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Mathematical Thinking Isn't What You Think It Is
- ivansavz 2y agoI like the idea of math as "self help." People don't realize it, but the more math you learn, the easier/simpler life becomes... In other words, people learn math not because they like complexity, but because they are lazy and don't want complexity in their life. For a specific example, consider some complicated arithmetic expression involving a dozen numbers and repeated operations +/-/*/÷. A person who knows high school algebra, could introduce some structure in the expression (e.g. by defining variables), then use the rules of algebra to simplify the expression, and end up doing much arithmetic overall to compute the answer. The more (as in abstraction and modelling) math you know, the less math (as in arithmetic) you'll have to do!
- card_zero 2y agoThat's not what I call laziness. Laziness is doing a half-assed, inefficient job that you don't have to concentrate on. Putting underwear away by throwing it. Spilling your drink on yourself because you didn't want to sit up in bed. Trying repeatedly to flick a switch with your toes rather than bend down. Communicating in grunts because thinking of words is demanding. What you're describing is cleverness, and it's a strain.
- fluoridation 2y agoSure, that's one way to define it. But to people who think work (and effort) is in itself a virtue, optimization is lazy, because it reduces the total work you'll need to do. Even some of your examples I'm not convinced are lazy according to your own definition. Am I lazy for flicking a switch at ankle level with my toes if I can do it well enough, when bending down would take so much more effort? I think by your standard I should be commended for my foot dexterity! When does the desire to reduce effort cease to be vicious and become virtuous?
- almostgotcaught 2y ago> But to people who think work (and effort) is in itself a virtue ... Who thinks that? Is it the same people that think pre-marital sex is a vice?
- keithalewis 2y agoI work hard to be lazy.
- fdhfdjkfhdkj 2y ago[dead]
- havefunbesafe 2y agoRelated to another quantum mag article on the front page today: "Why everyone can benefit from something that isnt what you think it is"?
- auggierose 2y agoAlready discussed here: https://news.ycombinator.com/item?id=42200209 https://news.ycombinator.com/item?id=42200209
- nullhole 2y ago243 comments, posted 15 hours ago
- mdp2021 2y agoHow come they have the same URL?
- emptiestplace 2y ago42172857 vs 4220020 Edit: Sorry, I think maybe you are asking why HN doesn't enforce article URL uniqueness - I can't answer that.
- mdp2021 2y ago> maybe Yes. The system here normally seems to check uniqueness.
- Jtsummers 2y agoIt seems like submissions that don't get much traction after a day or so don't get counted as duplicates if resubmitted. There were 4 submissions of this article, and until this one turned back up today (second chance pool, this one was originally submitted 3 days ago) only one submission actually had any traction, and that was from yesterday evening.
- alganet 2y agoWe had enough already. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=mathematical+thinking+isnt&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...