Notes toward a theory of the corpus, Part 1: History

By corpus I mean a collection of texts. The texts can be of any kind, but I am interested in literature, so I’m interested in literary texts. What can we infer from a corpus of literary texts? In particular, what can we infer about history?

Well, to some extent, it depends on the corpus, no? I’m interested in an answer which is fairly general in some ways, in other ways not. The best thing to do is to pick an example and go from there.

The example I have in mind is the 3300 or so 19th century Anglophone novels that Matthew Jockers examined in Macroanalysis(2013 – so long ago, but it almost seems like yesterday). Of course, Jockers has already made plenty of inferences from that corpus. Let’s just accept them all more or less at face value. I’m after something different.

I’m thinking about the nature of historical process. Jockers’ final study, the one about influence, tells us something about that process, more than Jockers seems to realize. I think it tells us that cultural evolution is a force in human history, but I don’t intend to make that argument here. Rather, my purpose is to argue that Jockers has created evidence that can be brought to bear on that kind of assertion. The purpose of this post is to indicate why I believe that.

A direction in a 600 dimension space

In his final study Jockers produced the following figure (I’ve superimposed the arrow):

Each node in that graph represents a single novel. The image is a 2D projection of a roughly 600 dimensional space, one dimension for each of the 600 features Jockers has identified for each novel. The length of each edge is proportional to the distance between the two nodes. Jockers has eliminated all edges above a certain relatively small value (as I recall he doesn’t tell us the cut off point). Thus two nodes are connected only if they are relatively close to one another, where Jockers takes closeness to indicate that the author of the more recent novel was influenced by the author of more distant one.

Each node in that graph represents a single novel. The image is a 2D projection of a roughly 600 dimensional space, one dimension for each of the 600 features Jockers has identified for each novel. The length of each edge is proportional to the distance between the two nodes. Jockers has eliminated all edges above a certain relatively small value (as I recall he doesn’t tell us the cut off point). Thus two nodes are connected only if they are relatively close to one another, where Jockers takes closeness to indicate that the author of the more recent novel was influenced by the author of more distant one.

You may or may not find that to be a reasonable assumption, but let’s set it aside. What interests me is the fact that the novels in this are in rough temporal order, from 1800 at the left (gray) to 1900 at the right (purple). Where did that order come from? There were no dates in 600D description of each novel. As far as I can tell, that must be a product of the historical process that produced those texts. That process must therefore have a temporal direction.

I’ve spent a fair amount of effort explicitly arguing that point [1], but don’t want to reprise that argument here. For the purposes of this piece, assume that that argument is at least a reasonable one to make.

What is that direction? I don’t have a name for it, but that’s what the arrow in the image indicates. One might call it Progress, especially with Hegel looking over your shoulder. And I admit to a bias in favor of progress, though I have no use for the notion of some ultimate telostoward which history tends. But saying that direction is progress is a gesture without substantial intellectual content because it doesn’t engage with the terms in which that 600D space is constructed. What are those terms? Some of them are topics of the sort identified in topic analysis, e.g. American slavery, beauty and affection, dreams and thoughts, Greek and Egyptian gods, knaves rogues and asses, life history, machines and industry, misery and despair, scenes of natural beauty, and so on [3]. Others are stylistic features, such as the frequency of specific words, e.g. the, heart, would, me, lady, which are the first five words in a list Jockers has in the “Style” chapter of Macroanalysis(p. 94).

In a post back in 2014 I suggested that Jockers’ image depicts the Geistof 19th century Anglo-American literary culture [2]. That’s what interests me, the possibility that we’re looking at a 21st century operationalization of an idea from 19th century German idealism. Here’s what the Stanford Encyclopedia of Philosophy has to say about Hegel’s conception of history [4]:

In a sense Hegel’s phenomenology is a study of phenomena (although this is not a realm he would contrast with that of noumena) and Hegel’s Phenomenology of Spirit is likewise to be regarded as a type of propaedeutic to philosophy rather than an exercise in or work of philosophy. It is meant to function as an induction or education of the reader to the standpoint of purely conceptual thought from which philosophy can be done. As such, its structure has been compared to that of a Bildungsroman (educational novel), having an abstractly conceived protagonist—the bearer of an evolving series of so-called shapes of consciousness or the inhabitant of a series of successive phenomenal worlds—whose progress and set-backs the reader follows and learns from. Or at least this is how the work sets out: in the later sections the earlier series of shapes of consciousness becomes replaced with what seem more like configurations of human social life, and the work comes to look more like an account of interlinked forms of social existence and thought within which participants in such forms of social life conceive of themselves and the world. Hegel constructs a series of such shapes that maps onto the history of western European civilization from the Greeks to his own time.

Now, I am not proposing that Jockers’ has operationalized that conception, those “so-called shapes of consciousness”, in any way that could be used to buttress or refute Hegel’s philosophy of history – which, after all, posited a final end to history. But I am suggesting that can we reasonably interpret that image as depicting a (single) historical phenomenon, perhaps even something like an animating ‘force’, albeit one requiring a thoroughly material account. Whatever it is, it is as abstract as the Hegelian Geist.

How could that be? Continue reading “Notes toward a theory of the corpus, Part 1: History”

Report on Cultural Evolution for the National Humanities Center, Revised Edition

Back in 2010 I wrote a piece for the National Humanities Center (USA), Cultural Evolution A Vehicle for Cooperative Interaction Between the Sciences and the Humanities, which is online at their Forum along with comments. I have since revised it to include a section on Jockers, Macroanalysis: Digital Methods in Literary History (2013). You can download the revised version from my SSN page. I’ve placed the added section below.

* * * * *

A Start: 19th Century Anglophone Literary Culture

Let me set the stage by quoting a passage from the excellent review Tim Lewens (2014) wrote for the Stanford Encyclopedia of Philosophy:

The prima-facie case for cultural evolutionary theories is irresistible. Members of our own species are able to survive and reproduce in part because of habits, know-how and technology that are not only maintained by learning from others, they are initially generated as part of a cumulative project that builds on discoveries made by others. And our own species also contains sub-groups with different habits, know-how and technologies, which are once again generated and maintained through social learning. The question is not so much whether cultural evolution is important, but how theories of cultural evolution should be fashioned, and how they should be related to more traditional understandings of organic evolution.

Building on discoveries made by others, we can see that kind of process in a graphic that Matthew Jockers used late in Macroanalysis: Digital Methods in Literary History (2013), though that’s not what Jockers had in mind in that particular investigation. He was working with a corpus of 3346 Ninetheenth Century novels by American, British, Irish and Scottish authors and was interested in tracking influence among them. It is one thing to track influence among a handful of texts; that is the ordinary business of traditional literary history. You read the texts, look for similar passages and motifs, read correspondence and diaries by the authors, and so forth, and arrive at judgements about how the author of some later text was influenced by authors of earlier texts.

It’s not practical to do that for over 3000 texts, most of which you’ve never read, nor has anyone read them in over 100 years. Jockers was using recently developed techniques for analyzing “big data,” in this case, a pile of 19th Century Anglophone novels. Without going into the details – you can find most of them in Jockers, pp. 156 ff.) – Jockers had the computer ‘measure’ each text on almost 600 different traits and then calculated the pair-wise similarity of all the texts. He then tossed out all values below a certain relatively high threshold and then had the computer create a network visualization of the remaining connections. Each text is represented as a ‘node’ in the network and the similarity between two texts is represented by the ‘edge’ (of link) connecting them. The length of the edge is proportional to the degree of similarity. Jockers then had the computer create a visualization of this network, where each text would be next to similar texts in the resulting image. Here’s that image (Figure 9.3 in the book, p. 165, color version from the web):

9dot3

It turns out that the visualization routine laid the graph out more or less in chronological order, going from older to newer, left to right. Note that there was no temporal information in the data from which that graph was derived (pp. 164-65):

The fact that they line up in a chronological manner is incidental, but rather extraordinary. The chronological alignment reveals that thematic and stylistic change does occur over time. The themes that writers employ and the high-frequency function words they use to build the frameworks for their themes are nearly, but not always, tethered in time. At this macro scale, style and theme are observed to evolve chronologically, and most books and authors in this network cluster into communities with their chronological peers. Not every book and not every author is a slave to his or her epoch.

On Jockers’ first sentence, it’s neither incidental nor extraordinary IF an evolutionary process regulates cultural change. For evolution proceeds through “descent with modification,” as Darwin put it, and that goes for cultural as well as biological evolution. If a later individual is modified from its immediate predecessors, it will in fact resemble them a great deal; the modifications do not change the basic character of the descendants.

As his language indicates, Jockers wasn’t looking for THAT result. It surprised him. Though he alludes to cultural evolution here and there in the book, he rejected it as a basic premise of his investigation (pp. 171-172). The evolutionary interpretation is mine, not his.

We must further realize that that interpretation is an assertion about the collective mentality. Jockers wasn’t examining the minds of millions of 19th century readers of English-language novels in Britain and America, but the history of those novels is a function of the tastes and interests of those readers. Those books wouldn’t have been written if publishers didn’t think they could see them to the public. Those tastes changed gradually, with the themes and styles of novels appealing to those tastes changing gradually as well.

The study of cultural evolution is thus the study of collective mentality. We are interested in the collective psyche. How can we think of the collective psyche without falling into hopeless mysticism?

From Macroanalysis to Cultural Evolution

The purpose of this post is to recast the work reported in Macroanalysis: Digital Methods & Literary History in terms appropriate to cultural evolution. The idea is to propose a model of cultural evolution and assign objects from Jockerss analysis to play roles in that model. I will leave Jockers’ work untouched. All I’m doing is reframing it.

Before doing that, however, I should note that in the last quarter of a century or so there has been quite a lot of work on cultural evolution in a variety of discipline including linguistics, anthropology, archaeology, and biology. Though it must be done at some time, I have no intention of even attempting to review that work here and so to place the scheme I propose in relation to it. That’s a job for another time and another venue. I note, however, that I have done quite a bit of work on cultural evolution myself and that some of that discussion can be found in documents I list at the end of this post.

Why Evolution?

First of all, why bother to recast the processes of literary history in evolutionary terms at all? Jockers wrote an excellent book without creating an evolutionary model, though he mentioned evolution here and there. What’s to be gained by this recasting?

As far as I can tell, much of the work that has been done on cultural evolution has been undertaken simply to exercise and extend the range of evolutionary discourse. It has not, as yet, resulted in an understanding of cultural process that is deeper than more conventional forms of historical discourse. Much of my own work has been undertaken in this spirit. I believe that, yes, at some point, evolutionary explanation will prove more robust that other forms of explanation, but we’re not there yet.

This work in effect is looking to evolutionary accounts as exhibiting something like formal cause in Aristotle’s sense. Evolutionary accounts are about distribution of traits across populations. In biology such accounts have a characteristic formal appearance so that, e.g. phylogenetic analysis of a population of entities tends to “look” a certain way. So, in the cultural sphere, let’s conduct a similar analysis and see how things look even if we don’t have our entities embedded in the kind of causal framework that genetics and population biology, molecular biology, and developmental biology provide the biologist.

That’s fine, as long as we remind ourselves periodically that that’s what we’re doing. But we must keep looking for the terms in which to construct a causal model.

What I specifically want from an evolutionary approach to culture is

  • a way to think about Said’s autonomous aesthetic realm,
  • a way to prove out Shelley’s assertion that “poets are the unacknowledged legislators of the world,”
  • a way of restoring agency to writers and readers rather than casting them as puppets of various vast and impersonal forces, and
  • a way of thinking about the canon in relation to the whole of literary culture.

That’s what I want. Those requirements imply having a causal model. Whether or not I’ll get it, that’s another matter.

Current critical approaches, however, in which individual humans are but nodal points in the machinations of vast and impersonal hegemonic forces, have trouble on all these points. Individual human beings are deprived of agency thus turning readers into zombies watching the ghosts of dead authors flicker on the remaining walls of Plato’s cave. The canon is captive to those same hegemonic forces, which have promulgated Shelley’s defense as an opiate for the masses, which R’ us.

The critical machine is broken. It’s time to start over. Before we do that, however, I need to dispense with one objection to seeking an evolutionary account of cultural phenomena. Continue reading “From Macroanalysis to Cultural Evolution”

UFO Events, a Thought Experiment about the Evolution of Language

The problem of human origins, of which language origins is one aspect, is deep and important. It is also somewhat mysterious. If we could travel back in time at least some of those mysteries could be cleared up. One that interests me, for example, is whether or not the emergence of language was preceded by the emergence of music, or more likely, proto-music. Others are interested in the involvement of gesture in language origins.

Some of the attendant questions could be resolved by traveling back in time and making direct observations. Still, once we’d observed what happened and when it happened, questions would remain. We still wouldn’t know the neural and cognitive mechanisms, for they are not apparent from behavior alone. But our observations of just what happened would certainly constrain the space of models we’d have to investigate.

Unfortunately, we can’t travel back in time to make those observations. That difficulty has the peculiar effect of reversing the inferential logic of the previous paragraph. We find ourselves in the situation of using our knowledge of neural and cognitive mechanisms to constrain the space of possible historical sequences.

Except, of course, that our knowledge of neural and cognitive mechanisms is not very secure. And large swaths of linguistics are mechanism free. To be sure, there may be an elaborate apparatus of abstract formal mechanism, but just how that mechanism is realized in step-by-step cognitive and neural processes, that remains uninvestigated,  except among computational linguists.

The upshot of all this is that we must approach these questions indirectly. We have to gather evidence from a wide variety of disciplines – archeology, physical and cultural anthropology, cognitive psychology, developmental psychology, and the neurosciences – and piece it together. Such work entails a level of speculation that makes well-trained academicians queasy.

What follows is an out-take from Beethoven’s Anvil, my book on music. It’s about a thought experiment that first occurred to me while in graduate school in the mid-1970s. Consider the often astounding and sometimes absurd things that trainers can get animals to do, things the don’t do naturally. Those acts are, in some sense, inherent in their neuro-muscular endowment, but not evoked by their natural habitat. But place them in an environment ruled by humans who take pleasure in watching dancing horses, and . . . Except that I’m not talking about horses.

It seems to me that what is so very remarkable about the evolution of our own species is that the behavioral differences between us and our nearest biological relatives are disproportionate to the physical and physiological differences. The physical and physiological differences are relatively small, but the behavioral differences are large.

In thinking about this problem I have found it useful to think about how at least some chimpanzees came to acquire a modicum of language. All of them ended in failure. In the most intense of these efforts, Keith and Cathy Hayes raised a baby chimp in their household from 1947 to 1954. But that close and sustained interaction with Vicki, the young chimp in question, was not sufficient. Then in the late 1960s Allen and Beatrice Gardner began training a chimp, Washoe, in Ameslan, a sign language used among the deaf. This effort was far more successful. Within three years Washoe had a vocabulary of Ameslan 85 signs and she sometimes created signs of her own. Continue reading “UFO Events, a Thought Experiment about the Evolution of Language”

Retiring Procrustean Linguistics

Many of you are probably already aware of the Edge 2014 question: what scientific ideas are ready for retirement? The question was derived from the Kuhnian-esque, and somewhat tongue-in-cheek, quote by theoretical physicist Max Planck:

A new scientific theory does not triumph by convincing its opponents and making them see the light, but rather because its opponents die, and a new generation grows up that is familiar with it.

Some of the big themes that jumped out at me were bashing the scientific method, bemoaning our enthusiasm for big data and showing us how we don’t understand and routinely misapply statistics. Other relevant candidates that popped up for retirement were culturelearninghuman natureinnateness, and brain plasticity. Lastly, on the language front, we had Benjamin Bergen and Nick Enfield weighing in against universal grammar and linguistic competency, whilst John McWhorter rallied against strong linguistic relativity and Dan Sperber challenged our conventional understanding of meaning.

And just so you’re aware: I’m not necessarily in agreement with all of the perspectives I’ve linked to above, but I do think a lot of them are interesting and definitely worth a read (if only to clarify your own position on the matters). On this note, you should probably go over and read Norbert Hornstein’s post about the flaws of Bergen’s argument, which basically boil down to a conflation between I-languages and E-languages (and where we should expect to observe universal properties).

If I had to offer my own candidate for retirement, then it would be what Anne Buchanan over at the excellent blog, The Mermaid’s Tale, termed Procrustean Science:

In classical Greek mythology, Procrustes was a criminal who produced an iron bed and made his victims fit the bed…by cutting off any parts of their bodies that didn’t fit. The metaphorical use of the word means “enforcing uniformity or conformity without regard to natural variation or individuality.” It is in this spirit that Woese characterized much of modern biology as procrustean, because rather than adapt its explanations to the facts, the facts are forced to lie in a bed of theory that is taken for granted–and thus, the facts must fit!

Continue reading “Retiring Procrustean Linguistics”

The Evolution of Speech: Lip-smacking monkeys

In January, Ghazanfar, Morrill & Kayser published a paper in PNAS entitled “Monkeys are perceptually tuned to facial expressions that exhibit a theta-like speech rhythm”. The abstract is below:

Human speech universally exhibits a 3- to 8-Hz rhythm, corresponding to the rate of syllable production, which is reflected in both the sound envelope and the visual mouth movements. Artificial perturbation of the speech rhythm outside the natural range reduces speech intelligibility, demonstrating a perceptual tuning to this frequency band. One theory posits that the mouth movements at the core of this speech rhythm evolved through modification of ancestral primate facial expressions. Recent evidence shows that one such communicative gesture in macaque monkeys, lip-smacking, has motor parallels with speech in its rhythmicity, its developmental trajectory, and the coordination of vocal tract structures. Whether monkeys also exhibit a perceptual tuning to the natural rhythms of lip-smacking is unknown. To investigate this, we tested rhesus monkeys in a preferential-looking procedure, measuring the time spent looking at each of two side-by-side computer-generated monkey avatars lip-smacking at natural versus sped-up or slowed-down rhythms. Monkeys showed an overall preference for the natural rhythm compared with the perturbed rhythms. This lends behavioral support for the hypothesis that perceptual processes in monkeys are similarly tuned to the natural frequencies of communication signals as they are in humans. Our data provide perceptual evidence for the theory that speech may have evolved from ancestral primate rhythmic facial expressions.

Writing in Nature, last week, Techumseh Fitch wrote a short news article on Ghazanfar’s findings including a very concise but clear outline on the two main hypotheses for the evolutionary origin of human speech, which he also goes over in his 2010 book. Namely, the hypothesis that speech is derived from primate vocalizations as the same vocal production system (lungs, larynx and vocal tract) is used to produce both primate calls and speech. However, as Fitch states, “a problem is that human speech is unique among primate vocalizations in being a very flexible, learned signal, whereas most primate calls have a strong, species-specific genetic determination. The ‘vocal origins’ hypothesis favours evolutionary continuity of vocal production over a hypothetical discontinuity in vocal control and vocal learning.”

The second hypothesis is MacNeilage’s hypothesis that speech rhythms originated not in the vocal, but in the visual domain. As the mouth generates not just vocal, but also visual, signals. The strength in this hypothesis lies in the fact that these articulators are under learned voluntary control in non-human primates. MacNeilage argues that speech develops in babies’ babbling as a lip-smacking behaviour superimposed on a vocal signal. Fitch states: “This rhythmic stream is then differentially modified, by learned tongue and lip movements, into the vowels and consonants of speech. Support for this hypothesis comes from previous work demonstrating that the detailed kinematics of lip-smacking are strikingly similar to those of speech. But Ghazanfar and colleagues’ work adds support from the domain of perception, indicating that perceptual tuning for the two signal classes is also consistent with MacNeilage’s hypothesis.”

As has been covered on this blog before, a lot of research on speech evolution has focused on the descended larynx. This new research adds to the body of work that suggest that anatomy might not be as important as first imagined, and that neural control and vocal learning may be much more important.

10th International Conference on the Evolution of Language, 14th – 17th April 2014, Vienna: Call for Papers

The 10th International Conference on the Evolution of Language will take place in the beautiful capital of Austria, Vienna, from April 14th to April 17th 2014.

The plenary speakers are:

“Plenary Speakers

The Call for Papers can be found here (Deadline for paper & poster submission is September 1, deadline for workshop proposals April , 2013).

To quote from the website:

“The Evolang conference series provides the major meeting for researchers worldwide in the origins and evolution of language. The Evolang conferences are interdisciplinary, with contributions from disciplines including, but not limited to: anthropology, archeology, artificial life, biology, cognitive science, genetics, linguistics, modeling, paleontology, physiology, primatology, and psychology. Typically, about 300 delegates attend, with representatives from all these disciplines. Additional information on Evolang can be found here.”

More information can be found on the website

1st International Winter School on Evolution

I don’t think anyone’s posted this yet:

1st International Winter School on Evolution – March 11th – 15th, 2013 University of Lisbon

The International Winter School on Evolution aims to better prepare a future generation for inter- and transdisciplinary evolution research by providing courses on cutting edge research in biological and sociocultural evolutionary sciences for Master, Doctoral and Postdoctoral students. Emphasis lies on topics that are currently underrepresented in (post)graduate curricula.

International experts will teach 9 courses on critical aspects of biological and socio-cultural evolution. The Winter School courses are centred around the following themes:

  • Macroevolution and the major transitions
  • Symbiogenesis, lateral gene transfer and hybridization
  • Language evolution

Visiting speakers include:

  • Michael Arnold
  • Folmer Bokma
  • Bill Croft
  • Daniel Dor
  • William Martin
  • Eörs Szathmáry
  • Mónica Tamariz
  • Douglas P. Zook

More info here: http://evolutionschool.fc.ul.pt

The Evolution of Speech: Learned Vocalisations in Mice

Mice can learn vocalisations! A new article realised today on PLOS ONE by Gustavo Arriaga, Eric Zhou and Erich Jarvis, shows that mice share some of the same mechanisms used to learn vocal patterning in songbirds and humans.

Mice can learn vocalisations! A new article realised today on PLOS ONE by Gustavo Arriaga, Eric Zhou and Erich Jarvis, shows that mice share some of the same mechanisms used to learn vocal patterning in songbirds and humans.

Very few animals have the capacity for vocal learning. This ability allows species to modify the sequence and pitch of sounds that create songs or speech. Currently, only three groups of birds – parrots, hummingbirds and songbirds – and some mammalian species – humans, whales, dolphins, sea lions, bats and elephants – have demonstrated vocal learning. This ability is still yet to be found even in non-human primates.

This study looks at the ultrasonic vocalizations known as mouse ‘song’ and provides evidence that mice can change at least one acoustic feature of these vocalizations based on their social exposure.

Two mice were put together and over time learned to match the pitch of their songs to one another. The paper suggests this is a limited form of vocal learning.

The paper also shows evidence that the mice can control their vocal motor neurons. In the press release, Erich Jarvis states, “This is an exciting find, as the presence of direct forebrain control over the vocal neurons may be one of the most critical aspects in the human evolution of speech.”

While this vocal learning in mice seems to be much more primitive than in songbirds or humans, it may reveal some of the intermediate steps in the process by which vocalization evolved in advanced vocal learners like songbirds and humans.

Exciting stuff!

 

References

Arriaga G, Zhou EP, Jarvis ED (2012) Of Mice, Birds, and Men: The Mouse Ultrasonic Song System Has Some Features Similar to Humans and Song-Learning Birds. PLoS ONE 7(10): e46610. doi:10.1371/journal.pone.0046610

Jim Hurford: What is wrong, and what is right, about current theories of language, in the light of evolution? (2)

This post continues my summary of Jim Hurford’s discussion of two contrasting extreme positions on language evolution in his plenary talk at the Poznan Linguistic Meeting. Here’s the summary of these two positions from my last post:

Position A:

(1) There was a single biological mutation which (2) created a new unique cognitive domain, which then (3) immediately enabled the “unlimited command of complex structures via the computational operation of merge. (4) This domain is used primarily for advanced private thought and only derivatively for public communication. (5) It was not promoted by natural selection.

Position B:

(1) There were many cumulative mutations which (2) allowed the expanding interactions of pre-existing cognitive domains creating a new domain, which however is not characterized by principles unique to language. This then (3) gradually enabled the command of successively more complex structures. Also, on this view, this capacity was used primarily for public communication, and only derivatively for advanced private thought and was (5) promoted by natural selection.

Hurford criticized the position that the biological changes enabling languages primarily evolved for private thought, because this would imply that the first species in the Homo lineage that developed the capacity for unlimited combinatorial private thought (i.e. “merge”) were non-social and isolated clever hominids. This, as Hurford rightly points out, is quite unrealistic given everything we know about human evolution regarding, for example, competition, group size, neocortex side and tactical deception. There is in fact very strong evidence that what characterizes humans the most is the exact opposite as would be predicted by the “Merge developed in the service of enhancing private thought” position: We have the largest group size of any primate, the largest neocortex (which has been linked to the affordances of navigating a complex social world) and have the most pronounced capacity for tactical deception.

Continue reading “Jim Hurford: What is wrong, and what is right, about current theories of language, in the light of evolution? (2)”