developing, these agents are characteristically creative in the "non-algorithmic" sense discussed in connection with Kauffman (2019) and the Duncker Candle Task above. They have the banal but preeminently human capacity to deploy material artifacts for purposes other than those to which they are conventionally put. Like successful Duncker Candle Taskers, it was the researchers, specifically Hua and colleagues (2002) in the Inchworm Episode, who had the "insight" to introduce a new empirical criterion—torque generation—and who thereby functionally redeployed the material conditions characteristic of the single-molecule motility assay in order to test for it.

So, as I characterize it, the research platform relevant to the Inchworm Episode consists of its epistemological conventions (empirical criteria), its material conditions (the technological and biological "stuff" of the single-molecule motility assay), and its researchers (creative epistemic agents). Lastly, a research platform is "entangled" with other research platforms within a broader field of research (Cartwright et al. 2023). Other molecular motors researchers studied kinesin using x-ray crystallography, electron microscopy, and various other tools of the cell biologist’s trade to produce structural and biochemical data that single-molecule researchers could draw upon in formulating hypotheses—both live and dead—about kinesin’s stepping pattern.^{Footnote 21} In more general terms, hypotheses about the phenomenon formulated within one research platform can be—perhaps typically are—motivated by information coming from outside of that platform through the variety of communicative channels that characterize the entangled social organization of scientific research in which creative scientists are embedded.

This organizational entanglement is also key to understanding the exercise of the form of creativity I attribute to researchers in my analysis of the Inchworm Episode. As Bollhagen (2021a) notes, the researchers who, in 2002, conducted the key study were inspired by a 1996 review article. This article put forward the possibility that, during its walk, kinesin’s tail might "wind up like the rubber band on a toy airplane" (Howard 1996, p. 724). This nudged them into having the creative insight that they could use the material conditions of their research platform to assay for torque generation rather than merely processivity and coordinated head activity. Why this key idea from a 1996 article lingered somewhere in the communicative channels running through the entangled web of research platforms characteristic of single-molecule kinesin research from 1989 to 2002, I do not know. But that is an important question that a more complete analysis than the one I can give here would seek to answer.

A final note about entanglement in the social organization of scientific fields. It is because of something about the character of that "tangle" that the key idea of the 1996 review article that inspired Hua et al. (2002) only nudged someone to have their insight as late as 2002. However, it is also because of that "tangle" that the insight was communicated at all. For my purposes here, the importance of this point is that we cannot simply say that single-molecule kinesin research was functionally fixed from 1989 to 2002 because people were just not thinking creatively enough. After all, humans cannot simply will themselves to think more creatively. A bald injunction to "think more creatively" is unintelligible as advice for how researchers should break through their functional fixity. Rather, the exercise of scientific creativity and the occurrence of creative insights in science are scaffolded, for better or for worse, by the entanglements characteristic of the social organization of research. I suggest that it is due to the character of these entanglements that, on the one hand, it took the time it did after the publication of the key idea in 1996 for that idea to inspire Hua and colleagues’ (2002) creative insight and, on the other hand, for that idea to finally give the nudge that was needed to break the single-molecule kinesin research platform out of its functionally fixed state. In short, the structure of entanglements between research platforms in a broader field of research is responsible for both the fixity and the insight.

I have discussed various ways in which I draw on Griesemer (2013) to build on the conceptual apparatus that I introduced in Bollhagen (2021a). I mentioned in my introduction that I was also going to build on this prior work by identifying an experimental dead-space with an epistemic adjacent possible. To close the loop, call the single-molecule research platform from 1989 to 2002—the period during which it was functionally fixed—"the actual." Call the experimental dead-space (Fig. 4) that persisted during that time "the epistemic adjacent possible." The story of the Inchworm Episode is the story of how epistemic agents "stepped into" the epistemic adjacent possible by creatively introducing torque generation as a new empirical criterion into the conventions regulating and standardizing the functional deployment of their research platform. This is just to say that they realized creatively that the material conditions characteristic of their research platform could be functionally redeployed to assay for features other than those for which it was conventionally used to assay in light of the 1989–2002 empirical criteria. This concomitantly generated a new epistemic adjacent possible—a "new crack in the floor of knowledge" into which the research platform could develop—in the form of an experimental dead-space occupied by inchworm and asymmetric hand-over-hand. Researchers, in turn, stepped into this adjacent possible as they creatively introduced limping, another new empirical criterion. Thus, to follow Kauffman (2019), from the point of view of the pre-2002 history of the development of the single-molecule research platform, its post-2002 development could not be prestated.^{Footnote 22} Such is the nature of the discontinuous change that the single-molecule research platform underwent over the course of its development from 1989 to 2005. Indeed, I would suggest, such is the nature of scientific change generally.

I opened this article with a claim that I take to be obviously true. Humans can use artifacts for purposes other than those to which they are conventionally put. While the fact that humans have this capacity is banal, the consequences of making this realistic attribution to epistemic agents in models of how they cope with practical underdetermination problems is anything but. As the analysis of the Inchworm Episode shows, in making this capacity central to our conception of scientists, we can understand at least one way in which experimental practice in science works such that it can develop in genuinely novel "unprestatable" ways. We can appreciate, in other words, a sense in which experimental science is a genuinely creative enterprise.

Granted, that humans have this capacity—and the capacity to get functionally fixed, for that matter—calls out for further explanation. While I will not offer a full explanation here, I do think the work of two other thinkers intersects interestingly on this capacity in a way that dovetails with the analysis given above.^{Footnote 23} In this concluding section, I situate the above analysis with respect to some remarks from Rheinberger (2011, 2012, 2016) on "experimental systems" and Nersessian (2010) on two forms of creativity that she distinguishes, following Boden (2004), as "P-" and "H-creativity." Finally, I discuss the ways in which I believe my "experimental dead-space" analysis of practical underdetermination problems improves philosophical understanding of the nature and structure of such problems.

In a sense that I take to be aligned with my claim that experimental practice in science works such that it can develop in unprestatable ways, Rheinberger (2011, 2012) characterizes what he calls "experimental systems" as "generators of surprise" and "machines for making the future" (2011, p. 314). A key to understanding this is that experimental systems "must be able to be differentiated.. They must be capable of ‘differing’ in the sense of being differentially iterated. Only then do they remain arrangements in which ... is generated ... knowledge that lies beyond what can be anticipated and imagined at a particular point in time" (2011, p. 313).^{Footnote 24}

Although I use the term "research platform" to characterize the unit of analysis that underwent creative historical change in the Inchworm Episode, what Rheinberger says of experimental systems seems to me straightforwardly applicable in my case. Indeed, I would follow Rheinberger and characterize Hua et al.’s (2002) version of the microtubule gliding assay as a "differentiated" iteration of the single-molecule research platform. Where Rheinberger (2016) emphasizes the role of unexpected or "serendipitous" events occurring within an experimental system as important drivers of differentiation, the key point I want to make here is that it was by means of the distinctive form of creativity I have discussed that this "difference" was introduced in the single-molecule research platform. I have characterized this form of creativity as "banal." My choice of the Duncker Candle Task underscores this point. With Rheinberger, however, I would emphasize that, in the context of sophisticated experimental research using materials far less banal than a box of tacks, the ability to exercise this form of creativity may require the kind of "virtuosity" that he maintains is necessary for a researcher to recognize a serendipitous epistemic opportunity in the context of an experimental system (Rheinberger 2012).

Nersessian (2010) distinguishes two forms of creativity: "‘P-creative’" ideas ... arise from episodes in which an individual creates something that is already culturally available, but novel for the individual in question ... ‘H-creative’ ideas arise from episodes in which something fundamentally new in human history is created" (2010, p. 15). Nersessian’s analysis of P-creativity is rooted in an extended discussion of a particular experimental subject’s performance in a "think-aloud protocol experiment" formulated by cognitive scientist John Clement in which the subject was tasked with solving the following problem:

A weight is hung from a spring. The original spring is replaced with a spring: made of the same kind of wire; with the same number of coils; but with coils that are twice as wide in diameter. Will the spring stretch from its natural length more, less, or the same amount under the same weight? (Assume the mass of the spring is negligible compared to the mass of the weight.) Why do you think so? (Clement 1989, p. 342)

A think-aloud protocol experiment requires the subject to describe their reasoning process, in words or in pictures, in real time as they work out the problem. What is remarkable about subject S2’s solution to the problem is that, at the beginning of the task, their concept of a spring did not include the notion of torsion, but by the end of the session, it did. This idea was culturally available but novel for S2. S2’s problem-solving processes, therefore, involved the formulation of a P-creative idea. Since this idea was not "fundamentally new in human history," however, it is not H-creative.

Clearly, I cannot reconstruct the reasoning process of Hua and colleagues (2002) to the level of detail that a think-aloud protocol experiment allows. However, the notions of P- and H-creativity can help sharpen the analysis. The idea that kinesin generates torque as it walks was "culturally available." In fact, in addition to being in the 1996 review article cited by Hua et al. (2002), it was floated in the 1989 article that reported the initial development of the single-molecule motility assay (Howard et al. 1989). That said, the creative act did not involve the researchers developing this idea anew for themselves in the context of a problem-solving situation. As I mentioned earlier, the researchers cite the 1996 review article as their inspiration. Further, the product of the creative act was not merely the idea that kinesin generates torque, but a new iteration of the platform organized such that it would generate characteristic patterns of data that would indicate whether or not kinesin in fact generates torque while stepping. In other words, it was specifically the introduction of torque generation as an empirical criterion in the single-molecule platform that represents these researchers’ creative insight. The consequence was the dynamic reorganization of the overall space of hypotheses regarding kinesin’s stepping pattern and, concomitantly, a fundamentally new way of organizing the biological, technological, and conceptual resources of the research platform. So, while it might not have had the kind of widespread implications for science that the H-creative ideas of Newton, Einstein, or Maxwell enjoyed, it would count as H-creative nonetheless. The post-2002 single-molecule research platform was indeed something "fundamentally new in human history."

My introduction contrasted the approach I pursue with the "epistemic gap" analysis of practical underdetermination problems. The latter understands such problems to be ones in which "logic and evidence leave off." As is clear (I hope) from the discussion above, it is important to recognize that the data-to-phenomenon inferences that researchers in the Inchworm Episode drew were not logical, at least in the sense that identifying them in terms of their logical form would not enable the analysis to capture the dynamics of case, that is, how the introduction of torque generation dynamically reorganized the overall space of alternative hypotheses rendering inchworm experimentally live. Rather, that inferential work was facilitated by substantive local knowledge about kinesin’s behavior expressed in empirical criteria.^{Footnote 25} These inferences, in other words, were material in the sense of Norton (2021) as opposed to formal. As we saw, the creative introduction of torque generation as a new empirical criterion changed the structure of the overall space of hypotheses and, concomitantly, enabled a new material inference to be drawn from data observable in the single-molecule assay (microtubule rotations or the lack thereof) to the hypothesis that kinesin walks in an inchworm (or asymmetric hand-over-hand) fashion. This is just another way of putting the point I made above, namely, that with the introduction of torque generation, "inchworm" became an experimentally live hypothesis—one that data can bear on materially as evidence. Indeed, we can only appreciate the way in which the single-molecule research platform developed in the creative way that it did by acknowledging that the inferences researchers drew were material as opposed to formal. The more immediate point, however, is that contrary to what the "epistemic gap" approach suggests, problems of practical underdetermination are not realistically analyzed as circumstances in which "some ... hypotheses ... are underdetermined by logic and the currently available evidence (Biddle 2013; my emphasis). Rather, they represent circumstances in which the possibilities of material inference from evidence to hypothesis are limited by the empirical criteria that constrain such inferences.

Finally, I suggest that, realistically construed, problems of practical underdetermination just are what I have called "experimental dead-spaces" and that understanding them as such discourages thin "logical" characterizations of practical underdetermination problems. In other words, I aim to offer an analysis of practical underdetermination problems alternative to the standard "epistemic gap" analysis. In my case, attending closely to empirical criteria, and hence the material character of the inferences single-molecule researchers drew, enabled me to identify in the Inchworm Episode the exercise of a form of human agency involved in scientists’ coping with practical underdetermination problems beyond that which the values in science literature identifies with valuing. I take this to be a key takeaway of the article. The analysis running through the article, however, is merely one model of what it looks like to analyze the kind of scientific work involved in coping with practical underdetermination problems on the "experimental dead-space" analysis—one on which researchers accessed the dead-space by means of this kind of creativity. This conception of creativity, at least as it was exercised in the Inchworm Episode, is most immediately relevant to how scientists interface with the material circumstances characteristic of their research platforms. By no means do I mean to suggest, however, that this form of creativity can solve all problems of practical underdetermination. More generally, any of the epistemic, conceptual, administrative, political, ethical, and financial dimensions of science as an institutionalized form of human intellectual activity might be implicated in a space’s being experimentally dead. Therefore, different forms of agency relevant to how humans interface with the various aspects of the "tangle of science" may be required to access them on a case-by-case basis.^{Footnote 26} Attending to these factors in diagnosing problems of practical underdetermination may, therefore, yield new insights into what holds scientific research platforms up at the thresholds of their epistemic adjacent possibles and also help identify still other forms of agency relevant to how human scientists interface with any of the threads constituting the tangle of science to move research forward in unprestatable ways.