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Conference Paper/Proceeding/Abstract 755 views 188 downloads

Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things

Alan Dix

Theoretical Aspects of Computing – ICTAC 2021, Pages: 18 - 35

Swansea University Author: Alan Dix

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DOI (Published version): 10.1007/978-3-030-85315-0_2

Abstract

Qualitative–quantitative reasoning is the way we think informally about formal or numerical phenomena. It is ubiquitous in scientific, professional and day-to-day life. Mathematicians have strong intuitions about whether a theorem is true well before a proof is found – intuition that also drives the...

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Published in: Theoretical Aspects of Computing – ICTAC 2021
ISBN: 978-3-030-85314-3 978-3-030-85315-0
ISSN: 0302-9743 1611-3349
Published: Cham Springer International Publishing 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa58133
first_indexed 2021-09-28T13:57:42Z
last_indexed 2021-10-28T03:23:17Z
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spelling 2021-10-27T15:38:36.1704526 v2 58133 2021-09-28 Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things e31e47c578b2a6a39949aa7f149f4cf9 Alan Dix Alan Dix true false 2021-09-28 Qualitative–quantitative reasoning is the way we think informally about formal or numerical phenomena. It is ubiquitous in scientific, professional and day-to-day life. Mathematicians have strong intuitions about whether a theorem is true well before a proof is found – intuition that also drives the direction of new proofs. Engineers use various approximations and can often tell where a structure will fail. In computation we deal with order of magnitude arguments in complexity theory and data science practitioners need to match problems to the appropriate neural architecture or statistical method. Even in the supermarket, we may have a pretty good idea of about how much things will cost before we get to the checkout. This paper will explore some of the different forms of QQ–reasoning through examples including the author’s own experience numerically modelling agricultural sprays and formally modelling human–computer interactions. We will see that it is often the way in which formal and mathematical results become useful and also the importance for public understanding of key issues including Covid and climate change. Despite its clear importance, it is a topic that is left to professional experience, or sheer luck. In early school years pupils may learn estimation, but in later years this form of reasoning falls into the gap between arithmetic and formal mathematics despite being more important in adult life than either. The paper is partly an introduction to some of the general features of QQ-reasoning, and partly a ‘call to arms’ for academics and educators. Conference Paper/Proceeding/Abstract Theoretical Aspects of Computing – ICTAC 2021 18 35 Springer International Publishing Cham 978-3-030-85314-3 978-3-030-85315-0 0302-9743 1611-3349 Informal reasoning; Estimation; Mathematical models; Order of magnitude; Covid models; Monotonicity 20 8 2021 2021-08-20 10.1007/978-3-030-85315-0_2 COLLEGE NANME COLLEGE CODE Swansea University 2021-10-27T15:38:36.1704526 2021-09-28T14:56:31.1757062 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Alan Dix 1 58133__21040__38551b86f3754abdbdb2f1dcc31fcffe.pdf ICTCS-QQ-2021-keynote.pdf 2021-09-28T15:46:14.6328231 Output 5533136 application/pdf Accepted Manuscript true true eng
title Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
spellingShingle Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
Alan Dix
title_short Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
title_full Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
title_fullStr Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
title_full_unstemmed Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
title_sort Qualitative–Quantitative Reasoning: Thinking Informally About Formal Things
author_id_str_mv e31e47c578b2a6a39949aa7f149f4cf9
author_id_fullname_str_mv e31e47c578b2a6a39949aa7f149f4cf9_***_Alan Dix
author Alan Dix
author2 Alan Dix
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issn 0302-9743
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hierarchy_parent_id facultyofscienceandengineering
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department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description Qualitative–quantitative reasoning is the way we think informally about formal or numerical phenomena. It is ubiquitous in scientific, professional and day-to-day life. Mathematicians have strong intuitions about whether a theorem is true well before a proof is found – intuition that also drives the direction of new proofs. Engineers use various approximations and can often tell where a structure will fail. In computation we deal with order of magnitude arguments in complexity theory and data science practitioners need to match problems to the appropriate neural architecture or statistical method. Even in the supermarket, we may have a pretty good idea of about how much things will cost before we get to the checkout. This paper will explore some of the different forms of QQ–reasoning through examples including the author’s own experience numerically modelling agricultural sprays and formally modelling human–computer interactions. We will see that it is often the way in which formal and mathematical results become useful and also the importance for public understanding of key issues including Covid and climate change. Despite its clear importance, it is a topic that is left to professional experience, or sheer luck. In early school years pupils may learn estimation, but in later years this form of reasoning falls into the gap between arithmetic and formal mathematics despite being more important in adult life than either. The paper is partly an introduction to some of the general features of QQ-reasoning, and partly a ‘call to arms’ for academics and educators.
published_date 2021-08-20T05:09:31Z
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