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My AI doctorate used a lot of group theory. I use came up with the following analogy for explaining what it is and what it's used for to fellow non-mathematicia
by lifebeyondfife 14y ago
My AI doctorate used a lot of group theory. I use came up with the following analogy for explaining what it is and what it's used for to fellow non-mathematicians:
If you want to measure and describe the number of occurrences of something, use an integer. If you want to measure and describe the amount of something, use a rational number. If you want to measure and describe the symmetry of a structure, use a group.
When programmatically dealing with objects that contain symmetry - e.g. physical objects like a cube, a set of identical resources like a fleet of lorries - having an understanding of group theory allows you another layer of abstraction in your computation, potentially greatly reducing runtime or memory consumption.
- pmelendez 14y agoWow.. I think this is the first time I actually get what means group theory. Excellent analogy! That was a very elusive concept to me when I took an abstract algebra course back in my undergraduate life. Thanks!
- themstheones 14y agoAnd I never had a prof who didn't describe groups as encoding symmetry. Strange.
- lifebeyondfife 14y agoI launched into a rant about this in a recent blog post[1]. The maths lecturer I had said, "A group theorist aims to classify and categorise the whole world..." and then he went straight into writing the four axioms of a group. [1] http://lifebeyondfife.com/the-difference-between-mean-and-median/ http://lifebeyondfife.com/the-difference-between-mean-and-me...
- pfortuny 14y agoGroups are just the abstraction of "transformations of something", the usual example being "symmetries" but it leaves out a bunch of other natural ideas like translations, movements, etc. Any teacher not mentioning "shape" when explaining group theory is either a bad teacher or a bad teacher.
- paulrademacher 14y agoGroup theory can be taught and appreciated without the geometric approach, but instead as a pure abstract concept. Different textbooks reflect this: Herstein is very abstract, Dummit and Foote uses probably more geometric examples, and Fraleigh relies heavily on geometric cases. I've personally always preferred the Herstein/abstract approach.
- pfortuny 14y agoOh certainly: that is the way I studied and enjoyed it but a book is not a teacher. I am not claiming books should always be "imagination" driven, on the contrary. But teachers should.