Author Archives: Rob

About Rob

Passion for studying history and philosophy of science & religion and everything in between.

Trump’s Fascism is Trumpism

From the early stages of his campaign and right into the Oval Office, Donald Trump has spoken harshly about the institutions and principles that make up the foundations of open government. In the process, he has systematically degraded political discourse in the United States, shown an astounding disregard for facts, libeled his predecessors, threatened to “lock up” political rivals, referred to mainstream journalists as “the enemy of the American people,” spread falsehoods about the integrity of the U.S. electoral process, touted mindlessly nationalistic economic and trade policies, vilified immigrants and the countries from which they come, and nurtured a paranoid bigotry toward the followers of one of the world’s foremost religions. (Albright 2018, 5)

(….) He is president because he convinced enough voters in the right states that he was a teller of blunt truths, a masterful negotiator, an effective champion of American interests. That he is none of those things should put us on edge, but there is a larger cause for unease. Trump is the first anti-democratic president in modern U.S. history. On too many days, beginning in the early hours, he flaunts his disdain for democratic institutions, the ideals of equality and social justice, civil discourse, civic virtues, and America itself. If transplanted to a country with fewer democratic safeguards, he would audition for a dictator, because that is where his instincts lead. (Albright 2018, 246)

Spreading Group Hatred

The psychic health of a society can be measured by the extent to which its policies and laws exclude and constrain prejudices. One sign of social stability is the degree to which a community and the individuals who compose it are willing to acknowledge the humanity and learn from the cultures of other people. Many cultures have resorted to discrimination and prejudice despite their self-destructive consequences. Dehumanizing representations of minorities disseminated through social discourse [e.g., social media] are integral to the formation of movements bent on harming outgroups. (Tsesis 2002, 99)

The victims of hate speech are at greater risk form groupwide threats than from personal attacks. Counterspeech is less effective against a group with deeply held beliefs, which feels the power of its numbers and the passions of its hateful convictions, than against an individual expressing only his or her biased ideas. Labels reify prejudices through stories that exaggerate and falsify outgroup traits and extol the presumed advantages of excluding minorities from ingroup privileges. The broad dark strokes that are then applied to scapegoats make for an auspiciously hostile environment filled with slights and vilifications. Aggressive names schematize the world into groups of good guys and bad guys…. Destructive messages are the main vehicles for spreading ideology. Hate speech is an essential means for popularizing hate groups. (Tsesis 2002, 1010)

Hate Speech qua Free Speech

Freedom of speech is critical to the growth and maturation of societies and is a much vaunted benefit of living in the United States. However, that freedom has not always led to the collective improvement of all citizens. History is littered with examples of harmful social movements, in various countries and cultures, employing violent racist rhetoric. Such hate-filled ideologies lie at the heart of human tragedies such as the Holocaust, U.S. slavery in the antebellum South, nineteenth-century Indian removal, and present-day slavery in Mauritantia. (Tsesis 2002: 1)

Donald Trump’s Racist Rhetoric

Propaganda [link] is essential for eliciting widespread cultural acceptance of exclusionary and supremacist ideologies. When hate speech is systematically developed, it sometimes becomes socially acceptable, first, to discriminate and, later, to oppress identifiable groups of people. Racialist rhetoric has been effectively harnessed to formulate and spread racism on national and even international scales…. Bigots have rationalized all these biases through threads of thought that are subtly woven into the fabric of everyday language [i.e., dog whistles]. (Tsesis 2002: 1)

Speech plays a pivotal role in communicating ideas—both progressive and regressive. Over time, the semantics of a language will mirror the historical development of a people. The context of phrases and the subtle nuances of demonstrative messages can contain the kernels of a cultural worldview. Traditionally accepted perspectives permeate the unconscious and form an often unquestioned social “reality.” Prejudices that reflect collective outlooks gradually find their way into laws. (Tsesis 2002: 1)

GOP/Trump’s Dog Whistles

People intent on maintaining power [such as demagogues like Trump] manipulate stereotypes that echo their followers’ preconceptions. Orators [and demagogues] and authors strategically exploit imbedded cultural meanings not just to create grammatically sentences, but also to persuade their audience. They use repeatedly uttered, dogmatic imagery to influence attitudes toward particular groups of people. Large audiences more readily recognize tenets when they draw on deeply held beliefs. (Tsesis 2002: 2)

Hate speech and the prejudice it fosters deny individuals [like the] fundamental rights like autonomy and tranquility…. “Misethnicity” [i.e., the institutionalized hatred of ethnic groups, something Trump has facilitated] …. is sometimes preferable to “racism” and “ethnocentrism.” “Racism” is the diminished respect and unequal treatment of people based on their biological particularities. “Ethnocentrism” is the sense of superiority of one’s own ethnic group. “Misethnicity” is more specific in recognizing that ethnic prejudice is a groupwide hatred. (Tsesis 2002: 2)

They were innocent … which to this day Trump denies …

Misethnicity is deeply nestled within conventional practices [such as Donald Trump’s full-page ad in the Daily News on May 1, 1989 calling for the death penalty for five innocent black teenagers]. By drawing attention to the centrality of language in perpetuating discrimination, we may be able to dislodge some deep-rooted racist thoughts and behaviors. Charismatic leaders can harness subtle and explicit misethnic statements to instigate active or complicit participation in hate crimes. Expressions such as these create an atmosphere of combustible intolerance: “Most Indians are drunks, but he’s a hard worker”; “He may be a Jew, but he’s not greedy”; “I’m usually careful around blacks, but he can be trusted.” These statements reflect the same animosity as their more flagrant counterparts; “Indians are drunks,” “Jews are greedy,” and “blacks are dangerous.” Studying the linguistic development of Misethnicity and its relation to socially destructive conduct is critical to realizing, anticipating, and thwarting its potentially catastrophic consequences. (Tsesis 2002: 2)

(….) Historical analysis is crucial because it exposes the association between hate propaganda and discriminatory action. Oppressors justify inequities by making their targets out to be less than human, unworthy of fair treatment or even of mercy ordinarily shown to animals…. Negative stereotypes and ideological schemas, designed to rationalize power in the hands of dominant groups, precede crimes against humanity such as genocide. Many lives may be ruined before the views of those who rebuff popular prejudices trickle into the community conscience. Even societies striving for equality, steeped in natural rights theory, and vigilant against intolerant majorities are not wholly immune from becoming havens for supremacists promulgating aggressive ideologies. (Tsesis 2002: 2-3)

Pondering the effectiveness of anti-Semitic and racist messages brings into stark relief the dangers that purveyors of hate pose to representative democracies. Scrutinizing the foundations of genocidal hatred in Germany and of dehumanizing and devaluing dogma in the United States yields abundant information about how, particularly in times of social and economic unrest, hate speech builds upon established ideologies. By understanding the progression from hatred to destruction, we can know better how to prevent Misethnicity from being exploited by provocative rhetoricians intent on generating dangerous social movements. Studying how unjust political movements, such as the National Socialist party or the Confederate Nullificationists [or Donald Trump’s “America First” rallies in which he incites the “angry mob” with such rhetoric like the free press and democratic party are the enemies of the people, or his attacks on the justice system and separations of power, etc.], manipulated cultural stereotypes is instructive in avoiding future calamities. (Tsesis 2002: 3)

How Economics Lost Sight of Its Goal

Back in Ancient Greece, when Xenophon first came up with the term economics, he described the practice of household management as an art. Following his lead, Aristotle distinguished economics from chrematistics, the art of acquiring wealth—in a distinction that seems to have been all but lost today. The idea of economics, and even chrematistics, as an art may have suited Xenophon, Aristotle and their time, but two thousand years later, when Isaac Newton discovered the laws of motion, the allure of scientific status became far greater. Perhaps this is why, in 1767—just 40 years after Newton’s death—when the Scottish lawyer James Steuart first proposed the concept of ‘political economy’, he defined it no longer as an art but as ‘the science of domestic policy in free nations’. But naming it as a science still didn’t stop him from spelling out its purpose (Raworth 2017, 28-29, Kindle Edition):

The principal object of this science is to secure a certain fund of subsistence for all the inhabitants, to obviate every circumstance which may render it precarious; to provide every thing necessary for supplying the wants of the society, and to employ the inhabitants (supposing them to be free-men) in such a manner as naturally to create reciprocal relations and dependencies between them, so as to make their several interests lead them to supply one another with their reciprocal wants (Raworth 2017, 29, Kindle Edition).

A secure living and jobs for all in a mutually thriving community: not bad for a first stab at defining the goal (despite the tacit disregard of women and slaves that came with the times). A decade later, Adam Smith had a go at his own definition but followed Steuart’s lead in considering political economy to be a goal-oriented science. It had, he wrote, ‘two distinct objects: to supply a plentiful revenue or subsistence for the people, or, more properly, to enable them to provide such a revenue or subsistence for themselves; and secondly, to supply the state or commonwealth with a revenue sufficient for the public services’. This definition not only defies Smith’s ill-deserved modern reputation as a free-marketeer but also keeps its eyes firmly on the prize by articulating a goal for economic thought. But it was an approach that would not last (Raworth 2017, 29, Kindle Edition).

Seventy years after Smith, John Stuart Mill’s definition of political economy started the shift in focus by recasting it as ‘a science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth’. With this, Mill began a trend that others would further: turning attention away from naming the economy’s goals and towards discovering its apparent laws. Mill’s definition came to be used widely but by no means exclusively. In fact for nearly a century, the emerging science of economics was defined rather imprecisely, leading the early Chicago School economist Jacob Viner, in the 1930s, to quip simply that ‘Economics is what economists do.’ (Raworth 2017, 29, Kindle Edition)

Not everyone found that a satisfactory answer. In 1932, Lionel Robbins of the London School of Economics stepped in with intent to clarify the matter, clearly irritated that ‘We all talk about the same things, but we have not yet agreed what it is we are talking about.’ He claimed to have a definitive answer. ‘Economics,’ he declared, ‘is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.’ Despite its contortions, that definition seemed to close the debate, and it stuck: many mainstream textbooks still start with something very similar today. But although it frames economics as a science of human behaviour, it spends little time enquiring into those ends, let alone into the nature of the scarce means involved. In Gregory Mankiw’s widely used contemporary textbook, Principles of Economics, the definition has become even more concise. ‘Economics is the study of how society manages its scarce resources,’ it declares—erasing the question of ends or goals from the page altogether (Raworth 2017, 29-30, Kindle Edition).

It is more than a little ironic that twentieth-century economics decided to define itself as a science of human behaviour and then adopted a theory of behaviour—summed up in rational economic man—which, for decades, eclipsed any real study of humans, as we will see in Chapter 3. But, more crucially, during that process, the discussion of the economy’s goals simply disappeared from view. Some influential economists, led by Milton Friedman and the Chicago School, claimed this was an important step forwards, a demonstration that economics had become a value-free zone, shaking off any normative claims of what ought to be and emerging at last as a ‘positive’ science focused on describing simply what is. But this created a vacuum of goals and values, leaving an unguarded nest at the heart of the economic project. And, as every cuckoo knows, such a nest must be filled (Raworth 2017, 30, Kindle Edition).

Dumuzid and Enkimdu

This is a debate between Dumuzid, the shepherd, and Enkimdu, a minor deity associated with cultivation and here representing the interests of the farmer…. Shepherds and farmers coexisted in the Mesopotamian economy and, while they may have had their differences, in many ways their interests were complementary. (Black 2004, 40)

Here the debate is out in a dramatic context, since Inana’s brother the sun-god Utu is urging her to marry Dumuzid the shepherd (11-19), whereas Inana is more inclined to marry Enkimdu the farmer (7-10, 20-34). The shepherd insists that nothing which the farmer can offer—woven garments, bear, bread, or beans—is superior to the sheep, milk, curds, cheeses or butter that he, the shepherd, can produce. (Black 2004, 40-64)

But just at the point when the debate might have become heated, following provocation from the shepherd, the farmer declines to argue, and good-naturedly allows the shepherd to graze his sheep on the stubble of the fields, and to water his flocks in the farmer’s canal. The two end up friends, and the farmer will provide the shepherd with wheat, beans, and barley. He will also continue to bring presents for Inana, even when she is married to Dumuzid. (Black 2004)


20-34 ‘The shepherd shall not marry me! He shall not make me carry his garments of new wool. His brand new wool will not influence me. Let the farmer marry me, the maiden. With the farmer who grows colourful flax, with the farmer who grows dappled grain ….’

35-9 These words … the shepherd, Dumuzid … to say …:

40-54  ‘In what is the farmer superior to me …? Enkimdu, the man of the dykes and canals—in what is that farmer superior to me? Let him give me his black garment, and I will give the farmer my black ewe for it. Let him give me his white garment, and I will give the farmer my white ewe for it. Let him pour me his best beer, and I will pour the farmer my yellow milk for it. Let him pour me his fine beer, and I will pour the farmer my soured (?) milk for it. Let him pour me his brewed bear, and I will pour the farmer my whipped milk for it. Let him pour me his beer shandy, and I will pour the farmer my … milk for it.

55-64 ‘Let him give me his best filtered beer, and I will give the farmer my curds (?). Let him give me his best bread, and I will give the farmer my … milk for it. Let him give me his little beans, and I will give the farmer my small cheeses for them. After letting him eat and letting him drink, I will even leave extra butter for him, and I will leave extra milk for him. In what is the farmer superior to me?

65-73  He was chearful, he was chearful, at the edge of the river bank, he was chearful. On the riverbank, the shepherd on the riverbank, now the shepherd was even pasturing the sheep on the riverbank. The farmer approached the shepherd there, the shepherd pasturing the sheep on the riverbank; the farmer Enkimdu approached him there, Dumuzid … the farmer, the king of dyke and canal. From the plain where he was, the shepherd from the plain where he was provoked a quarrel with him; the shepherd Dumuzid from the plain where he was provoked a quarell with him.

74-9 ‘Why should I compete against you, shepherd, I against you, shepherd, I against you? Let your sheep eat the grass of the riverbank, let your sheep graze on my stubble. Let them eat grain in the jewelled (?) fields of Unug, let you kids and lambs drink water from my Surungal canal.’

80-3 ‘As for me, the shepherd: when I am married, farmer, you are going to be counted as my friend. Farmer Enkimdu, you are going to be counted as my friend, farmer, as my friend.’

84-7 ‘I will bring you wheat, and I will bring you beans; I will bring you two-row barley from the threshing-floor. And you, maiden, I will bring you whatever you please, maiden Inana, … barley or … beans.’

88-9 The debate between the shepherd and the farmer: maiden Inana, it is sweet to praise you! (Black, Jeremy et. al., eds. The Literature of Ancient Sumer. Oxford: Oxford University Press; 2004.)

American Taliban: It Is Happening Here

What was emerging from this and similar meetings was a political force — the so-called Religious Right — that injected into the Republican Party a new emphasis on the promotion of religious morality (an area of concern which most early Goldwater activists thought belonged in the private, not public, and not political, arena). The focus of this new religion-centered “conservatism” was not on liberty and limited government but on what Russell Kirk had called the “transcendent moral order.”

By 1989, the Moral Majority, the late Jerry Falwell’s organization which had emphasized religious values across sectarian lines and often shared a common purpose with many conservatives and orthodox Jews, had all but disappeared. In his place rose the Christian Coalition, led by Pat Robertson and Ralph Reed. The Religious Right had become the overtly Christian Right. (Edwards 2008: 40-41)

(….) Through aggressive grassroots activism the movement’s members and supporters won elections, took over party organizations, and dominated party conventions. Later, when George W. Bush’s political advisor Karl Rove would speak of “the Republican base,” this was who he had in mind. (Edwards 2008: 41)

The Christian Right was hardly the Republican base (the party’s voters were often much more moderate in their views than were Robertson and his followers), but because Robertson’s forces tended to dominate conventions and primaries in which voter turnout is often low, they exerted influence far beyond their numbers. In the process, they transformed the republican Party and indeed the conservative movement itself into an arm of religion, precisely the outcome the First Amendment of the Constitution was designed to prevent. There were instrumental in galvanizing the conservative opposition to death with dignity laws in Oregon, private medical decisions in Florida, and scientific advances in the nation’s medical laboratories. (Edwards 2008: 41)

A wall was erected between church and the state … as an extension of the founder’s experience with religious persecution in Europe. Placing religion in a position to dictate, or heavily influence, national policy had led to sanctions, torture, murder, and war. European battlefields were littered with the corpses of men sent to war on behalf of one religious sect or another. In a nation founded on Lockean principles of individual rights, there would be no place given to sectarian terror. (Edwards 2008: 64)

The wall between religion and statecraft serves an additional purpose. The enemy of civility (a necessary ingredient in the governance of a diverse society) is certitude. And nothing breeds certitude more than religious belief. Religion is often a positive force in the lives of individuals, but when the true believer feels compelled to impose upon the whole of the society the truths that have enriched his or her life, the threads that bind us as a nation begin to fray. (Edwards 2008: 123)

(….) Conservatism’s central philosophy has long been based on the regard for the individual rather than the collective. Yet today many are willing to support the imposition of the personal beliefs of some, be they a majority or a minority, on others, who do not subscribe to those beliefs. The title of Sinclair Lewis’s novel about a politician who rose to power on a wave of religious fervor was ironic: It Can’t Happen Here. Its message was: yes, it can. (Edwards 2008: 124)

Because the Constitution’s central premise is liberty — it is a document designed for a free people–it was created to prevent both the concentration of power in a few hands … and the ability of the majority to impose its will on the minority… The rule of law, not the rule of the masses or rulers, defines American constitutional government. But that is a lesson conservatives have forgotten. (Edwards 2008: 128-129)

The Constitution is for all Americans — Catholic, Protestant, Jewish, Buddhist, Muslim, and nonbeliever alike. We are free to practice or not as we deem fit. Religion is a personal thing; government is what we hold in common, and that distinction lies at the heart of American conservatism [opposed to extremist fundamentalism as exhibited above]. Community is not the same thing as government. The U.S. government is a secular institution, and its policy decisions should not be required to conform to religious doctrine. (Edwards, Mickey. Reclaiming Conservatism. Oxford: Oxford University Press; 2008; pp. 40-166) 

Now is the time to remember that our great religious traditions, notably Christianity, once upon a time could not even conceive of reducing religious engagement with public life to a narrow list of hot-button issues. They were too concerned with the whole person and the whole of society to limit their reach to a handful of questions. Now is the time to heed the call to social justice and social inclusion embedded deeply in in the scriptures. (E. J. Dionne Jr., Forward, in Lew Daly (2009) God’s Economy: Faith Based Initiatives & the Caring State. University of Chicago Press)

We Were Warned

America’s Founders and Abraham Lincoln warned us of the danger of elevating a demagogue such as Donald Trump to the highest office in the land and the virulent nature of the “angry mob” of sycophants easily manipulated by such demagogues making up the political base of such right-wing populism as we are witnessing today at the heart of the GOP:

In an 1838 address to the members of the Young Men’s Lyceum of Springfield, Illinois, Lincoln warned that since American democracy could never be overthrown by a foreign invader, the only enemy to be feared was one within: undisciplined passion. Pointing to several recent examples of frontier lynchings, Lincoln deplored “the increasing disregard for law which pervades the country; the growing disposition to substitute the wild and furious passions, in lieu of the sober judgment of the Courts; and the worse than savage mobs, for the executive ministers of justice.” (….) Lincoln warned the young men of his home town that during the generations to come ambitious demagogues would seek to prey upon the passions of the people, unless these were kept under stern control. “Passion has helped us” in rallying the people to the cause of the Revolution, Lincoln acknowledged, “but can do so no more. It will in future be our enemy.” He cautioned: “Reason, cold, calculating, unimpassioned reason, must furnish all the materials for our future support and defence.” Only by the control of passion could American democracy keep from degenerating into anarchy or demagogy. When Lincoln declared that America would stand or fall by “the capability of a people to govern themselves,” he meant this in both a political and a psychological sense.

Howe, Daniel Walker. Making the American Self: Jonathan Edwards to Abraham Lincoln (pp. 142-143). Oxford University Press. Kindle Edition.

Alexander Hamilton, James Madison, and John Hay were the authors of The Federalist Papers:

No document relating to the Constitution of the United States has received more attention than The Federalist Papers. The papers were written in 1787–88 for the purpose of persuading the people of the state of New York to elect a convention that would ratify the proposed Constitution of the United States…. The authors of The Federalist—Alexander Hamilton, James Madison, and John Jay—were practical men, writing under intense pressures, with a strong sense of the campaign strategy they were pursuing. They submerged their individual differences in the collective persona of Publius, who for our purposes may be treated as a single author (Howe 2009, 78-79)…. What Publius fears is that “a torrent of angry and malignant passions will be let loose,” frustrating all attempts at rational discourse. He himself will engage in rational argument, without impugning the motives of individuals…. However he may feel provoked, Publius will take his stance with Prospero in The Tempest:

“Though with their high wrongs I am struck to the quick,
Yet with my nobler reason ‘gainst my fury
Do I take part.” (Howe 2009, 85)

“In all very numerous assemblies, of whatever characters composed, passion never fails to wrest the scepter from reason,” and the more numerous the assembly, “the greater is known to be the ascendancy of passion over reason.” Once dominated by passion, an assembly became a “mob.” (Howe 2009, 86) (….) Publius complained that the Anti-federalists’ rhetoric suggested “an intention to mislead the people by alarming their passions, rather than to convince them by arguments addressed to their understandings.” (….) Publius’s line of argument was not unprecedented: the seventeenth-century English classical republican theorist James Harrington had argued that government should be designed to maintain the supremacy of reason over passion, and had blamed passion for the degeneration of monarchy into tyranny, aristocracy into oligarchy, or democracy into anarchy….. The Federalist quoted Jefferson with approval: “An elective despotism was not the government we fought for.” (….) The demagogue is a sinister figure in The Federalist. He lurks ready to exploit the passions and create a faction. He is the natural enemy of the statesman, who has virtue and the common interest at heart. The Constitution, Publius argues, will provide a context within which the statesman can defeat the demagogue. Fittingly, he both begins and ends his series of letters with warnings against demagogues.

Howe, Daniel Walker. Making the American Self: Jonathan Edwards to Abraham Lincoln (pp. 90-95). Oxford University Press. Kindle Edition.

This very generation is witnessing with the rise of Trumpism an insidious form of right-wing populist extremism and “faction” that seeks to gratify “private passion by public means.” This is the exact kind of “faction” (i.e., the elevation of personal bias and opinion into absolutist totalitarian rhetoric) our Founders feared; the collective expression of “some common impulse of passion, or of interest, adverse to the rights of other citizens, or to the permanent and aggregate interests of the community.” Factions stem from passions writ large inflamed by ambitious demagogues, as we witnessed during Trump’s many campaign rallies were he regularly incites violence, boasting he could murder someone in the street and the “angry mob” would still vote for him. Hamilton warned that in this form, passions become more dangerous than ever: “a spirit of faction” can lead men “into improprieties and excesses for which they blush in a private capacity.” (Howe 2009, 95)

Donald Trump’s demagoguery directed at his ignorant base is aimed at inciting their passions and is bent upon ripping apart the social fabric of our society and tearing down our democratic institutions. The GOP has mainstreamed extremism, and by so doing has signaled the death of any semblance of classical principled conservatism. In the words of the 18th Century Irish statesman Edmund Burke, “All drapery of life is to be rudely torn off… Their liberty is not liberal. Their [anti-science] is presumptuous ignorance. Their humanity is savage and brutal.” By elevating license over liberty, zealotry and extremism over moderation and reason, the GOP has set America on a course Lincoln warned us would happen when we lost our ability to reasonably govern our own passions and prejudices. Trumpism is an existential threat to the very existence of America’s Constitutional form of government and balanced separation of powers. Time is swiftly running out and if we don’t augment our political discourse with a heavy dose of wisdom we will plunge ourselves over the cliff into another “dark ages” of the interregnum of wisdom bearing witness to the inexorable consequences of confusing license for liberty.

Charmed by Dimensional Analysis

I was charmed when as a young student I watched one of my physics professors, the late Harold Daw, work a problem with dimensional analysis. The result appeared as if by magic without the effort of constructing a model, solving a differential equation, or applying boundary conditions. But the inspiration of the moment did not, until many years later, bear fruit. In the meantime my acquaintance with this important tool remained partial and superficial. Dimensional analysis seemed to promise more than it could deliver. (Lemons 2017, ix, emphasis added)

Dimensional analysis has charmed and disappointed others as well…. The problem for teachers and students is that … [t]he mathematics required for its application is quite elementary — of the kind one learns in a good high school course — and its foundational principle is essentially a more precise version of the rule against “adding apples and oranges.” Yet the successful application of dimensional analysis requires physical intuition — an intuition that develops only slowly with the experience of modeling and manipulating physical variables. (Lemons 2017, Preface ix, emphasis added)

A Mistake to Avoid

A model of a state or process incorporates certain idealizations and simplifications. Skill and judgement are required to decide which quantities are needed to describe the state or process and what idealizations and simplifications should be incorporated. Similar skill and judgement are required in dimensional analysis, for the analysis in dimensional analysis is the analysis of a model. And the model we adopt in a dimensional analysis is determined by the dimensional analysis variables and constants we adopt and the dimensions in terms of which they are expressed. (….) While a certain part of dimensional analysis reduces to the algorithmic, no algorithm helps us answer [certain physical questions]. Rather, our answers define the state or process we describe and the model we adopt. We will, on occasion, make mistakes. (Lemons 2017, 11, emphasis original)

Dimensional analysis makes it possible to analyze in a systematic way dimensional relationships between physical quantities defining a model (Higham 2015, 90-91, emphasis added). Dimensional analysis is a clever strategy for extracting knowledge from a remarkably simple idea, nicely stated by Richardson[,] “… that phenomena go their way independently of the units whereby we measure them.” Within its limits, it works excellently, and makes possible astonishing economies in effort. The limits are soon reached, and beyond them it cannot help. In that it is like a specialized tool in carpentry or cooking or agriculture, like the water-driven husking mill … which husks rice elegantly and admirably but cannot do anything else. (Palmer 2015, v, emphasis added)

Hubris leads some to claim to be engaged in modeless modeling despite evidence plainly to the contrary (e.g., stylised facts, etc.). Whether talking of applied mathematics or dimensional analysis, one is by the very nature of the process engaged in mathematical modeling. Those who are arrogant enough to abuse mathematics for polemic purposes are breaking mathematical sense and are often, to put it kindly, philosophically naïve blinded by their own mathematical pride.

Physical (material) things have quantitative relationships that are measurable. A dimensional model uses a number of dimensional variables (physical variables) and constants that describe the model. Dimensional analysis is not a straightforward task for it requires skill and judgment — the same kind of skill and judgment needed to construct a model of a physical state or process. Add the complexity of open social systems and this requires even more skill, judgment, and frankly, enough wisdom to know the difference between a physical quantitative fact and qualitative mind-value judgement.

Some blinded by mathematical pride and/or statistical egotism and/or confused by philosophical materialism/monistic reductionism, not to mention spiritual blindness, fail to make a distinction between quantitative and qualitative observations, both dependent upon concepts experienced in the mind of the scientist whose very supermaterial insight formulates such a misguided self-contradictory monistic and reductive metaphysics.

What is Applied Mathematics?

The Big Picture

Applied mathematics is a large subject that interfaces with many other fields. Trying to define it is problematic, as noted by William Prager and Richard Courant, who set up two of the first centers of applied mathematics in the United States in the first half of the twentieth century, at Brown University and New York University, respectively. They explained that:

Precisely to define applied mathematics is next to impossible. It cannot be done in terms of subject matter: the borderline between theory and application is highly subjective and shifts with time. Nor can it be done in terms of motivation: to study a mathematical problem for its own sake is surely not the exclusive privilege of pure mathematicians. Perhaps the best I can do within the framework of this talk is to describe applied mathematics as the bridge connecting pure mathematics with science and technology.

Prager (1972)

Applied mathematics is not a definable scientific field but a human attitude. The attitude of the applied scientist is directed towards finding clear cut answers which can stand the test of empirical observation. To obtain the answers to theoretically often insuperably difficult problems, he must be willing to make compromises regarding rigorous mathematical completeness; he must supplement theoretical reasoning by numerical work, plausibility considerations and son on.

Courant (1965)

Garrett Birkhoff offered the following view in 1977, with reference to the mathematician and physicist Lord Rayleigh (John William Strutt, 1842-1919):

Essentially, mathematics becomes “applied” when it is used to solve real-world problems “neither seeking nor avoiding mathematical difficulties” (Raleigh).

Rather than define what applied mathematics is, one can describe the methods used in it. Peter Lax stated of these methods, in 1989, that:

Some of them are organic parts of pure mathematics: rigorous proofs of precisely stated theorems. But for the greatest part the applied mathematician must rely on other weapons: special solutions, asymptotic description, simplified equations, experimentation both in the laboratory and on the computer.

Here, instead of attempting to give our own definition of applied mathematics we describe the various facets of the subject, as organized around solving a problem. The main steps are described in figure 1. Let us go through each of these steps in turn. (Higham 2015, 1)

Modeling a problem. Modeling is about taking a physical problem and developing equations—differential, difference, integral, or algebraic—that capture the essential features of the problem and so can be used to obtain a qualitative or quantitative understanding of its behavior. Here, “physical problem” might refer to a vibrating string, the spread of an infectious disease, or the influence of people participating in a social network. Modeling is necessarily imperfect and requires simplifying assumptions. One needs to retain enough aspects of the system being studied that the model reproduces the most important behavior but not so many that the model is too hard to analyze. Different types of models might be feasible (continuous, discrete, stochastic), and for a given type there can be many possibilities. Not all applied mathematicians carry out modeling; in fact, most join the process at the next step. (Higham 2015, 2)

Analyzing the mathematical problem. The questions formulated in the previous step are now analyzed and, ideally, solved. In practice, an explicit, easily evaluated solution usually cannot be obtained, so approximations may have to be made, e.g., by discretizing a differential equation, producing a reduced problem. The techniques necessary for the analysis of the equations or reduced problem may not exist, so this step may involve developing appropriate new techniques. If analytic or perturbation methods have been used then the process may jump from here directly to validation of the model.

Developing algorithms. It may be possible to solve the reduced problem using an existing algorithm—a sequence of steps that can be followed mechanically without the need for ingenuity. Even if a suitable algorithm exists it may not be fast or accurate enough, may not exploit available structure or other problem features, or may not fully exploit architecture of the computer on which it is to be run. It is therefore often necessary to develop new or improved algorithms.

Writing software. In order to use algorithms on a computer it is necessary to implement them in software. Writing reliable, efficient software is not easy, and depending on the computer environment being targeted it can be a highly specialized task. The necessary software may already be available, perhaps in a package or program library. If it is not, software is ideally developed and documented to a high standard and made available to others. In many cases the software stage consists simply of writing short programs, scripts, or notebooks that carry out the necessary computations and summarize the results, perhaps graphically.

Computational experiments. The software is now run on problem instances and solutions obtained. The computations could be numeric or symbolic, or a mixture of the two.

Validation of the model. The final step is to take the results from the experiments (or from the analysis, if the previous three steps were not needed), interpret them (which may be a nontrivial task), and see if they agree with the observed behavior of the original system. If the agreement is not sufficiently good then the model can be modified and the loop through the steps repeated. The validation step ma be impossible, as the system in question ma not yet have been built (e.g., a bridge or a building).

Other important tasks for some problems, which are not explicitly shown in our outline, are to calibrate parameters in a model, to quantify the uncertainty in these parameters, and to analyze the effect of that uncertainty on the solution of the problem. These steps fall under the heading of UNCERTAINTY QUANTIFICATION [II.34].

Once all the steps have been successfully completed the mathematical model can be used to make predictions, compare competing hypotheses, and so on. A key aim is that the mathematical analysis gives new insights into the physical problem, even though the mathematical model may be a simplification of it.

A particular applied mathematician is most likely to work on just some of the steps; indeed, except for relatively simple problems it is rare for one person to have the skills to carry out the whole process from modeling to computer solution and validation.

In some cases the original problem may have been communicated by a scientist in a different field. A significant effort can be required to understand what the mathematical problem is and, when it is eventually solved, to translate the findings back into the language of the relevant field. Being able to talk to people outside mathematics is therefore a valuable skill for the applied mathematician. (Higham 2015, 2)