Talk:Variational principle

message: Should this article be merged with the calculus of variations page?  It seems like this page only details some basic applications to the calculus of variations and explains some general aims of the calculus of variations.  The C of V page could use a better explanation on its overall aims.  --69.180.18.247 14:42, 4 September 2006 (UTC)
thread_title:  Merge with Calculus of Variations? 

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thread_title:  External links modified 

message: The article mentions “Any physical law which can be expressed as a variational principle describes a self-adjoint operator.” with a reference to Lanczos' The Variational Principles of Mechanics. What does it mean for a principle to describe an operator? I briefly read through Lanczos' book and didn't find any mention of this anywhere, but the fact that no page or chapter is mentioned in the citation doesn't really help. Michal Grňo (talk) 14:31, 17 August 2020 (UTC)
thread_title:  What is it with self-adjoint operators? 

message: This page is weak and stationary action principle is weak. They should be merged, under "Action principle" Johnjbarton (talk) 23:09, 13 November 2023 (UTC)
replies: text: It is not the same as "action principle", it is more general. At best we could merge stationary action principle here but  I would prefer if we did not, or merge Variational principle with calculus of variations. Action principles have always been for me for mechanics and dynamics, while variational calculus in general covers the action principles, other physics methods that do not minimize an action like Ritz method or variational method (quantum mechanics) and non physics stuff like the ones listed in "Examples".--ReyHahn (talk) 08:14, 22 November 2023 (UTC)
replies: text: I agree. Johnjbarton (talk) 16:51, 22 November 2023 (UTC)
thread_title:  Merge with [[Stationary-action principle]]? 

message: Variational logicism (or variant logicism) means that infinite logical foundations are possible. It's based on the term variety and not on the mathematical term variational but it doesn't exclude it. The axiomatic system of all axiomatic systems doesn't exist because mutually exclusive axiomatic systems are logically possible (the omniaxiomatics doesn't exist = the universal axiomatics doesn't exist). Also the set of all sets doesn't exist (if we accepted a stationary = set pseudoomniaxiomaticity = a set of all axiomatic systems which doesn't actively engage their logic as a true axiomatic system). Neologicists supposedly wanted to remove the biases of logicists, but actually most of them erroneously claim that a single fundamental/foundational logic is possible; which is proven to be wrong, because logic is always axiomatic and contextual, but infinite axiomatic systems are logically possible (list-based, algorithmic, programs and hybrid axiomatics) and infinite logical contexts. Variational logicism accepts the fact that logic is rule-based, but the rules can vary per axiomatic system or other logical context. Infinite axiomatic systems are logically possible. We can experiment by creating axiomatic systems. Most axiomatic systems are weird and useless. Some axiomatic systems are allomathematics = mathematics (proof systems) of different axiomaticity/ axiomatic foundations. Some axiomatic systems are substantiality axiomatics = physioaxiomatics = physical axiomatics = physical foundations (the quantum foundations is the foundations of our universe). The physical axiomatics have to be more logically coherent = with more self-engaged foundations than the proof-system axiomatics, but they don't have to be as crystal clear as the proof-system (mathematical) axiomatics. The axioms of mathematics don't originate from a single logical kernel and according to the foundations of mathematics they aren't maximally coherent (they are eclectic; see: eclecticism). The axioms of mathematics aren't a physical foundations; they would disperse without causing a universe. Proof systems and universes don't have the same foundations. Both 1. mathematics and the infinite allomathematics and 2. the infinite universes are logical systems based on logical foundations, but that doesn't mean they have the same foundations. Informational entropy and thermodynamic entropy are intertwined in the physical foundations. The "axiomatic prerequisites of the physical foundations" is a field of study hypernymic/hypernymous/superordinate to the quantum foundations which is about our own universe. The infinite alternative physical foundations of the infinite logically achievable universes don't have strictly common rules because the axiomatic system of all axiomatic systems doesn't exist, but still we can postulate some basic prerequisites. 2A02:2149:8B83:6500:9464:BD1F:2B81:D064 (talk) 01:52, 3 April 2024 (UTC)
thread_title:  ''create page'': [[variational logicism]] because even neologicism is single-logic biased