PKT message, Fw: Past as Prologue - Physics and Economics

The following message to Gang8 may be of interest.

Gunnar

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I just had an exchange on the New York Times Science Forum, which [so and so] may find interesting - please forward this to him.

At issue were aspects of Newtonian gravitational mechanics - my first post read as follows:

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Newton made it emphatically clear (a) that he did not know what "gravity" was, and (b) that he would not speculate on the subject matter.

For example, with respect to a contemporary's construction of his work as implying that "gravity was an innate attribute of matter", Newton's response is summarized by a 20th century author as follows:

Several times in his Bentley letters Newton took occasion to object to the doctor's assumption that gravity is an essential quality of bodies. This his own experimental principles had led him to refuse to do... At the same time the prestige of his law of gravitation, and its apparent universality in the world of matter, had encouraged a general impression that gravity was innate in matter according to Newtonian principles, an impression that was further advanced by Cotes' explicit championship of the doctrine in his preface to the second edition of the Principia. "You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me; for the causes of gravity is what I do not pretend to know, and therefore would take more time to consider it."

Later, Einstein predicated his General Theory of Relativity on the notion that gravity is an essential attribute of mass ("bodies") - while I do not have the exact reference at hand, I recall reading Einstein's comment to the effect that his i working hypothesis on the relationship between gravity and mass was "wildly speculative".

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A follow-up post of mine read as follows:

One of the last things which Newton had to work out before publishing his gravitational equations was to demonstrate mathematically that, for the purposes thereof, gravitational attraction between two spherical bodies of mass may be represented by a force line extending from the center of one mass to the center of the other.

Gravity is a tricky thing!

Given the inverse square of the distance rule for the strength of gravitational interaction, Newton's demonstration means that the strength of gravity at the center of a spherical body is at (a) maximum? or (b) minimum?

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In the context of an ongoing Forum discussion, another Forumite posted the following a few minutes later:

OK try this one.

You are floating in space between two large equally massive spherical objects. You are exactly equidistant from both. What net gravitational force do you experience?

ZERO!

OK now subdivide the spheres into four spheres spaced around you in a tetrahedron. You are located at exactly the center of the tetrahedron. What net gravitational force do you experience.

ZERO!

Divide the speheres into 8 equal spheres and repeat above. Still ZERO net force.

Now you are getting it. Keep on going as far as you like maintaining the basic geometry and making as many spheres as you wish.

What net gravitational force do you experience as the number of spheres increases and their individual masses approach zero? Right! ZERO again!

Now bring those tiny little guys in towards your position keeping all the arrangements symmetrical. What gravitational force do you experience now? Right! ZERO!.

Finally arrange the spheres in concentric circles as many as you like and as close together as you like. What is the net force you experience at the center?

The final answer is left to the student as an exercise (but not much of one).

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In response to which, I posted the following - summarizing stuff that I had figured out back in 1976:

As you have so elegantly shown, the proposition that gravity is an innate attribute of matter invites but one answer to my quiz:

And the right answer is (b)!

No!

According to Newton's gravitational equations, the right answer is (a)!

But, of course, it makes no sense to suppose that both (a) and (b) are the right answer.

And therein lies an important clue to the nature of what I choose to label "structural gravity" associated with solar system bodies in stable orbital motion as distinct from whatever gravity may be associated with their mass content.

Briefly, Newton's mathematical demonstration falsifies the hypothesis that structural gravity is an attribute of the mass content of solar system bodies!

Now, why have all the mathematical geniuses who have given us modern physics failed to see this most nearly self-evident point?

            "...the reason why mathematicians are not intuitive," Blaise Pascal suggested, "is
            that they cannot see what is in front of them: for being accustomed to the clearcut,
            obvious principles of mathematics and to draw no conclusions until they have
            clearly seen and handled their principles, they become lost in matters requiring
            intuition, whose principles cannot be handled in this way. These principles can
            hardly be seen," Pascal continued, "and it is with endless difficulty that they can be
            communicated to those who do not perceive them for themselves. These things are
            so delicate and numerous that it takes a sense of great delicacy and precision to
            perceive them and judge correctly and accurately from this perception: most often it
            is not possible to set it out logically as in mathematics, because the necessary
            principles are not ready to hand, and it would be an endless task to undertake. The
            thing must be seen all at once, at a glance, and not as a result of progressive
            reasoning, at least up to a point."

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And how might all this relate to the problems which Gang8 has with Mainstream Economics Paul A. Samuelson style?

Briefly, Samuelson suffers from the intellectual myopia which, for some reason, seems to be packaged with whatever mathematical smarts Nature has bestowed upon mainstream economic scholars - yet, here is Samuelson in 1964 playing footsie with Newton's name as if the old man might have taken Foundations of Economic Analysis as evidence that its author was what Samuelson loftily termed "a fruitful contributor to knowledge":

Past As Prologue

In 1947 kind reviewers hailed this book as a culmination of a great tradition. IN the field of, say, music this would be the highest praise. But in the dynamic field of science the most important goal is to be seminal and pathbreaking, to look forward boldly even if imperfectly.

Perhaps the significant difference between a science and an art resides in the cumulative aspect of scientific knowledge. The best artist today cannot be expected to sculpt better than Michelangelo, or as well. But any schoolboy knows more than Archimedes, even though Archimedes was the greatest genius of ancient times. And most college graduates in physics know more then Isaac Newton: for as Newton himself said, a scientist sees further than his predecessors because he stands on the shoulders of earlier giants. (But do not misinterpret his modesty: bring Isaac Newton back to life today, give him a couple of years [sic!] of training, and prepare to see how he forges ahead of the pack! ) And yet, though it be important in science to codify the past and generalize it elegantly, we must remember that the future is longer than the past.

Thus, the parts of Newton's Principia that embalm in chaste geometry his universal law of gravitation are there to be admired. Blah, blah, blah.

Gunnar