section_path: Heuristics/Confirmation theory/Invariance
section_name: Invariance
paragraph_text: Invariance
  
  Principles of invariance have been a theme in scientific writing, and especially physics, since at least the early 20th century. The basic idea here is that good structures to look for are those independent of perspective, an idea that has featured earlier of course for example in Mill's Methods of difference and agreement—methods that would be referred back to in the context of contrast and invariance. But as tends to be the case, there is a difference between something being a basic consideration and something being given weight. Principles of invariance have only been given weight in the wake of Einstein's theories of relativity, which reduced everything to relations and were thereby fundamentally unchangeable, unable to be varied. As David Deutsch put it in 2009: "the search for hard-to-vary explanations is the origin of all progress".
  
  An example here can be found in one of Einstein's thought experiments. The one of a lab suspended in empty space is an example of a useful invariant observation. He imagined the absence of gravity and an experimenter free floating in the lab. — If now an entity pulls the lab upwards, accelerating uniformly, the experimenter would perceive the resulting force as gravity. The entity however would feel the work needed to accelerate the lab continuously. Through this experiment Einstein was able to equate gravitational and inertial mass; something unexplained by Newton's laws, and an early but "powerful argument for a generalised postulate of relativity".
  
  The feature, which suggests reality, is always some kind of invariance of a structure independent of the aspect, the projection.
  
  The discussion on invariance in physics is often had in the more specific context of symmetry. The Einstein example above, in the parlance of Mill would be an agreement between two values. In the context of invariance, it is a variable that remains unchanged through some kind of transformation or change in perspective. And discussion focused on symmetry would view the two perspectives as systems that share a relevant aspect and are therefore symmetrical.
  
  Related principles here are falsifiability and testability. The opposite of something being hard-to-vary are theories that resist falsification—a frustration that was expressed colourfully by Wolfgang Pauli as them being " not even wrong ". The importance of scientific theories to be falsifiable finds especial emphasis in the philosophy of Karl Popper. The broader view here is testability, since it includes the former and allows for additional practical considerations.