Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-22T21:23:16.125Z Has data issue: false hasContentIssue false

5 - Relationships

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
Get access

Summary

This chapter introduces the idea of studying things via their relationships with other things. We start with family relationships and the idea of depicting relationships with arrows, and building up relationships by composition. We revisit some of the concepts already discussed, and reframe them as types of relationship. This includes symmetry, basic arithmetic, and modular arithmetic. We look at the relationships between different types of quadrilateral and explore how depicting the relationships with arrows is more powerful than using a Venn diagram. We explore diagrams of factors, fixing a number n and then drawing a lattice of its factors and factor relationships among them. We show that abstracting from this gives us a lattice of subsets of the prime factors of n and that a further abstraction gives us lattices of subsets of any sets. We show that this further abstraction enables us to include a much wider variety of examples, including an analysis of interactions between people with different types of privilege. The idea is to start seeing relationships as something quite general, and to start seeing how abstraction gives us structures that are more widely applicable.

Type
Chapter
Information
The Joy of Abstraction
An Exploration of Math, Category Theory, and Life
, pp. 52 - 66
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Relationships
  • Eugenia Cheng, School of the Art Institute of Chicago
  • Book: The Joy of Abstraction
  • Online publication: 13 October 2022
  • Chapter DOI: https://doi.org/10.1017/9781108769389.007
Available formats
×

Save book to Dropbox

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 Dropbox.

  • Relationships
  • Eugenia Cheng, School of the Art Institute of Chicago
  • Book: The Joy of Abstraction
  • Online publication: 13 October 2022
  • Chapter DOI: https://doi.org/10.1017/9781108769389.007
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.

  • Relationships
  • Eugenia Cheng, School of the Art Institute of Chicago
  • Book: The Joy of Abstraction
  • Online publication: 13 October 2022
  • Chapter DOI: https://doi.org/10.1017/9781108769389.007
Available formats
×