The common name for several genera of the free-living (turbellarian) flatworms belonging to the order Tricladida, a name that derives from their characteristic three-branched digestive cavities.
Bilharziasis, or snail fever, parasitic disease caused by blood flukes, trematode worms of the genus Schistosoma. Three species are human parasites: S. mansoni, S. japonicum, and S. haematobium.
by Michael Mann & Gavin Schmidt
The precise factors underlying the so-called “Little Ice Age” (LIA) have been intensely debated within the scientific community. One key metric in this debate is the spatial pattern of cooling which may provide a ‘fingerprint’ of the underlying climate change, whether that was externally forced (from solar or volcanic activity) or was part of an intrinsic mode of variability.
- Inductive – Declare answer first from observation, then proceed to prove; eg. mathematical induction.
- Deductive – Proceed to prove then find answer; eg. Sherlock Holmes, Clue. Answer is confirmed at the end.
- Abductive – Abduction is a form of logical inference that goes from observation to a hypothesis that accounts for the reliable data and seeks to explain relevant evidence. The American philosopher Charles Sanders Peirce first introduced the term as “guessing“. …
Abductive reasoning is the third form of logical reasoning and is somewhat similar to inductive reasoning, since conclusions drawn here are based on probabilities. In abductive reasoning it is presumed that the most plausible conclusion also the correct one is. Example:
Major premise: The jar is filled with yellow marbles
Minor premise: I have a yellow marble in my hand
Conclusion: The yellow marble was taken out of the jar
The abductive reasoning example clearly shows that conclusion might seem obvious, however it is purely based on the most plausible reasoning. This type of logical reasoning is mostly used within the field of science and research.
a : a statement offered in explanation or justification
b : a rational ground or motive
c : a sufficient ground of explanation or of logical defense; especially something (as a principle or law) that supports a conclusion or explains a fact
d : the thing that makes some fact intelligible :
- a (1) : the power of comprehending, inferring, or thinking especially in orderly rational ways : intelligence (2) : proper exercise of the mind (3) : sanity
- b : the sum of the intellectual powers
- archaic : treatment that affords satisfaction
- in reason
within reasonable limits
with good cause
definition from Merriam-Webster
Abductive Reasoning– In laymen’s terms abductive reasoning is an argument to the best explanation. It is a form of reasoning that concludes in an abductive argument of what is plausible or most possibly true. Abductive logic is also considered inference to the best explanation. It is choosing the most likely or best hypothesis or explanation based upon the (most) relevant evidence. Some people think that it is closer to inductive reasoning because it is not as sound logically as deducing an argument using pure logic as in deductive reasoning. Others think it is closer to deductive reasoning, because using sound logic one eliminates the most unlikely argument to come to the most reasonable solution. I like to call it, the best compromise between an inductive and deductive argument.
Abduction is normally thought of as being one of three major types of inference, the other two being deduction and induction. The distinction between deduction, on the one hand, and induction and abduction, on the other hand, corresponds to the distinction between necessary and non-necessary inferences. In deductive inferences, what is inferred is necessarily true if the premises from which it is inferred are true; that is, the truth of the premises guarantees the truth of the conclusion. A familiar type of example is inferences instantiating the schema
All As are Bs.
a is an A.
Hence, a is a B.
But not all inferences are of this variety. Consider, for instance, the inference of “John is rich” from “John lives in Chelsea” and “Most people living in Chelsea are rich.” Here, the truth of the first sentence is not guaranteed (but only made likely) by the joint truth of the second and third sentences. Differently put, it is not necessarily the case that if the premises are true, then so is the conclusion: it is logically compatible with the truth of the premises that John is a member of the minority of non-rich inhabitants of Chelsea. The case is similar regarding your inference to the conclusion that Tim and Harry are friends again on the basis of the information that they have been seen jogging together. Perhaps Tim and Harry are former business partners who still had some financial matters to discuss, however much they would have liked to avoid this, and decided to combine this with their daily exercise; this is compatible with their being firmly decided never to make up.
Since Charles Sanders Peirce, it is standard practice to group non-necessary inferences into inductive and abductive ones.
Read more on abduction from the Stanford Encyclopedia of Philosophy.
Other types of reasoning
Reductive Reasoning– Reductive reasoning is a subset of argumentative reasoning which seeks to demonstrate that a statement is true by showing that a false or absurd result/circumstance follows from its denial. It is proving a statement true by reducing to the opposite of it and showing the absurdity of the opposite result. It is logically reasoning to the absurd or reducing to the absurd; hence the name why reductive reasoning is also called Reductio ad absurdum (Latin: “reduction to absurdity”). Reductive Reasoning is also considered a mixture of deductive & inductive reasoning. Inductive, because it strives to prove understanding of what is likely to be true. And deductive because it does resemble traits of critically and rationally of deductively reducing down to a conclusive or non-conclusive argument.
Fallacious Reasoning– Fallacious Reasoning is not real reasoning, it is the faulty premises for critical thinking and logic. One of the tall tell signs of fallacious reasoning is a logical fallacy. A fallacy is usually an error in reasoning and argumentation often due to a misconception, false premises, or presumptuous conclusions.
- Circular Reasoning is actually considered more of a form of fallacious reasoning. It would not be considered valid nor useful in a live debate.
- Deductive Reasoning: What is (absolutely) true?
- Inductive Reasoning: What is observably (most) true?
- Abductive Reasoning: What is most likely true?
- Reductive Reasoning: What is NOT true?
- Fallacious Reasoning: What you think is true?
Reason by Analogy
An analogy is a comparison between two objects, or systems of objects, that highlights respects in which they are thought to be similar. Analogical reasoning is any type of thinking that relies upon an analogy. An analogical argument is an explicit representation of a form of analogical reasoning that cites accepted similarities between two systems to support the conclusion that some further similarity exists. In general (but not always), such arguments belong in the category of inductive reasoning, since their conclusions do not follow with certainty but are only supported with varying degrees of strength. Here, ‘inductive reasoning’ is used in a broad sense that includes all inferential processes that “expand knowledge in the face of uncertainty” (Holland et al. 1986: 1), including abductive inference.
There are three basic types of programming languages.
THE SOUTHERN COMMUNICATION JOURNAL 55 (SUMMER, 1990), 337-354
WORDS AND NUMBERS: MATHEMATICAL DIMENSIONS OF RHETORIC
BY ALLEN H. MERRIAM
This essay investigates how numbers function rhetorically by influencing persuasive appeals, the structure of messages, and our use of .language. The author argues that “three” is the dominant numerical motif of rhetoric in the English language.
“All things are numbers.”1 – Pythagoras sixth century B.C.
“We went from the Seven Dwarfs to the Magnificent Seven.”2 – Richard Gephardt, 1987
Words and numbers represent major elements in human symbol systems. Language and mathematics both communicate ideas through symbols and, indeed, mathematics is a kind of language with its own structures, vocabulary, and capacity to elicit meaning. Although language and mathematics serve complementary functions in communication they have generated a schism within the academic world. Increasingly since the Scientific Revolution scholarship has split between those who seek Truth through language and verbal texts, and those who emphasize numbers, formulas, and statistical analysis. By midtwentieth century C. P. Snow lamented the emergence of “two polar groups,” epitomized by literary intellectuals and scientists, who seemed unable and even uninterested in understanding each other.3 This division prompted poet John Ciardi to suggest that the challenge of the atomic age was to “humanize the scientist and simonize the humanist.” A schism between qualitative and quantitative orientations also fractured the speech communication discipline, provoking calls for rapprochement by Miller and by Sillars.4
The purpose of this article is to demonstrate the overlap between rhetoric and numbers by investigating the uses and significance of numerical phenomena in human discourse. This demonstration in turn suggests that words and numbers serve complementary rather than competing ends.
Kenneth Burke acknowledged the rhetorical potential of numbers when noting that symbolicity includes not only speech but also “all other human symbol systems, such as mathematics, music, sculpture, painting, dance, architectural styles, and so on.”5 If a primary motivation for speech is the ordering of reality then numbers would appear a natural ally of language. Philosophers have long portrayed numbers as a key to apprehending the order of the universe. Plato, whose Academy had inscribed over its entrance “Let no one ignorant of geometry enter here,”6 claimed that the study of arithmetic has an “elevating effect, compelling the soul to reason.”7 An Old Testament poet wrote that God “hast ordered all things in number and measure and weight.”8 St. Augustine believed that number and wisdom are “one and the same thing” because both are unchanging and always true.9 Kepler found inspiration for astronomers in his assumption that “the movements [of the planets] are modulated according to harmonic proportions.”10 Whitehead claimed that pure mathematics may be “the most original creation of the human spirit.”11 Le Corbusier called numbers “weapons of the gods. “12 A recent author even suggested that perhaps God is a number.13
The appeal of numbers as a source of rational order and harmony derives in part from their perceived precision. In contrast to the inevitable ambiguities and abstractions of language numbers seem to possess exactness and objectivity. An old Latin saying held that numbers are incorruptible: Hanc ergo incorruptibilem numeri veritatem. The demands of modern empirical science for precision may imitate, Capra suggested, the ancient Greek belief that mathematical proportion and harmony undergird all Nature.14 Foremost among the Greeks in respect for numbers were the Pythagoreans of the sixth century B.C., whose cult-like devotion was observed by Aristotle:
all other things seemed in their whole nature to be modeled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole of heaven to be a musical scale and a number.”15
Inheriting a reverence for mathematics from the Greeks and Hebrews, medieval Christianity intensified a mixing of theology and “the science of numbers.” Isodore of Seville, Cassiodorus, Bede, and Alcuin all compiled encyclopedias of numbers while Augustine, Hugh of St. Victor, and Aquinas used numbers in the exegesis and allegorical interpretation of the Bible. A literterized preoccupation with order, beauty, and harmony characterized the Renaissance and several Latin treatises detailed the alleged magical powers of “sacred” numbers. Among these were Gergio’s Harmonia Mundi (1533), Agrippa’s De Occulta Philosophia (1533), Du Barta’s Sepmaine (1578), and Bongo’s De Numerorum Mysteria (1618).
NUMBERS AND INVENTION: PERSUASION THROUGH MYSTIFICATION
One of the major ways numbers function rhetorically relates to invention, the source of arguments. Given their inherent symbolic potency, numbers can produce persuasive effects by inducing deeply imbedded connotations and beliefs. Much of the impact of numbers grows out of philosophical and religious systems, given their propensity to uncover metaphysical meaning in symbols.16 But the origins of mystical numbers also emanate from the very nature of the physical universe, the physiology of the human body, and legends and myths. Many numbers have enjoyed special significance; the ancient Babylonians revered every number from one to 60 and associated each with a god.17
A brief survey may illustrate the mystique attached to numbers: Three has enjoyed prominence in many cultures, with the ancient Sumerians, Hindus, Greeks, Egyptians, Buddhists, Chinese, and Christians all conceptualizing deities or cosmologies in terms of a trinity.18 The triangle is thought to be the most stable shape in nature.
Four has been revered as the number of seasons, points of the compass, sides of a square, and, for ancient Greeks, the elements. Indian society was traditionally divided into four major castes and Hinduism viewed the world’s cycles and individual stages of spiritual development in terms of four.19 Buddhism preached “Four Noble Truths” while Christianity used four Gospels and related the points of the cross to “the four winds. “20
Five, as the number of fingers per hand, toes per foot, and senses, was important in China with Confucian philosophy centered on the five relationships, education based on the “Five Classics,” and Sun Tzu’s famous military treatise permeated with five-part categories.21 The Greeks and Romans developed five canons of classical rhetoric, Muslims promulgated the “five pillars” of Islam, and in Indonesia the five taboos (pancha-sila) formed the code of virtue in Hinayana Buddhism supplanting the earlier Javanese cosmology of five finas (celestial beings) thought to represent the five cosmic forces, five elements, five colors, and five directions.22
Seven was significant for the Chinese (who observed the human head has seven openings), Greeks (whose mythology told of Artemus’ seven nymphs becoming the Pleiades or Seven Sisters, a stellar configuration 400 light years from Earth), and Hebrews who observed the seventh day (Shabbath) as a time of rest and based many rituals on the symbolic seven.23 There were seven wonders of the ancient world, seven liberal arts, and cities built on seven hills (Rome, Lisbon, Constantinople). Roman Catholicism formulated the Seven Deadly Sins, Seven Spiritual Works of Mercy, Seven Corporal Works of Mercy, Seven Gifts of the Holy Ghost, Seven Penitential Psalms, and seven sacraments. Shakespeare’s Jaques spoke of the “seven ages” of man.24
Ten assumed practical use in arithmetic calculation, decimal currencies, and the nearly universal metric system of measurement. Hinduism’s Rig Veda consists of ten books, Mosaic Law was codified as Ten Commandments, the Jewish custom of tithing grew out of a belief that “the tenth shall be holy unto the Lord” (Leviticus 27:32), and Jesus gave parables about ten virgins (Matthew 25:1) and ten lepers (Luke 17:17).
Twelve has a distinguished history including the twelve labors of Hercules in Greek mythology, the twelve tables of Roman law, the twelve tribes of Israel, and Jesus’ twelve disciples. A prominent sect of Shi’ites in Iran, the “Twelvers,” awaits the return of the Twelfth Imam to reform the world through Islamic purity.25 Twelve avenues emanate from the Arc d’ Triumph, the symbolic center of Paris. Modern timekeeping is based on twelve months in a year, twelve signs of the Zodiac, and 24 (12 times 2) hours in a day.26
While certain numbers have been viewed historically as auspicious, others assumed negative associations. Evil connotations of “thirteen” can be traced to Norse mythology and early Christian thought; fear of thirteen has been so pervasive in Western societies that it has its own folklore and psychological term-triskaidekaphobia.27 The number “69” has invited cultural taboos, undoubtedly due to its overt sexual connotations. And “666” has been denigrated as the supposed sign of the beast in Revelation 13:18.28 Clearly, that aspect of symbolism which allows man beings to distinguish between socially positive language prayers, euphemisms) and negative language (obscenity, profanity) also applies to numbers.
Besides evoking culturally based assumptions of mystical power, numbers also function rhetorically as sources of legitimation. For example, much advertising seeks to persuade consumers of the value of products with slogans such as “100% Natural” ”20% More,” and “3 of 4 doctors recommend.” The practice of identifying machines, models, and electronic equipment by number (the Pontiac 6000, Boeing 747, Atari 5200, M-16 rifle, etc.) represents a strategy designed to create an aura of precision and technological sophistication. Kenneth Burke, whose own critical theories used mathematical forms including the Demonic Trinity and dramatistic pentad, explained the persuasive power of such a legitimation technique by observing that when symbols possess enigmatic, mysterious, or magical qualities, their rhetorical potential is enhanced .29 Numbers thus assume suasory capacity because their inherent abstraction induces mystification.
Given their ability to generate credibility, the accouterments of mathematics have gained wide acceptance in the discourse of the behavioral and human sciences. Koblitz noted that numbers, equations, graphs, and formulas now penetrate disciplines from anthropology and psychology to history and medical science. But he cautioned that manipulative uses of quantitative argument can produce “mystification, intimidation, an impression of precision and profundity” amounting to “mathematical quackery. “30 McCloskey demonstrated that much mathematical theorizing in economics uses language, metaphor, archetypes, and analogies so that the distinction between “scientific objectivity” and value-laden, intuitive subjectivity is often blurred.31 Davis and Hersh showed how mathematicians were mystified for nearly 1900 years into accepting as true certain logical gaps in Euclidean geometry.32 More recently, they analyzed what they call “rhetorical mathematics,” a kind of academic gamesmanship where elaborate schemes are developed-often with models, axioms, matrices, and sets of variables-to seduce the unsuspecting into believing an unproven theory.33 Clearly, numerically based argument requires checks for logical consistency just as does verbal reasoning.
DISPOSITION: NUMBERS AND MESSAGE STRUCTURE
Numbers also function rhetorically when they influence the ways humans structure thought and process information. Frequently the very architecture of discourse is based on concepts of mathematical proportion and balance. A common method of organizing information involves enumeration, by which evidence is itemized according to numbered sequence. This widely used compositional device was familiar to Aristotle who in the Rhetoric enumerated 28 lines of argument on which enthymemes can be based.34
When used in the structural organization of a speech, numbers can later serve as the rallying cry for an entire campaign or movement. Sun Yat-sen promoted revolution in China beginning in 1905 with his San Min Chu I or “Three Principles of the People” which formed the core of his ideology.35 Woodrow Wilson’s “Fourteen Points” speech of January 8, 1918 set forth his vision of European reorganization following World War 1.36 Mohammed Ali Jinnah’s “Fourteen Points,” issued in March, 1929, outlined a plan for political reform in British India.37 Franklin Roosevelt’s “Four Freedoms” speech of January 6, 1941 became a popular summary of American goals in World War II.38 In Indonesia, Sukarno’s Pantja Sila (“Five Principles”) speech of June 1, 1945 conveyed the essential elements of Indonesian nationalism while appealing to the powerful connotations of “five” in that culture noted above. Sukarno in 1959 developed an acrostic of five principles (USDEK) which formed his political manifesto and the outline for much subsequent oratory.39 Ronald Reagan summarized his economic policies in the “Four Economic Freedoms” speech of July 3, 1987.40
Numbers have often been used to structure literary works, as poets deliberately constructed numerological allegories to “reveal the structure of reality.”41 Thus, writers from Boccacio, Spenser and Milton to James Joyce, Thomas Mann, and Erik Lindegren have created works according to mathematical patterns.42 The ancient Chinese book of wisdom, I Ching, and Dante’s Divine Comedy (1321) are among the most striking examples of number symbolism in world literature.43 Japanese haiku utilize rigid number patterns, as seventeen syllables typically appear in a ratio of 5:7:5 in three lines corresponding to the “where, what, when” of a poem.44
Many themes and legends in contemporary folklore, children’s stories, and Hollywood films have origins in numerically structured literature, from the Arabic classic The Thousand and One Nights to Grimm Brothers’ stories such as “The Twelve Dancing Princesses” and “The Six Swans.” The perusal of a typical newsstand or bookstore in modern America can reveal an extensive amount of number-oriented articles and ideas, such as, McCall’s “10 Tips for a Happier Marriage,” Dale Carnegie’s “6 Ways to Make People Like You,” Fortune’s 500 biggest corporations, and college basketball’s “Top Twenty.” Numbers often form the organizing pattern for books, such as Marshall Fishwick’s Seven Pillars of Popular Culture, John Reed’s Ten Days That Shook the World, Charles Fillmore’s Twelve Powers of Man, and Gustave Miller’s 10,000 Dreams Interpreted. Clearly, numbers possess considerable popular appeal in the rhetorical structuring of our world.
While mathematical patterns influence thought and language, they also permeate musical composition. Since rhetoric and music both employ symbols and sounds to communicate ideas and feelings, they share an inherent concern with beauty and order.45 The structure of music requires rhythmic patterns and sound sequences often expressed in numbers: three-four time; quarter, half, and eighth notes; octaves; minor sixths; etc. Leibnitz observed that “music is a secret mathematical exercise, and he who engages in it is unaware that he is manipulating numbers.”46 Thus musical creativity from the Pythagoreans to Schoenberg has involved mathematical patterns of proportion and structure,47 with some compositions of J, S. Bach based on the overt exploitation of numbers such as three, ten, 21 and 356.48
NUMBERS AND LANGUAGE STYLE
An important rhetorical function of numbers involves their extensive use in naming our reality. Schiappa observed that “the most persuasive metaphors are those drawn from ordinary discourse”49 since commonplaces underscore unity among users of such language. Not only do numbers achieve immediacy in impact but they also tend to be easily remembered. The mnemonic quality of numbers derives from their clarity and specificity, because they are normally learned early in childhood thus becoming ingrained in our mind, and because unlike other abstractions they possess a precise meaning.50 All of these characteristics-simplicity, exactness, dramatic impact, and ease in recall-are observable in film titles such as “2001,” “10,” “Fahrenheit 451,” and “The Seventh Seal.” When names employ numbers with positive connotations, their impact intensifies. Thus, modern Americans drink “7-Up,” shop at “7-Eleven” stores, and enjoy James Bond as “Agent 007.”
Numbers also affect style in the form of witticisms, sayings, and idioms. Such phrases as being on “cloud nine,” feeling “all sixes and sevens,” and getting “behind the eight ball” have specialized meanings within American culture. The words “lucky seven” and “third time’s a charm” conjure mystical qualities long associated with those numbers. We use idiomatic expressions such as “killing two birds with one stone” and having “two strikes against you.” The journalistic “30” signals the end of an article or essay.
The number “1000” has served as a vivid metaphor for bigness or eternity. For example, Moses wrote that “a thousand years in thy sight are as yesterday “51 and a Hindu portrayal of God was recalled by physicist Robert Oppenheimer at the explosion of the first atomic bomb in New Mexico on July 16, 1945:
“If the radiance of a thousand suns
Were to burst at once upon the sky
That would be like the splendor of the Might One. . .
I am become Death, the destroyer of worlds.”52
Images of immortality were likewise implicit in Hitler’s 1934 proclamation that the Third Reich would last a thousand years,53 and in Nehru’s eulogy for Gandhi: “. . . a thousand years later that light will still be seen.”54 Speakers use this metaphor when trying to achieve emphasis, as in 1972 when George McGovern said he supported Thomas Eagleton “1,000 per cent” and during the 1988 campaign when George Bush promoted volunteerism by envisioning a “thousand points of light.”
Numbers also influence style in the form of dates. Synecdoches like “the fourth of July” in the United States and “el cinco de mayo” in Mexico, and “Double Ten Day” (October 10th) in Taiwan name holidays which elicit national pride. Dates can evoke powerful feelings in specific audiences (1066 to Britons. 1517 to Protestants, 1492 and 1776 to Americans, 1933-45 to Holocaust survivors, August 6, 1945 to anti-nuclear activists, etc.). Functioning enthymemically, a single date can encapsulate an entire reservoir of meaning within listeners. The use of precise dates can also add emphasis to an idea. Franklin Roosevelt achieved more dramatic impact by saying “Yesterday, December 7, 1941, a date that will live in infamy . . .” than if he had omitted the date. Similarly, Martin Luther King, Jr. derived symbolic effect in his 1963 “I Have a Dream” speech when referring to the Emancipation Proclamation of “five score years ago,” thereby connecting his message to Abraham Lincoln’s “four score and seven” phrasing at Gettysburg. In turn, that Biblical style undoubtedly gave Lincoln’s rhetoric greater impact than if he merely had said “a few generations ago . . .”
Numbers also are used to name historical periods, events, and persons. The “Hundred Years’ War” (conflicts between England and France from 1337 to 1453), the “Thirty Years’ War” (from 1618 to 1648 in Europe), and Franklin Roosevelt’s First Hundred Days” represent popular terms to simplify complex historical phenomena. Such naming can be persuasive when used to stir pride in an audience, as in the allusion to Roosevelt’s presidency in John Kennedy’s Inaugural Address:
“All this will not be finished in the first hundred days.
Nor will it be finished in the first one thousand days,
nor in the life of this administration, nor even perhaps
in our lifetime on this planet. But let us begin. “55
When used in the assumed name or title of political or religious leaders numbers connect their holders to their predecessors. Thus, titles like King George VI, Pope John XXIII, and the 14th incarnation of the Dalai Lama communicate a sense of tradition and continuity. Protest groups, when labeled with a number, seem to assume a legal identity of their own as seen in the “Chicago Seven,” the “Catonsville Nine,” the “Wilmington ‘Fen,” the “Siberian Seven,” the “Sharpeville Six,” and the “Gang of Four.”
Finally, numbers influence language when they name a goal or challenge to be met. The 3000 mark for the Dow Jones Industrial Average, a 300 game in bowling, a .500 average (winning as many as one loses) in competition, the “four minute mile” for runners, the “million dollar club” in real estate sales, or “living to be 100” provide targets for which to strive. When so used numbers operate both descriptively (by labeling the goal) and persuasively (by encouraging people to reach it). The numbers represent both a name and a motivation.
THE DOMINANCE OF “THREE” IN RHETORIC
Of all the numbers undergirding human discourse, “three” appears to stand out as the dominant numerical motif for users of the English language. People in the United States, for example, tend to speak in clichéd phrases with three components:
tall, dark, and handsome
Tom, Dick, and Harry
win, lose, or draw
wine, women, and song
eat, drink, and be merry
lock, stock, and barrel
a hop, skip, and a jump
hook, line, and sinker
the good, the bad, and the ugly
stop, look, and listen
ready, get set, go
morning, noon, and night
fair, fat, and forty
mind, body, and spirit
beg, borrow, or steal
thought, word, and deed
vim, vigor, and vitality
Americans talk about the “three R’s” of education, expect stories to have a beginning, middle, and end, and view life from the temporal perspective of past-present-future. Political views often are described as conservative, moderate, or liberal; social stratification focuses on lower, middle, and upper classes; and witnesses in court swear to tell “the truth, the whole truth, and nothing but the truth.” The U.S. flag has three colors, there are three branches of government, and horse racing and baseball have “triple crowns.” First, second, and third prizes (gold, silver, and bronze) often are awarded in competitions; circuses typically have three rings; and speeches are thought to have three sections (Introduction, Body, Conclusion). Hair colors are frequently divided into blondes, brunettes, and redheads; eating utensils consist of forks, knives, and spoons; and military strategy often is conceived in terms of land, sea, and air. Children are taught stories like “Goldilocks and the Three Bears” and “The Three Musketeers” and songs such as “Three Blind Mice” and “I Saw Three Ships.” Even jokes often contain three elements (e.g., priest, minister, rabbi) with the first two creating tension resolved by the third. So pervasive is the propensity to think and speak in threes that Condon and Yousef portrayed it as a fundamental hallmark of American cultural rhetoric.56
A few examples can illustrate this tendency to structure language in patterns of three. In the Declaration of Independence Thomas Jefferson enumerated the inalienable rights of “life, liberty, and the pursuit of happiness.” Lincoln at Gettysburg said “we cannot dedicate, we cannot consecrate, we cannot hallow this ground” and celebrated government “of the people, by the people, for the people.” Thoreau, in Walden, extolled “Simplicity, simplicity, simplicity!” and poet Gertrude Stein wrote “a rose is a rose is a rose.” George Wallace in 1963 advocated “segregation now, segregation tomorrow, and segregation forever” while Martin Luther King, Jr. countered with a dream of “free at last, free at last, thank God Almighty we’re free at last.” Edward Kennedy eulogized his brother Robert in 1968 as a man who “saw wrong and tried to right it, saw suffering and tried to heal it, saw war and tried to stop it.” Ronald Reagan in 1988 blamed the national deficit on the “iron triangle” of the media, lobbyists, and Congress. Students Against Drunk Driving sponsored a terse radio message: “You drink, you drive, you die.”
The predilection for saying things in threes extends to the common usage of initials. For example, in the USA there are businesses like AT&T, IBM, and TWA, usually headed by a CEO. There are governmental agencies such as the IRS, FBI, CIA. and FDA. The mass media involve such terms as ABC, NBC, CNN, HBO, and VCR. Sports organizations include the NFL, AFL, NBA, and AAU. There are professional societies such as the AMA, APA, SCA, and ICA and social and political groups like the GOP, KKK, VFW, NRA, and PTA. Concepts and products in daily conversation might include ESP, IRA, UF0, DWI, GNP, EKG, IUD, etc. Americans even name their presidents with three initials: FDR, JFK, LBJ.
Another illustration of the apparent preference for three-based language was provided in D’Souza and Fossedal’s satire on espionage. They proposed a scheme for creating impressive-sounding political talk by combining any word from each of .three columns:
Thus, one can speak of a “profound harmonious consensus” or a “complex societal network,” etc., forming phrases with strong appeal to American intellectuals, bureaucrats, and media.57 But our survey has indicated that three-part discourse is not restricted by ideology: conservatives (Wallace, Reagan) and liberals (King, Kennedy) both employ it. Numerical patterns appear to be an integral element of American speech regardless of political orientation or persuasive purpose.
All of this is not to deny that people in other cultures and nations also speak in patterns of threes; they obviously do, and have since at least 47 B.C. when Julius Caesar declared “Veni, vidi, vici” following the Battle of Zela. Additional examples include Shakespeare’s “Friends, Romans, countrymen,” the French slogan of 1789 (“Libertie, Equalitie, Fraternitie”), the Nazi cry of “Ein volk, ein Reich, ein Fuhrer,” the Olympic motto (“Faster, Higher, Stronger”), and the Beatles’ song “Yeah, yeah, yeah.”
Nor is it to deny that within English language rhetoric other numerical patterns are used; they certainly are. For example, a two-based pattern is evident in initials such as TV, IQ, UN, OK, and TM, and in Patrick Henry’s “Give me liberty or give me death,” slogans such as “Better dead than Red,” phrases like “the pros and cons,” “the birds and the bees,” “ups and downs,” and Jesse Jackson’s advice: “don’t put dope in your veins, put hope in your brains. “58 A pattern of four undergirds initials like ICBM, NCAA, and RSVP and language used by Malcolm X in 1964: “a problem that will make you catch hell whether you’re a Baptist, or a Methodist, or a Muslim, or a nationalist. “-59 Even five-part phrasing can be effective, as in Martin Luther King, Jr.’s “With this faith, we will be able to work together; to pray together; to struggle together; to go to jail together; to stand up for freedom together knowing that we will be free one day”60 and Robert G. Ingersoll’s “He believed that happiness was the only good, reason the only torch, justice the only worship, humanity the only religion, and love the only priest.61 But the dominant numerical motif seems to be three.
How can we explain the preeminence of three in English language rhetoric? Several explanations might be advanced:
(1) the positive connotations and even mystical powers associated with three in Western civilization, typified by the Christian doctrine of the Trinity, created a mindset favorably disposed to three;
(2) the rhythmic and metrical cadences of English allow three words or phrases to sound pleasing to the ear. Four or five-part rhetoric places heavier burdens on listeners due to the more complex sentence structure involved, while two-part patterns may sound aesthetically incomplete;
(3) the grammatical structures of English encourage thinking in threes. The conjugation of verbs normally corresponds to past-present-future tenses, personal pronouns are organized in sets of three (I, you, he-she-it; we, you, they), and adjectives usually have three forms (slow, slower, slowest, etc.). If, as argued by the Sapir-Whorf Hypothesis,62 language influences our thinking by predisposing us toward certain perceptual tendencies, then the grammar of English subtly guides its users toward speaking in triads;
(4) three-part phrasing seems to function as a signal to one’s audience to respond. In a provocative analysis of the rhetorical devices effective in eliciting audience reactions, Atkinson demonstrated that often the first two items in a series are delivered with rising intonation with the third word or phrase accompanied by falling intonation. This vocal shift, when combined with changes in volume, rhythmic stress and nonverbal behaviors, seems to invite applause ;63
(5) perhaps the very nature of argument supports a three-based pattern of evidence. While two-part reasoning can prove useful in formal debating and “either-or” messages, realism may often cause speakers to move beyond “black/white” thinking to shades of gray. In Hegelian terms, a thesis and antithesis resolve into a synthesis. Two pieces of evidence may be perceived as exceptions and two assertions can be denied, but a third statement lessens resistance to persuasion. As Lewis Carroll put it, “What I tell you three times is true. “64
(6) Holmes suggested that the practice of stringing adjectives and modifiers together in triads (as in “He was honorable, courteous and brave”) results from “an instinctive and involuntary effort of the mind to present a thought or image with the three dimensions that belong to every solid,-an unconscious handling of an idea as if it had length, breadth, and thickness.”65
(7) speaking in threes derives subtle reinforcement from cultural institutions, notably baseball. A sport whose terminology permeates American speech, the national pastime is built on threes: three strikes, three outs, three bases (plus home), three fields (left, center, right), nine players, nine innings, etc. Perhaps Jacque Barzun was correct in advising: “Whoever wants to know the heart and mind of America had better learn baseball. “66
We have demonstrated an intimate connection between mathematics and language. Numbers function rhetorically when they influence how people use words, structure messages, and respond to persuasive appeals. Cultures from India and Indonesia to ancient China and medieval Italy have attributed mystifying powers to numbers; “three” is arguably the dominant numerical motif of English speakers in the United States.
Rhetorical critics and theorists can find it productive to analyze discourse influenced by number patterns, mathematical metaphors, and quantitative argument. Specific areas for further research might include: (1) how do prominent rhetors use mathematical elements in their speaking? (2) what numerical patterns dominate other languages and cultural rhetorics? (3) in terms of the brain’s processing of symbols, how does being “numerate” relate to being “literate?” (4) what can quantitative argument teach us about the nature of persuasion? and (5) does the plethora of numbers in modern life, compounded by the computer revolution, indicate shifts from analogic reasoning toward more digital thinking?
Popular interest in horoscopes, astrology, biorhythmic analysis, and related phenomena suggests that some of the impulses which motivated the Pythagoreans 2600 years ago remain active today.67 As long as numbers influence the speech, behavior, and perceptions of people their rhetorical significance must be acknowledged and understood.
1 Fritjof Capra, The Tao of Physics (New York: Bantam, 1984) 19.
2 Missouri congressman commenting after televised debate of Democratic presidential candidates, Time: July 13, 1987 16.
3 C. P. Snow, The Two Cultures: and a Second Look (New York: Mentor, 1963)
4 Gerald R. Miller, “Humanistic and Scientific Approaches to Speech Communication Inquiry: Rivalry, Redundancy, or Rapprochement,” The Western Journal of Speech Communication 39 (1975) 230-239, and Malcolm O. Sillars, Communication Research: The Uncertain 80’s,” Spectra: February, 1981 5-6.
5 Kenneth Burke, Language as Symbolic Action: Essays on Life, Literature, and Method (Berkeley: University of California Press, 1966) 28.
6 Morris Kline, Mathematics in Western Culture (Oxford: Oxford U P, 1953) 110.
7 Plato, The Republic, Book VII (525b) in The Dialogues of Plato trans. by Benjamin Jowett, Great Books of the Western World, Vol. 7 (Chicago: Encyclopaedia Britannica, 1975) 393.
8 Song of Solomon 11:21.
9 Augustine, “On Free Will,” Book 11, xi, 30 in Augustine: Earlier Writings .rans. by John Burleigh (Philadelphia: Westminster Press, 1953) 154.
10 Christopher Butler, Number Symbolism (London: Routledge and Kegan Paul, 1970) 89.
11 Alfred North Whitehead, Science and the Modern World (1925; New York: Mentor, 1962) 25.
12 Le Corbusier, The Modulor (Cambridge: Harvard U P, 1954) 220.
13 Keith Ellis, Numberpower in Nature, Art and Everyday Life (New York: St. Martin’s Press, 1978) 174.
14 Capra 19.
15 Aristotle, Metaphysics, Book I, Ch. 5. Some Greeks even reified numbers as when Plutarch described odd numbers as male and even numbers as female. See Plutarch’s Essays and Miscellanies ed. by A. H. Clough and W. W. Goodwin, IV (New York: Colonial, 1905) 485.
16 See Paul Tillich, “The Meaning and Justification of Symbols” in Studies in Religious Philosophy ed. by Robert W. Hall (New York: American Book Co.,1969) 809.
17 Tobias Danzig, Number, the Language of Science (New York: Free Press, 1954) 41.
18 See Emory B. Lease, “The Number Three: Mysterious, Mystic, Magic,” Classical Philology 14 (1919): 56-73; and Carl Jung, “A Psychological Approach 10 the Dogma of the Trinity” in The Collected Works of C. G. Jung, XI (Princeton: Princeton U P, 1962) 107-200.
19 Heinrich Zimmer, Myths and Symbols in Indian Art and Civilization, Bollingen Series VI (Princeton: Princeton U P, 1972) 13-42.
20 A. W. Buckland, “Four as a Sacred Number,” Journal of the Anthropologic Institute of Great Britain and Ireland 25 (1896): 96-102.
21 Sun Tzu, The Art of War trans. by Samuel B. Griffith (New York: Oxford University Press, 1963).
22 Allen M. Sievers, The Mystical World of Indonesia (Baltimore: Johns Hopkins U P, 1974) 8-9.
23 See Genesis 2:2-3 and 7:2-3; Exodus 23:11; I Samuel 6:1; Numbers 19:11 and 23:1; etc.
24 As You Like It, II vii, 139-166.
25 See Abdul Aziz Sachedina, Islamic Messianism: The Idea of Mahdi in Twelver Shi’ism (Albany: State University of New York Press, 1981); and Carl Brockelmann, History of the Islamic Peoples trans. by Joel Carmichael and Moshe Perlmann (New York: Capricorn, 1973) who discusses (p. 425) the role of sacred numbers in Islam, especially “19” associated with Ali Muhammad, a mystic reformer executed in Iran in 1850.
26 An interesting alternative to our system of 1440 (24 times 60) minutes in a day involved water clocks created in the Western Han Dynasty in China (est. 202 B.C.) which divided days into 100 equal parts of 14.4 minutes each. See The Cambridge Encyclopedia of China (Cambridge: Cambridge U P, 1982) 391.
27 See “Why Is 13 Unlucky?” in Ellis 55-70.
28 Henry A. Sanders, “The Number of the Beast in Revelation,” Journal of Biblical Literature 36 (1918): 95-99.
29 Kenneth Burke, A Rhetoric of Motives (Berkelev: University of California Press, 1969) 174.
30 Neal Koblitz, “Mathematics as Propaganda” in Mathematics Tomorrow ed. by Lynn A. Steen (New York: Springer-Verlag, 1981) 111-120.
31 Donald N. McCloskey, The Rhetoric of Economics (Madison: University of Wisconsin Press, 1985) 42-83.
32 Philip J. Davis and Reuben Hersh, Descartes’ Dream: The World According to Mathematics (New York: Harcourt Brace Javanovich, 1986) 68.
33 Philip J. Davis and Reuben Hersh, “Rhetoric and Mathematics” in The Rhetoric of the Human Sciences; Language and Argument in Scholarship and Public Affairs ed. by John S. Nelson, et. al. (Madison: University of Wisconsin Press, 1987) 53-68.
34 Aristotle, Rhetoric, Book II, Ch. 23.
35 Sun Yat-sen in Sources of Chinese Tradition comp. bv William Theodore de Bary, et. al. (New York: Columbia U P, 1960) 767-786
36 Fourteen Points Address” in Papers of Woodrow Wilson ed. by Arthur S. Link, et al. 45 (Princeton: Princeton U P. 1984) 534-539.
37 See Sharif Al Mujahid, Quaid-i-azam Jinnah, Studies in Interpretation (Karachi: Quaid-i-azam Academy, 1981) 473-481.
38 Franklin D. Roosevelt, “Four Freedoms Speech” in Nothing to Fear ed. by B. D. Zevin (Boston: Houghton Mifflin, 1946) 258-276.
39 See Sievers 7-8; and Bernhard Dahm, Sukarno and the Struggle for Indonesian Independence trans. by Mary Ellen Heidhues (Ithaca: Cornell U P 1969).
40 “Reagan Vows to Alter Budget Process,” The New York Times 4 July 1987 5.
41 Butler 132.
42 See Vincent Foster Hopper, Medieval Number Symbolism (New York: Peter Cooper, 1969); Alastair Fowler, Spenser and the Numbers of Time (London: Routledge and Paul, 1964); and Gunnar Qvarnstrom, Poetry and Numbers; on the Structural Use of Symbolic Numbers (Lund: CWK Gleerup, 1966).
43 See Robert T. Oliver, Communication and Culture an Ancient India and China (Syracuse: Syracuse U P, 1971) 157-160; and John J. Guzzardo, Dante: Numerological Studies (New York: Peter Lang, 1988).
44 Kenneth Yasuda, The Japanese Haiku; its Essential Nature, History and Possibilities in English (Rutland, VT: Charles E. Tuttle, 1968) 27-68.
45 See Gregory C. Butler, “Fugue and Rhetoric,” Journal of Music Theory 21:1 Spring, 1977) 49-109, and Wilibald Gurlitt, “Musik und Rhetorik,” Helicon 5 : 944) 67-86.
46 Le Corbusier 74.
47 See Andre Barera, “The Consonant Eleventh and the Expansion of the Musical Tetractys: a Study of Ancient Pythagoreanism,” Journal of Music Theory 28 (Fall, 1984): 191-223 and Martha M. Hyde,
“Musical Form and the Development of Schoenberg’s Twelve-Tone Method,” Journal of Music Theory 29 (1985): 85-143.
48 See Robert L. Weaver (ed.), Essays on the Music of J. S. Bach (Louisville: University of Louisville Press, 1981), and Martin Jansen, “Bach’s Zahlen-Symbolik,” Bach Jahrbuch (1937) 96-116.
49 Edward Schiappa, “The Rhetoric of Nukespeak,” paper presented at the Central States Speech Association convention, St. Louis, MO (April, 1987) 1.
50 W. F. Leopold, “A Child’s Learning of Numerals,” Quarterly Journal of Speech 35 (April, 1949): 202-209.
51 Psalm 90:4.
52 Bhagavad Gita 11:12 and 32; see Robert Jungk, Brighter Than a Thousand Suns; a Personal History of the Atomic Scientists (New York: Harcourt, Brace, 1958) 201.
53 William L. Shirer, The Nightmare Years, 1930-1940 (Boston: Little, Brown, 1984) 121.
54 Jawaharlal Nehru, eulogy for Mohandas Gandhi, in A Treasury of the World’s Great Speeches ed. by Houston Peterson (New York: Simon and Schuster, 1965) 810.
55 John F. Kennedy, Inaugural Address, in Peterson 834.
56 John C. Condon and Fathi Yousef, .An Introduction to Intercultural Communication (Indianapolis: Boobs-Merrill, 1975) 233-235.
57 Dinesh D’Souia and Gregory Fossedal, My Dear Alex; Letters from the KGB (Washington, D.C.: Regnery Gateway, 1987) 6-7.
58 Quoted in William Safire, “Ringing Rhetoric: the Return of Political Oratory” The New York Times Magazine: August 19, 1984 108.
59 Malcolm X, “The Ballot or the Bullet,” in The Voice of Black America ed. by Philip S. Foner, II (New York: Capricorn, 1975) 370.
60 Martin Luther King, Jr., “I Have a Dream,” in Peterson 860.
61 Robert G. Ingersoll, eulogy for Ebon Ingersoll, in Peterson 620.
62 See Harry Hoijer (ed.), Language in Culture (Chicago: University of Chicago 1954).
63 Max Atkinson, Our Masters’ Voices; the Language and Body Language of Politics London: Methuen, 1984) 63.
64 Lewis Carroll, “The Hunting of the Snark,” 1, 8 in The Complete Works of Lewis Carroll (New York: Modern Library, n.d.) 757.
65 Oliver Wendell Holmes, The Autocrat of the Breakfast Table (Boston: Ticknor and Fields, 1865) 100.
66 Quoted in Lawrence Frank, Playing Hardball: the Dynamics of Baseball Folk Speech (New York: Peter Lang, 1983) 5.
67 For descriptions of the philosophy and practices of numerology see Gopi Sharma, The Science of Numbers (Delhi: Ajanta,1984); and Juno Jordan, Numerology (Marina del Rey, CA: De Vorss, 1977)
Dr. Allen Merriam is Professor of Communication at Missouri Southern State University. He can be reached by email at email@example.com.
Newton’s Laws of Motion were first published in his work Philosophiae Naturalis Principia Mathematica (1687). Newton used them to prove many results concerning the motion of physical objects. In the third volume (of the text), he showed how, combined with his law of universal gravitation, the laws of motion would explain Kepler’s laws of planetary motion.
- 1 Newton’s First Law: Law of Inertia –
Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
"An object at rest or traveling in uniform motion will remain at rest or traveling in uniform motion unless acted upon by a net force."
- 2 Newton’s second law: Law of Motion –
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimtur.
"The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction."
- 3 Newton’s third law: law of reciprocal actions –
Lex III: Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones is se mutuo semper esse aequales et in partes contrarias dirigi.
"All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction."
Any muscle having three heads, or points of attachment, but especially the triceps brachii at the back of the upper arm. One head originates on the shoulder blade and two on the upper-arm bone, or humerus. Uniting part of the way down the arm, the heads swell into the belly, or muscle proper. This tapers to a tendon that rounds the elbow and attaches to the ulna, the larger of the two forearm bones. Since contraction of the triceps straightens the arm, the muscle is called an extensor. It also helps lock the elbow when the forearm pushes forward against resistance. The triceps works in coordination with a flexor muscle, the biceps brachii of the upper arm.
Triple point is the intersection on a phase diagram where three phases coexist in equilibrium. The most important application of triple point is water, where the three-phase equilibrium point consists of ice, liquid, and vapor. Before discussing triple point further, a basic understanding of the lines from Figure 1, the phase diagram of water, are first considered. Continue reading Triple Point
Concerning the redundancy of all mission equipment, we have adhered to NASA policy requiring double redundancy for all mission critical factors and triple redundancy for all life critical factors. The redundancies are most clearly explained by breaking down the entire mission into two different phases, transport and surface. We define a transport phase to be any period of time spent traveling to or from mars, for example the T.M.I. journey. The surface phase is simply the period of time spent inhabiting the mars surface.
The structure of the human body is organized into groups of three with remarkable frequency. I have listed several examples of this tendency by region. This list does not include structures contributing to form the many “triangles” in the body. If you know of any more, please let me know.
John A. McNulty, Ph.D.
Historically, this was the first hyperlink to the Book of Threes in 1996 thanks to John McNulty . . .
To visit John McNulty’s amazing list, click here.
(Adapted from "The Twenty-fifth Anniversary Year Book", The Radio Club of America, Inc., 1934)
A HISTORY OF THE
RADIO CLUB OF AMERICA, Inc.
by: George E. Burghard
The story of the Radio Club of America begins over a quarter of a century ago, during the really dark ages of the radio art, about 1907