LMS General Meeting & Hardy Lecture 2023
The lectures are aimed at a general mathematical audience. All interested, whether LMS members or not, are most welcome to attend this event.
Programme (all timings are in BST)
3.30 pm Opening of the meeting and LMS Business (open to all)
- Election of the LMS Honorary Members in 2023.
- Announcement of the 2023 LMS Prize winners.
- Agenda and Papers
3.45 pm First Lecture: Sir Roger Penrose FRS (Oxford)
Non-computability in Physics?
Abstract: Three lecture courses I attended in Cambridge, in the early 1950s (not part of my official PhD topic in algebraic geometry) had a profound influence on my later research. These were by Steen, on mathematical logic, Bondi, on general relativity, and Dirac on quantum mechanics. Steen showed, in effect, via Gödel’s theorems and Turing computability, why conscious understanding could not be a purely computational process. But if our brains and bodies are, in essence, just physical systems, albeit very sophisticated ones, how could they be capable of non-computable tasks, as seem to be implied by an ability to appreciate the truth of Gödel’s statements?
Elsewhere I have made a case that a missing ingredient lies in an incompleteness of quantum theory, namely that the process referred to as “wave-function collapse” may objectively underlie this essential missing ingredient, allowing non-computable conscious actions. In this talk, I explore an alternative possibility, arising from a gap occurring in the behaviour of classical systems, pointed out by Dirac in 1938.
5.15 pm LMS Hardy Lecture 2023: Eva Miranda (UPC, Barcelona)
From Alan Turing to Fluid computers: Explored and unexplored paths.
Abstract: The notion of Chaos was coined by Edward Lorenz in 1961 with the simple statement
"Chaos: When the present determines the future, but the approximate present does not approximately determine the future".
A different sort of chaos was discovered by Cris Moore in 1990 with a 2D Turing-type dynamical system via generalized shifts. The existence of a Turing machine associated with the dynamical system added a new intrigue to the plot: the undecidability of the halting problem (Alan Turing, 1936) yielded the impossibility of logical predictions in the new models. However, those 2D systems given by mappings on the square Cantor set are not realized by a physical system. Can a mechanical system (including a fluid flow) simulate a universal Turing machine?
In this talk, I will present a 3D physical (and/or "almost" physical) constructions of logical chaos using fluids. Against all expectations, the main ingredient of this construction is geometrical. It relies on a mirror, unveiled in 2000 by Etnyre and Ghrist, between Beltrami fields and Reeb vector fields native to contact geometry.
Many questions around such construction are pending, including the connection among different levels of complexity (dynamical and logical) and the (non)existence of a hierarchy among them. The association of a “computer” to Fluid dynamics is a question which dates back to the work of Roger Penrose and Cris Moore and is connected to a recent programme of Terence Tao to address the Navier-Stokes conjecture. In his program. Tao speculates with the possibility of finding a counterexample to the Millennium problem using ideas closely related to Turing machines.
This construction of a "fluid computer" realizes the science fiction dream of Stanisław Lem in his novel Solaris. But could such a fluid computer be used to realize Tao’s dream?
6.15pm Close of meeting
6.30pm LMS Reception at Mary Ward House
7.30pm Society Dinner at The Wendy House, Bedford Hotel, Southampton Row
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