On 03/11/2015 03:41 PM, lrudo...@meganet.net wrote:
I'm trying to get at some aspects of the actual behavior of mathematicians.
Hardy_1 - "The function of a mathematician is [...] to prove new theorems" "Hardy wrote his Apology at the end of his mathematical career, when he was convinced, perhaps correctly, that “his creative powers as a mathematician at last, in his sixties, [had] left him" Hardy_3 - "The function of a mathematician is [...] to observe the facts about his own intricate system of reality, [...] to record the results of his observations in a series of maps, each of which is a branch of pure mathematics." Rudolph - "truth is what they come to believe more firmly as they function better [...] As such, truth is always conditional and subject to amendment: but it has, always and unconditionally, a net or web of meaning that anchors it pretty firmly to many places" You're spot on to note the change in defn before and after Hardy felt his powers had left him. And I'd like to use your own acuity to challenge your defn of math truth. One of the things that _all_ of us do, mathematicians included, is become more conservative as we age. As whatever powers we had leave us, we are left with the fossils of the exercising of those powers. This is true of both the complete structure as well as the more sparse anchors set more firmly amongst the less firm surroundings. My guess is that it's those anchors that _seed_ the crystal. Whatever anchors we become convicted of ... convinced of ... while younger, tend to accumulate cruft and barnacles, leading to a stigmergic mess of arbitrarily decided and inflexible dogma ... that we then carry to our graves. (Unless we have a near-death epiphany ... no atheists in foxholes, etc.) What Hardy successfully exhibits with his change is the path from ideological conviction to transpersonal _artifact_. Just like science, what matters are the artifacts you produce, the less semantically (and metaphorically) laden, the better. For math, it comes in the form of proofs. For science, it comes in the form of recipes that anyone with an equivalent sensorimotor manifold can execute. p.s. Just for full disclosure, I only read the first 6 and the last 3 pages of your chapter ... just enough to form the above premature opinion in the context of metaphor. But the rest of it looks appetizing! Thanks. -- ⇔ glen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
