#TDAC (The Discrete And Continuous, December 23, 2017):
Is grey ‘real’? Is all discretization perspectival? Can there be absolute notions of discreteness and continuity? Is time eternal? Is the world continuous but we perceive it as discrete? Are micro and macro objects continuous, but the meso discrete? Can real numbers be ‘made’ from integers? Are real numbers continuous (analog), & integers discrete (digital)? Do we don’t have access to ‘most’ of the real numbers? Did God make integers – or only 1 (& 0?)? What does Fourier Transform imply? What is the most fundamental signal? When does sampling not lead to loss of information? Can the sense of touch be discretized? Can surgeries be performed remotely? Does discretization happen in Nature? Is noise always continuous? Is speech predictable even if the underlying phonemes seem discrete? Do all manifolds lie on a continuum? Is making linear (analog) circuits difficult? Are higher order infinities deeper forms of ‘silence’? Does mathematics understand the ‘ambiguous’ ways in which things are (sometimes…) equal? Would a world without continuity (& community) be doomed? SynTalk thinks about these & more questions using concepts from logic & philosophy (Prof. Mihir K. Chakraborty, ex-University of Calcutta, Kolkata), mathematics (Prof. Kiran S. Kedlaya, University of California San Diego, La Jolla, California), & electrical engineering (Prof. D. Manjunath, IIT Bombay, Mumbai).
SynTalk is pleased and privileged to have hosted the following SynTalkrs (in alphabetical order) on its #TDAC show.
Prof. Mihir K. Chakraborty (logic, philosophy) is currently a visiting Professor in the School of Cognitive Science, Jadavpur University, and at the Department of Humanities, Indian Institute of Engineering, Science and Technology (IIEST), Shibpur, West Bengal. He retired in 2010 as a Professor from the Department of Pure Mathematics, University of Calcutta. His research interests are theory of graded consequence, rough set theory & its logic, fuzzy set theory, paraconsistent logic, inconsistent tolerant logic, philosophy of mathematics, logic of diagrams, rationality & reasoning. Prof. Chakraborty completed his Masters in Mathematics from University of Calcutta (1967), & then joined University of Kalyani (West Bengal) as a research scholar and worked under Prof. B. K. Lahiri to complete his Ph.D. in Functional Analysis in the year 1972. During the same period he also faced arrest for involvement in non-conformist radical politics. He later moved into research in non classical logics, such as fuzzy set theory and rough set theory, areas which were then considered peripheral by the main-stream mathematicians. Prof. Chakraborty has held honorary & visiting positions at numerous institutions such as Indian Statistical Institute (ISI, Kolkata, 2010-2013), Institute of Logic and Cognition (Sun Yat-Sen University, Guangzhou, China, 2011 & 2008), IRIT University Paul Sabatier (Toulouse, France, 2009), & University of Helsinki (Finland, 2008). He has also been an elected Fellow of the West Bengal Academy of Science and Technology, Rheinisch-Westfälische Technische Hochschule, Aachen (Germany, 1986, as a DAAD Fellow), and Indian Institute of Advanced Studies (IIAS, Shimla, 1986). Prof. Chakraborty is one of the three founding members of Calcutta Logic Circle (CLC, a study group found in 1987 with constant inspiration from Prof. H. N. Gupta, University of Regina, Canada), and has organized the annual CLC workshops for 15 years (1999-2014).
Prof. Kiran S. Kedlaya (mathematics) is Professor & Stefan E. Warschawski Chair in Mathematics, Department of Mathematics, University of California, San Diego, USA. He has also taught at Massachusetts Institute of Technology (MIT, 2003-2009), & at University of California, Berkeley (2001-2002). Prior to joining MIT, he was a postdoctoral fellow at the Institute for Advanced Study (IAS Princeton, 2003) & Mathematical Sciences Research Institute (MSRI Berkeley, 2000). His research interests are number theory, arithmetic algebraic geometry, with special focus on p-adic analytic methods in arithmetic geometry, p-adic Hodge theory, p-adic differential equations, algorithms in arithmetic geometry, interactions between arithmetic geometry and computer science. Prof. Kedlaya received a Bachelors in Mathematics & Physics from Harvard University (1996), an M.A. in Mathematics from Princeton University (1997), and Ph.D. from MIT (2000). He has held visiting positions, & summer positions at numerous institutes such as Institute for Computational and Experimental Research in Mathematics (Providence, 2015), Institute for Pure and Applied Mathematics (Los Angeles, 2014), MSRI (2014 & 2011), IAS (2009-2010), & Université de Rennes 1 (France, 2002-2003). He is also a Guggenheim Foundation Fellow (2015), an elected Fellow of American Mathematical Society (AMS, 2012), a Sloan Foundation Fellow (2006), the Liftoffs Fellow of the Clay Mathematics Institute (2000), & a three time Putnam Fellow (1993, 1994 & 1995). He won the International Mathematical Olympiad (gold medal in 1990 & 1992, and silver medal in 1991). Prof. Kedlaya is on the editorial board of ’Algebra and Number Theory’, an editor of ‘Nagoya Mathematical Journal’, & the editor of ‘L-functions and Modular Forms Database’. He has co-edited three books, & authored two books, titled, ‘p-adic Differential Equations’ (Cambridge Studies in Advanced Mathematics, 2010), & ‘Geometry Unbound’ (an open-source e-book).
Prof. D. Manjunath (electrical engineering) is Professor, Department of Electrical Engineering, Indian Institute of Technology Bombay (IITB), Mumbai. He has also worked at Indian Institute of Technology, Kanpur (IITK, 1994-1998), University of Delaware (1992-1993), & was also the post doctoral fellow at Department of Computer Science, University of Toronto (Canada, 1993-1994). His research interests are in the general area of networking, queueing and other stochastic systems, and performance modeling. More specifically, he focuses on distributed computation in sensor networks and distributed optimization for network resource provisioning, random geometric graph models for wireless networks and stochastic coverage processes, queueing system models for wireless networks, self tuning mechanisms for optimal resource allocation in computer systems, & design and algorithms for traffic engineering in optical networks. Prof. Manjunath did his B.E. in Electronics and Communication Engineering from University of Mysore (1986), an M.S. in Electrical Engineering (IIT Madras, 1989), & then completed his Ph.D. in Electrical Engineering from Rensselaer Polytechnic Institute (New York, 1993). He has held visiting positions at multiple universities, such as, University of Bristol (Benjamin-Meaker Visiting Professor, England, 2010), Microsoft Research (Cambridge, England, 2008), University of California (Riverside, USA, 2004), & Indian Institute of Science (IISc, Bangalore, 1998, 2001 & 2007). Prof. Manjunath has co-edited two books, with Anurag Kumar & Joy Kuri, titled ‘Wireless Networking’ (Elsevier, 2008), & ‘Communication Networking: An Analytical Approach’ (Elsevier, 2004, as part of Networking series edited by David Clark). He also co-invented, with Mart L. Molle, the ‘Technique for Measuring Response Times in Local Area Networks’, an invention that is now assigned to University of Toronto, Canada.
Note: Any & all errors in the brief profiles above are SynTalk’s own.
#TDAC mentions: Archimedes, Euclid, Nagarjuna, Leibniz, G. W. F. Hegel, Joseph Fourier, Richard Dedekind, Leopold Kronecker, Georg Cantor, Giuseppe Peano, & Jan Łukasiewicz, among others.