The diagrams of the two cultures noted by C.P. Snow are the inverses of one another. On the humanities side, things come together as we progress, resulting in a pyramid (e.g., Maslow’s hierarchy of needs). On the technical side, things come apart as we progress (former synonyms no longer holding), resulting in an inverted pyramid. I call these instances of things coming apart ‘technical dissociations’. Here is a big list of technical dissociations (no doubt grossly incomplete):
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 closer to 0” are synonymous, but are not synonymous for the set of arbitrary 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 (e.g., ‘sunrise’ and ‘sunset’)
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 (e.g., a convex Jordan curve)
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. chemical compound versus chemical 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. synonymity of cardinality and measure for finite sets
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 (e.g., is the circle a 1-sphere or a 2-sphere?)
101. stable, versus merely long-lived
102. defining fields by polynomials giving different results in the finite and infinite cases
103. temperature versus conductivity (why water feels colder than air at the same temperature)
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 (e.g., the panda)
118. frequency of a burden versus its intensity
119. specification versus implementation
120. testing versus debugging
121. impossibility versus probability of 0 (things of probability 0 happening all the time, actually)
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
142. an analytic set versus a Borel set (Suslin’s theorem)
143. catastrophe versus tragedy (“If he were to fall in the Thames it would be a catastrophe. If someone were to pull him out again, it would be a tragedy.”)
144. The subgroup identity is equal to the group identity, but when we move up to rings, we find that a subring can have an identity different from the ring.
145. for organizations, normative control and a regime of collective interest versus rational
control and a regime of self-interest (as noted in ‘Metaphor and the Embodied Mind’ –
Boland and Tenkasi)
146. dice equivalence versus dice winning against each other with equal probability
147. conceptual simplicity versus computational simplicity (e.g., n! versus Stirling’s formula)
148. non-uniqueness of tetration (i.e., repeated, or iterated, exponentiation)
149. inequality between the Hausdorff dimension of a set and its topological dimension
150. multiplication as repeated addition, versus multiplication as an independent operation with a life of its own
151. Spheroidal coordinates are of two types: oblate and prolate.
152. divergence of direction between percentage retention (goes to zero) and amount of retention (goes to infinity). (e.g., progressive income tax)
153. ‘one’ now also means not only ‘exactly one’, but also ‘at least one’, as in the requirement that your password contain ‘one of the following special characters’.
154. danishes dissociate into donuts and cores
155. harmonic mean: distinction between the natural form of the formula and the pattern form of the formula
156. As a system becomes more sophisticated, its nodes undergo bifurcation. This may be why we have two forms of possessive in English: analytic (expressed by ‘of’) and synthetic (expressed by an apostrophe + ‘s’.
157. simple interest versus compound interest
158. mind versus body
see also the website ‘DifferenceBetween.net’:
