Are non-computerized mathematical "recreations" dead?

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pcallahan
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Are non-computerized mathematical "recreations" dead?

Post by pcallahan » January 7th, 2020, 2:34 pm

Sandbox for my rant, but I would be interested in hearing opinions, particularly from those who never knew a world where programmable computers were not ubiquitous and cheap.

First, to be clear, I think there will always be an interest in "puzzle math", competitive problem solving of the sort seen in Math Olympiad, and competitive solving of popular puzzles like Rubik's Cube. There will also be serious mathematicians who may have little use for computers except as word processors. I'm talking about something a little different here. Since it's hard to define, I'll give an instance: flexagons, which I would explain as a method by which a strip of paper can be folded so it is isomorphic to an oriented binary tree and a traversal can be carried out by a series of folding and unfolding steps. I first encountered them in Madachy's Mathematical Recreations (hence my subject line) as a teen and I forget the other ones in that book. I guess magic squares would qualify as a mathematical recreation, but I have always been more excited by those that involve some craft: cutting, folding, gluing, etc.

Of course, since I did have access to a microcomputer at the time (though it was less common) one of the things I did a few years later was to code up the algorithm from the book on a computer (which is optimized for a human writing out a paper table, as I eventually realized).

So, examples aside, I have kids in their teens, and throughout their childhood I have shown them some "craft" mathematics that I find interesting (admittedly often using a computer as a time-saver, but it's not required). Here, for instance is an icosahedron and dodecahedron colored to illustrate how their rotation groups are equivalent to the group of 60 even permutations of five elements (pardon the sloppy glue work).
49661459_2248103755513182_6065936909488619520_o.jpg
49661459_2248103755513182_6065936909488619520_o.jpg (17.42 KiB) Viewed 1928 times
Anyway, they were underwhelmed, as with most such examples. "Cool thingy, dad! Now let me get back to my computer."

It may be an overall lack of interest, since this kind of activity has always had limited appeal, but I find that I am increasingly fascinated by the process of pulling mathematics away from electronic computers where everything is just way too easy, and constructing physical analogs. My kids think this is just weird, and they may be right.

In my estimation, we ought to be living in a "golden age of non-computerized mathematical recreations" since computers themselves can be used to discover and optimize the kinds of things that can be built with crafts (e.g. use a 3D printer to make prototypes until you find one that is easy to craft by hand). There are also newer craft products like polymer clay and a lot of interest in crafts in general (stores like Michaels), though rarely aimed at mathematics. The field looks wide open.

So what I wonder is if the main historical appeal of these crafts, such as flexagons, is that they could be used as analog devices before computers existed. In this view, they are now as obsolete as slide rules, given the existence of computers--in which not only can a binary tree be constructed, but a flexagon itself can be modeled and rendered in animation.

The question is whether it's interesting to have touchable mathematics. I mean, aside from manipulatives in a Montessori preschool. Are these things of any interest to teens and adults with access to powerful electronic computers?

JP21
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Re: Are non-computerized mathematical "recreations" dead?

Post by JP21 » February 19th, 2020, 6:30 am

Well, computers are really the only things nowadays.
A 13 year old guy that have useless discoveries about life and other rules.

Code: Select all

x = 13, y = 20, rule = B3/S23
11b2o$11b2o4$8b2o$8b2o2$2o$2o3$3b2o$3b2o2$11b2o$10b2o$12bo$3b2o$3b2o!

Hunting
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Re: Are non-computerized mathematical "recreations" dead?

Post by Hunting » February 21st, 2020, 8:50 am

JP21 wrote:
February 19th, 2020, 6:30 am
Well, computers are really the only things nowadays.
I wish we could go back to the world of 1970, but we cannot.
MLP will live on forever, so does John Horton Conway.
Moosey wrote:
February 5th, 2019, 7:51 pm
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“Quick, hide it!”
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pcallahan
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Joined: April 26th, 2013, 1:04 pm

Re: Are non-computerized mathematical "recreations" dead?

Post by pcallahan » February 25th, 2020, 10:40 am

Hunting wrote:
February 21st, 2020, 8:50 am
JP21 wrote:
February 19th, 2020, 6:30 am
Well, computers are really the only things nowadays.
I wish we could go back to the world of 1970, but we cannot.
You've persuaded me that if my CA tiles are ever going to take off, I probably need a phone app to go with them. This might even be fun (I am not a great judge of this). After placing the physical tiles, you should be able to snap a picture and have the whole layout scanned and imported into your phone. This is easier than most image recognition problems and shouldn't be too hard to code. Of course, if you have your phone, you don't need the tiles... I still like manipulating physical objects.

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GUYTU6J
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Re: Are non-computerized mathematical "recreations" dead?

Post by GUYTU6J » February 26th, 2020, 3:37 am

pcallahan wrote:The question is whether it's interesting to have touchable mathematics.
I'm sure it is, for me, who is fond of chemical structures and therefore the underlying mathematics. For instance, sometime ago I was really longing for a flexible physical model of Goldberg polyhedra, visualizing how the icosahedral symmetry groups are applied to fullerene geometry. But it turns out that magnetic ball-and-stick models can't construct stable pentagons/hexagons with variable sides, while Zometool, a model that is good at handling icosahedral symmetry(no ad intended), doesn't support the rotational group.
Another stuff I'm concerned about are the space-filling polyhedrons, for a better understanding about crystallography.
Glimmering Garden是怎么回事呢?各向同性非总和性细胞自动机相信大家都很熟悉,但是Glimmering Garden是怎么回事呢,下面就让GUYTU6J带大家一起了解吧。
---
Someone please find a use for this:

Code: Select all

x = 9, y = 7, rule = B3/S23
6bo$6bobo$5bo2bo$b2o3b2o$o2bo$bobo$2bo!

Hunting
Posts: 2964
Joined: September 11th, 2017, 2:54 am

Re: Are non-computerized mathematical "recreations" dead?

Post by Hunting » February 26th, 2020, 6:21 am

GUYTU6J wrote:
February 26th, 2020, 3:37 am
pcallahan wrote:The question is whether it's interesting to have touchable mathematics.
I'm sure it is, for me, who is fond of chemical structures and therefore the underlying mathematics. For instance, sometime ago I was really longing for a flexible physical model of Goldberg polyhedra, visualizing how the icosahedral symmetry groups are applied to fullerene geometry. But it turns out that magnetic ball-and-stick models can't construct stable pentagons/hexagons with variable sides, while Zometool, a model that is good at handling icosahedral symmetry(no ad intended), doesn't support the rotational group.
Another stuff I'm concerned about are the space-filling polyhedrons, for a better understanding about crystallography.
I'd say I agree with that. It is interesting enough to have such things demonstrating chemistry. It is better than something like MolView MooseyView. I don't think they are serious enough to be researched though. Though, LeapLife isnt serious too but it could be investigated...
MLP will live on forever, so does John Horton Conway.
Moosey wrote:
February 5th, 2019, 7:51 pm
“New knightship tagalong!”
“Quick, hide it!”
My TODO list

LeapLife - DirtyLife - LispLife

I could make a rule in ten seconds flat

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