From 7025874e457b6b096eba838a9c328c0b6ef66320 Mon Sep 17 00:00:00 2001 From: Joe Corneli Date: Wed, 31 May 2017 11:57:27 +0100 Subject: [PATCH] minor --- org/farm-2017.org | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/org/farm-2017.org b/org/farm-2017.org index 318184a..9d42794 100644 --- a/org/farm-2017.org +++ b/org/farm-2017.org @@ -1,7 +1,7 @@ #+TITLE: Functional models of mathematical reasoning #+AUTHOR: Joseph Corneli and Raymond Puzio #+EMAIL: contact@planetmath.org -#+DATE: May 27, 2017 for Thursday 1 June, 2017 deadline +#+DATE: May 27, 2017 for Thursday 1 June, 2017 deadline #+DESCRIPTION: Outline and draft of 12 page paper on math text analysis for FARM workshop at ICFP 2017 #+KEYWORDS: arxana, hypertext, inference anchoring theory #+LANGUAGE: en @@ -50,9 +50,9 @@ within the scope. ** 0.1 CONTEXT OF APPLICATION - modelling mathematical dialogues, people don't just write their things in metamath - people may make different expository choices -- mathematical text contains argumentation an narrative in addition to logic and calculations ([[1.2][1.2]]) +- mathematical text contains argumentation an narrative in addition to logic and calculations ** 0.2 FORCES -- push to make everything formal (QED, Tarski, LCF) [[1.1][1.1]] +- push to make everything formal (QED, Tarski, LCF) - push to make everything understandable (Alexander) ** 0.3 PROBLEM - each different user will have a different "way in", depending on their background knowledge ([[3.2][3.2]]) @@ -99,7 +99,9 @@ structures used so as to develop our formalism for representing mathematical knowledge in an informed matter. For the purposes of illustration, we will examine four short texts: -- *MPM* :: Mini-polymath thread 11. +- *MPM* :: Mini-polymath 3, thread 11 - part of a collaborative online + effort to a problem from the 2011 International Mathematics + Olympiad.[fn:: https://polymathprojects.org/2011/07/19/minipolymath3-project-2011-imo/] - *GCP* :: Timothy Gowers - What is the 500th digit of $(\sqrt{2}+\sqrt{3})^{2012}$? @@ -188,7 +190,7 @@ register also makes use of looser judgements of plausibility and heuristics. For instance, in the first example, the adjectives ``superficial'' and ``deeper'' appear. Terms such as these are not formally definable but refer to approximate notions which inform -heuristic choices. +heuristic choices. Allowing such loose notions and non-deductive reasoning serves an important purpose because, quite often, the exact deduction of some @@ -445,7 +447,7 @@ collaborative mathematics possible?" This project was convened by Gowers in 2009, and he developed 15 rules to address the "questions of procedure" that he anticipated would arise in the project.[fn:: http://gowers.wordpress.com/questions-of-procedure/ ] The basic premise was that people would work together on a shared blog to discuss a given mathematical problem in the open, -and jointly work out a solution.[fn:: Incidentally, the conclusion to the main motivating question was a tentative ``yes'' \cite{gowers2009massively}. New Polymath projects continue to be run to the present day. Four Minipolymath projects (including the one we refer to here as "MPM") have been convened in the same spirit.] +and jointly work out a solution.[fn:: Incidentally, the answer to the main motivating question was at least a tentative ``yes'' \cite{gowers2009massively}. New collaborative Polymath research projects continue to be run to the present day. Four Minipolymath projects (the third of which we refer to here as "MPM") have been convened in the same spirit, focusing on competition problems rather than research problems. However, these projects cannot be said to be "massive," if we use collaborations in other scientific disciplines as our standard.] Gowers carefully explicated the imperative to share comments that are "not fully thought out."[fn:UMEM] A good contribution to the project -- 2.11.4.GIT