The Nature of Natural Law

Course Description

Introduction

Why should the natural world obey ‘laws’?    How do ‘scientific theories’ come about, eventually gaining credence?

              We shall be especially concerned in this module with the nascent phase of scientific discovery, for it is here that the “thematic” content of science, a dimension quite distinct from its empirical and analytic content, may usefully be examined. “Themata” play a dominant role in the initiation and acceptance or rejection of certain key scientific insights. Broadly speaking, the course seeks to acquaint students of diverse academic interests with modes of scientific thought. It hopes to introduce students to some key concerns and methodologies of science; that is to say, to basic epistemological and ontological issues which underlie the construction of physical theories.

               A chief aim is to inquire, by means of specific case studies of scientists such as Kepler, Galileo and Newton among others, how the scientific mind works.

The context we shall focus on will be the Copernican Revolution, culminating as it did in the late 17th century with Newton’s law of universal gravity and his ‘System of the World’.

  

                The guiding idea underlying the module is to examine how a specific physical theory – Newtonian dynamics and gravitation - came to be regarded as the archetypal example of a fundamental ‘law’ of Nature, as well as to explore the significance of this process within the broader context of its intellectual history.

                 The main pedagogical components of the module are:

  • to examine the assumptions and primitive concepts that ‘laws’ of Nature rely on for their articulation and, especially, to consider the special role which mathematics occupies in this
  • the sense in which such natural laws are held by science to ‘explain’ the physical world
  • to understand, as a historical process, the gradual refinement or evolution of scientific laws
  • to discuss the nature of a ‘scientific revolution’ and how this involves changes, often radical, of paradigms through which scientists view the physical world
  • to explore the complex relationship between theory and experiment as a means of establishing ‘laws of nature’.

                  The module also aims to question, at a meta-level, the nature of ‘scientific explanation’; further, how these inevitably have to be modified over time in order to take into account new ‘facts’ provided by observation and experiment.

                  In sum, the aim of the course is to examine and in a sense, take apart the nature of scientific explanations of the real, physical world.

                 The student should begin to appreciate that the actual practice of science dispenses with certainties, that doubt and scepticism are a permanent condition of science and in fact largely what propels it forward. Apart from a better understanding of the nature of science and indeed, of human scientific creativity, the student should gain some appreciation of the intricate processes through which science progresses and should take away from this module the ability and confidence to critically evaluate the logical and evidential basis of scientifically framed questions and be able to independently, examine, assess and discriminate between alternatives.

Schedule

Schedule

The module commences on Tuesday, 10th August 2021 at 12 noon with an on-line lecture (via Zoom).
Thereafter, the schedule is as follows:

Lectures:

  • Tuesdays, 2.00 pm - 4.00 pm; Venue: Online class (refer to LumiNUS for details)

Tutorials:

  • Group 1: Thursdays, 12 noon to 2.00 pm; Venue: SR-2
  • Group 2: Fridays, 12 noon to 2.00 pm; Venue: SR-2

Structure

Structure

Week 1: The Nature of Physical Reality & Science

"To see what is general in what is particular and what is permanent in what is transitory is the aim of scientific thought."

A.N. Whitehead (1911)

“The aim of science is, on the one hand, a comprehension, as complete as possible, of the connection of the sense experiences in their totality, and on the other hand, the accomplishment of this aim by the use of a minimum of primary concepts and relations.”

Albert Einstein from Physics and Reality (1936), reprinted in Ideas and Opinions (p.293)

Reading Assignments:

  • The Copernican Revolution: Planetary Astronomy in the Development of Western Thought; Chap.1, pp. 2-4, ‘Copernicus and the Modern Mind’
  • Physics, the Human Adventure: From Copernicus to Einstein and Beyond; Chap. 3 'On the Nature of Scientific Theory', sections 3.1 & 3.4
  • Victory & Vexation in Science; Chap. 10 'Perspectives on the Thematic Analysis of Scientific Thought', p. 140-151, ‘The Thematic Approach’

         What is this thing called Science?;  Introduction, Chap. 1 ‘Science as knowledge derived from the facts of experience’ 

     Tutorial 1

     

Week 2-3: Space, Time & the Riddle of Motion

Reading Assignments:     

  • Physics, the Human Adventure: From Copernicus to Einstein and Beyond; Chap 3. 'On the Nature of Scientific Theory', section 3.2 & Chap. 5 ‘Galileo and the New Astronomy’
  • Foreword by Albert Einstein to Galileo Galilei's Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake
  • Galileo’s preface to the Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake
  • The Birth of a New Physics by I. Bernard Cohen, Chaps. 2 'The Old Physics'; Chap. 5 'Toward an Inertial Physics' (pages 81-106) & Supplement 10 'A Summary of Galileo’s Major Discoveries in the Science of Motion'

         Cosmological Koans by Anthony Aguirre, Chap. 1 The Arrow

         Resolving Zeno's Paradoxes by W.L. McLaughlin; Scientific American, Vol.271, no. 5, p.84-89 (1994)

         Understanding Physics; Vol. I, Chap. 2 'Falling bodies'

         Physics: Structure & Meaning by Leon Cooper, Chap. 3 'The Tower of Pisa' & Chap. 4 'A Very New Science'

         Feynman Lectures on Physics; Chap. 8 ‘Motion’

         What is this thing called Science?; Chap 2. ‘Observation as Practical Intervention’ 

  

Tutorial 2

Video on demand:

Starry Messenger [go to LumiNUS > Multimedia]

Week 4-5: The Dynamics of Motion: Force & Momentum

Reading Assignments:

  • Physics, the Human Adventure: From Copernicus to Einstein and Beyond; Chap. 9 Newton’s Laws of Motion
  • The Birth of a New Physics by I. Bernard Cohen; Chap. 5 ‘Toward an Inertial Physics’: Formulating the Law of Inertia (pages 106-126)
  • The Construction of Modern Science: Mechanisms and Mechanics; Chap. VII The Science of Mechanics & Chap, VIII Newtonian Dynamics                                                                                                 
  • Isaac Newton, Mathematical Principles of Natural Philosophy and System of the World (trans by Andrew Motte) 
  • Inertia by Dennis Sciama, Scientific American, Vol. 196, No. 2 (February 1957) pp. 99-109                                                                                                                                                                                                                                                                                                        

What is this thing called Science? Chap 3. ‘Experiment’

    Understanding Physics Vol. I, Chap. 3 'The Laws of Motion'

    Physics: Structure & Meaning by Leon Cooper, Chap. 3 'What is a Force' & Chap. 4 "The Lion is Known by His Claw"

    Feynman Lectures on Physics, Chap. 9 ‘Newton’s Laws of Dynamics’ and Chap. 10 ‘Conservation of Momentum’

    Motion of a Spring Pendulum

    Motion of a Simple Pendulum

    Elastic and Inelastic Collisions

    Tutorial 3

    Week 6-7: Newton’s 'System of the World': the law of universal gravity

    Reading Assignments:

    • Physics, the Human Adventure: From Copernicus to Einstein and Beyond; Chap. 10 Rotational Motion & 11 Newton’s Law of Universal Gravitation (sections 11.1 to 11.5)
    • Newton’s Principia for the Common Reader; Chap. 1 ‘The beginnings and the writing of the Principia’
    • The Birth of a New Physics by I. Bernard Cohen; Chap. 7 ‘The Grand Design- A New Physics’ (pp. 148-158); Supplement 11, Newton’s Debt to Hooke: The Analysis of Curvilinear Orbital Motion; Supplement 12, The Inertia of Planets and Comets; Supplement 14, Newton and the Apple: Newton’s Discovery of the v2/r Law; Supplement 15, Newton on “Gravitational” and “Inertial” Mass; Supplement 16, Newton’s Steps to Universal Gravity
    • George Smith, Newton's Philosophiae Naturalis Principia Mathematica (Stanford Encylopedia of Philosophy)                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

    What is this thing called Science? Chap 4. ‘Deriving theories from the facts: induction’

    Understanding Physics Vol. I; Chap. 4 ‘Gravitation’; Chap. 5 ‘Weight’

    Physics: Structure & Meaning, Chap. 6 ‘Newton's System of the World’

    Feynman Lectures on Physics; Chap. 7 'The Theory of Gravitation'

    Uniform Circular Motion

    Tutorial 4

    Week 8-11: The Motion of the Planets

    Reading Assignments:

    • Physics, the Human Adventure: From Copernicus to Einstein and Beyond; Chap. 1 ‘The Astronomy of Ancient Greece’, Chap. 2 ‘Copernicus’ Heliocentric Theory’, Chap 4. ‘Kepler’s Laws’ & Chap.11 Newton’s Law of Universal Gravitation (Sections 11.6 to 11.11)
    • The Birth of a New Physics by I. Bernard Cohen; Chap. 7 ‘The Grand Design - A New Physics’ (pp.158-184);  Supplement 12, The Inertial of Planets and Comets; Supplement 13, Proof that an Elliptical Planetary Orbit Follows from the Inverse-Square Law
    • The Copernican Revolution: Planetary Astronomy in the Development of Western Thought; Chap. 1, pp. 25-44, ‘The Birth of Scientific Cosmology – The Two-Sphere Universe’, Chap. 2, ‘The Problem of the Planets’ & Chap. 5, ‘Copernicus’ Innovation’                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Feynman's Lost Lecture: The Motion of the Planets Around the Sun ed. by D.L. & J.R. Goodstein; Chap. 1: 'From Copernicus to Newton'

    Gravitational Orbits: two-body

    Gravitational Orbits: two & three-body

    The Solar System

    Kepler’s First Law

    Kepler’s Second Law

    Tutorial 5

    Videos on demand:

    Conservation of Energy (IVLE)

    Energy and Eccentricity (IVLE)

    Potential Energy (IVLE)

    Week 12-13: Relativity in Physics & the Physics of Relativity

    Reading Assignments:

    • The Copernican Revolution: Planetary Astronomy in the Development of Western Thought; Chap. 7, ‘The New Universe’
    • The Birth of a New Physics by I. Bernard Cohen; Chap. 7 ‘The Grand Design- A New Physics’ (pp.180-184)
    • Physics: Structure & Meaning, Chap. 25 'The Union of Newton's Laws with the Principle of Relativity'; Chap. 27 'The General Theory of Relativity (Einstein's Theory of Gravitation)'

    Tutorial 6

    Gravitational Orbits of a Black Hole

    Readings

    Course Reference Texts

    The course reference texts will include various chapters or extracts from the following:

    • Physics, the Human Adventure: From Copernicus to Einstein and Beyond by Gerald Holton & Stephen G. Brush; Rutgers Univ. Press, ISBN 0-8135-2908
    • The Copernican Revolution: Planetary Astronomy in the Development of Western Thought by Thomas S. Kuhn; Harvard Univ. Press, ISBN 0-674-17103-9
    • The Birth of a New Physics by I. Bernard Cohen (Penguin 1985; ISBN 0 14 013633 9)

    The above books should be available in the Scholar’s reading room (or the NUS Central/ Science Library).

    Note: To follow this course, it is important that the relevant weekly readings and tutorial questions are completed during the assigned week(s) and not ‘postponed’ to later on in the course. Students should manage their time to allow for this!

    Additional Reading Material

    For various parts of this module, students will benefit from consulting relevant sections or chapters of some of the following books. They may also serve as useful resource materials for class discussions during the course, as well as your essays or term paper.

    HISTORICAL & GENERAL

    Thematic Origins of Scientific Thought: Kepler to Einstein by Gerald Holton (Harvard University Press, 1988; ISBN 0-674-87748-9)

    The Construction of Modern Science: Mechanisms and Mechanics by Richard S. Westfall; Cambridge Univ. Press, ISBN 978-0-521-29295-5

    The Scientific Renaissance 1450-1630 by Marie Boas Hall (Dover 1994; ISBN 978-0486-28115-5)

    Newton selected & edited by I. Bernard Cohen & R.S. Westfall (W.W. Norton & Co, 1995; ISBN 0 393 95902 3) Selected texts and commentaries on Newton’s scientific and other writings.

    Newton’s Principia for the Common Reader by S. Chandrasekhar (Oxford University Press, 1997; ISBN 0-19-851744-0)

    The Principia: Mathematical Principles of Natural Philosophy by Isaac Newton, translated by I. Bernard Cohen, Anne Whitman, Julia Budenz (University of California Press, 1999; ISBN-13: 978-0520088177)

    Galileo: A Very Short Introduction by Stillman Drake ( Oxford University Press, 1996; ISBN 0-19-285456-9)

    Galileo Galilei: Sidereus Nuncius or The Sidereal Messenger translated by Albert Van Helden (Univ. of Chicago Press, 1989: ISBN 0-226-27903-0)

    Galileo: Dialogue Concerning the Two Chief World Systems translated by Stillman Drake (University of California Press 1967)

    The Copernican Revolution: Planetary Astronomy in the Development of Western Thought by Thomas S. Kuhn (Harvard University Press, 1992; ISBN-13: 978-0674171039)

    The Ascent of Man by J. Bronowski (BBC Publications, 1975; ISBN 0 563 104988) Chapters five (The Music of the Spheres), six (The Starry Messenger) and seven (The Majestic Clockwork).
    A historical analysis of the development of key ideas in science from a civilizational perspective (albeit somewhat Eurocentric) perspective; available as DVDs from the Scholar’s reading room.

    Understanding Physics by Isaac Asimov (QC23UND1993); (Barnes & Noble Books,1993; ISBN 0-8802-9251-2)  

    The Evolution of Physics by A. Einstein and L. Infeld (Simon & Schuster, 1966; ISBN0-671-20156-5)

    What is this thing called Science?  by A.F. Chalmers (Hackett Publishing Co., 3rd Edition,  ISBN 0-87220-452-9)

    Discovering the Natural Laws by M.A. Rothman (Dover Publications 1972; ISBN 0-486-26178-6

    The Logic of Scientific Discovery by Karl Popper (Harper Torchbooks, Harper & Row 1968; SBN 06-130576-6)

    Conjectures And Refutations: The Growth of Scientific Knowledge by Karl Popper ( Harper Torchbooks, Harper & Row; SBN 06-131376-9)

    The Nature of Physical Reality: A Philosophy of Modern Physics by Henry Margenau (Ox Bow Press, 1977; ISBN 0-918024-02-1)

    Science and Philosophy by A.N. Whitehead (Philosophical Library, New York, 1948; ISBN- 8022-1864-4)

    The Philosophy of Space & Time by Hans Reichenbach (Dover Publications, 1957; ISBN 0-486-60443-8)

    NEWTON ’S THEORY OF GRAVITY & CLASSICAL MECHANICS

    The Character of Physical Law by R.P. Feynman (MIT Press, 1967; ISBN 0262560038)

    Feynman's Lost Lecture: The Motion of the Planets Around the Sun ed. by D.L. & J.R. Goodstein (Vintage, 1997; ISBN 0 09 97362)

    Physics: Structure & Meaning by Leon N Cooper (QC21PHY1992); University Press of New England, ISBN 0-87451-592-0

    Six Easy Pieces by R.P. Feynman (NL018); Addison-Wesley Publishing Co., ISBN 0-20140-825-2 (a reprint volume of selected chapters from The Feynman Lectures, see below)

    Feynman Lectures on Physics Vol. 1 by R.P. Feynman (NL214FEY); Addison-Wesley Publishing Co.

    EINSTEIN’S THEORY OF SPECIAL RELATIVITY

    Relativity Simply Explained by Martin Gardner; (Dover, 1997; ISBN 0-486-29315-7)

    Relativity by A. Einstein (Routledge, 2001; ISBN 0 415 25384 5)

    Great Ideas in Physics by Alan Lightman (McGraw Hill, 2000; ISBN 0-07-135738-6)

    EINSTEIN’S GENERAL THEORY OF RELATIVITY & GRAVITATIONAL PHYSICS

    Einstein’s Universe: The Layperson’s Guide by Nigel Calder ( Penguin, 1990; ISBN 0 14 013516 2)

    Was Einstein Right? Putting General Relativity to the Test by Clifford M. Will (The Perseus Books Group, 1993; ISBN 0465090869)

    Assessment

    Assessment

    Assessment will be on the basis of the following continuous assessment criteria:

    Tutorials & Class Participation: 20%
    Mid-term Essay Assignment: 25%
    Group Projects: 20%
    Final Term Paper: 35%
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