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

Getting ready for 1st plenary session of #SPSP2013 “Some roles of mathematics in some scientific practices” by Ian Hacking

Hmm … #SPSP2013 seems to be in use already, so I’ll use #SPSP2013Toronto

Getting ready for 1st plenary session of #SPSP2013Toronto “Some roles of mathematics in some scientific practices” by Ian Hacking #BetterTag

Actual title of Ian Hacking’s talk: “Some roles of some mathematics in some scientific practices” (Maybe some summing?) #SPSP2013Toronto

Hacking: will mostly be talking about “applied math”, concept that arose ~1780 #SPSP2013 #SPSP2013Toronto

Marc Steiner claims no applied math, just math & its applications. Hacking disagrees #SPSP2013 #SPSP2013Toronto

App 0: Math applied to math. App 1: “Pythagorean dreams”. App 2: theoretical physics of most general sort. #SPSP2013 #SPSP2013Toronto

App 3: math modeling in “disinterested” sci research, App 4: mission oriented math modeling, App 5 everyday #SPSP2013 #SPSP2013Toronto

App 6: unintended uses (educational screens, like req’d calculus 4 med school), App 7: bizarre applications #SPSP2013 #SPSP2013Toronto

Representationaldeductive picture: model phenomenon of interest, play w/model, draw conclusions #SPSP2013 #SPSP2013Toronto

A C Crombie on “enigmatic matching” of nature w/ math & vice versa #SPSP2013 #SPSP2013Toronto

David Bloor’s book, _The Enigma of the Aerofoil_;”Why did the British fight WWI w/ wrong theory of aerofoil?” #SPSP2013 #SPSP2013Toronto

British mathematicians were trying to be “practical”, German ones looking for what worked (Hmm) #SPSP2013 #SPSP2013Toronto

Hacking’s example: rigidity (structure that can’t be deformed) – but in real life, too much rigidity is bad! #SPSP2013 #SPSP2013Toronto

Hurricanes, earthquakes make quick work of overly rigid structures. 101 bldg in Taipei uses pendulums to cope. #SPSP2013 #SPSP2013Toronto

Birds’ nests also need to be rigidenoughbutnottoomuch #SPSP2013 #SPSP2013Toronto

Some concept of rigidity probably came into human consciousness pretty early, Hacking says #SPSP2013 #SPSP2013Toronto

Mathematics of rigidity. Cauchy (1814) proved thm about convex polyhedra w/rigid plates and hinges at edges #SPSP2013 #SPSP2013Toronto

James Clerk Maxwell developed geometrical results on rigidity (general thm abt # of pts & lines needed) #SPSP2013 #SPSP2013Toronto

Exceptions to thm –> anomalies end up being very interesting #SPSP2013 #SPSP2013Toronto

Discipline of rigidity that becomes part of pure topology, but mathematicians still learned from engineers #SPSP2013 #SPSP2013Toronto

Buckyball tents for sale! Tensegrity (tensional integrity) used in pure math and in structural engineering #SPSP2013 #SPSP2013Toronto

Also fullerenes (smallest humanbuilt structures using Fuller’s principles). #SPSP2013 #SPSP2013Toronto

In 1992 geologists detected natural fullerenes in surface of earth! #SPSP2013 #SPSP2013Toronto

Late 19th C, R Bricard discovered flexible nonconvex polyhedra #SPSP2013 #SPSP2013Toronto

1977 Robert Connelly elaborated class of flexible polyhedra; constructed some w/ cardboard & ducttape #SPSP2013 #SPSP2013Toronto

Examples illustrate complex intermingling between clearcut cases of pure math and handson engineering. #SPSP2013 #SPSP2013Toronto

Representationaldeductive picture doesn’t capture variety of interactions that come from mathematical practices #SPSP2013 #SPSP2013Toronto

Q: Is math a *special* representational strategy? (We have lots of representational strategies in science) #SPSP2013 #SPSP2013Toronto

Hacking: we owe our idea that math is a way of finding out abt deep ways of the world to Pythagorean wackiness #SPSP2013 #SPSP2013Toronto

Maybe an anthropomorphic bent to our minds, looking at how nature does things #SPSP2013 #SPSP2013Toronto

Q: is there a particular mathematical style of thinking, or a plurality of them? Hacking: a distinct genre … #SPSP2013 #SPSP2013Toronto

… but distinct mathematical style of thinking keeps interacting w/ diff styles of thinking used in science #SPSP2013 #SPSP2013Toronto

Diff people better at diff reasoning styles. (Hacking outs self as terrible natural historian) #SPSP2013 #SPSP2013Toronto

Most interesting mathematical problems begin w/ material problems or attempts to model material concepts #SPSP2013 #SPSP2013Toronto

Only good arg for Platonism: show there are these possibilities out there; eliminate some, refine what’s left #SPSP2013 #SPSP2013Toronto

Deepening the realworld structures in our heads #SPSP2013 #SPSP2013Toronto

Mathematicians distinguish pure vs. applied by whether the problem itself is “mathematically interesting” #SPSP2013 #SPSP2013Toronto

Mathematically interesting vs physically interesting a useful distinction? Hacking adds”organically interesting” #SPSP2013 #SPSP2013Toronto

Does adding complexity leave everything the same or open up new possibilities that weren’t there before? #SPSP2013 #SPSP2013Toronto

Competing histories of how pure vs. applied math separation came to be (German, French, and British) #SPSP2013 #SPSP2013Toronto

Interweaving of pure & applied in aerofoil case. Cambridge mathematicians wouldn’t listen to the engineers. #SPSP2013 #SPSP2013Toronto

Engineer’s sense of what would be likely to work; Mathematicians: “This is mathematically impossible!” #SPSP2013 #SPSP2013Toronto

Concept of how air as a fluid would interact w/ a surface in motion #SPSP2013 #SPSP2013Toronto

Q: is this really interplay of pure & applied math, or of different kinds of mathematical models? #SPSP2013 #SPSP2013Toronto

Mathematics put out axioms, engineers come up with counterexamples to them. #SPSP2013 #SPSP2013Toronto

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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