Hexaflexagons [video] (2012)
youtube.com
youtube.com
It takes a special place in my heart for being able to break apart and explain the effects of media and belief - especially of media referenced within media.
Genius.
So I went to the main branch of the NY public library ("reading between the lions") and looked up the article on microfiche. It was fascinating and fun - from how to make a row of equilateral triangles with nothing more than a ruler, pen and paper. Many, many hours were spent on the various flexagon derivatives.
Years later, I made a JS page to combine images and print hexaflexagons for my son's classmates. Had some fun with that as well; it was much more confounding than I expected.
Nowadays, microfiche is gone, the public library is unfortunately not in most kids vernacular, and the attention span that would be required to enjoy doing the math I did has been hijacked. (TikTok !== figure-out-flexagon)
https://www.tiktok.com/tag/flexagon
It’s also not intended for long-form content, which is fine. If someone is super interested in the topic, related math, etc — easy to find information elsewhere using search engine and the short videos are much more likely to get someone’s attention.
And my phone can keep track of more more phone numbers than I was ever able to memorize.
But, I know far fewer numbers now than I did as a kid, and my son will know far less than I did about flexagons. One reason may be because he knows it is readily available, he won't learn it himself. And one reason is because there is so much surface level learning available, which is so easy and interesting to consume, that anything that takes work and time is postponed, and eventually conditioned to be ignored.
This is true for porn, fast-food, caffeine, or what have you - easy, gratifying, effortless dopamine rushes will destroy the positive (and ultimately more gratifying) activities that the brain chemicals were supposed to encourage in the first place.
As someone who works with youth, the level of constant distraction that the smartphone has created is not plausibly denied.
1. The main issue I see is that smartphones are primarily devices for consumption (vs creation). The creation you can do easily are well established tools (digital writing, photography and videography). Where TikTok and Insta have succeeded is simple editing tools for the latter two (+ sharing and social algos etc).
2. To the action we as technologist need to take, is to build tools for smartphones that have a focus on creation rather than consumption (or to fuse the two, a la explorable explanations).
3. It may also be that the smartphone is a broken paradigm and we need to start thinking beyond smartphones, with a keen awareness that powerful corporations have a strong incentive to ensure that consumption is at the core of the technology experience (e.g. Meta and VR).
Seeing smartphone software as the complete editing tool - in the mold of desktop software - isn't that interesting, creatively speaking. It's very precise to use software in that way, to emulate professional workflows from generations ago and create all sorts of shortcuts and configurations. But it only affects decision-making workflows in a limited sense, because what the precision mostly does is pull you down the road towards polishing your output more and more, making smaller and smaller edits with more and more layers. Why are you polishing it? If you exit the software and change mediums, you can actually accomplish more with less, because then you can just accept the limitations and finish. Software is often at its best with mixed media approaches where it supplements a few tasks with a light layer of edits, a data processing step, or a preliminary design iteration. But there are many traditional techniques and technologies that don't need it, or amount to "we strap some AI onto it to turn an imprecise machine into a precise one".
The consumption-device viewpoint of the phone is an invention of the software industry. The reality is that people are doing a lot of productive things just by turning the phone into a portable scanner or audio recorder. It's already the fastest way to grab references for most media. If you set up a Bluetooth keyboard and a stand, the small screen works fine for typing up run-once code to solve immediate problems. The things blocking creativity are a combination of the software ecosystem being unready to deprofessionalize itself and exit the industrialized "app" model(and it is unready - we have a lot of maturation to do still to automate programmers out of their jobs), and the atmosphere of social media to engage in rat races for likes and follows, which is caused through incoherent models of assigning credit and blame, poor mechanisms of identity management, etc.
> The things blocking creativity are a combination of the software ecosystem being unready to deprofessionalize itself and exit the industrialized "app" model
Could you explain what you mean here? Not sure I quite follow.
So one example of an app that does allow you to do creative things effectively is grageband on iOS. It's an amazing tool for sketching musical ideas, which can later be more closely refined at a full desktop setup, so in a sense I agree that smartphone software can't be seen as a "complete editing tool", though it can be used much earlier in the creative process. DAWs are pretty complex tools and if you can get a decent version of a DAW on a phone, I see no reason why other tools shouldn't be possible.
I guess one way of looking at it would be to compare an artist's sketchbook vs what they produce on canvas. One is small, portable and allows the artist to capture moments as come up. The canvas however is much larger, essentially static and requires long, painstaking work to get right. I am sure that I am not the first person think of this analogy, but that seems like the level of creation that is suitable for the form factor.
> turning the phone into a portable scanner or audio recorder
Sure, but they also use the caluclator, spirit level etc, these are all pretty established tools, just made more readily accessible, rather than harnessing all that computing and visualisation power a smartphone can offer.
There is just too much to keep in a human brain. So, don’t, or, try and make an effort to separate the wheat from the chaff and know where it’s ok to give some up. No, your kids will probably not know as much about an origami trick, but they will know more about fusion or quantum computing or nanobots than you ever will. That doesn’t make them disadvantaged or you better. They might know more about Octaflexagons than you.
I’m sure my grand father that worked in a foundry making cast iron pipe would be horrified to discover I don’t know a lot about that process, but I could easily look up more than he ever knew.
So, this largely seems like a “kids these days” type of rant.
“[…] of making many books there is no end; and much study is a weariness of the flesh. ”
— Ecclesiastes 12:12
I read this to the backdrop of the movie "Idiocracy" playing in my mind. Especially the "porn, fast-food, caffeine" (aka Starbucks in the movie :P)
Most kids didn't randomly look up microfiche articles in libraries in your generation, even if some did. Most kids in this generation wont go deep with learning on the internet. Some 15 year olds find MIT open course ware and go wild. Its just the way of the world.
To leave off with a quote
"The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise." -- Socrates (allegedly)
I also work with youth. I don't agree. I see youth go broad and go deep. There's terrific variation in aptitudes to go deep, but it's certainly out there. Most of us didn't live at the library and look for deep resources (you and I did). I think a bigger fraction of youth accomplish high levels of aptitude and find areas to go deep in than ever before.
I do think there's fundamental change-- not all of it negative. We had to plan our next move at the library, right? We had to think a long time for what a good next move was in our area of interest. Youth now can afford to be infinitely more speculative than we ever were able to get away with.
And, yes, smartphones and their social pressures add completely new problems and distractions, and many educational environments do not manage them well.
And perhaps this is a general process when calculators, computers, phones, etc. automate activities which were mentally challenging (and so were good mental exercise) but ultimately not intellectually interesting?
The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise.
No one ever starts at a public library to study a particular topic, you almost always go to an internet resource first [usually Google]. And TikTok/the internet generally, has hijacked attention spans, but not just of children, but of adults as well.
I disagree. It verry much came across as a critique of the younger generation.
> So I went to the main branch of the NY public library ("reading between the lions") and looked up the article on microfiche.
Ouch. Now I feel old. I read that article in Dad's collection of Scientific American magazines...
TikTok is visible. Kids teaching themselves math isn’t. That doesn’t mean it isn’t happening.
The kids are alright.
https://m.youtube.com/watch?v=btPqKAGyajM
And of course the odd response from the UK government to the above petition was to basically say having a realistic football signs would increase the odds of accidents, lol:
https://aperiodical.com/2017/10/standupmaths-petition-has-ha...
Maybe the petition was done the wrong way:
It's not about geometry lessens. Soccer balls literally don't look like that. There are (most likely) way more people appreciating sports than geometry in the UK, so that'd be a better argument
Edit: looking for the original article from Martin Gardner; meanwhile: the submitted video was commented by the Scientific American (the original container) - https://blogs.scientificamerican.com/observations/flexagon-b...
The original article was Flexagons // In which strips of paper are used to make hexagonal figures with unusual properties, published on December 1, 1956. The Scientific American has it online, but paywalled.
Found it:
https://archive.org/details/martingardnerthecolossalbookofma...
in Martin Gardner - The Colossal Book Of Mathematics (page 385)
https://en.wikipedia.org/wiki/Martin_Gardner_bibliography#%2... - That's a list of the books (and on that page many other things) collecting Gardner's Scientific American "Mathematical Games" articles.
https://www.cambridge.org/us/academic/subjects/mathematics/s... - First 4 of the reprints available here (or a bookseller of your choice).
If you are interested in recreational mathematics, don't miss to checkout https://georgehart.com/.
https://www.youtube.com/user/Vihart/videos?sort=p, https://hn.algolia.com/?query=vi%20hart
[1] 'folding' in a different sense: How to fold a Julia fractal (2013) - https://news.ycombinator.com/item?id=32209192
If so, hexaflexagons (or general flexagons) could present interesting analogies to Calabi-Yau manifolds, especially in terms of holonomic properties, which might yield some insights or parallels for type II string theory. Or in more intuitive terms as I see it, a flexagon looks suspiciously similar to a string oscillating on a folded dimension, but discretized as some sort of torus/state machine. (not a physicist, worked at a HEP lab ages ago, I hope some of my comment made sense)
If interested, I've spend quite some time looking for more square flexagons, and made one with 12 and another with 14 faces (along with a puzzle version)! Tricky to build properly but stunning.
Happy to see Vi Hart’s still making videos: