The Nature of Normal Science
The Nature of Normal Science
I. Concept of a Paradigm
Established Usage vs. Scientific Usage:
In its established usage (e.g., grammar: "amo, amas, amat" as a pattern for "laudo, laudas, laudat"), a paradigm is an accepted model or pattern whose examples can be replicated or replaced.
In science, a paradigm is rarely an object for replication. Instead, it functions similarly to an accepted judicial decision in common law, serving as an object for further articulation and specification under new or more stringent conditions.
Initial Limitations and Success of Paradigms:
Paradigms are often limited in scope and precision at their first appearance.
They gain status by being more successful than competitors in solving a few acute problems recognized by practitioners.
Initial success is largely a promise, discoverable in selected and incomplete examples (e.g., Aristotle's motion analysis, Ptolemy's planetary computations, Lavoisier's use of the balance, Maxwell's electromagnetism).
II. Characteristics and Purpose of Normal Science
Definition: Normal science consists of the actualization of the promise of a paradigm.
Actualization Methods: This is achieved by:
Extending knowledge of facts that the paradigm reveals as important.
Increasing the match between these facts and the paradigm's predictions.
Further articulating the paradigm itself.
"Mop-Up Work": The bulk of scientific activity; most scientists engage in this throughout their careers.
Nature of the Enterprise: It is an attempt to "force nature into the preformed and relatively inflexible box that the paradigm supplies."
Aims of Normal Science:
Not to call forth new sorts of phenomena (those that don't fit the box are often not seen).
Not to invent new theories (scientists are often intolerant of new theories).
Instead, research is directed to the articulation of phenomena and theories already supplied by the paradigm.
Restricted Vision: Normal science investigates minuscule areas, leading to a drastically restricted vision.
Essence of Restrictions: These restrictions, born from confidence in a paradigm, are essential to the development of science because they:
Focus attention on a small range of esoteric problems.
Force scientists to investigate nature with unimaginable detail and depth.
Built-in Mechanism for Change: Normal science possesses a mechanism that ensures the relaxation of these restrictions when the paradigm ceases to function effectively, leading to a change in research problems and scientific behavior (prelude to scientific revolutions).
Achievement of Normal Science: During its successful period, a paradigm enables the profession to solve problems its members could not have imagined or undertaken otherwise, with a part of that achievement proving permanent.
III. Classification of Normal Scientific Problems: Fact-Gathering
Normal science primarily consists of three foci for factual scientific investigation, which are not always distinct:
Determining Facts the Paradigm Shows as Revealing:
The paradigm highlights certain facts as particularly significant to understanding the nature of things.
These facts are then determined with greater precision and in a wider variety of situations.
Examples:
Astronomy: Stellar position and magnitude, periods of eclipsing binaries and planets.
Physics: Specific gravities and compressibilities, wavelengths and spectral intensities, electrical conductivities and contact potentials.
Chemistry: Composition and combining weights, boiling points and acidity, structural formulas and optical activities.
Effort Involved: Increasing accuracy and scope for these facts occupies a significant portion of experimental and observational science. It requires complex special apparatus (e.g., synchrotrons, radio telescopes), first-rate talent, time, and significant financial backing.
Reputation: Scientists like Tycho Brahe and E. O. Lawrence gained fame not from novel discoveries, but from the precision, reliability, and scope of their methods for redetermining previously known facts.
Comparing Facts Directly with Paradigm Theory Predictions:
This class involves factual determinations that, though often lacking intrinsic interest, can be directly compared with theoretical predictions from the paradigm.
Difficulty: Direct comparison between theory (especially mathematical) and nature is often difficult and limited to few areas (e.g., only a few accessible areas for Einstein's general theory of relativity, such as Mercury's perihelion precession, red shift, bending of light; gravitational shift of Mossbauer radiation).
Approximations: Applications often demand theoretical and instrumental approximations, limiting expected agreement.
Challenge: Improving this agreement or finding new areas of demonstrable agreement is a constant challenge for experimentalists and observers.
Examples of Special Apparatus:
Special telescopes to demonstrate Copernican prediction of annual parallax.
Atwood's machine (century after Principia) for the first unequivocal demonstration of Newton's second law.
Foucault's apparatus to show light speed greater in air than water.
Gigantic scintillation counter to demonstrate neutrino existence.
Paradigm Dependency: This type of experimental work is highly dependent on the paradigm, which sets the problem and often informs the design of the apparatus (e.g., Atwood machine measurements would be meaningless without the Principia).
Articulating Paradigm Theory (Resolving Ambiguities):
Empirical work undertaken to resolve residual ambiguities in the paradigm theory and enable solutions to problems it had only highlighted.
This class is considered the most important.
Subdivisions:
Determination of Physical Constants:
In mathematical sciences, experiments aim to determine physical constants.
Example: Universal Gravitational Constant (G): Newton indicated its existence but didn't estimate its size. Cavendish finally determined it in the 1790s. Due to its central position, improved values have been sought repeatedly (e.g., G was measured about 24 times between 1741 and 1901).
Other Examples: Astronomical unit, Avogadro's number, Joule's coefficient, electronic charge.
Prerequisite: Such efforts require a paradigm theory to define the problem and guarantee a stable solution.
Discovery of Quantitative Laws:
Experiments aim at establishing quantitative laws.
Examples: Boyle's Law (gas pressure to volume), Coulomb's Law (electrical attraction), Joule's formula (heat generated to electrical resistance and current).
Paradigm as Prerequisite: The notion that these laws are found by aimless measurements is historically unsupported.
Boyle's Law: Required the recognition of air as an elastic fluid adaptable to hydrostatic concepts.
Coulomb's Law: Depended on constructing special apparatus to measure force between point charges, which in turn relied on the prior concept of electric fluid particles acting at a distance.
Theoretical Guesses: Since Galileo, quantitative laws have often been correctly guessed with paradigm aid years before experimental determination was possible.
Qualitative Ambiguity Resolution:
Prevalent in periods and sciences dealing with qualitative aspects of nature.
A paradigm developed for one set of phenomena might be ambiguous in related applications.
Experiments choose among alternative ways of applying the paradigm to a new area.
Example: Caloric Theory: Initially applied to heating/cooling by mixtures and phase change. When applied to other phenomena (chemical combination, friction, gas compression/absorption), ambiguities arose.
Problem: Heating by compression could be explained by mixing gas with void (if vacuum had heat capacity) or by a change in specific heat of gases with pressure, among others.
Experiments: Many experiments were devised to distinguish these possibilities, all arising from and exploiting the caloric theory for design and interpretation.
IV. Classification of Normal Scientific Problems: Theoretical
Theoretical problems in normal science largely mirror the experimental and observational classes.
Predicting Factual Information of Intrinsic Value (Small Part):
Using existing theory to predict intrinsically valuable factual information.
Examples: Astronomical ephemerides, computation of lens characteristics, radio propagation curves.
Often considered "hack work" relegated to engineers or technicians, rarely appearing in significant scientific journals.
Displaying New Applications or Increasing Precision (Main Part):
Manipulations of theory undertaken not for intrinsic value, but because they can be directly confronted with experiment.
Purpose: To show a new application of the paradigm or increase the precision of an existing one.
Need: Arises from immense difficulties in establishing points of contact between theory and nature.
Example: Newtonian Dynamics after Newton:
Principia's Success: By the early 18^{th} century, Newton's Principia was taken for granted due to significant increases in research scope and precision.
Derived Kepler's Laws and explained lunar deviations.
Derived results for pendulums and tides on Earth.
Derived Boyle's Law and sound speed formula (with ad hoc assumptions).
Newton's Limited Applications: Despite generality, Newton developed few applications, and these were not as precise as what a modern graduate student could achieve.
Terrestrial Applications: Principia was mainly for celestial mechanics; adapting it for terrestrial problems (especially motion under constraint) was unclear.
Continental scientists (Bernoullis, d'Alembert) used Galileo's and Huyghens' techniques successfully for terrestrial problems.
The goal was to show these techniques and Principia's as special cases of a more general formulation.
Problem of Precision:
Empirical Aspect: Required special equipment (Cavendish, Atwood, improved telescopes) for specific data.
Theoretical Aspect: Newton made approximations (e.g., pendulum bob as mass point, ignoring air resistance, neglecting inter-planetary gravitational attraction for Kepler's Laws) that limited perfect agreement between predictions and experiments.
Successors' Work: Newton's theory was more than satisfactory, but these limitations created fascinating theoretical problems for successors.
Europe's best mathematicians (Euler, Lagrange, Laplace, Gauss) worked to improve the match between Newton's paradigm and celestial observations (e.g., motions of more than two attracting bodies, stability of perturbed orbits).
They developed powerful mathematical techniques for hydrodynamics and vibrating strings for applications Newton hadn't attempted.
This type of work constitutes most theoretical work in mathematical sciences.
Paradigm Articulation (Theoretical Reformulation):
Even in mathematical sciences, and predominantly in qualitative sciences, theoretical problems involve paradigm articulation.
Clarification by Reformulation: Problems aim for logical and aesthetically satisfying reformulations.
Example: Principia: Was not always easy to apply due to clumsiness and implicit meaning.
Goal: Mathematicians (Euler, Lagrange, Hamilton, Jacobi, Hertz) reformulated mechanics to present explicit and implicit lessons of Principia and Continental mechanics in a more coherent, uniform, and unequivocal version for new problems.
Interconnectedness of Empirical and Theoretical Articulation:
Problems of paradigm articulation are simultaneously theoretical and experimental.
Example: Coulomb: Had to use electrical theory to design his equipment before making measurements, and his measurements refined that theory.
Example: Caloric Theory: Scientists who designed experiments to distinguish heating by compression theories were often the same ones who formulated those versions. Their work yielded both new information and a more precise paradigm by eliminating ambiguities.
V. Conclusion on Normal Science Problems
These three classes of problems (determination of significant fact, matching facts with theory, and articulation of theory) exhaust the literature of normal science, both empirical and theoretical.
They do not exhaust the entire literature of science, as "extraordinary problems" exist.
Extraordinary Problems: These are not readily available and emerge only on special occasions, prepared by the advance of normal research.
Majority of Work: The overwhelming majority of problems undertaken by even the best scientists fall into these three categories.
Paradigm's Role: Work under a paradigm can only be conducted in these ways; to desert the paradigm is to cease practicing the science it defines.
Lead to Revolutions: Such desertions do occur and are the pivots around which scientific revolutions turn, which are prepared by normal scientific pursuits.