The historical background to democracy, which good citizens must defend, started with the Greeks. Thucydides, Plato, Aristotle, and Polybius thought that political history was circular, which meant that good regimes, ruling on behalf of the people, held sway for a time but deteriorated into bad regimes – tyrannical – ruling for the rulers’ benefit. Their solution was to propose “mixed regimes,” containing monarchical, aristocratic, and democratic elements which, checked and balanced, would have to cooperate with each other by compromising different interests. Such a regime was the Roman Republic, which promoted both compromise and public virtue (“republicanism”) in the sense of devotion toward the state. During the Enlightenment, European political thinkers added the concepts of “sovereignty,” in order to impose public order, and “social contracts,” to make sovereigns at least somewhat answerable to subjects. Thus when the Founders convened to invent their government, they used “common sense,” prescribed by Paine, Jefferson, Madison, and others, to fashion a mixed government of special character. That government, which the Founders called “republican,” rested on a written “constitution,” which reined in “factions” via “checks and balances,” and which refrained from creating a “sovereign” who might, as in the French case almost immediately, plunge the nation into war.

Chapter VI provides case studies for the conceptual metaphor of conflict myth in the image reaching from the fourth in the first millennium BCE. Its approach is informed by Aby Warburg’s emphasis on gesture language and its history of reception as developed in his Mnemosyne Atlas and by Erwin Panofsky’s approach to iconology to develop the concept of interpictoriality as a network of pictorial references or Bildgedächtnis (collective pictorial memory).

13.1 Implementation of k-means Clustering and Hierarchical Clustering

In the previous chapter, we discussed various clustering algorithms. We learned that clustering algorithms are broadly classified into partitioning methods, hierarchical methods, and density-based methods. The k-means clustering algorithm follows partitioning method; agglomerative and divisive algorithms follow the hierarchical method, while DBSCAN is based on density-based clustering methods.

In this chapter, we will implement each of these algorithms by considering various case studies by following a step-by-step approach. You are advised to perform all these steps on your own on the mentioned databases stated in this chapter.

The k-means algorithm is considered a partitioning method and an unsupervised machine learning (ML) algorithm used to identify clusters of data items in a dataset. It is one of the most prominent ML algorithms, and its implementation in Python is quite straightforward. This chapter will consider three case studies, i.e., customers shopping in the mall dataset, the U.S. arrests dataset, and a popular Iris dataset. We will understand the significance of k-means clustering techniques to implement it in Python through these case studies. Along with the clustering of data items, we will also discuss the ways to find out the optimal number of clusters. To compare the results of the k-means algorithm, we will also implement hierarchical clustering for these problems.

We will kick-start the implementation of the k-means algorithm in Spyder IDE using the following steps.

• Step 1: Importing the libraries and the dataset—The dataset for the respective case study would be downloaded, and then the required libraries would be imported.

• Step 2: Finding the optimal number of clusters—We will find the optimal number of clusters by the elbow method for the given dataset.

• Step 3: Fitting k-means to the dataset—A k-means model will be prepared by training the model over the acquired dataset.

• Step 4: Visualizing the clusters—The clusters formed by the k-means model would then be visualized in the form of scatter plots.

The English language has been attested in Ireland since the late twelfth century but did not become widespread until the beginning of the seventeenth century when vigorous planting of English settlers took place. Distinct forms of Irish English began to develop which were a mixture of diverse dialectal inputs from England and transfer phenomena from Irish as the native population began to switch to the language of the colonisers. Almost as the same time as planting of English settlers started there was a movement out of Ireland, either by deportation or voluntary emigration, largely due to economic circumstances. This led to areas in overseas anglophone regions showing centres of Irish emigration, e.g. Appalachia with eighteenth-century Ulster Scots or the north-eastern coast of the USA with nineteenth-century southern Irish Catholics. At these locations the linguistic impact of Irish English was slight but traces can be found still which testify to this input.

The study of dialects in Britain and Ireland yields insight into the manner in which social forces affect the development of language. The history of English, outside of the trajectory which led to Southern Standard British English, shows a rich and varied tapestry of features, processes and interactions, which make this subject particularly rewarding in the context of an inclusive view of the language’s history. The identity function of local norms is apparent in all the studies of dialects in individual locations and ultimately accounts for the survival of local varieties despite the increasing pressure from supraregional forms of English represented in the educational system and very widely across the media landscape of modern Britain and Ireland. Looking beyond Britain and Ireland, factors that have influenced the English spoken in four small but significant locations in Europe (the Channel Islands, Malta, Cyprus and Gibraltar) are examined, revealing a rich interaction of colonial legacy, contact and national identity.

4.1 Motivations and Objectives

Taxation is the principal mechanism through which redistribution of income from the rich to the poor takes place. The analysis of taxation is one of the major pieces of tasks of economists who analyze public sector economics. Taxes can be distinguished with respect to the effects they generate on the distribution of income. While raising revenue for some specific welfare purposes, it is ethically desirable that a tax scheme should exert an equalizing effect on the distribution of income; the rich should bear a greater share of the tax burden than the poor. This makes the after-tax income distribution more equal than its before-tax twin. In the process, the tax burdens come to be more unequally distributed than the pre-tax incomes. These two effects of a tax system are referred to as the “redistributive” effect and the “disproportionality” (or “departure from proportionality”) effect of a tax system. (For a recent discussion on these features of a tax system, see Chakravarty and Sarkar, 2025.)

Now, the basic definition of progression of an income tax system is that the local measure “average rate progression,” the tax liability as a proportion of the income, should rise with income (Pigou, 1928). A local or structural indicator looks at the extent of progression along the income scale; it focuses on income-by-income progression.

This chapter begins the analysis of how American society prepared a space for someone like Trump to dominate public life. The major symptom was that citizens failed to not elect Trump and therefore twice elevated to be president a man who had no qualifications to administer the Executive Branch of a democratic government consisting of more than 4,000,000 employees and multiple responsibilities. He was, however, a “populist,” who promised to act on behalf of “the people” as if the people were entitled to throw off rule by “elites.” And together, he and his associates admired what scholars call “neoliberalism,” whereby many traditional, and democratic, political practices are overridden in favor of unleashing “private innovators” – such as Jeff Bezos and Mark Zuckerberg – to acquire enormous wealth and influence. Assuming that Trump is a populist, we should observe that America’s crisis is not so much a failure of democratic “institutions” – agencies, procedures, etc. – as it is that “citizens” have failed to vote to support those institutions. Thus Defending Democracy is about how citizens must do their job – their “vocation” – more and better.

Chapter 6 discusses the distinction between sense and reference. The sense of a term is its general meaning as captured in the semantic properties of its dictionary definitions. This is what underlies generic and descriptive terms in trademark law. Unique identification of one particular entity requires some special and different “mapping” between language and the world: an “arbitrary” or “fanciful” link between e.g. APPLE and KODAK and their respective companies; a “suggestive” extension of ROACH MOTEL to its producer; or a “secondary meaning” for an otherwise descriptive term. The chapter argues, on the basis of grammatical and corpus evidence, that POST OFFICE is a generic term and not a source identifier for the US Postal Service. It analyses a set of trademarks involving ELASTIC, which are shown to make a clear and unique identification of the source company in question. Finally the difference between “referential” and “attributive” uses of definite descriptions is exemplified for THE POLICE in a dispute over who exactly was being accused of a certain crime.