SPSP 2013 Plenary session #1: Ian Hacking
Tweeted from the 4th biennial conference of the Society for Philosophy of Science in Practice in Toronto, Ontario, Canada, on June 27, 2013
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Getting ready for 1st plenary session of #SPSP2013 “Some roles of mathematics in some scientific practices” by Ian Hacking
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Hmm … #SPSP2013 seems to be in use already, so I’ll use #SPSP2013Toronto
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Getting ready for 1st plenary session of #SPSP2013Toronto “Some roles of mathematics in some scientific practices” by Ian Hacking #BetterTag
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Actual title of Ian Hacking’s talk: “Some roles of some mathematics in some scientific practices” (Maybe some summing?) #SPSP2013Toronto
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Hacking: will mostly be talking about “applied math”, concept that arose ~1780 #SPSP2013 #SPSP2013Toronto
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Marc Steiner claims no applied math, just math & its applications. Hacking disagrees #SPSP2013 #SPSP2013Toronto
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App 0: Math applied to math. App 1: “Pythagorean dreams”. App 2: theoretical physics of most general sort. #SPSP2013 #SPSP2013Toronto
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App 3: math modeling in “disinterested” sci research, App 4: mission oriented math modeling, App 5 everyday #SPSP2013 #SPSP2013Toronto
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App 6: unintended uses (educational screens, like req’d calculus 4 med school), App 7: bizarre applications #SPSP2013 #SPSP2013Toronto
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Representational-deductive picture: model phenomenon of interest, play w/model, draw conclusions #SPSP2013 #SPSP2013Toronto
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A C Crombie on “enigmatic matching” of nature w/ math & vice versa #SPSP2013 #SPSP2013Toronto
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David Bloor’s book, _The Enigma of the Aerofoil_;”Why did the British fight WWI w/ wrong theory of aerofoil?” #SPSP2013 #SPSP2013Toronto
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British mathematicians were trying to be “practical”, German ones looking for what worked (Hmm) #SPSP2013 #SPSP2013Toronto
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Hacking’s example: rigidity (structure that can’t be deformed) – but in real life, too much rigidity is bad! #SPSP2013 #SPSP2013Toronto
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Hurricanes, earthquakes make quick work of overly rigid structures. 101 bldg in Taipei uses pendulums to cope. #SPSP2013 #SPSP2013Toronto
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Birds’ nests also need to be rigid-enough-but-not-too-much #SPSP2013 #SPSP2013Toronto
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Some concept of rigidity probably came into human consciousness pretty early, Hacking says #SPSP2013 #SPSP2013Toronto
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Mathematics of rigidity. Cauchy (1814) proved thm about convex polyhedra w/rigid plates and hinges at edges #SPSP2013 #SPSP2013Toronto
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James Clerk Maxwell developed geometrical results on rigidity (general thm abt # of pts & lines needed) #SPSP2013 #SPSP2013Toronto
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Exceptions to thm –> anomalies end up being very interesting #SPSP2013 #SPSP2013Toronto
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Discipline of rigidity that becomes part of pure topology, but mathematicians still learned from engineers #SPSP2013 #SPSP2013Toronto
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Buckyball tents for sale! Tensegrity (tensional integrity) used in pure math and in structural engineering #SPSP2013 #SPSP2013Toronto
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Also fullerenes (smallest human-built structures using Fuller’s principles). #SPSP2013 #SPSP2013Toronto
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In 1992 geologists detected natural fullerenes in surface of earth! #SPSP2013 #SPSP2013Toronto
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Late 19th C, R Bricard discovered flexible non-convex polyhedra #SPSP2013 #SPSP2013Toronto
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1977 Robert Connelly elaborated class of flexible polyhedra; constructed some w/ cardboard & duct-tape #SPSP2013 #SPSP2013Toronto
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Examples illustrate complex intermingling between clearcut cases of pure math and hands-on engineering. #SPSP2013 #SPSP2013Toronto
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Representational-deductive picture doesn’t capture variety of interactions that come from mathematical practices #SPSP2013 #SPSP2013Toronto
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Q: Is math a *special* representational strategy? (We have lots of representational strategies in science) #SPSP2013 #SPSP2013Toronto
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Hacking: we owe our idea that math is a way of finding out abt deep ways of the world to Pythagorean wackiness #SPSP2013 #SPSP2013Toronto
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Maybe an anthropomorphic bent to our minds, looking at how nature does things #SPSP2013 #SPSP2013Toronto
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Q: is there a particular mathematical style of thinking, or a plurality of them? Hacking: a distinct genre … #SPSP2013 #SPSP2013Toronto
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… but distinct mathematical style of thinking keeps interacting w/ diff styles of thinking used in science #SPSP2013 #SPSP2013Toronto
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Diff people better at diff reasoning styles. (Hacking outs self as terrible natural historian) #SPSP2013 #SPSP2013Toronto
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Most interesting mathematical problems begin w/ material problems or attempts to model material concepts #SPSP2013 #SPSP2013Toronto
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Only good arg for Platonism: show there are these possibilities out there; eliminate some, refine what’s left #SPSP2013 #SPSP2013Toronto
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Deepening the real-world structures in our heads #SPSP2013 #SPSP2013Toronto
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Mathematicians distinguish pure vs. applied by whether the problem itself is “mathematically interesting” #SPSP2013 #SPSP2013Toronto
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Mathematically interesting vs physically interesting a useful distinction? Hacking adds”organically interesting” #SPSP2013 #SPSP2013Toronto
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Does adding complexity leave everything the same or open up new possibilities that weren’t there before? #SPSP2013 #SPSP2013Toronto
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Competing histories of how pure vs. applied math separation came to be (German, French, and British) #SPSP2013 #SPSP2013Toronto
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Interweaving of pure & applied in aerofoil case. Cambridge mathematicians wouldn’t listen to the engineers. #SPSP2013 #SPSP2013Toronto
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Engineer’s sense of what would be likely to work; Mathematicians: “This is mathematically impossible!” #SPSP2013 #SPSP2013Toronto
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Concept of how air as a fluid would interact w/ a surface in motion #SPSP2013 #SPSP2013Toronto
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Q: is this really interplay of pure & applied math, or of different kinds of mathematical models? #SPSP2013 #SPSP2013Toronto
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Mathematics put out axioms, engineers come up with counterexamples to them. #SPSP2013 #SPSP2013Toronto
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This was the first philosophical talk I tweeted. For some reason, philosophy seems harder to capture in tweets than does your typical ScienceOnline session, but I’m not giving up! By the end of the conference, maybe I’ll have the hang of it.
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