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The history of physics is full of examples of phenomena that used to be described independently, until additional insight proved they were the same thing.

Some famous instances are

  • motion of bullets and motion of stars and planets, until Newton unified Galileo and Kepler visions
  • mechanical work and heat each had their own unit (Joules and calories) until it was realized heat is just another form of energy
  • electricity and magnetism, until Maxwell unified Gauss and Ampere's laws
  • electromagnetism and light propagation
  • spin and special relativity until Dirac's equation
  • etc.

Throughout history, these unifying concepts have shaped the way we see the world, and it certainly seems to me as if the general trends is towards more unification.

Is the reverse process also an observed trend, though less famous? In other words, what are significant advances that have been made in the natural sciences from realizing that concepts that used to be thought the same were actually distinct?

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  • $\begingroup$ This question has no way to determine a single "best" answer, as it's essentially just asking for an unbounded list. Basically every answer could be as correct as any other. $\endgroup$ – V2Blast Jan 19 at 8:05
  • $\begingroup$ Depending on how settled you think it's become in recent years, we could go with Apatosaurus and Brontosaurus, and as an added bonus they've gone from distinct to the same to distinct. $\endgroup$ – J.G. Jan 28 at 6:26
  • $\begingroup$ @V2Blast I see your point but isn't this the purpose of the [examples] tag? $\endgroup$ – Alexis Jan 29 at 10:14
  • $\begingroup$ @Alexis: Hmm. I guess so. Though it's strange for there to be a tag for a type of question that explicitly goes against the StackExchange format (i.e. the part that says to avoid asking questions where "every answer is equally valid" - though it's not subjective, it's impossible to accept any answer as the best one because they're basically all correct). $\endgroup$ – V2Blast Jan 29 at 10:19
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The two most famous paradigmatic examples of de-unification are phlogiston and ether. The Kaluza-Klein theory of gravity and electromagnetism did not get to spread as far and wide before faltering. The splitting of jade into two distinct minerals, nephrite and jadeite, is a small scale example.

The phlogiston/caloric theory was able to unify chemical and thermal phenomena in a way that was eliminated by the mechanical theory of heat. Specifically, the processes of heating/cooling were assimilated to chemical reactions with phlogiston (later caloric), and this was one of the key arguments in 18-19th century for preferring this theory. Stahl explained burning and decalcination (formation of metals) by separation of phlogiston from matter in 1703. Black's work in 1757-1764 led to the explanation of latent heat by phlogiston's ability to combine chemically with matter, and of gaseous states as solutions of liquids in phlogiston. Even Lavoisier, who introduced the oxygenation theory of burning in 1780-s, needed a heat fluid (renamed into caloric) to make his theory work. For more details and references see What are the major flaws of the “caloric” theory of heat?

Ether offered a unification of wave phenomena with hopes of extending it to an intuitively appealing unified theory of matter. Kelvin's theory of vortex atoms and Lorentz's theory of electrons were steps in that direction. Suffice it to quote Michelson from 1902:

"The day seems not far distant when the converging lines from many apparently remote regions of thought will meet... Then the nature of the atoms, and the forces called into play in their chemical union... the explanation of cohesion, elasticity, and gravitation — all these will be marshaled into a single compact and consistent body of scientific knowledge... one of the grandest generalizations of modern science ... that all the phenomena of the physical universe are only different manifestations of the various modes of motion of one all-pervading substance — the ether."

The ether loss was taken particularly hard, it still has its adherents, and even Einstein (1920) mused about reconceptualizing it:"We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the general theory of relativity space without Aether is unthinkable...". Dirac (1951) suggested identifying it with the QED vacuum:"The Aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an Aether... We have now the velocity at all points of space-time, playing a fundamental part in electrodynamics. It is natural to regard it as the velocity of some real physical thing."

More generally, de-unifications are examples of what is termed Kuhn loss, benefits of a prior theory that do not carry over to its successors, see Examples of Kuhn loss? The topic is controversial. In recent decades the disunity of science thesis has gained popularity. It is argued that there are insurmountable obstacles to unifying physical and biological concepts, for example, or biological and psychological ones. In The Conceptual Foundations of Renormalization Theory (1993) Cao and Schweber describe the effective field theory approach that opposes the "theory of everything" even in physics:

"This position rejects uncompromisingly the idea successively advanced during the last fifteen years by grand unified theorists, supergravity theorists, and superstring theorists that the development of fundamental physics will end with the discovery of an ultimate, definitive, and conclusive mathematical formalism. Rather, the development is taken as a process of successive extrapolations that is assumed not to have an end, with every step of the extrapolation being justified by a collective reinterpretation of theory and observation before and after the extrapolation".

Presumably, the reinterpretations should be expected to involve de-unifications with previously unified phenomena coming apart at higher resolutions. This effect should be expected even under the most traditional views of the history of science: many early unifications are bound to be premature/superficial, and hence come to be broken in the course of further research.

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    $\begingroup$ Something similar has been happening in theoretical linguistic syntax over the last few decades. Chomsky's Universal Grammar is being disunified pretty thoroughly; while there are still True Believers, the emphasis of young researchers is very practical and data-oriented. $\endgroup$ – jlawler Dec 12 '18 at 15:23
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  1. number versus numeral (a distinction everyone learns in the third grade – except for those who played hooky that day)

  2. loss of unique-factorization as you move from the reals to the complex numbers – e.g., 26 = (2)(3) and 26 = (1 – 5i)(1 + 5i)

  3. for two distinct numbers, in the set of positive numbers “is to the left of” and “is farther from 0” are synonymous, but are not synonymous for the set of real numbers.

  4. For two distinct lines, in the plane “are everywhere equidistant from each other” and “do not intersect” are synonymous, but are not synonymous for 3D space.

  5. rotation versus revolution

  6. apparent astronomical movement versus actual astronomical movement

  7. dependence of final result on initial conditions, versus, independence

  8. rational versus irrational numbers

  9. a polynomial versus the polynomial function associated with it

  10. In foraging theory, time minimization versus energy maximization (pp. 8-9 of the book ‘Foraging Theory’ by Stephens and Krebs)

  11. explanation versus prediction

  12. tracking versus detection

  13. detection versus recognition

  14. ordinal numbers versus cardinal numbers

  15. In foraging, path depletion not equal to negative acceleration of the energy gain function

  16. complete information versus perfect information

  17. a function being analytic versus being infinitely differentiable

  18. two types of paraboloid (elliptic and hyperbolic)

  19. wave/particle duality of light

  20. MAD (median absolute deviation) has more than one meaning

  21. inertial mass versus rest mass

  22. domain of a partial function is ambiguous, depending on the discipline (logic or mathematics)

  23. multiple, and only partially satisfactory, definitions of tortuosity

  24. general life situation versus general life situation (terminology of Kurt Lewin)

  25. singularities of solutions not necessarily occurring only at singularities of the equation

  26. inequality of the types of cardinality for surface area and volume (e.g.: Gabriel’s horn)

  27. sometimes homeomorphism type is not determined by homotopy type

  28. “There are several definitions of R2 that are only sometimes equivalent.” (Wikipedia’s article on coefficient of determination)

  29. coverage probability splits into ‘actual’ and ‘nominal’

  30. utility versus exactness – e. g., Agresti and Coull's 1998 paper “Approximate is Better than ‘Exact’ for Interval Estimation of Binomial Proportions.” (cited in the Wikipedia article on binomial proportion confidence intervals)

  31. having to choose between a statistical estimator that is unbiased or which has better mean squared error

  32. There are two types of Hermite polynomials: the ‘probabilists’ Hermite polynomials and the ‘physicists’ Hermite polynomials.

  33. good for exploratory data analysis versus good for classification applications – e. g., Sammon mapping

  34. canonical form vs normal form (see the Wikipedia article on computer algebra)

  35. A subgroup of a finitely generated group need not be finitely generated.

  36. exploiting prey versus exploiting patches

  37. the zero-one law in foraging theory versus Kolmogorov’s zero-one law – the former being prescriptive, and the latter being descriptive

  38. double-entry bookkeeping versus single-entry bookkeeping

  39. agent-designer’s goals versus agent’s goals

  40. how the product topology is defined for finitely many spaces versus how it is defined for infinitely many spaces

  41. ‘heavy-tailed’ distribution has several meanings

  42. non-unique generalization of the single-variable derivative

  43. a series converging versus getting arbitrarily many digits correct

  44. convexity of a set versus convexity of the region bounded by the set

  45. dice equivalence versus dice winning against each other with equal probability

  46. connectedness versus i-connectedness

  47. connectedness versus path-connectedness

  48. leaves versus structures that look like leaves (such as that possessed by mosses and leafy liverworts)

  49. the polyphyletic nature of algae versus the situation of living in water and performing photosynthesis

  50. whether energy is present versus whether it is available

  51. sidereal time versus solar time

  52. rolling friction versus static friction

  53. planet versus star

  54. elastic versus inelastic collision

  55. heat versus temperature

  56. a removable versus a non-removable discontinuity

  57. blood versus type-distinguished blood

  58. vapor versus gas

  59. air versus oxygen

  60. whale versus fish

  61. gold versus fool’s gold

  62. rocket propulsion versus friction-based propulsion

  63. physical change versus chemical change

  64. chemical combustion versus stellar dynamics

  65. warm-blooded versus cold-blooded creatures

  66. robustness versus anti-fragility

  67. linear response versus nonlinear response

  68. chaotic versus non-chaotic phenomena

  69. continuity versus differentiability

  70. speed of sound in air versus speed of sound in water

  71. how others hear us versus how we hear ourselves

  72. compound versus element

  73. Bronze-Age creation myth versus Evolution

  74. jealousy versus envy

  75. perception controlling behavior versus behavior controlling perception

  76. conscious versus unconscious mind

  77. momentum versus energy

  78. potential energy versus kinetic energy

  79. radiant energy versus heat

  80. 24 hour period versus calendar day (as in ‘Around the World in 80 Days’)

  81. mass versus weight

  82. currency versus money

  83. sub-sonic versus super-sonic explosions

  84. cycloid versus circular arc

  85. coma versus death

  86. medical intervention versus palliative care

  87. data versus information

  88. macro versus micro economics

  89. weather versus climate

  90. strategy versus tactics

  91. longitudinal versus transversal waves

  92. traditional versus public-key cryptography

  93. the definition of uniform integrability in measure theory versus probability theory

  94. Nash equilibrium for a game repeated finitely many times versus infinitely many times

  95. looking only at truth values versus looking at content (material implication)

  96. Spheroidal coordinates are of two types: oblate and prolate.

  97. how symmetric groups behave on finite versus on infinite sets

  98. optimal behavior in the Prisoners’ Dilemma in the short run (betrayal) versus in the long run (cooperation)

  99. If W is a generalized complex subspace of a generalized complex vector space V, then V/W is not necessarily a generalized complex quotient of V.

  100. topological definition of an object versus geometrical definition

  101. stable, versus merely long-lived

  102. defining fields by polynomials giving different results in the finite and infinite cases

  103. temperature versus conductivity

  104. intensive versus extensive properties

  105. addition of heat versus a rise in temperature (i.e., the phenomenon of ‘latent heat’)

  106. Subsystems can be connected in series or parallel.

  107. distinct types of rock (igneous, sedimentary, metamorphic)

  108. musical time versus metronome time

  109. amortized update time of an algorithm versus worst-case update time

  110. absence of evidence versus evidence of absence

  111. simple versus small (e.g., uncompressed data versus compressed; cf: Pascal’s remark about not having time to make his letter shorter)

  112. ‘no students’ (but staff present) versus ‘no school’ (nobody present)

  113. a commonly accepted proxy for a hard-to-pin-down concept (e.g., variance as a proxy for risk); also: measure of an entity versus a (more convenient) proxy measure for the entity (e.g., weight as a proxy measure for mass)

  114. ‘good’ cholesterol versus ‘bad’ cholesterol

  115. cis versus trans configurations of unsaturated fatty acids

  116. direct current versus alternating current

  117. animal classification by its diet versus by the nature of its digestive system

  118. frequency of a burden versus its intensity

  119. specification versus implementation

  120. testing versus debugging

  121. impossibility versus probability of 0

  122. de jure versus de facto

  123. topological convergence versus convergence in measure

  124. frontier versus wilderness

  125. revenue versus profit

  126. voltage versus current

  127. dictionary versus encyclopedia

  128. conservation as wilderness preservation versus as resource management

  129. background versus foreground

  130. short term versus long term

  131. duality in terms of polar reciprocation versus topological duality

  132. a candid photo versus a posed photo

  133. mixture versus solution

  134. billable time versus elapsed time

  135. independent generalizations (such as how Newton’s work stands in relation to Kepler’s work) versus dependent generalizations (such as how the Law of Cosines stands in relation to the Pythagorean Theorem, or how Taylor’s Theorem stands in relation to Maclaurin’s Theorem)

  136. ability as a conversationalist versus ability as a lecturer

  137. archival storage versus working storage

  138. complex versus complicated

  139. powdered chocolate mix for a cold drink versus for a hot drink

  140. form determined by gravity versus by capillarity

  141. vector as an arrow (‘something with magnitude and direction’) versus as an element of a vector space

see also the website ‘DifferenceBetween.net’: http://www.differencebetween.net/

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    $\begingroup$ Nice answer! Many examples are from mathematics though, not natural sciences. $\endgroup$ – Alexis Dec 3 '18 at 7:34
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    $\begingroup$ Add language vs writing, words versus thoughts, words versus things, grammar versus correctness. $\endgroup$ – jlawler Dec 12 '18 at 15:25
  • $\begingroup$ @jlawler: Ho hum. $\endgroup$ – EulerSpoiler Dec 14 '18 at 23:52
  • $\begingroup$ "number versus numeral"? What are you referring to, specifically? $\endgroup$ – Geremia Jan 29 at 23:58
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    $\begingroup$ The second item makes no sense. The fields of real and complex numbers, as well as polynomials in 1 or more variables with coefficients in the real or complex numbers, have unique factorization. There is no "loss" in either case unless you were not writing what you meant to say there. $\endgroup$ – KCd Jan 30 at 1:09
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Mass & weight. It’s easy enough to make that mistake since we see objects in a uniform gravitational field.

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  • $\begingroup$ But the joke about how you would 'weigh less on the moon' is well known. $\endgroup$ – EulerSpoiler Mar 10 at 15:11

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