Year: 2022

Believe it or not, this little person came up to me in the woods. I am trying to locate its home. Mythical experience. View in LinkedIn

FRAGMENT FROM NATURE features an extraordinary article by an extraordinary man. Professor J. Butterfied was Regius Professor of Physic at the University of Cambridge where he led the re-establishment of the School of Clinical Medicine, at the University of Cambridge, and was Master of Downing College, Cambridge. I had a long meeting with this man and was stunned by his extreme gentle humility and his effortless gravitas. https://lnkd.in/dTSsKks View in LinkedIn

QUANTUM GRAVITY. “The discovery of a satisfactory quantum theory of gravity has been widely regarded as the Holy Grail of theoretical physics for some forty years. The senses in which our standard ideas of time, and more generally spacetime, might be not fundamental to reality, but instead ‘emergent’ as an approximately valid concept on sufficiently large scales.” https://lnkd.in/dMm_YkR View in LinkedIn

EMERGENT TIME. “The idea of the emergence of time is, roughly speaking, that the concept of time as a continuum ordering of events is only an approximation, valid for sufficiently large scales of time and length (and, correspondingly, sufficiently low energies), to what is expected to be a quite different concept in the, as yet, unknown full quantum theory of gravity.” https://lnkd.in/dMm_YkR View in LinkedIn

POINTS IN TIME. “Those who have succumbed to the seductive allure of the archetype of ‘eternal recurrence’—for example, in our own time: Nietzsche and T.S. Eliot—would want to model points in time by the points on a circle, rather than the real line. In a quantum theory, the scales of time or length are related to the inverse of energy via Planck’s constant.” https://lnkd.in/dMm_YkR View in LinkedIn

SETS AT THE HEART. “By concatenating such deductions with judiciously chosen definitions, one shows in effect that all of classical pure mathematics can in this sense be deduced from the theory of sets. This remarkable result, showing how large an expressive power can be obtained by applying this small stock of logical operations to a small initial family of predicates, is the source of the traditional philosophical restriction to considering just these logical operations.” https://lnkd.in/dMm_YkR View in LinkedIn

MATHEMATICAL HIERARCHY. “Even quite simple physical theories such as, for example, Newtonian mechanics of point particles interacting just by gravity, are complicated from the viewpoint of logic and foundations of mathematics; simply because such theories use mathematical apparatus (for example, calculus) that is ‘high up’ in the deductive chain from basic logic and set theory.” https://lnkd.in/dMm_YkR View in LinkedIn

BEDROCK LOGIC. “When we undertake to express such a theory in a formal language, we naturally envisage adding the theory’s distinctive physical vocabulary, and axioms governing it, to a so-called ‘underlying logic’ that is much stronger than just basic logic and set theory; i.e., to one that contains standard mathematical operations sufficient to yield the mathematical apparatus; for example, calculus, which is needed by the theory.” https://lnkd.in/dMm_YkR View in LinkedIn

EXTENDING DEDUCTIVE REACH. “In effect all of classical pure mathematics was a definitional extension using just logical operations, of set theory. But it is equally remarkable how many examples of definitional extension there are in physics, at least once we give the reducing physical theory a suitably strong underlying logic (i.e., a rich enough set of operations) so as to ‘extend its deductive reach’.” https://lnkd.in/dMm_YkR View in LinkedIn

DEDUCTIVE EXTENSION. “For example: the elementary theory of equilibrium classical statistical mechanics for a strictly isolated system, which postulates the microcanonical measure on the energy hypersurface, is a definitional extension of the mechanics of the micro-constituents, once we use an underlying logic strong enough to express calculus (of many variables).” https://lnkd.in/dMm_YkR View in LinkedIn