Humanities meets Natural Science: Entropy and the Prediction of Language Change

Facultad de Filología Universidad de Sevilla Trabajo de Fin de Grado Humanities meets Natural Science: Entropy and the Prediction of Language Change Autor: Fco. Javier González Del Valle Mezo Tutor: Julia Fernández Cuesta Curso Académico 2022/2023 2 Table of Contents 1. Introduction ................................................................................................................. 3 2. Science:Philosophy and Methodology ........................................................................ 6 2.1 Philosophy of Science: Uniformitarianism .............................................................. 6 2.2 The Scientific Method ........................................................................................... 10 3. Entropy and Language .............................................................................................. 14 3.1 An Introduction to the concept of Entropy ............................................................ 14 3.2 Word Entropy and Metaphoric Change................................................................. 18 3.3 Entropy and Sound Change ................................................................................... 22 4. Conclusion ................................................................................................................. 25 5. References ................................................................................................................. 26 6. Annex………………………………………………………………………………30 3 1. Introduction Humans tend to categorize everything in nature , from human beings and animals to physical entities and abstract ideas. Fields of study are not an exception. The usual categories in the academic world are as follows: Natural Sciences, Social Sciences and Humanities. Linguistics is traditionally placed within the category of ‘Humanities’, and there is a plethora of reasons to support this categorization. Language is undeniably a human product, and humans are arguably the only animals on earth to have developed such a rich and complex method for communication, as far as we know. Linguistics, by definition, is the scientific study of human language. Yet science tends to be associated with the strict application of the well-known scientific method prediction and testable hypotheses. It still needs to be shown that the scientific method, , is also applicable to the study language change. This distinction relies on whether the phenomena studied have a human origin or exist outside the human sphere. Art, language, and philosophy are the representatives of ‘the Humanities’, and there is no denying their human origin, but other disciplines like medicine are also of human origin and yet there are not not grouped within the ‘Humanities’ The same applies to formal sciences, which can be said to have evolved from philosophy, but they form their own. The usual answer to these questions is that medicine, as well as the formal sciences apply the scientific method, but so does Linguistics, and more specifically, Historical Linguistics, which is in the ‘Humanities’ group. The origin of this distinction might be in the range of applications of the knowledge generated. The natural sciences are applicable to virtually anything because the natural laws affect everything that exists, but the humanities are not applicable outside the human world. Physics can be applied to virtually anything in the world, but Linguistics is much more restricted within the range of its application, in other words, it is more specialized, and the same is true for other natural sciences: chemistry originates as a specific application of the laws of physics, while biology at the same time stems from chemistry, but they deal with matters that are too restrictive for physics to effectively deal with. Of course, this argumentation is not supposed to discredit the validity of Linguistics and Historical 4 Linguistics as non-scientific, but rather to showcase that this is simply a matter of nomenclature and range of application. The aim of this Final Degree Project is by no means to discuss or argue the role of Linguistics as a science, since linguistics has been considered a scientific field since the Neogrammarians, but rather to discuss its role as one by determining what constitutes a real scientific discipline and whether historical linguistics, which has traditionally borrowed methods from other disciplines such as geology or biology, which may seem in principle completely unrelated to the phenomenon of language change. can be considered a true scientific pursuit. As a physicist, who is also a linguist, I am interested in the relationship between physics and language, beyond the direct applications of wave properties in the acoustic study of phonetics, given the ordered nature of language, and being familiar with physics, I thought of a possible entropic understanding of language and of all its components, and as showcased in this paper, physics, particularly the second law of thermodynamics, has been applied to the study of language change (Hume et al 2013; Shclechtweg et al. 2017) with different degrees of success, which will be discussed in section 3, as well as its inconvenients and advantages. This law constructed a new variable of systems known as entropy, which refers to the energy of systems that is not usable in any process, that is, the loss of energy in processes that involve energy transfer, usually in the form of heat. The concept of entropy was further studied by Boltzmann in the 1870s. Boltzmann developed an equation for the evolution of an ideal gas modelling the molecules of said gas as spheres or punctual masses. This equation became very importance for various reasons since the evolution of ideal gases in equilibrium had already been proven previously using other means such as kinetic theory. Its importance lay in the fact that Boltzmann equation (see section 3.1, equation 3) proved the Second Principle of Thermodynamics by applying it to systems that were not in equilibrium, which had not been accomplished until then; and instead of using an energetic concept, he relied on sheer probability. This led to the birth of mechanical statistics as a subfield of physics which is based on Boltzmann’s interpretation of Entropy. (Cercignani 2006:35). This will be explained in more detail in Section 3 below. 5 Entropy was later introduced into mathematics in the early 20th century, in the subfield of information theory, which considers information (also known as ‘surprise’ or ‘surprisal’) as the probability of a certain symbol occurring, a symbol being any independent observable event in the universe that contains new information for its observer, (i,e., tossing a coin and later knowing the result). For sources of information in which symbols are emitted independently (i.e,. binary code of 0s and 1s), the weighted average of information obtained from this source, happens to behave in a similar manner as physical particles do in terms of the probability of possible ordinations for discrete elements; in fact, the mathematical expression for information (Shannon 1948: 379, 623) mirrors that of Boltzmann. Because of this, the average of information delivered by any source is also entropic in nature and referred to as entropy as well (Carter 2011: 15, 26). Language is a form of information in which symbols are not emitted independently of one another, in other words, the previous symbol will condition the emission of the next one to codify the information in a way that it makes sense to the end receiving it. Furthermore, language is not a system in equilibrium given that it varies from speaker to speaker, although the common code that we generally refer as ‘English, Spanish, Dutch’ may be recognized by speakers of that ‘language’ as “the same.”. historical linguistics, the study of language evolution, shows that linguistic change does not occur at the same pace in languages (even languages belonging to the same family) and that some languages are much more stable than others (at various linguistic levels) for reasons which are hard to determine. The purpose of this essay is to explore whether an entropic approach can be helpful within the field of historical linguistics. 2. Science: Philosophy and Methodology 2.1 Philosophy of Science: Uniformitarianism Uniformitarianism has been established as the foundational principle of science and it is defined and presented as an axiom by Gordon (2013: 79): “the assumption that all natural 6 laws and processes that operate in the universe and in present-day scientific observations have always operated in the universe in the past and apply everywhere within the boundaries of the universe”. Gordon (2013: 82) also refers to uniformitarianism as the invariance of the metaphysical underpinning science, such as the constancy of cause and effect through space and time, historical linguistics, like all scientific disciplines, also subscribes to the uniformitarian principle, i.e. that the present is the key to understand the past. As a matter of fact, it is safe to say that the entirety of scientific knowledge relies on this untestable, axiomatic principle. Yet the uniformitarian principle is somewhat contradictory, since it states that the way everything functions in the universe has remained unchanged since its origin. If this were the case, no system subject to the universal laws would ever be prone to suffer any change whatsoever, at no point in time or space, and all changes, would always be in the same direction (the uniformitarian principle, in a narrow sense, would rule out the possibility of emergence). To summarize, one might abstract from the principle that the whole universe would remain static or in a regular-paced change. As far as we know that has never been the case for any system within the boundaries of the universe. In fact, quite the opposite is true, i.e., systems evolve from abrupt, spontaneous events that are unpredictable in many cases. Thus, uniformitarianism can be understood from multiple points of view, or in other words, it has many faces. The case of uniformitarianism in Linguistics is no different. According to this principle, human behavior, anatomy, and thinking capabilities would have remained the same since our first steps into this world, and the same can be said for language. Yet, if that were the case, it is hard to explain the language diversity that exists and how every language evolves differently from others, even in the same family or subfamily. This issue is still a topic of discussion in the academic world and there seems to be no definite answer. Walkden (2019) discusses every facet of the uniformitarian principle through the scope of Linguistics and the applications that it has had in this field of knowledge. He argues that “Uniformitarianism as understood in linguistics is not itself a uniform notion and does not reflect the conceptual or empirical advances in other areas of historical science.” (Walkden, 2019. 11). He concludes that uniformitarianism does not reflect the advances of knowledge because it has had as many readings and interpretations as historical linguists. Gould (1965: 256), for instance, argued that the uniformity of rate as described by Lyell (1833) to be false, since Lyell had willingly left aside abrupt, catastrophic 7 changes in favor of steady and relatively constant natural phenomena; in recent times, scholars have gone as far as to state that uniformitarianism in geology has been “entirely falsified” (Romano 2015: 73). This opposition to uniformitarianism has gone beyond geology, affecting cosmology and physics as well. These concerns were brought to light by Balashov (1994), who argued that given the widespread acceptance in the academic world of the ‘Big Bang Theory’, uniformitarianism, as it had been understood so far, had no place in science; since the ‘Big Bang theory’ was an example of extreme catastrophism which led to everything that exists abruptly coming to life out of a singularity of nothingness, it ruled out the narrowest face of uniformitarianism. Uniformitarianism has also been challenged with the emergence of quantum physics, since classical physics failed miserably at explaining the behavior of subatomic particles, which function in a probabilistic way; yet it still worked in the macroscopic scale, this being fully deterministic (Planck 1900). Nevertheless, this does not mean that uniformitarianism is an invalid proposal, but that its conception has had the need to evolve and change as new questions have appeared with every discovery. The case of historical linguistics is complicated, since uniformitarianism is necessary in practice when reconstructing languages, but it is quite problematic other ways. In his book on historical linguistic and language change, Roger Lass (1997:29), which has always been preoccupied with the application of philosophy science to linguistics, expresses his view of the uniformitarian principle as follows argued that “Here is a short and largely methodological example of how these principles would operate…. Say somebody reconstructs a past state of some language with a vowel system /y, ø, u, ɔ/. We could reject this out of hand on the no miracles principle: to the best of our knowledge no language has only rounded vowels.” He then rejects his own line of reasoning by saying that “to the best of our knowledge” is not an argumentation based on inductive knowledge, since no one has recorded every single language that exists now, existed in the past, or will do so in the future. Lass revisits uniformitarianism in Lass (2000: 216-218), where he claims that the theory that “all grammatical material has its origin in lexical material implies that there was once a stage at which all languages were isolating, with only lexical material, which is in itself a violation of uniformitarianism since at no times in recorded history has this been the case, with the problem being the paradox of uniformitarianism that apparently denies the 8 possibility of emergence, hence making it impossible for grammaticality to originate in bare lexical components. Despite being a violation of the uniformitarian principle in the sense that this could be considered a catastrophic event of emergence, such a claim is valid. The following hypothetical example by Walkden explains why: “No living language contains the words wulfaz ‘wolf’ and hwaþeraz ‘which of two’ nor does it allow referential pronominal subjects to remain unexpressed; yet we have no qualms about reconstructing this state of affairs for Proto-Germanic (Walkden 2014; Ringe 2017), despite being in clear violation of the General Uniformity Principle. This is perhaps an extreme case, but no one would maintain that reconstructing a language with these properties is inadmissible.” (Walkden 2019: 6). This raises the question of why such violation of the uniformity principle rules the rounded vowel theory, yet it does not so for the language containing both wulfaz and hwaþeraz. To this question, Lass (1997: 26) tries to solve the problem by distinguishing between the “immanent” and the “configurational”, or in other words, the natural and permanent (not in the sense of immutable) part of something and the non-permanent characteristics or principles that condition the state of affairs, in other words, the vowel asset of a language is inherent to said language, even though it can mutate (i.e., phonological change), as is the lexicon of a language (a language that contains both of the afore mentioned words) whereas the capacity of a language for allowance of referential nominal subjects while remaining unexpressed is configurational due the fact that it conditions the language, it is a grammatical asset. The first example given by Lass can be ruled out immediately because it references just an immanent asset of languages, the second one is different because there is no correlation between two specific examples of lexicon and a grammatical property of the same, one being immanent while the other configurational; it makes no sense to discard the possibility of such a language existing despite there being no historical records of such. This distinction is always made in advanced physics (e.g., quantum physics) in the form of ‘initial conditions’ and ‘boundary conditions’, but the difference is that the problems and inquiries of physics are met with fewer conditioning factors that determine the evolution and behavior of the systems studied, as well as to which degree and in which form these conditions are correlated. On the contrary, the case of language change is obscured by the fact that the number of factors that cause it are too numerous to create mathematical equations that represent them accurately. Physical phenomena depend on factors that are 9 easily quantified and translated into equations, whereas the conditions that trigger language change tend to be qualitative and not quantitative; for instance, sociolinguistics studies variation of language depending on social factors such as gender, social class, age, and others, many of which are not quantifiable and thus, not transformable into equations, demanding other methods such as statistical analysis, a method whose results are extremely dependent on the conditions of each study, this will be explained in more depth in section 3. To sum up, while uniformitarianism is necessary for the study of any scientific field, it is flawed for many reasons. The first one is its unverifiability and infallibility, the second one that it relies on inductiveness, which is misleading and, as previously stated, might lead to claims based on no knowledge. Thus, uniformitarianism has been considered at least incomplete if not entirely wrong and continues to be object of debate to date. According to a narrow view of uniformitarianism, historical linguistics, being founded on the uniformitarian principle would, therefore, be fundamentally flawed. The paradox is that the results obtained are considered to be true since they explain best the evolution of language (e.g., Grimm’s Law); for instance, take mathematics, the fundamental language for natural sciences; they are built upon an incomplete number of axioms (Gödel 1931) that lead to formulations that cannot be consistent and complete at the same time; despite this, no one rejects mathematics nor questions its reliability and usefulness when describing the natural eventualities of our universe. The same should be taken into account when discussing the reliability of uniformitarianism in historical linguistics, take for instance the reconstruction of Proto-Indo European (PIE) through the use of the comparative method between its daughter languages (Encyclopædia Britannica), since there is no record of the language, that has been estimated to have been spoken between 4500 BCE – 2500 BCE (Powell 2017), the reconstruction is incomplete and inferential, based in the recurrent similarities among the differences and similarities of the daughter languages of PIE, as an illustration, the English words foot, father and fish compared to the Spanish words pie, padre and pez show a consistence correspondence between the initial consonance between /f/ and /p/, there also being a correspondence between meanings too frequent to be fruit of casualty, thus suggesting a system of phonetic laws from which the hypothetical language of PIE to the modern ones. These laws had become so detailed and reliable that the Neogrammarians managed to create a law that stated that phonetic changes from PIE occur without exception. Indeed, this rule 16 the integral will always be greater than 0. This theory was later transferred to systems that were not adiabatic, and later to the universe, and the law still stood, in fact, it was reinforced. The inequality (2) also contains the first equation: if both variables are equal, then the process is reversible, if 𝛥𝑆 is greater than the other variable, then the process is irreversible. The theoretical question of a possible system where the inequality was satisfied but lesser than or equal to 0 was also raised, but no observation of the phenomenon had ever happened either in nature or in a laboratory setting. The theory establishes that any process in which the increment of entropy is lesser than 0 is impossible, and 0 only in absolute zero temperature. That is, the universe always increases its entropy, which means that energy is finite and at some point, there will be no energy left for any process in it, reaching a final state of pure equilibrium and bringing all processes of the universe to an inevitable end. Later, in 1877, entropy was introduced in statistical mechanics by Austrian physicist Ludwig Boltzmann, and his is the current definition of entropy up to this day. Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system (Boltzmann 1877). He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called ‘statistical mechanics’, and found the link between the microscopic interactions, which fluctuate about an average configuration to the macroscopically observable behavior in form of a simple logarithmic law with a proportionality constant, the Boltzmann constant, which has become one of the defining universal constants for the modern International System of Units (SI). In short, the thermodynamic definition of entropy provides the experimental verification of entropy, while the statistical definition of entropy extends the concept, providing an explanation and a deeper understanding of its nature. Specifically, entropy is a logarithmic measure of the number of system states with significant probability of being occupied: 𝑆 = −𝑘𝐵𝛴𝑝𝑖𝑙𝑛 𝑝𝑖 (3) where pi is the probability that the system is in ith state, usually given by the Boltzmann distribution, kB is a constant named after Boltzmann, and 𝛴 is a mathematical operator that adds every element of a discrete series (in a microscopical setting, this number is too vast for 17 the human mind to even grasp); if states are defined in a continuous manner, the summation is replaced by an integral over all possible states. This new scope gave entropy a new sense of uncertainty rather than unprofitable energy, and processes that were deemed impossible or irreversible within the second law of thermodynamics are now understood as extremely unlikely; for instance, water can freeze spontaneously above freezing temperature, but a higher temperature enables more states to operate, and thus, the probability of virtually endless particles that are constantly changing microstates to match that of ice 2 becomes practically null when the vast majority of states possible are for particles to be in the liquid state. As an estimation, imagine a bag with trillions of grains of salt in it, most of them are white, but only one or two are black; if you were to draw one grain out of the bag, it would always be white, even if there were black grains in the bag. This is why some processes seem to be impossible, because the probability of its microscopic components to arrange in that state is one among an absurd number of possible states, which is essentially zero. To simplify, the importance of Boltzmann’s discovery lied in his ability to convert an energetic magnitude into sheer probability, calling into question the determinism that had governed natural sciences up to then, and eventually ruling it out thanks to the success of quantum physics, which were heavily influenced by Boltzmann’s input. Moreover, this entropic measure of probability has been successfully imported to other disciplines with great success, as mentioned above. It is this probabilistic reading of entropy that linguistics has borrowed from Physics to apply it either directly to a language or through means of computational science to Computational Linguistics. Sections 3.2 and 3.3 will deal with how entropy has been used to explain both sound change and semantic change (word entropy). 3.2 Word Entropy and Metaphoric Change As stated in the introduction, entropy has gone through a great deal of changes in its interpretation. As has already been mentioned, in the present day Boltzmann’s interpretation of entropy still stands as the most accurate physical description of what 2 since ice is solid, its particles are bound to a minuscule number of states compared to a liquid in which every single molecule has significantly more freedom of movement) 18 entropy is. Yet with the introduction of computer science, a new interpretation appeared. It has turned out that entropy, while still belonging to the physical, can also have a purely abstract interpretation in the form of information (see section 1). Information theory, a relatively new subfield of mathematics that studies how bits of information are codified and packed, is also based on Boltzmann’s theory of entropy, the only difference being that if for microscopical systems, possible states of being for each particle are independent of each other, for information, every state is dependent of the previous one (except for computed binary codes). Unfortunately, the mathematics and level of abstraction begin to get excessively complicated for a full development of these theories; thus, for the sake of simplicity, let us just state that for each random process in the universe that has an informational value, there is an entropic value , i.e. the level of disorder or number of possible disposition of the elements in a system associated to it; the higher the value, the more informative the process will be and vice versa. This entropic interpretation of information is constantly used in computer science, and thus, it could also be applied for linguistic purposes, since human language has been coded in the binary system, to which entropy is entirely applicable; and that is exactly what Dominik Schlechtweg and others have done. In their paper ‘German in Flux: Detecting Metaphoric Change Via Word Entropy’ (2017), Schlechtweg et al. explain the process of such application as well as the results obtained. Using a Semantic Distributional Model with the Deustches Textarchiv corpus of the German language as a source, they exploit the idea of semantic generality applied to hypernym detection in order to detect metaphoric change as a special process of meaning innovation through distributional. First defining metaphoric change as a mapping from a source domain to a target domain, in this case, the source domain being existing meanings (MA) and the target domain being acquired meanings (MB), where MB is relatod to MA by similarity or reduced comparison. As an illustration, Schlechtweg (2017: 356) offers the following example of what is referred to as metaphorical change:” While language is often used ad hoc in a non-literal meaning in discourse, not every of these uses constitutes an instance of metaphoric change. Only when a metaphoric innovation is conventionalized within the language, we can speak of metaphoric meaning change (cf. Koch, 2016, p. 27). Consider German umwälzen as an example. In Early New High German the word was only used in the sense ‘to turn around something or someone physically’ (MA) as in (1). In Contemporary New High German, though, the word is also frequently used in the sense ‘to change something (possibly abstract) radically’ (MB) as in (2). 19 (1) ...muß ich mich umbweltzen / und kan keinen schlaff in meine augen bringen ‘...I have to turn around and cannot bring sleep into my eyes.’ (2) Kinadon wollte den Staat umwälzen... ‘Kinadon wanted to revolutionize the state...’ These metaphorical changes create polysemy, extending the meaning of a word, and such extension implies an increase in the context of appearance of said word. This extension distinguishes between semantically stable words and words undergoing such a change, but also other changes where the opposite is to be expected: reduction in meaning. Polysemization is not a typical property of metaphoric change alone, but of all types of innovative change such as metonymic change, specialization, etc. However, unlike any other innovative change, metaphoric change essentially requires a mapping (a univocal, sometimes multi-univocal correspondence) between two different domains, hence, a relatively strong effect on the contextual distribution of words is to be expected. Moreover, the range of a word’s meanings is not the sole influential factor in the range of occurrence contexts, but also the particular nature (semantic generality) of any individual meaning produces an effect in the range as well, in other words, semantically more general words are less informative since they occur in more general contexts (a narrower variety of contexts). As an example, Schlechtweg (2017: 356): proposes the following: “the development of German glänzend with ‘luminous’ as source and ‘very good’ as target concept. The source concept only applies to a rather limited range of entities, i.e., physical ones. The target concept, on the contrary, given its abstractness, applies to nearly every entity. Interpreting such changes of words as a change in their semantic generality, we now aim to examine how well it is measurable with distributional methods”. For such a purpose, they applied the concept of word entropy, introduced by Santus (2013), who stated that: “In fact, contexts such as bark and has fur are likely to co-occur with a smaller number of words than move and eat. Starting from this hypothesis and using entropy as an estimate of context informativeness (Shannon, 1948), we propose SLQS, which measures the semantic generality of a word by the entropy of its statistically most 20 prominent contexts.”, and for which Schlechtweg and their team give the following explanation: “Examining language statistically, a word w may be represented by its distribution in a corpus. This distribution is determined by the contexts of w, i.e., the words it cooccurs with, and how often it co-occurs with them.” What Santus (2009) meant by his definition of word entropy, is that words such as bark and fur are less likely to occur in language because they have less possible association with other words, i.e., a lower entropic value, since the number of combinations that these words may form with their peers is much lesser than the words move or eat. As an illustration, the word move can be associated with many other words, basically any object in the world that is susceptible to be moved in every possible direction or place, etc., whereas the word fur is likely to occur in fewer contexts since its associations with other words are much more restricted, given the specificness of this lexical item For the purpose of their research, Schlechtweg and his team developed the following entropic formula based on Bolztmann’s equation: 𝑯(𝒄)= −∑𝑷(𝒄𝒊|𝒘)𝒍𝒐𝒈𝟐𝑷(𝒄𝒊|𝒘) 𝒏 𝒊=𝟏 (4) where H(c) is the entropy associated to a word w in a co-occurrence context c and where 𝑷(𝒄𝒊|𝒘) is the conditioned probability of said word occurring in said context. Of course, to measure metaphorical change, they could not rely only on this mathematical model, they had to determine a metaphor for the model to work, that is, they had to create a golden standard with which they could compare the results of their model with. What differentiates this study to predict semantic change from previous ones that also employed distributional methods, is, according to Schlechtweg (2017: 355) that most similarity models limit themselves to quantifying the degree of general change rather than qualify various types of semantic change, and by not doing so, computing them all together leads to misinformation, since, as previously established in this section, ignoring the effects of certain types of meaning change in the distribution, and thus effecting the results obtained, creating difficulties for analysis of the results: “Similarity metrics, in particular, were shown not to distinguish well between words on different levels of the semantic hierarchy (Shwartz 21 et al 2016). Thus, we cannot expect diachronic similarity models to reflect changes in the semantic generality of a word over time, which was described to be a central effect of semantic change (Bybee 2015: 197). Another problems of analysis that do not distinguish types of meaning change is that they cannot establish a clear correspondence between two vectorial spaces 3 for the sole reason that every type meaning change would form their own vectorial space, that is, that previous studies merged elements from different vectorial spaces without transforming or reducing them to a common space, making it topologically impossible to establish a clear correspondence between the different sets MA and MB because not all of the data would entirely correspond to MA but to its own vectorial space MX with X being the correspondent type of meaning change particularly, expressed in the following quotation: “Additionally, they often pose the problem of vector space alignment (especially when relying on word embeddings), occurring when word vectors from different time periods have to be mapped to a common coordinate axis (Hamilton et al., 2016: 1492).” The conclusion derived from the data obtained through the application of equation (4) to different periods in the history of the German language and through comparison with modern German (see Annex) was that there was a significant correlation between the level of disorder in meaning (a higher number of contexts of co-occurrence for any w word compared to its frequency of appearance) and metaphorical change, implying that the equation (4) was somewhat successful as it predicted the annotations made by semanticists previously needed to stablish a golden rank, or summing up: it agreed with the results expected, while at the same time confirming hypotheses constructed by methods of historical linguistics, with a correlation index of r2 = 0.64, as a reference. In natural sciences, correlation indexes below a value of 0.98 are usually disregarded and always imply that the data is poor in number or that the equations used need revision, whereas in other disciplines this is usually overlooked because lower values of r2 also hint to correlation if it is higher than 0, usually because of the number of data being not enough, with the following quotation as an illustration: “Different distributional measures based on the information-theoretic concept of entropy were compared against the annotators judgments and it was found that raw word entropy 3 A vectorial space is a dataset containing a finite number of data for which there is a transformational function that is capable to convert one dataset into another dataset that usually exists in other dimension (e,g., a vectorial space in this experiment could be the meaning of a word in German in the XVIIIth century) 22 correlates strongly and significantly with the gold rank in different settings in contrast to most other entropy measures and frequency.” (Schelchtweg et al 2017: 362). It also implied that for a higher value of word entropy, there was a higher probability of metaphoric change for said word, which also correlated with the findings of Historical Linguistics and the model is transferable to any other type semantic change, rather than just metaphoric, as well as to other languages, having the potential to become a powerful tool for research purposes in the field of linguistic change. Summarizing, the model that Schlechtweg developed could predict the metaphorical change of the words in the corpus used in the period of 1700-1800 based on the entropic value of the words, i.e., the probability of certain words appearing in more contexts rose the likelihood of the same words changing their meanings in a metaphorical way because of simple association. 3.3 Entropy and Sound Change The next model that will be dealt with in this essay not based on experimentation, it is purely theoretical. This model makes uses the entropic principle to tackle the question of why certain phonological changes occur given certain factors that are treated independently of one another, when they could all be treated at once when considering an entropic reading, according to Hume et al (2011): “While there is ample evidence showing the impact of these diverse forces on language systems, they are often treated independently of one another (though see Blevins and Wedel 2009). As such, the literature on language change is replete with arguments for why one factor, as opposed to another, underlies a particular modification. In this chapter we propose a unified account of the influence of these and other factors (phonetic factors, usage factors such as familiarity and procedural factors due to structural complexity) is possible when we view the phenomena of phonologization through the lens of information theory (Shannon 1948), in particular making use of the concepts of surprisal and entropy. Not only do the tools of information theory allow us a deeper understanding of why these factors influence language systems in the way that they do, they also provide insight into the process of phonologization.” This opens up discussion as to which specific factors are to be included in the model, for instance, sociolinguistics takes into account factors previously mentioned in this paper, such as gender, age, profession, 23 social class, etc. If one were to apply these factors to the model, the first step should be to determine whether or not these could propel phonologization in the right context, and what their probability for doing so would be by studying how informative these are, as an example, the Labov’s experiment (1984) previously used in this paper, could be considered as a candidate for the entropic model to be proposed (5) if it was able to determine the entropic contribution of social class, that is, how social class affects the probability 4 of postvocalic /r/ being produced. Taken from the book Origins of Sound Change Ch. 2, this model applies a similar formula to that seen in section 3.2, reached after an extensive discussion about what factors are to be taken into account in the process of phonologization and the productions of sounds to which humans associate a meaning. They explain and debate which entropic function is to be used for such a purpose (see section 3.1 above), but instead of using the probability of a word co-occurring in a certain, real context, it associates a probability of a certain sound to always be conditioned by the probability of events that can alter the perception of that sound (acoustic phenomena, cognitive phenomena, physical impediments, etc…, and are not specified). Entropy is interpreted with a wholistic sense, that is, it is a magnitude attributed to a system and not its components individually. However, the following equation is applied considering a phoneme its own system: 𝑺(𝑿 = 𝒗𝒊)= −𝒍𝒐𝒈𝟐𝑷(𝑿 = 𝒗𝒊|𝒌, 𝒂, 𝒇, 𝒆𝒊) (5) Where X is a set of vowels for any language, and vi is each vowel, k is confusability (the likelihood of a sound not being successfully precepted), a is articulatory precision, f is contextual frequency and ei is any grammatical context of the language studied in which the vowel vi can be observed (either produced or perceived). Nevertheless although this model can be used to a certain extent, it is not easy to assign a numeric value to all possible conditioning factors, given that there is no scale on which to base those values, which means that they would have to be chosen arbitrarily; in fact, the authors do so to test how the surprisal (informational value, entropy) varies depending on whether the sounds have an equal possibility of occurring, or different 4 Porbability differs from Statistics in that the results of Probability are fixed, whereas the results of Statistics will vary greatly with each application. As an example, probability explains that the possible outcomes of tossing a coin that is not loaded, which will be 0.5 for each of its faces (this does not mean that the coin will land 50 times on one face and fifty on the other) whereas statistics will experiment by tossing the coin 100 times and with each trial, the number of times that heads or tails will appear is going to be different. 24 probabilities. They reach the conclusion that if a set of sounds is equiprobable, its entropic contribution or the entropic value is lower and less likely to mutate. Despite the low reliability of any attempt of measurable experimentation with this model, it still is a good tool and a step further in the study of sound change, since it diversifies the discussions and serves as an idealistic proposal that can help future research take form and improve. What can be concluded from this study is that, even though a calculation of this caliber is not entirely possible yet, a higher entropic value (associated to complex, uncommon sounds), as well as a lower entropic value (associated to simple, common sounds) have a pretty low surprisal contribution. Surprisal, in this context, is defined as the informative value of a sound, and thus, prone to phonologization. As an example, the sound /ə/ in English is pretty common, while /ʒ/ being one of the most infrequent sounds in Standard English, both being at opposite ends of a spectrum, have a similar contribution to the entropic distribution in (5), since one is so common that any variant is likely to go unnoticed due to its low surprisal in case of /ə/, while variation of /ʒ/ is also likely to go unnoticed for the opposite reason, a gradual mutation in these sounds is much more probable than in others such as /t/ because they are easier to be confused with other sounds due to their frequency. The extremes of an entropic distribution add very little to its value in physical systems as well, and any state in the middle is more stable and likely to happen. In other words, attribution of entropic values to sound change explain the variety of sound changes that have happened throughout history; why certain changes are more common in languages, such as lenition (Grimm’s Law, common for Germanic languages), but the opposite changes such as fortition do also happen (for instance, the High German Consonant Shift, which is unique to the High German dialect). This means that voiced plosives (/b/,/d/, /g/) are more stable, in entropic terms, than their voiceless counterparts (/p/,/t/,/k/) since the phonetic change occurred more often in the direction of voiceless to voiced than the other way around, concluding that /p/,/t/ and /k/ are less informative than /b/,/d/, and /g/ and more unstable. According to entropic models, attribution of one cause for certain phenomena to occur is out of the question, as it rules out determinism in favor of probability; in historical linguistics, this is the case of assuming a change happened for a sole reason, for example, language contact in the case of non-palatalization of /k/ in northern dialects of OE due to higher contact with ON in the region, would be deterministic if considered as the only factor 25 that led to such a change, whereas, in reality, it can be interpreted as just another condition that altered the probability of the change to not happen, always among other reasons ; or in other words, phenomena that increase the entropic value of a language’s phonetic inventory, by adding new sounds with a higher surprisal, i.e. easier to perceive and thus more informative, make said language more prone to change its phonetic repertoire, by either adding or deleting sounds. The only problem with this approach is that of acknowledging the conditioning factors that may cause the changes, as there might be a number too high to compute, as well as the need for inductive reasoning in order to support the knowledge stablished by historical linguistics. However, this does not rule out its capacity for predicting sound change in the future and might become an indispensable tool for future research in the field. 4. Conclusion This essay has discussed the place of Linguistics, and more specifically, Historical Linguistics, within the scientific paradigm and its categorization within the ‘Humanities’. It has also discussed the qualities and status of Historical Linguistics as a science, both from a philosophical and methodological points of view. It has been concluded that historical linguistics is well established as an empirical science, despite the fact that language change cannot be predicted as is the case in all natural sciences (as opposed to the ‘hard sciences, such as physics and mathematics). I have also tried to show that interdisciplinarity, that is, borrowing knowledge and methodology from other scientific fields, specifically physics, which might seem in principle completely unrelated, has proven to be quite useful in determining the accuracy of certain theories of Historical Linguistics, while at the same time grounding knowledge that could be disputed due to its inductive origin, and directing Historical Linguistics a step closer to prediction. I have particularly focused on the power of Boltzmann’s entropic theory and equation and its possible application to the study of language change. The fact that language is a system in a constant state of non-equilibrium, formed by discreet elements, makes it a perfect candidate for such an approach, more so given the computational capacity to translate human language into binary code, which facilitates the work.