Ancestors

Toot

Written by Anthony Cowley on 2024-09-30 at 12:54

My young son crafts these elaborate TTRPG-style gaming scenarios, and has been on a sci-fi kick of late because we’ve dipped back into No Man’s Sky on screens. He employs a lot of toys in the physical gaming, and now I’m the player in this saga with upgradeable ships and characters like Luke Slime Walker (using a crocheted Dragon Quest Slime my wife made for him) and Carth Vader (a toy car with a cape).

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Descendants

Written by Asta Halkjær From on 2024-09-30 at 12:55

@acowley omg I want a crocheted Dragon Quest Slime too!

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Written by Leon P Smith on 2024-09-30 at 13:03

@acowley I've been interested in the early childhood math curriculum ever since I was a young child myself, and I finally wrote down my philosophy of math education over the pandemic, which focused on adding well-considered examples from abstract algebra and number theory to the earliest math lessons.

You might be interested in this: https://github.com/constructive-symmetry/constructive-symmetry

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Written by Boarders on 2024-09-30 at 14:24

@leon_p_smith @acowley I haven’t studied this properly yet, but I love the idea of developing curricula that properly get at the amazing examples in mathematics and doesn’t stick to what we have been doing for the last 100 years for high school math

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Written by Leon P Smith on 2024-09-30 at 14:33

@boarders @acowley

You might try solving Project Euler #192, that's the exact problem that helped spawn the insights that lead to all of this.

I mean, at first I had no idea how to even approach the problem, but somehow I stumbled into the answer, realized that the answer wasn't really that difficult, and was shocked how few people managed to solve that problem successfully.

At that point it was obvious that continued fractions were an underappreciated thing... I don't know how long I spent fumbling with them fruitlessly as an undergrad, but I made several efforts. "The Higher Arithemetic", which Wiles considers his favorite introduction to number theory (mentioned in the preface to the 6th edition of Hardy and Wright), has an explanation that might have clicked had I saw it as an undergrad, as it's morally the same explanation as the one I remember seeing on cut-the-knot.

So yeah, there's something that's definitely a non-obvious leap, but once you know how to use a tiny bit of linear algebra to make that leap, it somehow seems manageable, even if it's something nobody is likely to find for themselves. Thus part of the reason to make the Stern-Brocot tree the frontispiece.

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Written by Boarders on 2024-09-30 at 14:39

@leon_p_smith @acowley I think that is a very pretty part of mathematics, but what is important to me is getting across to students that mathematics is about deep structures where one can ask and answer questions and feel a sense of mystery. High school mathematics essentially doesn’t contain any important objects of mathematics of this form

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Written by Leon P Smith on 2024-09-30 at 14:44

@boarders @acowley

Yeah, I can see that too. I mean, I had a sense of how important it was, but I really had no idea about how well connected it really was until I started working on writing my ideas down.

Many, most of the connections I've found in the literature, I honestly don't understand. Conway's rational tangles are cool, for example, but I haven't the foggiest idea why it works at this point.

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