Some thoughts on the shape rotator vs worcel meme

Here’s some background reading if you’re unfamiliar with this meme. I was going to write “new meme” but think by now it’s an idea that’s rather thoroughly entrenched in sufficiently large Twitter communities. Namely Crypto Twitter and Machine Learning Twitter, and by tech VCs that lurk both.

I don’t agree with the bucketing of deep learning and crypto, but it’s a snappy tweet regardless.

I think it defines an interesting dichotomy. I think it puts forward a novel division that previous dichotomies of a similar flavour have not; e.g., left vs right brain, good at math vs good at writing. It gets closest to the essence of what these ideas are approximating.

On shape rotation

The ability to expertly rotate shapes isn’t the same thing as being good at math. Mathematical thinking itself can be split into its shape rotation and wordcel elements. There are generally two approaches to developing a mathematical proof:

  1. One can prove a mathematical statement by simply playing with mathematical language in a grammatical way, or
  2. One can prove a mathematical statement by first seeing its truth visually (or sensing it, in a rather parasensory way) and then translating that into mathematical language.

Good mathematicians do the latter.

Consider the following two explanations/proofs for the correctness of the decryption function in the Data Encryption Standard. Namely, that the first step of decryption reverses the last step of encryption.

A wordcel-esque proof:

“Ah, yes, substitute this for that, move the brackets around, and then some terms cancel out and we have our equivalence!”

A shape rotator proof:

A visual, “intuitive” understanding of equivalence. Identical colours represent equal values.

I should note that all proofs in their final form take on a wordcel appearance. However, one can’t tell — unless the mathematician reveals their process — how the proof came about, whether it was a play of mathematical grammar or whether it was first seeded in the mind’s eye.

A tangent: This gets really close to implications from every stoner mathematician’s favourite subject, Gödel’s Incompleteness Theorem. When we visualize the essence of a mathematical truth, is that our mind rendering our brain’s electrical circuits into a sense perception? So then we simply decode the visual to its circuit board-like original form? Does our brain generate wordcel proofs before converting them to images? Or is it some precognitive thing? Can we visualize or intuit the truths of certain mathematical statements but never be able to prove them? Puff puff.

A video from the Essence of Linear Algebra YouTube series by 3Blue1Brown.

(I wasn’t sure where to fit this, so it’s going here. Linear algebra is one of the most wordcel-y classes taught in university when it’s actually perfect subject matter for the shape rotator. Anyone who’s taken a linear algebra course would know what I mean. This series of YouTube videos — with sharp visuals and animation — helped really solidify fundamental concepts in linear algebra for me, something two university courses couldn’t.)

On wordcels

-cel is a derogatory suffix used in internet parlance. Describing a wordcel is best illustrated with an example. Here’s an abstract from a recent paper in a journal called Leisure Sciences:

Philosopher Henri Lefebvre claimed that exultations such as “Change life! Change society!” — or, more appropriately, “Change your habits!” — mean nothing “without the production of an appropriate space” where these changes can occur. Adapting Lefebvre’s theories on the production of space to leisure, this paper celebrates how our participation in collectivistic online communities helps reconcile our need for distraction and connection during quarantine, aided by the practice of “space-building.” Through this process, leisure develops as both a visual and physical practice, the apathy (and boredom) resulting from inertia circumvented by space-building. By constructing relatable spaces that strive to mimic “real-world” locales, the dissonance created by the dialectical relationship between the objective truth (I’m stuck at home … ) and our subjective projections is temporarily resolved.

While the author clearly has a strong command of English vocabulary, grammar, and phraseology; his entire thesis is essentially: During quarantine, the physical spaces that traditionally play a social function (e.g., cafes, clubs, bars) have been replaced by our own homes and digital spaces. This makes physical isolation a bit more enjoyable. This abstract is a lot of words that don’t really say much. Do you think reading the full paper would meaningfully change the way you understand or experience reality?

A wordcel — at least in its derogatory connotation — is someone who has a strong commandment of language (high verbal IQ) but doesn’t really say much. A wordcel does not describe reality interestingly, and sometimes not even accurately. Nor do they necessarily create new useful concepts, forms, or processes.

Screenshot of an example text from Postmodernism Generator. I originally considered using an example from this website— a shape rotator invention created to mimic the wordcel — but I decided upon something written by an actual human wordcel for the analysis above.

So is every writer a wordcel? No! The conversation from here gets hairy. It essentially boils down to: What makes a writer a good writer? (What makes them not a wordcel?)

A good writer doesn’t merely play with language, they actually say something of substance. Note that this presupposes that they’ve rotated a concept in their mind and steadied upon an interesting and novel angle. Or — even better — they have so comprehensively rotated a thing in their mind’s eye that they’ve steadied and absorbed the essence of the thing itself. Then their words must gracefully pass through a proverbial eye of a needle so that this essence is undisturbed and emerges reassembled in the reader’s consciousness.

Aurora / Goddess sparkle / A mountain shade / Suggests your shape / I tumbled down / On my knees / Fill the mouth / With snow / The way it melts / I wish / To melt / Into you / Aurora

— Björk, “Aurora”

I argue that art comes from the future (and I can prove it?!) It’s my job to sort of channel it into the present in words … I believe art is a way to talk about the way things are in general … I believe art is a way to attune to what reality is, which is a weird reality … I could find a million examples in your work. The description of the snow in “Aurora” leaves the snow to be exactly what it is, yet at the same time there is this tantalizing sensual appearance, yet one can’t quite grasp it, which is why it’s beautiful (‘The way it melts …?’). Kant said something very similar about raindrops in his funny old clunky way.

— Timothy Morton in an email exchange with Björk

Transforium by Tammy Lu (detail)

What may be the nature of objects considered as things in themselves and without reference to the receptivity of our sensibility is quite unknown to us. Not only are the raindrops mere appearances, but even their circular form, nay, the space itself through which they fall, is nothing in itself, but both are mere modifications or fundamental dispositions of our sensible intuition, whilst the transcendental object remains for us utterly unknown.

— Emmanuel Kant, Critique of Pure Reason

Conclusion

Okay, so what’s my conclusion? Truthfully, I just needed to write down some thoughts that have been swirling in my mind for a while and be at peace with leaving some dots unconnected. Here are a few things I can safely conclude.

  • There’s a good reason why this meme has become so popular so quickly. It captures a dichotomy that is so palpable and seemingly ever-present but yet hasn’t been approximated successfully. And there’s something a little tantalizingly elusive about it too. It’s difficult to really define — nay, impossible — because the meme pierces beyond the veil of language itself.
  • It’s not really like a yin/yang thing. Shape rotation — or, more accurately, the mysterious mechanism guiding it — is strictly better than wordcel-dom. It seems like language is a crippling barrier between the (proto-)thoughts of two minds. (Here’s a conversation I had with Andryl that gets into those things.)
  • I hope I managed to convey something of the fuzzy boundary between math and language, if there truly is a meaningful boundary at all. And perhaps given you a sense of the tantalizing ether beyond these words themselves.

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