Origami: Reutersvärd Triangle

Reutersvärd Triangle

Reutersvärd Triangle, designed by me

Many years ago, I designed the origami Arrow Illusion–an arrow that points in the opposite direction when viewed in a mirror.  It’s probably the biggest “hit” among my designs.  Recently, CFC (an Origami community) had a monthly challenge to create optical illusions, and it featured Arrow Illusion as an example.  So, I thought I’d design another.

I went through several ideas, but ultimately settled on the Reutersvärd Triangle.  It’s similar to the better-known Penrose triangle, but was actually created independently by Oscar Reutersvärd in 1934–before the Penrose triangle.

Like the Penrose triangle, the Reutersvärd Triangle is just an illustration–it’s impossible to actually make something shaped that way.  And yet, you can find many very convincing 3D-printed implementations of the Reutersvärd Triangle.  I felt this was a sign that I needed to origamize it.  (Note that the Arrow Illusion, too, was inspired by 3D printing!)

Actually designing the thing was fairly challenging, and I went through over half a dozen prototypes.  Even once I got the basic form down, I tried many ideas to optimize for simplicity and stability.  The end result is so elegant that its instructions fit on a single page.  Note: if you try to fold this, I suggest trying the “easy” version first, and make one with just 6 pieces of paper. It will look like this:

Reutersvärd Triangle, with 6 cubes
How does the illusion work?  The cubes are actually inverted.  Although it pretends to be a collection of cubes pointing outwards towards the camera, they’re actually internal corners pointing inwards.  It’s… not very convincing when you have the physical object right in front of you.  It’s most convincing when you take a photo in ambiguous lighting, and then sometimes it helps to turn the photo upside-down.  The lighting of the cubes doesn’t match the shadows behind the model, which may have caused some of you to see through the illusion already.  But in case you don’t see it, here’s a photo from the side:

Reutersvärd Triangle, seen from the side

LLM error rates

I worked on LLMs, and now I got opinions. Today, let’s talk about when LLMs make mistakes.

On AI Slop

You’ve already heard of LLM mistakes, because you’ve seen them in the news. For instance, some lawyers submitted bogus legal briefs–no, I mean those other lawyers–no the other ones.  Scholarly articles have been spotted with clear chatGPT conversation markers. And Google recommended putting glue on Pizza. People have started calling this “AI Slop”, although maybe the term refers more to image generation rather than text? This blog post is focused exclusively on text generation, and mostly for non-creative uses.

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Link Roundup: July 2024

In the past month, I wrote an article for The Asexual Agenda discussing causality.  And on a more personal front, I composed a couple short songs for music box.  (Did you know, I made an EP back in 2022?)  Anyways, onwards with the roundup.

Seeing Beyond the Veil | Bullet Points Monthly – This article discusses the association of psychosis and spiritualism, through the lens of Senua’s Saga: Hellblade II (a game I have little familiarity with).  In the first game, the protagonist’s psychosis is a source of suffering; in the second game, it’s a source of spiritual power.  This serves a narrative of empowerment–but it takes place in a world where giants and fairies exist.  In the real world, people may have more complicated feelings about attempts to turn their suffering into something mystically useful.

‘Cis by Default’, ‘Cis-genderless’, and ‘Gender detachment’: Three Terms You’ll Hopefully Be Hearing More Of | Ace Film Reviews – Blue Ice-Tea discusses three independently created concepts, each describing experiences of people who are not necessarily trans or non-binary, but lack a strong sense of identity.  I think by the nature of the thing, people with these experiences may not be very vocal about it, and may not even think much about it.  Creating labels for the experience has the disadvantage of drawing unwanted attention to the question of who is or isn’t.  But I do think it’s worth being aware of this side of gender experience, and at least some people may find the words useful.

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Origami: Ixora

Ixora

Ixora, designed by Meenakshi Mukerji

I’m saddened to hear that Meenakshi Mukerji recently died.  I almost had an opportunity to meet her at a convention, but there was a pandemic and it never happened.  I’d give her a lot of credit for getting me into modular origami, and many of my earliest models were from her books.  I love her work.  This is a simple model that I have folded many times; it can be found in Ornamental Origami.

Environmental impact of LLMs

A reader asked: what is the environmental impact of large language models (LLMs)? So I read some articles on the subject, and made comparisons to other technologies, such as video games and video streaming. My conclusion is that the environmental footprint is large enough that we shouldn’t ignore it, but I think people are overreacting.

Pricing

I’m not an expert in assessing environmental impact, but I’ve had a bit of experience assessing computational prices for LLMs. Pricing might be a good proxy for carbon footprint, because it doesn’t just represent energy costs, but also the costs of building and operating a data center. My guess is that across many different kinds of computation tasks, the carbon footprint per dollar spent is roughly similar. And in my experience, LLMs are far from the most significant computational cost in a typical tech company.

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I worked on LLMs

Generative AI sure is the talk of the town these days. Controversial, is it not? It’s with some trepidation that I disclose that I spent the last 6 months becoming an expert in large language models (LLMs). Earlier this year when I moseyed through the foundational LLM paper, that was where it began.

I’d like to start talking about this more, because I’ve been frustrated with the public conversation. Among both anti-AI folks as well as AI enthusiasts, people have weird, impossible expectations from LLMs, while being ignorant of other capabilities. I’d like to provide a reality check, so that readers can be more informed as they argue about it.

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Link Roundup: June 2024

Orientalism: Desert Level Music vs Actual Middle-Eastern Music | Fayra Faraji (video, 1:36 hours) – This video explains how orientalist music has virtually nothing to do with actual music from the Middle East.  The music uses a hodgepodge of different instruments and musical styles that come from vastly different contexts.  They nearly exclusively use the double-harmonic and phrygian mode, not because those are particularly common in Middle-Eastern music, but rather because it’s uncommon in other western music and yet fits within the 12TET system.

As a fan of xenharmonic/microtonal music, I know that many non-western music traditions use different tuning systems–the Maqam traditions are particularly notable.  I appreciate such music as it comes into my awareness, and definitely wish it were more widely distributed.  That said, I’m very aware that I come from a western musical tradition, and the very first thing I hear in microtonal music is a sense of uniqueness relative to my musical context and training.  When I think about non-Western musical traditions, I imagine a whole history and culture where these musical characteristics are just normal, just a medium used to express something else entirely.  That just isn’t my perspective, I cannot hear it that way.

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