HN Theater @HNTheaterMonth

Cute video on hexaflexagons:

https://youtu.be/VIVIegSt81k

⬐ sam_goody

I saw a reference to Martin Gardner's article when I was in, maybe, 9th grade.

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)

⬐ bigdict

National education crisis averted: https://www.maa.org/sites/default/files/pdf/pubs/focus/Gardn...

⬐ mulmen

Careful that you do not become the old man yelling at clouds.

TikTok is visible. Kids teaching themselves math isn’t. That doesn’t mean it isn’t happening.

The kids are alright.

⬐ bigiain

> I saw a reference to Martin Gardner's article when I was in, maybe, 9th grade.

> 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...

⬐ lmm

> 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)

The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise.

⬐ ChrisClark

Said every single generation once they got older.

⬐ miffy900

Weird you would re-surface that quote in response to that, since I don't think a reasonable person would interpret it as a criticism of younger generations, but of the changing times we now live in.

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.

⬐ lmm

The comment I replied to explicitly talks about "kids" not knowing about the public library.

⬐ miffy900

Even then, the OP mentioning that kids don't know about public libraries was NOT a criticism; you quoting Socrates is just bizarrely out of place as Socrates' quote was a strident critique on his perception of the behaviour of younger generations.

⬐ lmm

> the OP mentioning that kids don't know about public libraries was NOT a criticism

I disagree. It verry much came across as a critique of the younger generation.

⬐ marcelluspye

>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)

Ok, boomer.

⬐ collegeburner

your comment is agephobic

⬐ O__________O

TikTok has a lot of creative content on flexagons:

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.

⬐ sam_goody

Oh sure, the internet has a lot more related info readily available than was ever possible by using microfiche.

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.

⬐ bawolff

Pretty much every generation says this about the next generation.

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)

⬐ SV_BubbleTime

Counterpoint… there is too much information now.

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.

⬐ teddyh

> there is too much information now.

“[…] of making many books there is no end; and much study is a weariness of the flesh. ”

— Ecclesiastes 12:12

⬐ mlyle

> 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.

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.

⬐ wikfwikf

Perhaps with your phone being able to remember 10-digit numbers for you, this leaves you and/or young people today with more mental space and energy to do more interesting mental tasks such as exploring recreational mathematics.

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?

⬐ tomxor

> [...] 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.

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)

⬐ MrsPeaches

A few random thoughts on this.

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).

⬐ syntheweave

It's very easy to turn the smartphone into a reasonable creation tool, the trick is not act like the world ends at the bounds of the device.

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.

⬐ MrsPeaches

Thank you for your thoughts.

> 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.

⬐ pixl97

Hexagons are the bestagons

https://youtu.be/thOifuHs6eY

⬐ O__________O

To be fair, hexagons alone are unable to form a sphere like surface:

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...

⬐ Aardwolf

"The purpose of a traffic sign is not to raise public appreciation and awareness of geometry which is better dealt with in other ways."

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

⬐ O__________O

Agree. Video mentions that sports fans likely care and that they only wanted future signed updated, the petition though as far as I am able to tell mentions neither of these points:

https://petition.parliament.uk/archived/petitions/202305

⬐ mdp2021

I built so many, as a child, after reading Martin Gardner. Six faces for the basic ones, then many more. I used the tape of calculators with mechanical printing.

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)

⬐ tunesmith

The sixth video in the series is really a work of art: https://www.youtube.com/watch?v=DIyruYQ-N4Q&list=PLaNzoFtkQ7... I've thought a lot about arguments and premises and values and conclusions and how it connects with frustration and humiliation and shame, and really wasn't expecting all those subjects to come in in a video about hexaflexagons.

⬐ someweirdperson

Quote from part 6: "The pink side with the yellow center is a theoretical possibility that remains unobserved as in practice it seems to be unopenupable."

⬐ lupire

Strangely, in the Gardner article that she used for the outline of her video, it explicitly states that its eqivalent of the pink side with yellow center is theoretically impossible, in the hexahexafrustragon.

⬐ notRobot

I know about Vi Hart but hadn't seen this series before, I just watched the first two videos and my mind is so blown right now, this is incredible. I love fun math stuff like this.

⬐ Jtsummers

If you liked this, you ought to check out Gardner's articles themselves:

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).

⬐ anandology

When I saw the name Vi Hart, the author of the video, it sounded quite familiar. It turned out that She is the daughter of George W Hart, a mathematician and polyhedron man. I'm a big fan of work zome geometry and amazing polyhedron.

If you are interested in recreational mathematics, don't miss to checkout https://georgehart.com/.

⬐ nightchalk16

http://loki3.com/flex/

⬐ Klaster_1

Are there any practical applications to this, like making nanoscale structures that can change particle or surface properties? What's the smallest possible structure that enables bending? This looks like one of those mundane problems that yields unexpectedly impactful applications, like moiré pattern and magic angle graphene.

⬐ tocs3

I do not how practical but maybe a business card with different bits of information depending on how it is folded.

⬐ StephenAmar

I can think of https://youtu.be/ThwuT3_AG6w

⬐ mgdlbp

A recent submission[1] reminds me of the series on flexagons—folded paper with more than two faces that can be swapped via a 'flexing' operation—by Vi Hart, whose videos on mathematics were quite popular on YouTube around ten years ago.

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

⬐ mgdlbp

Interesting— Vi Hart was a PI for YC Research's HARC (known mostly for Bret Victor's Dynamicland) – small world

https://hn.algolia.com/?query=harc

⬐ O__________O

Yep, Vi Hart even posted single comment on HN years ago:

https://news.ycombinator.com/threads?id=vihart

⬐ omneity

Maybe someone with more specialized knowledge can shime in, but this looks awfully similar to me to a discretized SU(1) symmetry (maybe SU(2)? My intuition in Lie algebras is extremely rusty)

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)

⬐ CliffStoll

Vi Hart's videos -- terrific!

⬐ Despoisj

I made a 6 sided square flexagon puzzle for my dad, it's surprisingly simple yet can take forever to solve.

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.

⬐ ge96

Damn... I have not seen this in a long time

⬐ stevenjgarner

She had me at you "find that your new American paper doesn't fit in your old English binder."

⬐ AndrianV

I don't know why I had this image in my head, but I pictured Stone, Tuckerman, and Feynmann as being around the same age when this took place. Imagine how disheartened I was to learn that they were 23 years old, 24 years old, and 21 years old correspondingly.

⬐ 2muchcoffeeman

I thought Feynman Diagrams were for interactions of subatomic particles.

⬐ donclark

related:

https://www.alibris.com/search/books/isbn/9781944686109?invi...

https://www.etsy.com/listing/1231396190/tri-hexa-flexa-coder...

⬐ O__________O

(2012) is date for videos from this thread.

Happy to see Vi Hart’s still making videos:

https://m.youtube.com/user/Vihart/videos

⬐ None

None

⬐ None

None

⬐ bmorton

I absolutely cannot stand Vi Hart's delivery. I remember 2012 well and at the time this style was considered cutesy. It has not aged well. I don't think the term manic-pixie-dream-girl had been thought of at the time, but her message would have a much longer term impact if she hadn't chosen (yes, a conscious choice) such a one-sided character when narrating her videos.

⬐ jb1991

Weird flex, but okay.

⬐ washyourdishes

I love to recommend ViHart’s “Suspend your Disbelief” video: https://youtu.be/deg1wmYjwtk

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.

⬐ Nebasuke

Thanks for linking this, I loved this video. I'm surprised it's relatively unpopular compared to the rest of the channel, but I suppose that supports her point...

⬐ sn9

This is one of those rare videos that makes me feel less alone by describing something it seems like everyone online is unaware of.

⬐ JKCalhoun

I had not seen that one before. She truly is genius.

⬐ Karellen

Also, "How I Feel About Logarithms": https://youtu.be/N-7tcTIrers

Genius.

⬐ qwertox

"Sometimes, to make the harder things simple, you first need to make the simple things harder"

Vi Hart is amazing with flexagons [0].

[0] https://www.youtube.com/watch?v=VIVIegSt81k

⬐ skipnup

And of course the best of all hexaflexagon videos: https://youtu.be/GTwrVAbV56o

⬐ hadlock

Came here to post this

⬐ ketzo

This is where I first learned about them! Absolutely loved watching her videos when I was younger and just getting into math/science as a concept.

And more related, also from Vi Hart: https://www.youtube.com/watch?v=VIVIegSt81k, https://www.youtube.com/watch?v=paQ10POrZh8, https://www.youtube.com/watch?v=AmN0YyaTD60

Is this the same vihart of YouTube hexaflexagon fame?

https://youtu.be/VIVIegSt81k

⬐ ygra

Yes.

⬐ Udo

This is one of these things I feel a lot of hackers might know already but I only discovered them yesterday :)

When playing a nice pen and paper roleplaying game of Cthulhu, our GM had us trapped in a non-euclidean manor where the doors through which you went changed the configuration of the space. We had an insane clock device with us (in the shape of a symbol-ridden hexaflexagon as a playing aid on the table) that allowed us to eventually navigate through the thing.

The only catch was none of the players had ever heard of hexaflexagons and the GM flexed the device hidden from view. So we did an unspeakable amount of diagrams trying to figure out how the device might work. Good times.

Anyway, this is awesome and everybody should know about them.

⬐ weseven

related: http://www.youtube.com/watch?v=kFUyXWlObLw

⬐ todd8

Growing up, before the internet, I fell in love with libraries. I discovered Scientific American and it's regular column "Mathematical Games" by Martin Gardner. I eventually read every one of those columns written by Gardner and picked up a lot of science from the rest of the magazine along the way. When I discovered his 1950's column on hexaflexagons I introduced them at my junior high school where dozens of us carried them around and played with them at lunchtime. Several other diversions I learned from Martin Gardner also made the rounds at that school.

I highly recommend the Mathematical Games columns written by Gardner; many of the more interesting ones are available in his books as collections, for example [1], which is less than $5 on Amazon. (Equally fascinating to me then was the Scientific American column "Amateur Scientist", this went back decades farther than "Mathematical Games" and showed projects, actually built by readers, that were often completely over the top--atom smashers, x-ray machines, sophisticated seismographs, etc. Thank goodness I didn't kill myself in my homemade lab in the basement.)

For an up to date treatment of the flexigon see [2].

[1] My Best Mathematical and Logic Puzzles, Martin Gardner, Dover, 1994. [2] Flexagons Inside Out, Les Pook, Cambridge Univ Press, 2003.

Vi Hart is fantastic; I recommend watching all her videos [1] (though skip the very early music-only ones if that's not your thing). Particularly good are the hexaflexagon ones [2] and the plant spiral ones [3].

[1] https://www.youtube.com/user/Vihart/videos

[2] https://www.youtube.com/watch?v=VIVIegSt81k

[3] https://www.youtube.com/watch?v=ahXIMUkSXX0

⬐ dnautics

the snail one is uh, amazing, too.

⬐ leephillips

She deserves the Nobel Prize of the internet. Her Pythagoras video[0] is one of my favorites.

I was awestruck at the end of this one, after seeing the musical shapes. A well-spent 30 minutes.

I would only disagree with her listing of Stravinsky as an "atonal" composer. Although he did mess with 12-tone composition a bit very late in his career, he is not usually thought of this way, as he very much dealt with tonality in the vast majority of his work.

[0]http://www.youtube.com/watch?v=X1E7I7_r3Cw

⬐ stephencanon

Even Stravinsky's serial compositions aren’t so much atonal as they are post-tonal. There are relatively few composers whose work can be genuinely called “atonal”.

⬐ eli_awry

Vi Hart, who produces these videos, now works at Khan Academy. She's also one of the people to make tau (as an alternative to pi) go viral. http://www.youtube.com/watch?v=jG7vhMMXagQ

⬐ soapdog

I know I will sound like a fanboy but every morning before starting to work, I watch one vi hart video.

Starting the day with those fantastic videos is like kickstarting both my analytical mind and my creative mind or may be those videos just make me happy in a very geek sense and the day begins in a better mood.

Also, SPIRALS EVERYWHERE...

⬐ joeycfan

I had these things in my pencilcase in highschool in the seventies.

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