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3 - Patterns

from Part One - Building up to Categories

Published online by Cambridge University Press:  13 October 2022

Eugenia Cheng
Affiliation:
School of the Art Institute of Chicago
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Summary

A discussion of the role of pattern spotting in mathematics. This chapter still has little formality. The idea is that, in math and also in life, we might make abstract versions of things, then spot patterns in them or in common between different situations, and then ask if those patterns are caused by some abstract structure. We begin with some pattern spotting in number squares, and introduce the arithmetic of the 12-hour clock and look at the patterns on its addition table. We discuss patterns as analogies between situations, and discuss the relationship between visual patterns and abstract patterns, one example being the visual patterns made by multiples of 3 on a number square (or multiples of other fixed numbers). We introduce systemic power structures in society as another example of patterns caused by abstract similarities. We discuss how abstraction can help us spot patterns, with one example beingthe analysis of contentious arguments in society and politics, many of which follow a similar pattern.

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Chapter
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The Joy of Abstraction
An Exploration of Math, Category Theory, and Life
, pp. 35 - 43
Publisher: Cambridge University Press
Print publication year: 2022

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  • Patterns
  • Eugenia Cheng, School of the Art Institute of Chicago
  • Book: The Joy of Abstraction
  • Online publication: 13 October 2022
  • Chapter DOI: https://doi.org/10.1017/9781108769389.005
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  • Patterns
  • Eugenia Cheng, School of the Art Institute of Chicago
  • Book: The Joy of Abstraction
  • Online publication: 13 October 2022
  • Chapter DOI: https://doi.org/10.1017/9781108769389.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Patterns
  • Eugenia Cheng, School of the Art Institute of Chicago
  • Book: The Joy of Abstraction
  • Online publication: 13 October 2022
  • Chapter DOI: https://doi.org/10.1017/9781108769389.005
Available formats
×