A large number of the so‐called electronic balances, for example those using wire strain gauges, are based on the elastic deformation of solid materials, and on the electrical measurement of the resulting changes in length. Such instruments must therefore be grouped into the class of spring balances. The spring balance operates within the limits of proportionality according to the law discovered by and named after Robert Hooke. No precise information about the spring balance can be found so far in the (...) literature about balances: it is assumed that it was invented before 1700, without knowledge of the name of the inventor. As the result of a literature research it is shown that Robert Hooke found experimentally in 1676 with „ut tensio sic vis”︁ not only the physical principles which led to the law of elasticity: he also drew practical conclusions from it, and in the treatise De potentia restitutiva, published 1678, he described the most important types of spring balances. Experiments carried out by him to demonstrate the reduction of gravity with increasing altitude by using such a balance led, however, to a negative result because of its lack of sensitivity. Further developments for more than 100 years were necessary, until the spring balance come into more general application. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Una din cele mai disputate controverse privind prioritatea unor descoperiri științifice este cea privind legea gravitației universale, între Isaac Newton și Robert Hooke. În acest eseu extind o lucrare mai veche pe aceeași temă, ”Isaac Newton vs. Robert Hooke în legea gravitației universale”. Hooke l-a acuzat pe Newton de plagiat, preluându-i ideile exprimate în lucrările anterioare. În această lucrare încerc să arăt, pe baza unor analize anterioare, că ambii oameni de știință au greșit: Robert Hooke pentru că teoria sa nu (...) era în fond decât idei care nu s-ar fi materializat niciodată fără suportul matematic al lui Isaac Newton; iar acesta din urmă a greșit nerecunoscând niciun merit al lui Hooke în elaborarea teoriei gravitației. Mai mult, după moartea lui Hooke și preluarea prezidenției Societății Regale, Newton a înlăturat orice urmă din instituție a fostului președinte, Robert Hooke. De asemenea, La negarea contribuției lui Hooke a contribuit și statutul său social ”inferior”, fiind poreclit de contemporani ”mecanicul”, spre deosebire de Sir Isaac Newton cel nobil. Pentru aceasta detaliez acuzațiile și argumentele fiecăreia dintre părți, și cum a fost percepută această dispută de către contemporanii celor doi. Finalizez lucrarea cu concluziile desprinse din cuprins. (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies. Newton's (...) thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)