Showing posts with label david harriman. Show all posts
Showing posts with label david harriman. Show all posts

Monday, July 24, 2017

200,000 Pageviews

On or about July 17, 2017, this blog tallied its 200,000th page view. Launched on 2 January 2011, about 100 people per day read the posts, often as a result of Internet searches for topical information. Everyone can be a publisher, and perhaps too many people are. But I believe that we are experiencing a renaissance, a silver age, if not a golden age, in which the sharing of information – facts and opinions alike — creates a flourishing. Our lives are better.

In a previous post, I wrote about Jerry Emanuelson’s algebraic proof of Ricardo’s Law of Comparative Advantage. Emanuelson has other interests. He previously created and marketed a high school level kit for experimenting with superconductors. The Internet gave him an easy and extensive exposure.


Science hobbyists of our generation knew well the Edmund Scientific Catalog. Edmund also wrote about the scientific method. He taught it as a 14-step engagement in discovery. Norman W. Edmund lived long enough (1916-2012) to bring his work to the Internet (see here http://scientificmethod.com/index2.html ). It proved much more efficient than the U.S. Post Office.

The most popular articles from this blog so far are:
What (if anything) did Dorothy Learn? (4626)
Contradictions in the Constitution (2400)
Alongside Night to Run in Austin (1799)
Bob Swanson and Genentech (713)
William Sheldon: Psychologist, Numismatist, Thief (655)
Debt: the Seed of Civilization (556)
Crimes Against Logic: Exposing Bogus Arguments (409)
There is no John Galt and that’s Worse (356)
Supplies and Demands (340)
Romantic Realism (339)


Those numbers come from the Stats under the All time button on my control panel. However, I also have other numbers under View Count in the Posts:

Forgery and Fraud in Numismatics 1187
Debt: the Seed of Civilization 1183
Harriman’s Logical Leap Almost Makes it 884
(see, also, David Harriman’s Logical Leap 408)
Junk Criminology as Pseudo-Science 877
Nerd Nation: Natalie Portman, Danika McKeller, and Felicia Day 831
Unlimited Constitutional Government 797
ELI the ICE Man: Science and Technology 788
Hacking Computer Security: BSides Austin 2013 747
Art & Copy 729
Megacities 726
… that goddam Ayn Rand book 717
To Make Money 658
The Problem of Induction: Karl Popper and His Enemies 643
Employee Theft 639
The Fallibility of Fingerprinting 634
Sándor Kőrösi Csoma 626
Murray Rothbard: Fraud or Faker? 592
Shifting the Paradigm of Private Security 569
Venture Capital 566
Where All Children are Above Average 556
Karl Marx and the Dustbin of History 553
Gregory M. Browne’s Necessary Factual Truths 529
Republicans for Voldemort 528
Ayn Rand versus Conservatives 527
Firefly: Fact and Value Aboard “Serenity” 517
De Magnete by William Gilbert 466
George Boole’s Laws of Thought 459
Money as Press and Speech 439
Money as Living History 433
Against Gulching 396
Ma Kiley: Railroad Telegrapher 367
Short Snorters 354
The Virtues of Aviation Culture 339
A Successful Imitation of Alan Turing 335

The search terms that bring people here include Çatal Hüyük, (catal huyuk), supply and demand, supply and demand curve, contradictions in the Constitution, Merry Newtomas, and Employee Theft Facts. Although I write about Newtonmas every year, none of them makes the top of the lists.

Mirror sites
Among others…

PREVIOUSLY ON NECESSARY FACTS

Thursday, April 14, 2016

IMAGINARY NUMBERS ARE REAL. Pegasus is Not.


Technical language is derived from common language to allow more accurate and precise statements, and more penetrating and perceptive questions. Commonly, when we say “real” we mean “true”, independent of the observer, valid, or verifiable, actual; not imaginary or mythical. Pegasus was not a real animal.  Polyphemus the Cyclops was not real, though Odysseus may well have been. In mathematics, “real” numbers are the set that includes all integers, rational, and irrational numbers. “Imaginary” numbers are those whose square (or other “even” power) is a negative number; in other words, the square roots of negative numbers are imaginary. But imaginary numbers are real in the common sense.
Euler's Equation. As sin^2(x) + cos^2(x) = 1
this can be applied to the analysis of
alternating current electricity.
 
Imaginary numbers are important to the design and analysis of alternating current circuits. (See, for instance, the Wikipedia article on Volt-ampere-reactive.)   Without imaginary numbers we could not have complicated electrical power systems, just as we could not have modern commerce without negative numbers.  Overcoming the confusion and ignorance about the reality of numbers has been a historical process.

The Golden Ratio seen in the Parthenon
has many applications.
Geometrically pleasing,
its algebraic expression
(1 + sqrt(5))/2 is irrational
It is said that the followers of Pythagoras killed one of their disciples for revealing that the square root of two is irrational. Apparently, until about 5th century BCE, the Greeks accepted that every number must be rational, only that not all reductions were known. For example, the Egyptians chose to represent all fractions as sums of fractions with 1 in the numerator: ¾ = ½ + ¼ or 3/7 = 1/3 + 1/14 + 1/42.  

Diophantus of Alexandria (3rd century CE) denied the reality of negative numbers.  The Nine Chapters on Mathematical Art (Jiu zhang suan-shu) of about the same time accepted their reality. Although early conceptions of zero as a placeholder are known from Babylonian and Egyptian texts, zero was not accepted as a number in the modern sense until about 500 CE.  What is nothing? And in the technical language of metaphysics, nothing is not a different kind of something. “Nothing exists beyond the universe” does not mean that “beyond the universe” is “something else.” The confusion over zero comes from the difference between “nothing” and “none.”  The number 207 has no tens; it does not have metaphysical “nothing” in the tens place. 

But we are not confused by that in daily life.  When Mom asked “What’s going on?” and you replied “Nothing!” she was not thrown into a metaphysical conundrum.

So, too, with imaginary numbers. They have an unfortunate etymology, but we use them every day. If the operators in control rooms of electrical power plants could not manipulate reactive power – expressed in imaginary numbers—with real controls, we would suffer blackouts. 

My motivation here is a post on the Galt’s Gulch Online discussion board.  On April 5, 2016, about 7:00 AM local time, frequent contributor ewv wrote: “Mathematics by itself doesn't describe reality. It is the means by which you relate in terms of concepts what can be measured. Mathematics is a science of method, not about things like physics does.” (Reply here in "What is Science?" here.)


Her keyboading error aside (“physics does” for “physics is”), she is usually a very adept student of Objectivism. As a quip, I once accused her of being Dr. Leonard Peikoff.  Her comment about mathematics was a direct derivation of statements by Ayn Rand in Introduction to the Objectivist Epistemology, as well as elucidations by David Harriman in The Logical Leap. However, mathematics does describe reality, as does any language. 


We can give expression to falsehoods using common language, as when we attempted to deflect Mom’s inquiry about our noisy play. Pegasus and Nike of Samothrace are other examples. They are mathematically impossible. Whatever the wings represent symbolically, they cannot function from the meager muscles on the back of the horse or the girl. Arguments about politics and religion, and Monday morning quarterbacking supply a surfeit of such falsehoods. That silliness is impossible in mathematics.

Patent for application
of the Moebius strip
to a power conveyor.
Can you have a sheet of paper with only one side? Can you have a container with only an inside? The Möbius Strip and the Klein Bottle were inventions of topology, a study in mathematics that contravenes common sense. But they do exist; and they do have practical applications. As an investigation of relationships, topology is based on qualities, not quantities. Topology is nonetheless a study within mathematics. Topology is rigorous and consistent. It does not allow for internal contradictions, just as integer arithmetic does not.  

Mathematics does have unsolved challenges. Science always has frontiers.  However, anything that is proved to be mathematically true must be realizable, even if we have not found one or built one yet.

ALSO ON NECESSARY FACTS

Wednesday, August 29, 2012

Is Physics a Science?

In sociology, students at all levels are presented with some discussion about whether and how sociology is a science. Physics – especially Newtonian physics – is taken as a kind of standard against which sociology is measured. Actually, a scientific investigation of college textbooks revealed that physics education is deficient in presenting students with the methods and limits of experiment and theory. 

Since the Renaissance, the term experiment has been used in diverse ways to describe a variety of procedures such as a trial, a diagnosis, or a dissection … To examine changes in the textbook construction of experimental method, introductory texts in psychology, sociology, biology, and physics were surveyed during three time periods: 1930-1939, 1950-59, and 1970-79. […] … the percentage of texts with discussions of research methods increased from 50%-90% in psychology, from 25%-70% in sociology, from 20%-45% in biology, and from 16%-30% in physics. Even in the 1970s, such discussions were absent from the majority of biology and physics texts.
"What Counts as an Experiment?: A Transdisciplinary Analysis of Textbooks, 1930-1970," Andrew S. Winston and Daniel J. Blais. The American Journal of Psychology, Vol. 109, No. 4 (Winter, 1996), pp. 599-616.

Visiting the University of Texas Kuehne Library for Physics, Mathematics and Astronomy, I found that this is still true.

Another concept is missing, paradigm. Kuhn’s Structure of Scientific Revolutions was published in 1962. (See Necessary Facts here.) I was assigned it in a philosophy class at Lansing Community College in 1975. My last undergraduate class in physics was in 1982. Paradigm and experiment were never explicitly discussed.
  
At the UT Kuehne Library (honoring John Matthias Kuehne, 1872-1960), I checked nine recent physics textbooks, both for freshmen and for classes in modern physics, typically the second year for majors, seeking index entries for experiment and paradigm. The results were disappointing. Neither term appeared in these:
  • Bernstein, Fishbone, Gasiorowicz, Modern Physics (2000).
  • Benson University Physics, (1996)
  • Giancoli, Physics for Scientists and Engineers (2000)
  • Halliday, Resnick, Walker, Fundamentals of Physics (2005)
  • Hech, Physics: Calculus (2000)
  • Learner, Physics for Scientists and Engineers (1996)
  • Tipler, Physics for Scientists and Engineers (1991)
  • Young and Freedman, Sears and Zemansky’s University Physics (2004). 
Of those, the last was most disappointing being the 11th edition of the standard textbook that served the first post-war generation in the 1950s and 1960s. Tipler was one of the books we had at Lansing Community College because it was newly written in 1976 and because Paul Tipler taught at the University of Michigan. He, too, ignored Kuhn.
M31: Andromeda Galaxy, at first a "cloud"
then a spiral within our galaxy,
then an "island universe" like our
own Milky Way.

Better treatment appeared in Lea and Burke, Physics: the Nature of Things (1997). And this speaks to the validity of critical sociology: It is Susan M. Lea who made the effort to present students with discussions of experiment, including the nature of experiment, thought experiment (first Galileo, then Einstein: pp 11, 132, 445), and experiment and theory. As a woman in a man’s world, Dr. Lea easily adopted the sociological perspective of considering the accepted from a different point of view.

However, even Lea and Burke fall into positivist fallacies that plague science with “the problem of induction.”  (See Necessary Facts on David Harriman’s Logical Leap here and here.)  
They say (page 12): “Physics is an experimental science that prides itself in getting close to reality through laboratory testing of theory. … How can we be certain that the experimental process of dissecting nature into component part is ultimately correct? We can’t! Belief in experimental science depends on one’s worldview.” Again (page 14): “Consistency with experiment and usefulness in understanding nature are the properties of a good physical theory. The word truth is conspicuously absent. Aristotle… Kepler and Galileo… Newtonian physics, thought absolutely true for 250 years. In the twentieth century, we have learned that Newtonian physics is not exact but stands as an excellent approximation. Absolute truth is elusive. We continue to seek greater depth in our understanding, greater elegance in our theories, and greater precision in our experiments. Whether truth can be achieved in some approximate sense by this process is unanswerable. We believe in physics because we know we can organize our knowledge and employ it to describe the behavior of nature with greater accuracy using only a small number of fundamental ideas.”
 The objectivist answer is that rational-empiricism works. The physicists who are not sure about reality never think twice about getting into an elevator and expecting it to operate. And if it fails – despite the failsafe which was designed by the same laws – then some cause must be and can be found. In a lecture on “The Primacy of Existence,” Objectivist philosopher David Kelley notes that these doubters do not drive their cars according to the theory that we can never know anything for certain.

(Note the two words, lower case o-objectivist, and upper case. The first is the general rational-empirical method, the scientific method. Capital-O Objectivism derives explicitly from the published works of Ayn Rand and is a modern school of thought based on the objectivism of pre-Kantian Enlightenment )

Also, Lea and Burke gloss over the key problem with doubt: “Physics is an experimental science that prides itself in getting close to reality through laboratory testing of theory.”  What is this reality to which we can get close, but never discover?

To know that we are closer, not farther, requires some test. That test is reality.

In the history of science, few inventions came from engineering applications of scientific principles. Rather, engineering achievements provided data for theoretical explanation. The telegraphs of the world transmitted our ideas across continents, each click creating a magnetic field that collapsed, inductively broadcasting evidence of our existence into the Galaxy, all a generation before Maxwell.

The best sociology discovers facts, creates theories, identifies causes, and tests hypotheses. As passive description, ethnography is not highly regarded, though it is passionately defended. Passive description is good science – and good description is not passive. We bring our expectations to our observations. A scientist knows to be ware of preconceived notions and to be open to new perceptions. At the same time, the scientific observer often has good reason to seek exactly the phenomenon under investigation. It is not really passive. If only implicitly, certain factors are held constant, while others change. Aristotle’s description of the chick embryo is a paradigmatic example cited as one of the greatest scientific experiments in history. (See Necessary Facts here.)  

But sociology knows these facts. Sir Anthony Giddens’s international standard undergraduate textbook, Sociology, has an entire chapter (number 20) on Research Methods with three explicit discussions of experiment. It begins with two discussions of sociology as a science (pp 7-8; and 12-14).

Moreover, in sociology, we enjoy some self-criticism in examining the historical development of our field, from Comte (I prefer Spencer), Weber, Durkheim, and Marx, through to Parsons, Merton, and your choice of pop stars of the current generation. Physics students do not understand their science as a historical development. As Kuhn pointed out fifty years ago, physics is presented whole and complete, without development. No wonder they are surprised by a new explanation of a previously unperceived fact.

ALSO ON NECESSARY FACTS
The Sokol Affair
Reflections on the Sokol Affair
David Harriman's Logical Leap
David Harriman's Logical Leap Almost Makes It
"Big Bang Theory" and Modern Philosophy

Friday, August 3, 2012

Science in the Middle Ages

Objectivists value the scientific method as the cornerstone of the engineering achievements of our civilization from structural trusses and direct current to alternating current and cybernetics.  We too easily see the Middle Ages as a time of ignorance and barbarism in which learning was chained to (and by) theology.  The reality is more complicated.

“The Middle Ages was a period ruled by the Witch Doctor, in a firm, if mutually jealous alliance with Attila. The Witch Doctor controlled every aspect of human life and thought, while the feudal Attilas looted one another’s domains, collected material tributes from serfs – who worked, lived, and served in subhuman conditions – and maintained the power to burn heretics at the stake.
“Philosophy, in that era, existed as a “handmaiden of theology,” and the dominant influence was, appropriately, Plato, in the form of Plotinus and Augustine. Aristotle’s works were lost to the scholars of Europe for centuries. The prelude to the Renaissance was the return of Aristotle via Thomas Aquinas.” – Ayn Rand, “For the New Intellectual.”

Astronomy, in particular was not dormant, nor could it be.  The problem of Easter required bringing lunar and solar calendars into alignment.  Whether biology, botany, and medicine had any hint of modernism is a difficult question, but can only be answered with direct citations to contemporary works.  Like the revolution of the Earth on its axis and the orbit of the Earth about the Sun, proof contrary to spontaneous generation did not come until the 1840s. As with astrology versus astronomy, it is too easy to dismiss alchemy as not being "real" chemistry. While its paradigms are not ours, the practices were utilitarian: dying wool and leather were important crafts. Paints, pigments, and finishes also were consequential.

“Historians have long recognized that the rebirth of science in twelfth-century Europe flowed from a search for ancient scientific texts. But this search presupposes knowledge and interest; we only seek what we know to be valuable. The emergence of scholarly interest after centuries of apparent stagnation seems paradoxical. This book resolves that seeming contradiction by describing four active traditions of early medieval astronomy: one divided the year by observing the Sun; another computed the date of Easter Full Moon; the third determined the time for monastic prayers by watching the course of the stars; and the classical tradition of geometrical astronomy provided a framework for the cosmos. Most of these astronomies were practical; they sustained the communities in which they flourished and reflected and reinforced the values of those communities. These astronomical traditions motivated the search for ancient learning that led to the Scientific Renaissance of the twelfth century.” (Astronomies and Cultures in Early Medieval Europe by Stephen C. McCluskey. Cambridge University Press,  1997.) 

“Measurements by clepsydras prove … that although the earth is at the center of the universe, it is eccentric to the sun's orbit. At times the sun is borne at a greater distance from the earth than at other times. When the sun is climbing upwards in Cancer and Gemini, in the steeper tracts of its course, it takes longer, lingering 32 days in Gemini; but it requires less time in the lower tracts, 28 days in Sagittarius, the elapsed time for the other signs varying between those extremes (848-849) . “Dominant Traditions in Early Medieval Latin Science” by William H. Stahl, Isis, Vol. 50, No. 2 (Jun., 1959), pp. 95-124. 

Mean Speed from the Oxford
Calculators used by Galileo
"The sorry state of scientific studies at the close of the Roman Empire in the fifth century reflected Roman, not medieval, failures and short-comings." "How Science Survived: Medieval Manuscripts as Fossils” by Sharon Larimer Gilman and Florence Eliza Glaze. Science, New Series, Vol. 307, No. 5713 (Feb. 25, 2005), pp. 1208-1209.

“The dominant explanation of human behavior at this time was astrology.  Charles, like most of his contemporaries, ruled with the advice of the recognized social scientists of the day, the court astrologers. In this vein Oresme was ordered by Charles to translate Ptolemy's Quadripartitum from Latin into French. This order discharged, Oresme then attempted to debunk the popular conceptions in an attack on judicial astrology, Contra judiciaros astronomos (1360), which he later translated into French. There is no hint in the historical record that Oresme's efforts altered the predominance of astrology in the determinance of social policy; indeed, he returned to the attack ten years later with a treatise entitled Contra divinatores horoscopios, and in a series of Quaestiones (a stylized form of question and answer popular with academicians of the period).”
“Nicole Oresme and Medieval Social Science: The 14th Century Debunker of Astrology Wrote anEarly Monetary Treatise” by Kevin B. Bales, American Journal of Economics and Sociology, Vol. 42, No. 1 (Jan., 1983), pp. 101-111.

“WHEN historians and historians of science flatly state that Ptolemy's Almagest and Geography dominated the fields of astronomy and geography for fourteen centuries, they are apt to mislead unwary readers into supposing that Ptolemy was the supreme authority in Latin science during that period. Quite the contrary, his works might almost as well never have been written for all the influence they had in the Latin West until translations were produced from Greek or Arabic texts in Toledo and Sicily in the twelfth century.' If there was any dominant tradition of Latin science in the first thirteen centuries of the Christian Era, it was a stream of encyclopedic literature, the main course of which may be traced backwards through the Latin encyclopedist Varro and the Platonizing Stoic Posidonius; to trace sources beyond them is difficult indeed. In any case it is well to bear in mind that this stream of encyclopedic works skirts around Ptolemy without being appreciably influenced by him. We can trace its course through the extant writings of Pliny, Theon of Smyrna, Cleomedes, Geminus, and numerous others.

“Of the three, Martianus Capella offers the best account of encyclopedic science and will be discussed first. He seems to have flourished in the first half of the fifth century.  Martianus Capella wanted to produce an encyclopedia in the Varronian tradition and, by excluding two of Varro's disciplines, medicine and architecture, laid the foundation of the medieval trivia and quadrivia.

The first work of Archimedes translated into Latin was the Measurement of the Circle. It was translated from the Arabic twice in the twelfth century.' The first translation, which I have argued (but not surely) was done by Plato of Tivoli, was most inferior; just three manuscripts are known, only one of which is medieval. Apparently not long after this first translation the great translator Gerard of Cremona again used the Arabic text and rendered the Measurement of the Circle into Latin. This time the translation was quite accurate, and so before 1187 a faithful version of this short but important treatise became available. We are fortunate that this version was included in MS Bibliotheque Nationale, Fonds latin 9335, a handsome codex of Gerard translations. Incidentally, this manuscript is one of the best examples of intelligent copying of scientific works. It has marginal variant readings which cite alternate copies. The drawings are carefully made. Even more important the transcription of numbers - even of six places - is almost perfect. “The Impact of Archimedes on Medieval Science,” by Marshall Clagett, Isis, Vol. 50, No. 4 (Dec., 1959), pp. 419-429. 

"Among late thirteenth and fourteenth century philosophers, the Averroists have been particularly noticed by historians as advocates of the autonomy of the sciences. In arguing, for example, that physics might give an answer to the question of the eternity of the world different from the answer given in accordance with Christian belief, Boethius of Dacia based himself largely on a conception of physics as an independent discipline with its own principles, rational methods, and conclusions. This approach to the autonomy of the sciences was not, however, the only influential one in this period. Another basis for the autonomy of physics is found in the work of certain Oxford commentators on Aristotle's Physics, most prominently in William of Ockham's Expositio super octo libros Physicorum. This second approach makes physics autonomous by placing greatest confidence not in deductively and causally prior principles of physics, which some thought could be proved or made known by metaphysics, but rather in propositions accepted on the basis of experience, if not known in themselves. The primary evidence cited in the following paper." “The a Posteriori Foundations of Natural Science: Some Medieval Commentaries on Aristotle's Physics, Book I, Chapters 1 and 2” by Edith Dudley Sylla, Synthese, Vol. 40, No. 1, Jan., 1979, pp. 147-187.
 In The Logical Leap, Objectivist physicist and philosopher David Harriman denigrates medieval science. In Chapter 3 "The Mathematical Universe" under the subhead "The Birth of Celestial Physics" on page 85 (ppb), Harriman says that with the Ptolemaic Model, the relative sizes of the orbits of the planets could not be calculated.  That leads to an interesting contradiction.  If it is true that the Geocentric model prevents such calcuations, then they must have used some other model, because the relative sizes of the orbits were known.  On the other hand, perhaps the geometry and observations of the time did, indeed, allow them to make those calculations, even assuming the Geocentric model.  My reference for that is Astronomies and Cultures in Early Medieval Europe by Stephen McCluskey (Cambridge, 1998).  In fact, because of the religious viewpoint, the very scale of the measurable universe and the comparatively small size of the (spherical; not flat) Earth, were substantiating evidence to the relative unimportance of Earthly affairs. Saturn's orbit was estimated to be 72 million miles from Earth. (McCluskey, page 203).

Thursday, March 15, 2012

Harriman's Logical Leap Almost Makes It

The root of the problem with his presentation is that the audience is not defined.  If he were writing only for others in his peer group – he holds master’s degrees in physics and philosophy – then much of Harriman’s narrative could have been deleted.  That the book is mass-marketed indicates a wider audience for whom more or better explanation is needed. Rather than trying to replace the accepted meaning of the inductive method, Harriman should simply call his the objective (or Objectivist) method. 

The Logical Leap: Induction in Physics by David Harriman, with an introduction by Leonard Peikoff. New American Library, July 2010. Paperback, 279 pages + vi, illustrations. $16.00.
Despite some flaws in the presentation, David Harriman’s proposal for a new method of scientific methodology is interesting, valuable, and important.  Harriman’s thesis is that induction is actually the integration of a new experience with the totality of all previous experience for the purpose of creating a new generalization.  One example is enough for a generalization, if it is validly composed.  According to Harriman, to be valid, an induction must be derived from a first-level generalization.  To demonstrate the truth of his claim, Harriman provides examples from the works of Galileo, Newton, and Dalton, among others. 
[edited and shortened February 8, 2016]

In philosophy the “problem of induction” is defined by the question “How much evidence is enough?”  David Harriman’s answer is provocative on several grounds.  One fact is enough to validate a theory, if that fact is properly integrated with everything else known to be true.  That much alone would be challenging.  The back cover of this book credits Ayn Rand’s theory of epistemology as the starting point for Harriman’s work.  That flag is necessary for those who do not know Leonard Peikoff as Ayn Rand’s appointed “intellectual heir.”  Peikoff wrote the introduction, and, it is revealed, tutored Harriman in the use of induction in physics.  But Peikoff is a philosopher (doctorate from NYU) and so Harriman attempts the technical proof. 

The root of the problem with his presentation is that the audience is not defined.  If he were writing only for others in his peer group – he holds master’s degrees in physics and philosophy – then much of Harriman’s narrative could have been deleted.  That the book is mass-marketed indicates a wider audience for whom more or better explanation is needed. 

David Harriman is not the only working physicist to blunder about orbital mechanics.  It is an easy error to say that the path of a projectile is a parabola (p. 50).  Later, discussing Newton he does note that the path of an object in orbit under an inverse-square law of central force motion can be any conic section (though he leaves out the line). However, in this part he is explicit about the parabolic path of a projectile. Thirty years ago, I caught Scientific American in this same error; and for them, I photocopied a page from The Wonders of Physics by Irving Adler (Golden Books, 1966).


The Wonders of Physics:
an Introduction to the Physical World
by Irving Adler 
( Illus. by Cornelius De Witt); New York,
Golden Press [1966].
We take the parabola as an approximation for projectile motion by assuming that the Earth is flat. 

This is helpful to students for whom the mathematics of this curve is easier than that of an ellipse.  The ellipse is the most common orbital path in our immediate experience.  Harriman does not distinguish this.

If projectile motion can be explained to a child, then it should stated correctly in a technical treatise on the epistemology of science. 

This oversight is especially significant as the author claims to be explaining how the scientific revolution of the Renaissance replaced earlier mysticisms.  Galileo knew that the Earth is round; that fact was known to Aristotle.  The diameter of the Earth was measured by Eratosthenes. 

Galileo failed to make the logical leap that Newton finally did when he demonstrated via his calculus why an inverse-square force results in orbits that are conic sections.  In fact, in his introductions to editions of the Principia, Newton credits the ancients (“Chaldeans”) who “long ago believed that the planets revolve in nearly concentric orbits, around the sun and that comets do so in extremely eccentric orbits…” (Cohen/Whitman translation, 1999).

Newton’s works are prominent in this book, and rightfully so.  Newton was arguably the greatest scientist of all time.  However, Newton maintained that light consists of corpuscles; but Newton’s own experiments with optics argued against his theory of light.  Newton maintained faith in a hypothesis that he could not prove.  Harriman glides past this problem (pp. 50-67).  Later, Harriman derides the “wavicle” of modern physics.  He also denigrates Rene Descartes.  As an Objectivist, Harriman is opposed to Cartesian rationalism.  However, Descartes is credited with proving that light refracts according to the ratio of the sines of the angles of incidence and refraction.  In American schools, we call this “Snell’s Law” but Willebrord Snellius did not publish it.  So, Descartes is credited with the independent discovery that sin(I)/sin(R) = k.  Pierre de Fermat also proved this mathematically (rationalistically) from the principle of least time. 

Just as we speak too easily of parabolic motion, so, too, do we accept “white light.”  No such thing exists.  All electromagnetic phenomena exist in discrete wavelengths and white is not one of them.  It is true that if we project a mix of colors (red, blue, green; magenta, cyan, yellow) on a white screen, the screen remains white.  Projecting only a beam of red light on a white screen, the illuminated area appears red.  The perception of “white” is a consequence of perceiving several colors at once.  Harriman uses vernacular English to praise Newton for discovering that white light is composed of colors.

Attempting to explain the development of the atomic theory, Harriman offers an erroneous simile comparing a hydraulic pump to a lever (pp. 123-124).  Explaining the theory of the fluid barometer, he writes: “It is similar to the action of a lever; the weight of the air will raise the same weight of water (per unit surface area).  Here the weight of the entire atmosphere above a particular surface must be equal to the weight of thirty-four feet of water over the surface.”  It is true that all simple machines -- wedge, lever, wheel, axle, and screw – allow us to trade force, distance, time, speed, or work.  Considering conservation of energy, the liquid barometer could be likened to any of them, but it would be stretching the analogy.  A lever works by trading force and distance: the fifty-pound child at the end of a teeter-totter lifts the 150-lb. man sitting on the other side but closer to the center.  The hydraulic lift is not a lever any more than a screw is a pulley.

Harriman states in words what would be easier given as symbols.  Numbers are written out.  This reflects the lack of a defined audience.  Harriman explains some things but glosses over others; and it is hard to know when he is being technical or vernacular. 

Consider the allusions to elastic and inelastic collisions.  “… [Newton] deliberately varied the mass of the bobs and thereby proved that his law applied to both elastic and inelastic collisions.” (p. 127)  Referring to the standard college textbook by Sears and Zemansky (now 
Young and Freedman, Sears and Zemansky’s University Physics), in a perfectly inelastic collision the two bodies stick together, their kinetic energies before and after are not conserved, and the difference lost is converted to heat.  I believe that here Harriman is using the word “elastic” in its vernacular sense: balls of yarn or wood were deformed more or less by the impacts, having negligible consequences to the experiment.  However, discussing the kinetic theory of gases, Harriman uses elastic and inelastic in their proper technical senses (p. 166).

Kepler suggested that perhaps the sun attracts the planets with some kind of magnetism.  Newton ruled out magnetism in Corollary 5 to Proposition VI Theorem VI in the Principia.  However, magnetism had to be considered.  Newton’s measurements suggested that the power of magnetic attraction diminishes at a proportion between an inverse-square and an inverse-cube.  Today, we know that the field of a magnetic dipole diminishes as the inverse-cube, but that the force of attraction toward either pole follows the inverse-square rule.  Thus, gravity, static charge, and magnetism all were contenders to explain the motions of the moon and the falling apple.  As Harriman notes:  “Different causes can lead to qualitatively similar effects (e.g., a magnet with an electric charge on its surface will attract both straw and iron filings, but for different reasons” (p. 137).  But Harriman is in error when he continues: “However, when Newton proves that the moon and the apple fall with rates that were precisely in accordance with a force that varies as the inverse square of the distance from Earth’s center – then there can be no doubt that the same cause is at work” (p. 137).  Strictly on the basis of the inverse-square attraction, both magnetism and electric charge could have been the cause. 

Harriman says that Newton experimented with magnets floated on wood in a tub of water.  According to Harriman, that the magnets were mutually attracted without causing a net motion of the tub proved that the attractions were directed equal and opposite to each other (pp. 127-128).  That experiment proves nothing of the sort.  Placing the magnets in a tub of water and measuring their motions, one might discover several facts, for instance, that some materials magnetize more strongly than others or (counterfactually) that different objects are attracted with unequal accelerations.  But there is no way that they could move the tub, even if they banged into the sides.  It is a standard problem in freshman physics to determine whether a person standing on a (frictionless) rail car could move it by firing a bullet at an opposite wall. 

Harriman goes on to say
“Since Earth attracts all materials on its surface, it was reasonable to suppose (and it would later be proven) that every part of Earth attracts all other parts.  So consider the mutual attraction, say, of Asia and South America.  If these two forces were not equal and opposite, there would be a net force on Earth as a whole – and hence Earth would cause itself to accelerate.  This self-acceleration would continue indefinitely and lead to disturbances in Earth’s orbit” (p. 128).
  Again, Asia might be more strongly attracted to South America than that continent is to Asia.  All actions would take place on the “tub” of the Earth within the same inertial frame of reference.

Denigrating ancient and medieval astronomy, Harriman claims that the relative sizes of the orbits of the planets could not be computed (pp. 88-86).  This was not true; and Harriman must know that because he says that Ptolemy estimated the distance to the stars (p. 88).  Moreover, if it is true that the geocentric model prevents such calculations, then the ancient astronomers must have used some other model, because the relative sizes of the orbits were computed.  The ancients did not believe that all of the celestial lights were spread on a single sphere.  They knew that the moon is much closer than Saturn.  On the other hand, (more reasonably) the geometry and observations of the time did, indeed, allow them to make those calculations, even assuming the geocentric model.  In fact, because of the religious viewpoint, the very scale of the measurable universe and the comparatively small size of the (spherical; not flat) Earth, were substantiating evidence of the relative unimportance of Earthly affairs.  (See Astronomies and Cultures in Early Medieval Europe by Stephen McCluskey, Cambridge, 1998.)

Measurement was always important to the medieval astronomers who welcomed the new astrolabe imported from the Muslims.  Thus, it is no surprise that measurement of the Earth’s diameter and the distance to the moon were important to Sir Isaac Newton.  Harriman says that Newton accepted the numerical approximation of 60 Earth radii as the distance to the Moon (pp. 136-137).  In fact, Newton was not comfortable with these approximations, but he had to settle for them.  He was being stonewalled by John Flamsteed, the Royal Astronomer who also was working out the celestial mechanics of the Earth-Moon system and did not want to share his data.  These facts about Newton are in the standard modern biographies by Richard Westfall (Never at Rest), Michael White (Isaac Newton: the Last Sorcerer), and David Berlinski (Newton’s Gift: How Sir Isaac Newton Unlocked the System of the World.). 

Harriman has his own new theory of science, dismissing the accepted scientific method. 
“Today, it is almost universally held that the process of theory creation is nonobjective.  According to the most common view, which is institutionalized in the so-called “hypothetico-deductive method,” it is only the testing of theories (i.e., comparing predictions to observations) that gives science any claim to objectivity.  Unfortunately, say the advocates of this method, such testing cannot result in proof – and it cannot result even in disproof, since any theory can be saved from an inconvenient observation merely by adding more arbitrary hypotheses.  So the hypothetico-deductive method leads invariably to skepticism” (pp. 145-146). 
 Thus, to Harriman, Newton’s experiments did not validate Descartes’ (more correct) theory of light.

Harriman would do well to heed his own words.  “Introspection is clearly an indispensable source of data, since philosophy studies consciousness and an individual has direct access only to his own” (p. 233).  We have the introspective reports of Richard Feynman, Kary Mullis, Albert Einstein, Francis Crick and James D. Watson, and many others, all of whom report something different in their heads than what Harriman claims must be true of all humans, based, we can assume, on his own introspection. 

Richard Feynman’s The Character of Physical Law delivers an outstanding explanation of why the hypothetico-deductive method works.  Norman W. Edmund, the founder of Edmund Scientifics Corporation, created a superb website at www.scientificmethod.com/.  He teaches a 14-step process which touches on philosophy.  Any public school science teacher knows the many posters and other aids that present a 5 or 9-step method.  Regardless of the specifics, Harriman mischaracterizes the scientific method when he claims that it indulges in rationalist fantasies (p. 142). It is true that you can “make up” any airy explanations you want, but the only ones that count are the ones that can be tested.  Harriman ignores that. 

Arguing in the grand style of Ayn Rand he broadly accuses an unnamed collective of committing evils, and then draws his own conclusions about what they really believe.  “Today, it is almost universally held that the process of theory creation is nonobjective [p. 142].”  He does later resort to the Randian device of naming evil professors such as Paul Feyerabend, but nowhere does Harriman provide any support for his claim that what he opposes is “almost universally held.” 

For Ayn Rand, a person’s fundamental existential choice – to be or not to be – is to think or not to think.  Choosing to think is the essence of being human.  That raises the challenge, “Are you not thinking when you choose not to think?”  Rand’s answer came via psychologist Nathaniel Branden (at first an Objectivist himself, then developing his own Biocentric theories).  Psychological suppression is an avoidance mechanism to prevent unpleasant thoughts.  The thought process is abandoned before the thought can be fully formed.  This can begin as denial, justification, or rationalization, but typically is an emotional precognitive response to a potentially painful identification. 

Similarly, Harriman’s Objectivist theory of induction apparently rests on the very hypothetico-deductive method that he denies: in order to make a logical leap, do you not first carry out a series of experiments, any one of which could falsify the previous work until a better theory explains both?  Harriman praises Galileo and Newton both for their careful and repetitive work.  Then, he denies the repetitive aspect of induction, claiming that these scientists “leapt” to valid conclusions.  Harriman needs a meta-explanation. 

Is it inherent in human nature to think by induction?  Is this why we have superstitions as well as science because we leap to general conclusions based on single instances?  If so, what is the nature of this abstracting?  Where in the brain does it occur?  What chemicals cause it?  Can you go through life never doing it?  Or must you always do it?

Moreover, the hypothetico-deductive method is how we validate and verify the works of others.  Explanatory theories are easy to devise.  To be scientific an explanation must be tested.  The claim, no matter how compelling it seems, must be tried against new data, not in the original set.  And, best of all, a valid theory leads to new predictions not in the original data.  

Harriman requires that to be valid an induction must be integrated with all previously known truths.  If that alone were enough, then any theory might be falsified by the discovery of a new phenomenon.  That brings us back to the very problem Harriman claims to solve.  He wants to avoid the debilitating skepticism that hobbles philosophers of science.  We can never be sure of anything (they say) because something new might come along.  Thus, (it is claimed) science leads not to truth but to ignorance.  

Harriman’s beast is personalized by Paul Feyerabend.  Having recently completed a bachelor of science degree in criminology, I was assigned to read similar “post modernist” claims that there is no such thing as science, but only a “scientistic discourse” that excludes women and minorities, that criminology is only ideology in service to oppression.  Fortunately, our courts do not work on that theory any more than researchers in physics adhere to the "fashionable nonsense" of post-modernism.

While these shortcomings are bothersome, they are not fatal.  Harriman’s thesis deserves more than mere consideration.  Properly taught, it would be a revolution in science.  

Rather than trying to replace the accepted meaning of the inductive method, Harriman should simply call his the objective (or Objectivist) method. 

Objectivism (with or without the capital-O) is rational-empiricism and both sides of that equation are required.  Ayn Rand taught that existence exists, that reality is real, that A is A, entities have identities: to be is to be something.  Therefore, contradictions do not exist.  

Truth is rational and empirical, logical and evidentiary, analytic and synthetic, theoretical and experimental, ideal and practical, deductive and inductive, and even imaginary and experiential. Harriman’s book rests on those truths.  In that, its value cannot be overestimated.

ALSO ON NECESSARY FACTS
Is Physics a Science?
The Problem of Induction: Karl Popper and His Enemies
The Sokal Affair
The Structure of Scientific Revolutions