Paideia High School Curriculum Plan
Beginnings of a Paideia High School Curriculum Plan Skill-Based Focus
The three Paideia books argue that Column Two should rule the time spent in a paideia school. Some 65% to 75% of the time should be spent on the skills of learning, the liberal arts of reading, writing, speaking, listening, calculating, problem-solving, observing, measuring, and estimating. The traditional liberal arts are the trivium (grammar, logic, and rhetoric) and the quadrivium (arithmetic, music, geometry, and astronomy). In general, one may say that the liberal arts are the skills of learning. The two terms are interchangeable. The list provided in the Paideia books is simply an updated enumeration of these arts based on the very same principles as the more traditional list of seven. The paideia approach combines the best of innovation and tradition. These considerations lead to a clear conclusion: Any curriculum plan for a paideia school should be anchored in “Column Two.” This deduction is also based on the unspoken assumption that most contemporary public school curricula are not rooted in the “Column Two” skills of learning. What, then, is the guiding principle of contemporary curriculum plans that must be abandoned, the wrong grounding in which most modern curricula are based? The answer can be found in the three Paideia books. Column One currently reigns supreme. Knowledge, divided into component categories, governs curriculum plans and dominates schedules. A paideia school must abandon the current curricular paradigm, which may be called “content-based” or “subject-based” for an “arts-based” or “skills-based” model. Don’t Throw the Baby Out With the Bath Water One must be careful with this shift in thinking, however. Building a curriculum plan around “Column Two” does not mean that one should throw out knowledge, subjects, and memory work. Neither does it mean that one should deemphasize “Column Three,” which is arguably the crown of the “Three Columns.” While the curriculum plan must be firmly grounded in “Column Two,” it must also include both “Column One” and “Column Three.” Practice Flips Theory on Its Head The elements of the arts of learning line up one way from a theoretical point of view and the opposite way from a practical viewpoint. The cooperative art of education aims at producing good habits of body, will, and intellect. This listing, which puts body first, is practical. In theory, the development of good habits of mind, the intellectual virtues, is the ultimate aim of education in a paideia school. In theoretical order of importance, then, the list would line up as follows: intellect, will, and body. Yet, parents and teachers must begin in the practical order. Education is, after all, a practical art. As parents, we must begin teaching our own children the simplest bodily skills. A baby cannot even manage burping on his or her own. We then move on to “doing” and shape “good habits of doing,” traditionally known as the moral virtues. We teach our children not to bite their siblings but to share, for example. Finally, we begin teaching the intellectual virtues by coaching our children in the art of using words. Educational practice, then, must proceed from bodily skills to the arts of “doing” and then, finally, to the arts of the will and the intellect. We must first teach good habits of body, then action, and finally knowing and understanding. However, just as the “Three Columns” must be considered not as separate compartments but an integrated whole, so too must the art of education. In our example of the growing baby, we must integrate the skills of walking, behaving, and talking more or less simultaneously. True learning does not fit into airtight compartments. Teaching and learning progress as an integrated whole and cut across all three columns, often simultaneously. It is, though, useful to think in categories. So What Does This Kind of Curricular Plan Look Like? A paideia curricular plan must always see the parts from the point of view of the whole. Nevertheless, any practical scheme must have parts and begin with step one. Thus the arts of learning can be separated into four categories: “Physical and Bodily Arts,” “Scientific Arts,” and “Language Arts.” Each of these arts must be practiced within some subject. The difference in a paideia curriculum plan, however, is that the arts have a primary focus and must be given the time they demand—a full 75% of the time if necessary and not less than 65%. Finally, the intellect must be given its due. After competence in the “Column One” realm of memory, imagination, and skill, the intellect must be nurtured in the “Column Three” realm of understanding and wisdom. To this end, performance must be included for each of the arts of learning through seminars, demonstrations, contests, and involvement in artistic activities like music, drama, and visual arts. Curricular Schema Physical and Bodily Arts Scientific Arts Language Arts Primary Focus—Column Two (65%-75%) Gross Motor, Fine Motor, Exercise, Using Instruments of Observation and Music Calculating, Problem-Solving, Observing, Measuring, Estimating Reading, Writing, Speaking, Listening, Editing? Secondary Focus—Column Three (15% to 20%) Physical Performance and Contests Demonstrations and Presentations Seminars, Performance, Expository Writing, and Creative Writing Tertiary Focus—Column One (10% to 15%) Knowledge of Skills, Arts, and Games Scientific, Mathematical, and Artistic Knowledge Knowledge of Literature, Fine Arts, History, Geography, and Social Science
[insert more explanation of the table ]
Planning Units around Works How does a teacher implement a specific plan for student learning within this schema? The answer lies in the paideia school’s choice of works to be studied, the same works by every teacher and student. The work chosen will, first of all, exercise the arts of learning, secondly identify the ideas and values in the work, and finally determine the necessary background knowledge. In this way, every work will determine learning activities in “Column One,” “Column Two,” and “Column Three” with the primary focus being on “Column Two.” While not every work will be the subject of a separate “Column Three” activity, all such activities will draw upon some, perhaps most, of these works. In addition, seminar-type questions should be asked in the course of daily classroom work and they should form mini seminar-style class discussions. The question of order arises again. The order given in the last paragraph is a ranking of “focus,” meaning that most of the scheduled class time is given to “Column Two,” then “Column Three,” and finally “Column One.” However, when planning a unit, the reverse order will often govern the analysis of a work. For example, it is quite easy to recognize a term or topic in a work that assumes background knowledge. It is likewise simple to note that term or topic in a list for didactic instruction. Identifying exactly which “Column Two” arts are best practiced using a given work is less easy. The teacher must often complete a full inspection or analysis of the work before those arts become apparent. For example, Haldane’s On Being the Right Size lends itself well to three specific arts of analytical reading: Identifying the authors most important terms, sentences, and arguments. In this short essay, the arguments in particular are compact and fairly easy to find. However, in the planning stage, a teacher creating a plan from scratch would not be able to drill down to the suitability of this work for developing these specific reading skills right away, certainly not as easy as determining from the first paragraph that a reader must “know” the term “zoologist.” Finally, only with the help of reference materials like the “Syntopical Guide” in The Gateway to the Great Books or the Syntopicon itself can a teacher find all the important ideas in the work. In general, the planning order proceeds in the opposite direction of the order of importance. How does a work determine learning 10% to 15% of the learning activities in “Column One”? Background knowledge is necessary to comprehending any work. The unit developed around the work will include a listing of the background knowledge necessary to comprehend that particular work. If this listing has not been previously produced, the teacher or curriculum developer must create it. This sort of work, so necessary to curriculum development, should be filed for the future and shared. Both traditional and electronic means of filing ought to be considered. The latter has the advantage of providing access to students, parents, and staff both on and off campus. How does a work determine learning activities 65% to 75% of the learning activities in Column Two? The very best works available for the students engaged in learning are chosen precisely for their potential to exercise the skills of learning. The unit plan built around a particular work should list the skills that students can develop through facilitated learning activities. The teacher should choose one or two skills appropriate to the needs of the student or group of students and should avoid choosing too many skills. Over time, a teacher can focus equitably on all the skills of learning by carefully choosing different skills in a methodical manner, always suited to the needs of the students. How are the works used in units of study incorporated into “Column Three” activities comprising 15% to 20% of the learning time? The teacher who understands “Column Three” learning will likely find this to be the easiest of the questions to conceptualize and the most difficult to implement. The reason is that it is fairly simple to think about discussing a work or a collection of works in a seminar. This notion applies with equal ease to performances, publishing, creating works of art, delivering a paper, participating in games, demonstrating a scientific experiment, engaging in a debate, and delivering a speech. However, the skill a teacher needs to effectively lead seminars, performances, etc. are not commonly provided in teacher training programs. They must be a central focus of staff development in a paideia school. Planning a Unit around Activities Related to the Physical and Bodily Arts While the main purpose of a paideia school is to develop the liberal arts related to formation of intellect—knowledge, skills of learning, and understanding of ideas and values—attention to the health and fitness of the body is important too. The focus should be on lifetime skills and activities like golf, hiking, skiing, and games commonly played with friends and family throughout life. Communities have adult leagues for sports, games, and other activities. Family reunions and other gatherings often include various games like croquet, volleyball, bocce ball, horseshoes, and other regional and cultural activities. Before discussing the more obvious gross motor activities, sports, and games it will be good to briefly mention fine motor activities associated with drawing, measuring, building, and playing a musical instrument. The fine-motor skills of using a straightedge and compass are essential to studying geometry, for example. Likewise, fine-motor skills are essential to art, music, and scientific labs. All of these skills, so foundational to intellectual growth, begin at the physical and bodily level. They must not be neglected. Knowledge of specific sports, games, and other activities can and should be taught didactically and immediately coached and practiced. A coaching methodology should be employed. Coaching is used here in a slightly different sense than in the intellectual arts because the word is so much more commonly employed in sports, games, and activities. A good coach incorporates quite naturally each of the “Three Columns” in the paideia pedagogical model. While the coaching of skills is the obvious focus in sports, for example, good coaches spend 10%-15% of their time explaining the knowledge required to perform the skill and 65%-75% of their time coaching students (players, performers, etc.) in the practice of the skill. Finally, 15%-20% of the time is spent in competitive games, activities, and performances. In many important ways, the coaching of physical and bodily arts serves as a model for how all of education ought to be planned and implemented. Planning a Unit around a Work Related to the Scientific Arts Euclid’s Elements serves as an example in the Scientific Arts. “Book One” of the Elements can be completed by a first- or second-year cohort of high-school students. While the Elements would be chosen in the “Scientific Arts” column of the “Curricular Schema” table, it exercises nearly every art of learning in each column. In the physical and bodily arts column, teachers must coach students’ fine motor coordination in order for them to use a straightedge and compass effectively. Exercise of the “Scientific Arts” is mostly obvious. However, the Greeks had a differing concept than our own of calculation based on linear, square, and cubic geometric quantities. Measuring as a “Scientific Art” is not one of the most obvious exercised by Euclid either. Yet, it is not difficult to imagine how students do indeed “measure” with units defined by the distance between the points of a compass as well as squares and cubes of different sizes much the same as they calculate in the Greek way. The “Language Arts” must obviously be exercised when studying Euclid, including speaking and listening to deepen comprehension of the text. And, finally, examples of every skill of critical thinking and judgment come alive in Euclid. It is important, however, for the teacher to carefully teach the arts of learning and have students practice them one at a time. This does not mean that students practice only one art at a time; it simply means that, practically speaking, teaching and learning must focus on one art at a time. Consequently, the teacher must limit the number of arts for coaching and not try to cover them all for each work. Arts not covered using one work can be covered using another. Foundational arts like reading, can and should be a focus of many different units. Of the manifold arts available for practice in Euclid’s Elements, each should be chosen one at a time. A year-one or year-two cohort of students could tackle only “Book One” of Elements and focus on the physical fine-motor skills necessary for completing constructions and the deductive reasoning of an axiomatic system. Understanding Euclid requires much background knowledge. This is why a year-one or year-two cohort of high schools students should tackle a limited amount of the Elements—just “Book One” for example. What is an undefined term? A definition? What is an axiom? A postulate? A self-evident truth? What is an axiomatic system? How do all these elements combine to support such a system? Knowledge related to these questions, and more, is absolutely prerequisite to understanding Euclid’s Elements. Such knowledge must be identified and didactically taught to students who must exercise their memories and imaginations to develop the knowledge base necessary to tackle “Book One” of the Elements. Planning a Unit around a Work Related to the Language Arts While Euclid’s Elements is the second best-selling book of all time (after the Bible), Defoe’s Robinson Crusoe is the second best-selling work of fiction ever (after Homer’s Iliad and Odyssey). Defoe’s popular masterpiece serves well as an example of a work in the “Language Arts.” But so do the Bible, Iliad, and Odyssey. Any work involving reading, writing, speaking, or listening can form the basis of coaching the language arts. Through coaching students to read Robinson Crusoe using the rules described in “The Ways and Whys of Reading” or How to Read a Book, a teacher helps students exercise the language arts. The arts of reading and writing can be coached directly using the rules of reading and note-taking cited in the two works above, the shorter essay or the longer book. Of course, writing could be further exercised by asking for written plot summaries, character sketches, or other such elements of narrative fiction. While a teacher exercises the skills of speaking and listening in students through the questioning and answering proper to “Column Two” coaching, these skills could be further developed in a seminar on the work. “Column One” background knowledge depends completely on the work used to coach the language arts. Historical, cultural, and scientific elements of the time imbue works of narrative fiction like Robinson Crusoe and non-fiction works like Euclid’s Elements. These elements of knowledge must be carefully extracted, listed, and didactically taught and learned before a student can comprehend a work and understand its ideas and values. “Column Three” activities can take several forms if used in relation to specific works chosen to coach the language arts. Seminars will likely be the most frequent activity, but others can enlarge the understanding too. For example, students can publish essays, give speeches, and engage in debates. If the work is a play, students can perform it. There are many rewarding ways to engage in Column Three activities that draw on some (definitely not all) of the works used for coaching the skills of learning and didactically teaching the relevant knowledge. A Sample Unit Plan Planning a unit begins with analyzing the work to be studied. As mentioned above, the planning is likely to proceed in order from “Column One” to “Column Three.” However, the planning also organically integrates elements of each column. For example, a point suitable for “Column One” may trigger a plan for either of the other two columns. There is no substitute for a teacher’s experience of creating his or her own unit plan. A sample plan for Haldane’s On Being the Right Size is included as an appendix. APPENDIX List of Paideia High School Works Year One Cohort IMAGINATIVE LITERATURE •
- Defoe, Robinson Crusoe
Hugo, “The Battle with the Cannon” • Lawrence, The Rocking-Horse Winner • Maupassant, Two Friends • Molière, The Doctor in Spite of Himself • Poe, The Tell-Tale Heart • Scott, The Two Drovers • Shakespeare, Julius Caesar • Shaw, The Man of Destiny • Stevenson, The Strange Case of Dr. Jekyll and Mr. Hyde • Tolstoy, The Three Hermits • Twain, The Man That Corrupted Hadleyburg • Wilde, The Happy Prince CRITICAL ESSAYS • Lamb, My First Play • Woolf, How Should One Read a Book? THE HUMAN PERSON AND SOCIETY • American State Papers: Articles of Confederation • Crèvecoeur, “The Making of Americans” • Hawthorne, Sketch of Abraham Lincoln • Jefferson, Biographical Sketches • Lincoln o Letter to Horace Greely o The Gettysburg Address • Paine, “A Call to Patriots—December 23, 1776” • Pliny the Younger, “The Eruption of Vesuvius” • The English Bill of Rights • Whitman, Death of Abraham Lincoln NATURAL SCIENCE • Boeke, Cosmic View • Haldane, On Being the Right Size • Tyndall, “Michael Faraday” MATHEMATICS • Dantzig o Fingerprints o The Empty Column • Hogben, Mathematics, the Mirror of Civilization • Kasner and Newman o Beyond the Googol o The New Names for Old PHILOSOPHY AND RELIGION • Bible, Genesis • Erskine, The Moral Obligation to Be Intelligent • Plato, Meno MUSIC (PIANO AND MUSIC APPRECIATION ) LANGUAGE ARTS (ENGLISH AND LATIN) • Hutchins, Adler, and Fadiman (Eds.), Gateway to the Great Books, “The Ways and Whys of Reading” • Ørberg, Lingua Latīna Per Se Illustrata: Pars Prīma, Familia Rōmanā • Goldman, English Grammar for Students of Latin List of Paideia High School Works Year Two Cohort IMAGINATIVE LITERATURE • Crane, The Open Boat • Flaubert, The Legend of St. Julian the Hospitaller • Hemingway, The Killers • Homer, The Odyssey • Kipling, Mowgli’s Brothers • Melville, Billy Budd • Poe, The Masque of the Red Death • Shakespeare o The Taming of the Shrew o The Tempest • Swift, Gulliver’s Travels, Parts I-II • Tolstoy, What Men Live By • Virgil, The Aeneid, Books II-III CRITICAL ESSAYS • Hazlitt, Of Persons One Would Wish to Have Seen • Lamb, Dream Children, a Reverie THE HUMAN PERSON AND SOCIETY • American State Papers: The Constitution of the United States of America • Crèvecoeur, Declaration of the Rights of Man and of the Citizen • Herodotus, History, Books I-II • Hume, Of the Study of History • Lincoln o Second Inaugural Address o Last Public Address • Prescott, “The Land of Montezuma” • Stevenson, The Lantern-Bearers • Twain, “Learning the River” • The Virginia Declaration of Rights • Xenophon, “The March to the Sea” NATURAL SCIENCE • Curie, The Discovery of Radium • Fabre, The Sacred Beetle MATHEMATICS • Euclid, Elements, Book I PHILOSOPHY AND RELIGION • Aristotle, Politics, Book I • Bible o Proverbs o Luke • Plato, Republic, Books I, VI, and VII MUSIC (PIANO AND MUSIC APPRECIATION ) LANGUAGE (ENGLISH AND LATIN) • Adler and Van Doren, How to Read a Book • Ørberg, Lingua Latīna Per Se Illustrata: Pars Prīma, Familia Rōmanā • Goldman, English Grammar for Students of Latin List of Paideia High School Works Year Three Cohort IMAGINATIVE LITERATURE • Anderson, I’m a Fool • Apuleius, “Cupid and Psyche” • Aristophanes, The Clouds • Butler, “Customs and Opinions of the Erewhonians” • Chekhov, The Darling • Eliot, G., The Lifted Veil • Gogol, The Overcoat • Pushkin, The Queen of Spades • Shakespeare, The Merchant of Venice • Sophocles, Antigone • Virgil, The Aeneid CRITICAL ESSAYS • Arnold, The Study of Poetry • Bacon o Of Beauty o Of Discourse o Of Studies • Hazlitt, My First Acquaintance with Poets • Lamb, Sanity of True Genius • Whitman, Preface to Leaves of Grass THE HUMAN PERSON AND SOCIETY • Adams, “The United States in 1800” • Bacon o Of Youth and Old Age o Of Parents and Children o Of Marriage and Single Life o Of Great Place • Clausewitz, What is War? • Emerson, Thoreau • The Federalist, Nos. 1-10 • Franklin o A Proposal for Promoting Useful Knowledge among the British Plantations in America o Proposals Relating to the Education of Youth in Pennsylvania • James, W., The Energies of Men • La Bruyère, Characters • Lincoln o Address at Cooper Institute o Meditation on the Divine Will • Montaigne o To the Reader o Of Idleness o Of the Education of Children o Of Cannibals o Of Democritus and Heraclitus • Mill, J. S., “Childhood and Youth” • Plutarch o Of Bashfulness o Theseus o Pericles • Swift o Resolutions When I Come to Be Old o A Meditation Upon a Broomstick • Tacitus, The Life of Gnaeus Julius Agricola • Thucydides, The History of the Peloponnesian War, Bks. I-II, V • Thoreau, A Plea for Captain John Brown • Washington, Circular Letter to the Governors of All the States on Disbanding the Army • Woolf, The Art of Biography • Xenophon, “The Character of Socrates” NATURAL SCIENCE • Bacon, The Sphinx • Eddington, The Running-down of the Universe • Fabre, A Laboratory of the Open Fields • Faraday, The Chemical History of a Candle • Galileo, The Starry Messenger • Hippocrates, The Oath MATHEMATICS • Archimedes, The Sand Reckoner • Forsyth, Mathematics in Life and Thought • Poincaré, Mathematical Creation PHILOSOPHY AND RELIGION • Bacon o Of Truth o Of Death o Of Adversity o Of Love • Bible o Ecclesiastes o Acts • Cicero, On Friendship • Emerson, Self-Reliance • Pater, “The Art of Life” • Plato o Apology o Crito MUSIC (PIANO AND MUSIC APPRECIATION ) LANGUAGE (ENGLISH AND LATIN) • Ørberg, Lingua Latīna Per Se Illustrata: Pars I, Familia Rōmanā • Goldman, English Grammar for Students of Latin • Ørberg , Sermōnēs Rōmanī, Plautus, Cato, Cicero, Phaedrus, Horace, Tacitus, Martial, Pliny, Aulus Gellius, and Lucas • Ørberg, Lingua Latīna Per Se Illustrata: Pars II, Rōma Aeterna
List of Paideia High School Works Year Four Cohort IMAGINATIVE LITERATURE • Anonymous, Aucassin and Nicolette • Balzac, A Passion in the Desert • Cervantes, Don Quixote (inspectional reading only) • Chaucer, The Canterbury Tales, Prologue • Conrad, Youth • Dante, The Divine Comedy, Hell • Dickens, “A Full and Faithful Report of the Memorable Trial of Bardell against Pickwick” • Dostoevsky, White Nights • Euripides, Alcestis • Galsworthy, The Apple-Tree • Hawthorne, Rappaccini’s Daughter • Homer, The Iliad • Melville, Moby Dick • Milton, Paradise Lost • Shakespeare o Hamlet o Macbeth • Voltaire, Micromégas CRITICAL ESSAYS • Arnold, Sweetness and Light • De Quincey o Literature of Knowledge and Literature of Power o On the Knocking at the Gate in Macbeth • Sainte-Beuve, What is a Classic? • Schopenhauer, On Some Forms of Literature THE HUMAN PERSON AND SOCIETY • Bacon o Of Seditions and Troubles o Followers and Friends o Of Usury o Of Riches • Burke, Letter to the Sheriffs of Bristol • Carlyle, The Hero as King • Charter of the United Nations • Faraday, Observations on Mental Education • Hamilton, Madison, and Jay, The Federalist, Nos. 15, 31, 47, 51, 68-71 • James, W., Great Men and Their Environment • Jefferson o “The Virginia Constitution” o First Inaugural Address • Lincoln, First Inaugural Address • Long, The Power within Us • Lucian, The Way to Write History • Montaigne o Of the Inconstancy of Our Actions o Of Giving the Lie o Of Repentance o Of Experience • Plutarch o Themistocles o Alexander • Schopenhauer, On Education • Smith, The Wealth of Nations, Introduction and Bk. I • Swift o An Essay on Modern Education o A Modest Proposal • Universal Declaration of Human Rights • Washington, Farwell Address NATURAL SCIENCE • Carson, The Sunless Sea • Darwin, Autobiography • Eisley, “On Time” • Huxley, On a Piece of Chalk • Jeans, Beginnings and Endings MATHEMATICS • Euclid, Elements, Bks. II-V • Whitehead, “On Mathematical Method” PHILOSOPHY AND RELIGION • Aristotle, Nicomachean Ethics, Bk. I • Bacon o Of Friendship o Of Anger o New Atlantis • Bible o Psalms o Matthew • Cicero, On Old Age • Epictetus, The Enchiridion • Hazlitt, On the Feeling of Immortality in Youth • Locke, Concerning Civil Government • Plato, Phaedo MUSIC (PIANO AND MUSIC APPRECIATION ) LANGUAGE (ENGLISH AND LATIN) • Ørberg , Sermōnēs Rōmanī, Plautus, Cato, Cicero, Phaedrus, Horace, Tacitus, Martial, Pliny, Aulus Gellius, and Lucas • Ørberg, Lingua Latīna Per Se Illustrata: Pars II, Rōma Aeterna A SAMPLE UNIT PLAN BASED ON HALDANE’S ON BEING THE RIGHT SIZE The following unit plan demonstrates the analysis of an entire essay using Microsoft Word to emphasize the actual text of the document and to make comments on each paragraph in the margin. Links to Britannica Online and other web sources are provided within the analysis. The access codes and sites, accurate at the time of publication, may not currently be accurate, but they serve as an example of how planning links to resources. At the end of the documents, the elements of the planning for each of the three columns is presented based on the forgoing analysis. This example is relevant not only to short works, but also to the methodology necessary to planning for longer works. On Being the Right Size J. B. S. Haldane Analysis for Unit Planning The most obvious differences between different animals are differences of size, but for some reason the zoologists have paid singularly little attention to them. In a large textbook of zoology before me I find no indication that the eagle is larger than the sparrow, or the hippopotamus bigger than the hare, though some grudging admissions are made in the case of the mouse and the whale. But yet it is easy to show that a hare could not be as large as a hippopotamus, or a whale as small as a herring. For every type of animal there is a most convenient size, and a large change in size inevitably carries with it a change of form. Let us take the most obvious of possible cases, and consider a giant man sixty feet high—about the height of Giant Pope and Giant Pagan in the illustrated Pilgrim’s Progress of my childhood. These monsters were not only ten times as high as Christian, but ten times as wide and ten times as thick, so that their total weight was a thousand times his, or about eighty to ninety tons. Unfortunately the cross sections of their bones were only a hundred times those of Christian, so that every square inch of giant bone had to support ten times the weight borne by a square inch of human bone. As the human thigh-bone breaks under about ten times the human weight, Pope and Pagan would have broken their thighs every time they took a step. This was doubtless why they were sitting down in the picture I remember. But it lessens one’s respect for Christian and Jack the Giant Killer. To turn to zoology, suppose that a gazelle, a graceful little creature with long thin legs, is to become large, it will break its bones unless it does one of two things. It may make its legs short and thick, like the rhinoceros, so that every pound of weight has still about the same area of bone to support it. Or it can compress its body and stretch out its legs obliquely to gain stability, like the giraffe. I mention these two beasts because they happen to belong to the same order as the gazelle, and both are quite successful mechanically, being remarkably fast runners. Gravity , a mere nuisance to Christian, was a terror to Pope, Pagan, and Despair. To the mouse and any smaller animal it presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force. An insect, therefore, is not afraid of gravity; it can fall without danger, and can cling to the ceiling with remarkably little trouble. It can go in for elegant and fantastic forms of support like that of the daddy-longlegs. But there is a force which is as formidable to an insect as gravitation to a mammal. This is surface tension. A man coming out of a bath carries with him a film of water of about one-fiftieth of an inch in thickness. This weighs roughly a pound. A wet mouse has to carry about its own weight of water. A wet fly has to lift many times its own weight and, as everyone knows, a fly once wetted by water or any other liquid is in a very serious position indeed. An insect going for a drink is in as great danger as a man leaning out over a precipice in search of food. If it once falls into the grip of the surface tension of the water—that is to say, gets wet—it is likely to remain so until it drowns. A few insects, such as water-beetles, contrive to be unwettable; the majority keep well away from their drink by means of a long proboscis. Of course tall land animals have other difficulties. They have to pump their blood to greater heights than a man, and, therefore, require a larger blood pressure and tougher blood-vessels. A great many men die from burst arteries, greater for an elephant or a giraffe. But animals of all kinds find difficulties in size for the following reason. A typical small animal, say a microscopic worm or rotifer, has a smooth skin through which all the oxygen it requires can soak in, a straight gut with sufficient surface to absorb its food, and a single kidney. Increase its dimensions tenfold in every direction, and its weight is increased a thousand times, so that if it is to use its muscles as efficiently as its miniature counterpart, it will need a thousand times as much food and oxygen per day and will excrete a thousand times as much of waste products. Now if its shape is unaltered its surface will be increased only a hundredfold, and ten times as much oxygen must enter per minute through each square millimetre of skin, ten times as much food through each square millimetre of intestine. When a limit is reached to their absorptive powers their surface has to be increased by some special device. For example, a part of the skin may be drawn out into tufts to make gills or pushed in to make lungs, thus increasing the oxygen-absorbing surface in proportion to the animal’s bulk. A man, for example, has a hundred square yards of lung. Similarly, the gut, instead of being smooth and straight, becomes coiled and develops a velvety surface, and other organs increase in complication. The higher animals are not larger than the lower because they are more complicated. They are more complicated because they are larger. Just the same is true of plants. The simplest plants, such as the green algae growing in stagnant water or on the bark of trees, are mere round cells. The higher plants increase their surface by putting out leaves and roots. Comparative anatomy is largely the story of the struggle to increase surface in proportion to volume. Some of the methods of increasing the surface are useful up to a point, but not capable of a very wide adaptation. For example, while vertebrates carry the oxygen from the gills or lungs all over the body in the blood, insects take air directly to every part of their body by tiny blind tubes called tracheae which open to the surface at many different points. Now, although by their breathing movements they can renew the air in the outer part of the tracheal system, the oxygen has to penetrate the finer branches by means of diffusion. Gases can diffuse easily through very small distances, not many times larger than the average length traveled by a gas molecule between collisions with other molecules. But when such vast journeys—from the point of view of a molecule—as a quarter of an inch have to be made, the process becomes slow. So the portions of an insect’s body more than a quarter of an inch from the air would always be short of oxygen. In consequence hardly any insects are much more than half an inch thick. Land crabs are built on the same general plan as insects, but are much clumsier. Yet like ourselves they carry oxygen around in their blood, and are therefore able to grow far larger than any insects. If the insects had hit on a plan for driving air through their tissues instead of letting it soak in, they might well have become as large as lobsters, though other considerations would have prevented them from becoming as large as man. Exactly the same difficulties attach to flying. It is an elementary principle of aeronautics that the minimum speed needed to keep an aeroplane of a given shape in the air varies as the square root of its length. If its linear dimensions are increased four times, it must fly twice as fast. Now the power needed for the minimum speed increases more rapidly than the weight of the machine. So the larger aeroplane, which weighs sixty-four times as much as the smaller, needs one hundred and twenty-eight times its horsepower to keep up. Applying the same principle to the birds, we find that the limit to their size is soon reached. An angel whose muscles developed no more power weight for weight than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economize in weight, its legs would have to be reduced to mere stilts. Actually a large bird such as an eagle or kite does not keep in the air mainly by moving its wings. It is generally to be seen soaring, that is to say balanced on a rising column of air. And even soaring becomes more and more difficult with increasing size. Were this not the case eagles might be as large as tigers and as formidable to man as hostile aeroplanes. But it is time that we pass to some of the advantages of size. One of the most obvious is that it enables one to keep warm. All warm-blooded animals at rest lose the same amount of heat from a unit area of skin, for which purpose they need a food-supply proportional to their surface and not to their weight. Five thousand mice weigh as much as a man. Their combined surface and food or oxygen consumption are about seventeen times a man’s. In fact a mouse eats about one quarter its own weight of food every day, which is mainly used in keeping it warm. For the same reason small animals cannot live in cold countries. In the arctic regions there are no reptiles or amphibians, and no small mammals. The smallest mammal in Spitsbergen is the fox. The small birds fly away in winter, while the insects die, though their eggs can survive six months or more of frost. The most successful mammals are bears, seals, and walruses. Similarly , the eye is a rather inefficient organ until it reaches a large size. The back of the human eye on which an image of the outside world is thrown, and which corresponds to the film of a camera, is composed of a mosaic of “rods and cones” whose diameter is little more than a length of an average light wave. Each eye has about a half a million, and for two objects to be distinguishable their images must fall on separate rods or cones. It is obvious that with fewer but larger rods and cones we should see less distinctly. If they were twice as broad two points would have to be twice as far apart before we could distinguish them at a given distance. But if their size were diminished and their number increased we should see no better. For it is impossible to form a definite image smaller than a wave-length of light. Hence a mouse’s eye is not a small-scale model of a human eye. Its rods and cones are not much smaller than ours, and therefore there are far fewer of them. A mouse could not distinguish one human face from another six feet away. In order that they should be of any use at all the eyes of small animals have to be much larger in proportion to their bodies than our own. Large animals on the other hand only require relatively small eyes, and those of the whale and elephant are little larger than our own. For rather more recondite reasons the same general principle holds true of the brain. If we compare the brain-weights of a set of very similar animals such as the cat, cheetah, leopard, and tiger, we find that as we quadruple the body-weight the brain-weight is only doubled. The larger animal with proportionately larger bones can economize on brain, eyes, and certain other organs. Such are a very few of the considerations which show that for every type of animal there is an optimum size. Yet although Galileo demonstrated the contrary more than three hundred years ago, people still believe that if a flea were as large as a man it could jump a thousand feet into the air. As a matter of fact the height to which an animal can jump is more nearly independent of its size than proportional to it. A flea can jump about two feet, a man about five. To jump a given height, if we neglect the resistance of air, requires an expenditure of energy proportional to the jumper’s weight. But if the jumping muscles form a constant fraction of the animal’s body, the energy developed per ounce of muscle is independent of the size, provided it can be developed quickly enough in the small animal. As a matter of fact an insect’s muscles, although they can contract more quickly than our own, appear to be less efficient; as otherwise a flea or grasshopper could rise six feet into the air. And just as there is a best size for every animal, so the same is true for every human institution. In the Greek type of democracy all the citizens could listen to a series of orators and vote directly on questions of legislation. Hence their philosophers held that a small city was the largest possible democratic state. The English invention of representative government made a democratic nation possible, and the possibility was first realized in the United States, and later elsewhere. With the development of broadcasting it has once more become possible for every citizen to listen to the political views of representative orators, and the future may perhaps see the return of the national state to the Greek form of democracy. Even the referendum has been made possible only by the institution of daily newspapers. To the biologist the problem of socialism appears largely as a problem of size. The extreme socialists desire to run every nation as a single business concern. I do not suppose that Henry Ford would find much difficulty in running Andorra or Luxembourg on a socialistic basis. He has already more men on his pay-roll than their population. It is conceivable that a syndicate of Fords, if we could find them, would make Belgium Ltd or Denmark Inc. pay their way. But while nationalization of certain industries is an obvious possibility in the largest of states, I find it no easier to picture a completely socialized British Empire or United States than an elephant turning somersaults or a hippopotamus jumping a hedge.
Column One (10% to 15% of Scheduled Time for This Unit) BIOGRAPICAL INFORMATION • Haldane, J. B. S. (Username paideia10, Password: mortimer) • On Being the Right Size o Who wrote it? Haldane. Who published it? How? o What is it about as a whole? o Where did Haldane write it? o Why did Haldane write it? o When did Haldane write it? VOCABULARY (Britannica Online, username: paideia10, password: mortimer) Animals: • Eagle • Sparrow • Hippopotamus • Hare • Mouse • Rat • Horse • Whale • Herring • Gazelle • Rhinoceros • Giraffe • Daddy-Longlegs • Elephant • Land crabs • Kite • Tiger • Bear • Seal • Walrus • Cat • Cheetah • Leopard • Flea Specialized Terms: • zoology, zoologist • order (as in Linnaean Classification: kingdom, phylum, class, order, family, genus, species) • successful (in terms of evolution—i.e. successful mechanically meaning, for example, that the evolutionary form of a giraffe and a gazelle make them fast runners, or the term “successful mammal”) • gravity/gravitation • mammal • surface tension of water • proboscis • blood pressure • blood vessels/arteries • rotifer • oxygen • kidney • millimeter • intestine • gills, lungs • organs (biological) • higher animals, lower animals • higher plants, lower plants • green algae • cells (biological) • anatomy, comparative anatomy • adaptation (evolutionary) • vertebrates • resistance (to movement, to falling) • tracheae, tracheal system • gases • diffuse • molecule, gas molecule • inch, quarter of an inch • aeronautics • dimension, linear dimension • power, horsepower • limit (mathematical as applied to the size of a bird) • angel (Haldane uses the word incorrectly) • warm blooded animal • reptile • amphibian • rods and cones • energy • ounce • efficient, less efficient (in terms of an insect’s muscles) • democracy, Greek democracy • citizen • orator, representative orator • vote directly, vote indirectly • legislation • philosopher, Greek philosopher (name the most famous ones) • representative government • democratic nation (in contrast to democratic city) • broadcasting (in 1926) • referendum • biology, biologist • socialism, socialist, socialistic • Ltd, Inc • Nationalize, nationalization • Industry, industries Word Meanings (Use the Dictionary Link in Britannica Online): • inevitable, inevitably • oblique, obliquely • elegant • contrive • microscopic • altered, unaltered • absorb, absorptive • tufts • stagnant • principle, general principle • mosaic • distinguishable • image, definite image • relative, relatively • recondite • quadruple • contrary • institute (verb), institution of
REFERENCES • Pilgrim’s Progress (Username: paideia10; Password: mortimer); note references to: o Giant Pope o Giant Pagan o Christian o Jack the Giant Killer o Despair • British versus American spelling o millimetre versus millimeter (metre versus meter) o aeroplane versus airplane • Biographical o Galileo o Henry Ford Column Two (65% to 75% of Scheduled Time for This Unit) DO THE READING Haldane’s On Being the Right Size is an excellent essay for practicing all the arts of reading. It is especially suitable for practicing the analytical reading arts of finding the most important words, the most important sentences, and the author’s arguments. DO THE MATH • Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force. (Based on the principle—to be researched and verified below—that air resistance is proportional to the surface area of the moving object). • If it’s linear dimensions are increased four times, it must fly twice as fast. • So the larger aeroplane, which weighs sixty-four times as much as the smaller, needs one hundred and twenty-eight times its horsepower to keep up. • Five thousand mice weigh as much as a man (is this true?). Their combined surface and food or oxygen consumption are about seventeen times a man’s (again, this is a fact-check too). • Increasing the dimensions of a cube by ten times increases its volume by 1000 times • Reduction in the three dimensions of a cube reduces its volume to a thousandth but its surface area only to a hundredth • Given a number of lengths, compute the average length • Given the lengths of a number of airplanes of a given shape, compute the minimum speed necessary to keep them in the air (principle of aeronautics: minimum speed varies as the square root of length) o If its linear dimensions are increased four times, it must fly twice as fast. o So the larger aeroplane, which weighs sixty-four times as much as the smaller, needs one hundred and twenty-eight times its horsepower to keep up. o Applying the same principle to the birds, we find that the limit to their size is soon reached. (What is the limit to a bird’s size?) o An angel whose muscles developed no more power weight for weight than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economize in weight, its legs would have to be reduced to mere stilts. (Ignoring Haldane’s misuse of the word “angel,” suppose that an angel was corporeal rather than non-material and do the math to see if his claim is accurate.) • After researching the wavelengths of light, list them and compute the “length of an average light wave” (from the tenth paragraph).
FIND ON A GLOBE AND THEN ON A MAP (Username: paideia10; Password: mortimer) • Arctic Regions • Andorra • Luxembourg • Belgium • Denmark • Spitsbergen DO THE RESEARCH AND CHECK STATED FACTS (Username: paideia10; Password: mortimer) • For the resistance presented to movement by the air is proportional to the surface of the moving object. • The English invented representative government. • Aeronautical principle that the minimum speed needed to keep an airplane of a given shape in the air varies as the square root of its length (does the principle have a name? who discovered it? How is it stated in a mathematical equations? Is there a standard form or forms? Etc.) • oxygen absorption in differing animals (tall land animals versus microscopic worms and rotifers) • Now the power needed for the minimum speed [of an airplane] increases more rapidly than the weight of the machine. • All warm-blooded animals at rest lose the same amount of heat from a unit area of skin, for which purpose they need a food-supply proportional to their surface and not to their weight. • The back of the human eye on which an image of the outside world is thrown, and which corresponds to the film of a camera, is composed of a mosaic of “rods and cones” whose diameter is little more than a length of an average light wave. Each eye has about a half a million, and for two objects to be distinguishable their images must fall on separate rods or cones (research “human eye,” “rods and cones,” “wavelengths of light”). o It is obvious that with fewer but larger rods and cones we should see less distinctly. o If they were twice as broad two points would have to be twice as far apart before we could distinguish them at a given distance. But if their size were diminished and their number increased we should see no better. o But if their size were diminished and their number increased we should see no better. OBSERVE IN A LAB OR VIDEO • Diffusion of gases • Human eye (and/or other eyes of mammals) Column Three (15% to 20% of Scheduled Time for This Unit) CONCEPTS AND IDEAS TO ENLARGE THE UNDERSTANDING (SUITABLE FOR CLASS DISCUSSIONS) • GREAT IDEAS: ANIMAL 2b, 3; CHANGE 8; FORM, EVOLUTION o For every type of animal there is a most convenient size, and a large change in size inevitably carries with it a change of form (cf. Britannica Online’s sizes of organisms; Username: paideia10, Password: mortimer). o . . . the larger animal with proportionately larger bones can economize on brain, eyes, and certain other organs . . . • GREAT IDEAS: QUANTITY 3, SPACE 1c (Inventory of Terms: Dimensions and dimensionality) o Increasing the dimensions of a person or animal by ten times increases its volume by 1000 times (Galileo’s Square Cube Law). o reduction in the three dimensions of a physical object reduces volume to a thousandth but surface area only to a hundredth (in reference to “an animal’s length, breadth, and height) GREAT IDEAS: MATHEMATICS 4c; QUANTITY 1b, 5d, 6b; RELATION 1d, 5a(3); SAME AND OTHER 3b (Inventory of Terms: Proportion, proportionality) o resistance to movement is proportional to the surface [area] of the moving object o oxygen-absorbing surface in proportion to the animal’s bulk o increase surface [area] in proportion to volume o proportional to their surface and not their weight o more nearly independent of its size than proportional to it o an expenditure of energy proportional to the jumper’s weight GREAT IDEAS: CITIZEN; CONSTITUTION 9-9b; DEMOCRACY 5-5c; LAW; STATE 8a (Inventory of Terms: Representation, Representatives) o Greek type of democracy o Citizen o Legislation o Representative government o Possibility of a democratic nation o Referendum GREAT IDEAS: DEMOCRACY 4a(2); LABOR 5d, 7b; WEALTH 6a, 8a (Inventory of Terms: Socialism) o Socialism o a completely socialized British Empire or United States QUESTIONS (SUITABLE FOR SEMINAR PLANNING) • Why does Haldane conclude an essay on the optimal sizes of animals with observations about politics (democracy and socialism)? • There are two religious references in this essay: (1) The reference to Pilgrim’s Progress, and (2) The reference to an angel. In the latter, Haldane misuses the word “angel” by using it as if the word referred to a corporeal being; the word (and the first “great idea” in Great Books of the Western World) refers to incorporeal (meaning “non-material” and “spiritual”) beings. Why do you think Haldane does this? Is he uniformed? Misinformed? • Haldane uses arguments based on dimensionality and proportionality. How does he do this (cite text)? Do his mathematical arguments enhance his case? Why or why not? • Is there evidence of bias in Haldane’s essay? Identify whether your evidence is from the text, from other sources, or both. • What impact does Haldane’s essay have on you? Has it given you new things to think about? Changed your worldview at all?