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  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.

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


  1. "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."

    Are you implying that a bullet fired from a frictionless railcar could not move the car?

  2. If you fire from the car off the car - but not perpendicular to the rails - then, the car will move. But if all action is within the car, the net forces result in no motion.
    F = ma -> F - ma = 0.
    (Now... I wonder... what are the time slices like? What happens with losses to heat from the firing of the charge and the impact of the bullet? ... or the friction on your shoes? ...)

  3. What a wonderfully thought out analysis of this book. Such a refreshingly serious look at this issue so denigrated in academia (especially in my field - psychology).

    I assume you are not Objectivist? It struck me that you were speaking from an external position to the philosophy. If so then I applaud your reasoned approach to Ayn Rand's ideas.

    Thank you for this review. I will be sharing it.

  4. I am an Objectivist, though I prefer to spell it with a lower case o, just as a logical positivist is not a Logical Positivist. I believe that the so-called "problem of induction" is at once much larger and perhaps reducible to a simple statement. Either side of that equation is beyond my own scope.