Invariant Quotes

[Critical social science attempts] to determine when theoretical statements grasp invariant regularities of social action as such and when they express ideologically frozen relations of dependence that can in principle be transformed. (Jürgen Habermas)
To proceed from assumptions about an abstract theoretical set-up and from them to draw conclusions about the observable world and to test - by rough or more refined means - whether the conformity with observations is "good" enough, is indeed the time honoured procedure that all empirical sciences, including the natural sciences, have used. I shall therefore not plead guilty of heresy even if I do work with choice-theory concepts that are not invariant under a general monotonic transformation of the utility indicator. View quote
Ragnar Frisch
In some central and important cases, ... the existence of specific power relations in the society will produce an appearance of a particular kind. Certain features of the society that are merely local and contingent, and maintained in existence only by the continual exercise of power, will come to seem as if they were universal, necessary, invariant, or natural features of all forms of human social life, or as if they arose spontaneously and uncoercedly by free human action. View quote
Raymond Geuss
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant. Of course, the situation is different if the quantum mechanical predictions are of limited validity. Conceivably they might apply only to experiments in which the settings of the instruments are made sufficiently in advance to allow them to reach some mutual rapport by exchange of signals with velocity less than or equal to that of light. In that connection, experiments of the type proposed by Bohm and Aharonov, in which the settings are changed during the flight of the particles, are crucial. View quote
John Stewart Bell
The sequence of different positions of the same particle at different times forms a one-dimensional continuum in the four-dimensional space-time, which is called the world-line of the particle. All that physical experiments or observations can teach us refers to intersections of world-lines of different material particles, light-pulsations, etc., and how the course of the world-line is between these points of intersection is entirely irrelevant and outside the domain of physics. The system of intersecting world-lines can thus be twisted about at will, so long as no points of intersection are destroyed or created, and their order is not changed. It follows that the equations expressing the physical laws must be invariant for arbitrary transformations. View quote
Willem de Sitter
A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms. View quote
Roger Shepard
Further, as every law of nature implies the existence of an invariant, it follows that every law of nature is a constraint. View quote
W. Ross Ashby
[H]istorical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation. View quote
Stephen Jay Gould
[H]istorical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation (you don't see electrons, gravity, or black holes either). View quote
Stephen Jay Gould
I cannot without great astonishment - I might say without great insult to my intelligence - hear it attributed as a prime perfection and nobility of the natural and integral bodies of the universe that they are invariant, immutable, inalterable, etc., while on the other hand it is called a great imperfection to be alterable, generable, mutable, etc. For my part I consider the earth very noble and admirable precisely because of the diverse alterations, changes, generations, etc. that occur in it incessantly. If, not being subject to any changes. View quote
Galileo Galilei
Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects. (Max Born)
What does cultural pluralism signify in the absence of economic pluralism? Perhaps the question seems meaningless. Yet the apparent lack of meaning signals the intellectual retreat. The economic structure of society-call it advanced industrial society or capitalism or the market economy-stands as the invariant; few can imagine a different economic project. The silent agreement says much about multiculturalism. No divergent political or economic vision animates cultural diversity. From the most militant Afrocentrism to the most ardent feminists, all quarters subscribe to very similar beliefs about work, equality and success. The secret of cultural diversity is its political and economic uniformity. The future looks like the present with more options. Multiculturalism spells the end of utopia. View quote
Russell Jacoby