## Natural Philosophy: Including Mathematics, Optics, And Alchemy

## Introduction

**
Natural Philosophy Including Mathematics, Optics, and Alchemy
**

In Newton's day, the term "natural philosophy" referred to the physical sciences, and Newton's work in this area was informed by his belief in a universe which operated on mechanical principles and which was set into motion by God. His scientific study focused on identifying the nature of these mechanical principles. In the course of this study, Newton discovered, developed, and elucidated the mathematical rules by which motion is governed; the fruits of this labor are presented in *Philosophiae Naturalis Principia Mathematica* (1687). Newton also sought to examine through extensive experimentation the properties of light and color, and his findings are published in *Opticks* (1704). modern critics analyze and debate Newton's scientific and mathematical achievements as evidenced by these two works as well as by several of Newton's unpublished papers. Another area of critical discussion focuses on the historical sources that may have influenced Newton's work. Newton's interest in alchemy has proved to be a topic of controversy among critics, as many students and scholars of Newton find it difficult to reconcile his rational, scientific work with a subject deemed occult and false.

**
Major Works
**

Many of the calculations found in *Principia* were worked out by Newton many years earlier, after he had returned to his home in Woolsthorpe, when Trinity College closed due to the plague in 1665. In 1684 astronomer Edmund Halley approached Newton, asking him to describe the orbit of the planets. Newton responded that he had mathematically determined the orbit to be elliptical. Halley urged Newton to send him the calculations, which Newton did. With Halley's encouragement and patronage, Newton elaborated and expanded the work, which became the *Principia.* In this work, Newton explains the laws of the motion of the planets, moons, comets, the tides, and the earth. He also presents his theory of universal gravitation. The differential calculus Newton had earlier developed became a tool used for the calculations in *Principia.* In *Opticks,* Newton presents the results of his experiments with prisms, in which he had broken down white light into a spectrum of primary colors. This led to his theory that light was comprised of individual particles, or corpuscles. Also described in *Opticks* are Newton's experiments with colors of thin films. These experiments led to his theory that light could be both reflected and refracted. Additionally, *Opticks* contained a list of "Queries," in which Newton speculates not only about light and color, but other subjects of physics and philosophy as well.

**
Critical Reception
**

Modern critics have continued to assess the relevance and significance of Newton's mathematical and scientific achievements. After noting the influence of Johannes Kepler and Galileo on Newton, Albert Einstein examined Newton's approach to the problem of motion and comments on the importance of Newton's findings. Einstein noted that while the theories of electromagnetic fields and relativity have limited the significance of some of Newton's work, Newton's mechanics nevertheless paved the way in other areas, making a theory of fields possible. Unlike Einstein, Brian Ellis has argued that Newton's laws of motion are more historically related to Cartesian physics than to Galileo's work in kinematics. In addition to demonstrating Newton's debt to René Descartes, Ellis also emphasizes the conceptual nature of Newton's laws of motion, arguing that they are not deduced from or supported by observation or experimentation. Rupert Hall and Marie Boas Hall center their study on Newton's theory of matter, maintaining that his unpublished manuscripts on this subject help to demonstrate the development of his theory. The critics discussed Newton's exploration of the role of aether in the movement of particles and commented on the influence of Newton's theological beliefs on his theory of matter. Critics such as Robert B. Downs and I. Bernard Cohen focus on the subject matter and significance of the *Principia.* Downs surveys the content of the three books of the *Principia* and emphasizes Newton's application of mathematics to the movement of bodies. Likewise, Cohen states that "Newton's outstanding achievement was to show how to introduce mathematical analysis into the study of nature in a new and particularly fruitful way." Cohen goes on to identify the aspects of *Principia* which may be deemed "revolutionary."

Given that Newton's achievements in mathematics made his scientific discoveries possible, it is not surprising that much, criticism has been devoted to the discussion of Newton's mathematical studies and accomplishments. E. W. Strong explores the procedure Newton identified as a method for "mathematically determining all kinds of phenomena." In particular, Strong underscores the importance to Newton of measurement, experimental investigation, and demonstration from principles. In evaluating Newton's contributions to mathematics, D. T. Whiteside states that Newton "transmuted the received theoretical bases of infinitesimal calculus, dynamics, and optics into their classical forms." Whiteside also discusses Newton's discovery of the general binomial expansion and maintains that fluxional calculus is Newton's "undivided glory."

Just as aspects of Newton's thinking on matter and motion have been supplanted by twentieth-century developments in science, so has his corpuscular theory of light. Nevertheless, his work in the area of light and color laid the foundation for future study. I. Bernard Cohen, in his examination of the content, textual history, and contemporary reception of Newton's *Opticks,* demonstrates that while the work was an exposition of the corpuscular theory of light, it also contained many basic principles of "undulation," or wave theory. The fact that Newton adopted two competing theories in one essay, Cohen explains, accounts for the negative reception the work received in the nineteenth century. In the eighteenth century, *Opticks* had gained much more popular appeal than *Principia.* Cohen compares the two works and argues that while *Principia* is "forbidding" to the nonspecialist, *Opticks* is more able to capture and retain the interest of the layperson. Additionally, Cohen observes, *Opticks* was published in English and written in an intimate style, whereas *Principia* was written in Latin, which was characteristic of its emphasis on mathematical principles. Thomas S. Kuhn analyzes the content of the papers on optical theory that Newton published in scientific journals. While Kuhn identifies the significance of Newton's findings in these papers, he also identifies problem areas in Newton's experimental procedures and presentation, such as Newton's habit of failing to fully explain the intellectual extrapolations he makes.

Critics who study Newton's interest in alchemy, evidenced by his many notebooks on the subject, write against a tradition that downplays or ignores Newton's alchemical studies. P. M. Rattansi states that many critics find Newton's interest in a subject such as alchemy completely inconsistent with his rational, scientific studies. The relationship between these two areas of study may be better understood, Rattansi contends, if Newton's interest in both biblical studies and ancient natural philosophy are further examined. Rattansi explains that the underlying assumptions of Newton's study of biblical prophesy and ancient natural philosophy was that truth about the "true system of the world," among other things, was given to man in ancient times but in a veiled and mysterious way, as in Scripture. It is Rattansi's suggestion that Newton's alchemical studies represented, like the rest of Newton's interest, his search for truth. Similarly, Betty Jo Teeter Dobbs argues that for Newton and his search for truth, no singular approach to knowledge was sufficient. For Newton, Dobbs maintains, the search for the "alchemical spirit" was one way of identifying God's action in the world. Additionally, Dobbs stresses that Newton's work in alchemy influenced his scientific thought. As Dobbs and other critics have argued, Newton sought a unified system of God and nature, and his work in mathematics, optics, motion, matter, and alchemy all supported this goal.

## Criticism

## Albert Einstein (essay date 1927)

SOURCE: "Isaac Newton," in *Smithsonian Treasury of Science,* edited by Webster P. True, Simon and Schuster, Inc., 1960, pp. 278-86.

*[In the following essay, originally published in 1927, Einstein examines the methods by which Newton approached scientific inquiry and comments on the significance of Newton's achievement.]*

The two-hundredth anniversary of the death of Newton falls at this time. One's thoughts cannot but turn to this shining spirit, who pointed out, as none before or after him did, the path of Western thought and research and practical construction. He was not only an inventor of genius in respect of particular guiding methods; he also showed a unique...

(The entire section is 2975 words.)

## E. W. Strong (essay date 1951)

SOURCE: "Newton's Mathematical Way," in *Journal of the History of Ideas,* Vol. XII, No. 1, January 1951, pp. 90-110.

*[In the following essay, Strong analyzes Newton's method for "mathematically determining" natural phenomena. Aspects of this mathematical procedure, Strong states, include experimental investigation, demonstration from principles, and an emphasis on measurement.]*

The task of this historical essay is to make out the procedure which Newton designates as a "mathematical way" to be followed in physical science—a way of "mathematically determining all kinds of phenomena."^{1} This procedure with respect to the role of measurement in experimental...

(The entire section is 8576 words.)

## I. Bernard Cohen (essay date 1952)

SOURCE: A preface to *Opticks, or, a Treatise of the Reflections, Refractions, Inflections, and Colours of Light,* by Isaac Newton, Dover Publications, 1952, pp. ix-lxxvii.

*[In the following essay, Cohen reviews the content, textual history, and contemporary and later reception of Newton's* Opticks.]

Great creations—whether of science or of art—can never be viewed dispassionately. The *Opticks,* like any other scientific masterpiece, is a difficult book to view objectively; first, because of the unique place of its author, Isaac Newton, in the history of science, and, second, because of the doctrine it contains. One of the most readable of all the great books in...

(The entire section is 11328 words.)

## Rupert Hall and Marie Boas Hall (essay date 1960)

SOURCE: "Newton's Theory of Matter," in *Isis,* Vol. 51, No. 164, June 1960, pp. 131-44.

*[In the following essay, Hall and Hall examine several of Newton's unpublished manuscripts in order to better understand the development of his theory of matter.]*

*A* clear understanding of Newton's real thoughts about the nature of matter and of the forces associated with material particles has always been (to borrow his own phrase) "pressed with difficulties." That a corpuscular or particulate theory was unreservedly adopted by him has long been abundantly evident from many passages in the *Principia,* and from the *Quaeries* in *Opticks,* to mention only...

(The entire section is 7669 words.)

## Brian Ellis (essay date 1965)

SOURCE: "The Origin and Nature of Newton's Laws of Motion," in *Beyond the Edge of Certainty: Essays in Contemporary Science and Philosophy,* edited by Robert G. Colodny, Prentice Hall, 1965, pp. 29-68.

*[In the following essay, Ellis studies the historical origins of Newton's laws of motion and argues that contrary to popular belief the laws are more derivative of the physics of Descartes than the theories of Galileo. Ellis further emphasizes the conceptual nature of the laws, maintaining that they are not derived from or supported by observation or experimentation.]*

Are the laws of acceleration and of the composition of forces only arbitrary...

(The entire section is 19829 words.)

## D. T. Whiteside (essay date 1967)

SOURCE: "Sources and Strengths of Newton's Early Mathematical Thought," in *The Texas Quarterly,* Vol. X, No. 3, Autumn 1967, pp. 69-85.

*[In the following excerpt, Whiteside traces the development of Newton's mathematical thought and comments on his achievements in calculus.]*

In this tercentenary year we celebrate, in spirit if perhaps not with full historical accuracy, the first maturing of Newton the exact scientist. Persuaded by a wealth of pleasant traditional anecdote and autobiographical reminiscence, our thoughts go back three hundred years to a young Cambridge student, at twenty-three scarcely on the brink of manhood, working away undisturbed in a cramped,...

(The entire section is 6699 words.)

## Dudley Shapere (essay date 1967)

SOURCE: "The Philosophical Significance of Newton's Science," in *The Texas Quarterly,* Vol. X, No. 3, Autumn 1967, pp. 201-15.

*[In the following essay, Shapere explores the relationship of philosophy and science in Newton's thought, suggesting that Newton approached scientific study in a philosophical manner.]*

In a famous passage in the preface to the first edition of his *Principia,* Newton declared that:

I offer this work as the mathematical principles of philosophy, for the whole burden of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to...

(The entire section is 9056 words.)

## P. M. Rattansi (essay date 1972)

SOURCE: "Newton's Alchemical Studies," in *Science, Medicine, and Society in the Renaissance,* edited by Allen G. Debus, Science History Publications, 1972, pp. 167-82.

*[In the following essay, Rattansi emphasizes that examination of Newton's work in alchemy should not be divorced from the remainder of his scientific work, nor should such examination attemnpt to divide Newton into "irreconcilable 'scientific' and 'mystical' selves."]*

Newton's alchemical studies first came to public notice when Brewster published his magisterial biography of Newton in 1855. Brewster was troubled by Newton's obsessive interest in the subject, and confessed that:

...

(The entire section is 6303 words.)

## Robert B. Downs (essay date 1978)

SOURCE: "System of the World," in *Books That Changed the World,* Second Edition, American Library Association, 1978, pp. 334-74.

*[In the following essay, Downs surveys the content, scope, and reception of Newton's* Principia.]

*Sir Isaac Newton. Principia Mathematica*

Of all the books which have profoundly influenced human affairs, few have been more celebrated and none read by fewer people than Sir Isaac Newton's *Philosophiae Naturalis Principia Mathematica* ("Mathematical Principles of Natural Philosophy"). Deliberately written in the most abstruse and technical Latin, profusely illustrated by complex geometrical diagrams, the work's...

(The entire section is 4191 words.)

## Thomas S. Kuhn (essay date 1978)

SOURCE: "Newton's Optical Papers," in *Newton's Papers & Letters on Natural Philosophy and Related Documents,* Second Edition, Harvard University Press, 1978, pp. 3-24, 27-45.

*[In the following essay, Kuhn examines Newton's optical experiments and publications, commenting on the significance of his findings as well as the limitations of his experimental procedures and his presentation of results.]*

The original publication of the optical papers of Isaac Newton marked the beginning of an era in the development of the physical sciences. These papers, reprinted below, were the first public pronouncements by the man who has been to all subsequent generations the archetype...

(The entire section is 7547 words.)

## I. Bernard Cohen (essay date 1980)

SOURCE: "The Newtonian Revolution in Science," in *The Newtonian Revolution,* Cambridge University Press, 1980, pp. 1-37, 290-99.

*[In the following essay, Cohen offers an overview of the developments in the scientific community during Newton's time. Cohen then identifies the qualities of Newton's* Principia *that made the work so revolutionary.]*

**1.1 Some basic features of the Scientifc Revolution**

A study of the Newtonian revolution in science rests on the fundamental assumption that revolutions actually occur in science. A correlative assumption must be that the achievements of Isaac Newton were of such a kind or magnitude as to...

(The entire section is 18864 words.)

## A. T. Winterbourne (essay date 1985)

SOURCE: "Newton's Arguments for Absolute Space," in *Archiv fur Geschichte de Philosophie,* Walter de Gruyter, 1985, pp. 80-91.

*[In the following essay, Winterbourne offers a reading of Newton's "proofs" of absolute space that supports the claim that Newton's argument has been misrepresented by modern critics. Furthermore, Winterbourne suggests that Newton's argument may be interpreted more literally than has previously been the case.]*

In this paper I shall examine Newton's 'proofs' of absolute space, and try to justify the claim that the argument has been misrepresented by recent commentators, and that it can be given a rather more literal rendering than has been the...

(The entire section is 5135 words.)

## Betty Jo Teeter Dobbs (essay date 1991)

SOURCE: "Isaac Newton, Philosopher by Fire," in *The Janus Faces of Genius: The Role of Alchemy in Newton's Thought,* Cambridge University Press, 1991, pp. 1-18.

*[In the following essay, Dobbs challenges critics who have doubted or suppressed the influence of alchemy on Newton's scientific thought.]*

*Introduction*

Isaac Newton studied alchemy from about 1668 until the second or third decade of the eighteenth century. He combed the literature of alchemy, compiling voluminous notes and even transcribing entire treatises in his own hand. Eventually he drafted treatises of his own, filled with references to the older literature. The manuscript...

(The entire section is 7239 words.)

## Further Reading

Cohen, I. Bernard. *Introduction to Newton's 'Principia'.* Cambridge, Mass.: Harvard University Press, 1971, 380 p.

Book-length introduction to the *Principia* featuring a review of contemporary, eighteenth-, and nineteenth-century interest in the work; discussion of the problems of Newtonian scholarship; and analysis of Newton's writing, revision, and publication of the first and successive editions of *Principia.*

Hall, A. Rupert. *All Was Light: An Introduction to Newton's* Opticks. Oxford: Clarendon Press, 1993, 252 p.

Includes biographical discussion of Newton; examination of the experiments and lectures that provided the data for...

(The entire section is 506 words.)