number versus numeral (a distinction everyone learns in the third grade – except for those who played hooky that day)
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)
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.
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.
rotation versus revolution
apparent astronomical movement versus actual astronomical movement
dependence of final result on initial conditions, versus, independence
rational versus irrational numbers
a polynomial versus the polynomial function associated with it
In foraging theory, time minimization versus energy maximization (pp. 8-9 of the book ‘Foraging Theory’ by Stephens and Krebs)
explanation versus prediction
tracking versus detection
detection versus recognition
ordinal numbers versus cardinal numbers
In foraging, path depletion not equal to negative acceleration of the energy gain function
complete information versus perfect information
a function being analytic versus being infinitely differentiable
two types of paraboloid (elliptic and hyperbolic)
wave/particle duality of light
MAD (median absolute deviation) has more than one meaning
inertial mass versus rest mass
domain of a partial function is ambiguous, depending on the discipline (logic or mathematics)
multiple, and only partially satisfactory, definitions of tortuosity
general life situation versus general life situation (terminology of Kurt Lewin)
singularities of solutions not necessarily occurring only at singularities of the equation
inequality of the types of cardinality for surface area and volume (e.g.: Gabriel’s horn)
sometimes homeomorphism type is not determined by homotopy type
“There are several definitions of R2 that are only sometimes equivalent.”
(Wikipedia’s article on coefficient of determination)
coverage probability splits into ‘actual’ and ‘nominal’
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)
having to choose between a statistical estimator that is unbiased or which has better mean squared error
There are two types of Hermite polynomials: the ‘probabilists’ Hermite polynomials and the ‘physicists’ Hermite polynomials.
good for exploratory data analysis versus good for classification applications – e. g., Sammon mapping
canonical form vs normal form (see the Wikipedia article on computer algebra)
A subgroup of a finitely generated group need not be finitely generated.
exploiting prey versus exploiting patches
the zero-one law in foraging theory versus Kolmogorov’s zero-one law – the former being prescriptive, and the latter being descriptive
double-entry bookkeeping versus single-entry bookkeeping
agent-designer’s goals versus agent’s goals
how the product topology is defined for finitely many spaces versus how it is defined for infinitely many spaces
‘heavy-tailed’ distribution has several meanings
non-unique generalization of the single-variable derivative
a series converging versus getting arbitrarily many digits correct
convexity of a set versus convexity of the region bounded by the set
dice equivalence versus dice winning against each other with equal probability
connectedness versus i-connectedness
connectedness versus path-connectedness
leaves versus structures that look like leaves (such as that possessed by mosses and leafy liverworts)
the polyphyletic nature of algae versus the situation of living in water and performing photosynthesis
whether energy is present versus whether it is available
sidereal time versus solar time
rolling friction versus static friction
planet versus star
elastic versus inelastic collision
heat versus temperature
a removable versus a non-removable discontinuity
blood versus type-distinguished blood
vapor versus gas
air versus oxygen
whale versus fish
gold versus fool’s gold
rocket propulsion versus friction-based propulsion
physical change versus chemical change
chemical combustion versus stellar dynamics
warm-blooded versus cold-blooded creatures
robustness versus anti-fragility
linear response versus nonlinear response
chaotic versus non-chaotic phenomena
continuity versus differentiability
speed of sound in air versus speed of sound in water
how others hear us versus how we hear ourselves
compound versus element
Bronze-Age creation myth versus Evolution
jealousy versus envy
perception controlling behavior versus behavior controlling perception
conscious versus unconscious mind
momentum versus energy
potential energy versus kinetic energy
radiant energy versus heat
24 hour period versus calendar day (as in ‘Around the World in 80 Days’)
mass versus weight
currency versus money
sub-sonic versus super-sonic explosions
cycloid versus circular arc
coma versus death
medical intervention versus palliative care
data versus information
macro versus micro economics
weather versus climate
strategy versus tactics
longitudinal versus transversal waves
traditional versus public-key cryptography
the definition of uniform integrability in measure theory versus probability theory
Nash equilibrium for a game repeated finitely many times versus infinitely many times
looking only at truth values versus looking at content (material implication)
Spheroidal coordinates are of two types: oblate and prolate.
how symmetric groups behave on finite versus on infinite sets
optimal behavior in the Prisoners’ Dilemma in the short run (betrayal)
versus in the long run (cooperation)
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.
topological definition of an object versus geometrical definition
stable, versus merely long-lived
defining fields by polynomials giving different results in the finite and infinite cases
temperature versus conductivity
intensive versus extensive properties
addition of heat versus a rise in temperature (i.e., the phenomenon of ‘latent heat’)
Subsystems can be connected in series or parallel.
distinct types of rock (igneous, sedimentary, metamorphic)
musical time versus metronome time
amortized update time of an algorithm versus worst-case update time
absence of evidence versus evidence of absence
simple versus small (e.g., uncompressed data versus compressed;
cf: Pascal’s remark about not having time to make his letter shorter)
‘no students’ (but staff present) versus ‘no school’ (nobody present)
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)
‘good’ cholesterol versus ‘bad’ cholesterol
cis versus trans configurations of unsaturated fatty acids
direct current versus alternating current
animal classification by its diet versus by the nature of its digestive system
frequency of a burden versus its intensity
specification versus implementation
testing versus debugging
impossibility versus probability of 0
de jure versus de facto
topological convergence versus convergence in measure
frontier versus wilderness
revenue versus profit
voltage versus current
dictionary versus encyclopedia
conservation as wilderness preservation versus as resource management
background versus foreground
short term versus long term
duality in terms of polar reciprocation versus topological duality
a candid photo versus a posed photo
mixture versus solution
billable time versus elapsed time
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)
ability as a conversationalist versus ability as a lecturer
archival storage versus working storage
complex versus complicated
powdered chocolate mix for a cold drink versus for a hot drink
form determined by gravity versus by capillarity
vector as an arrow (‘something with magnitude and direction’) versus as an element
of a vector space
