since I seem to own the "hiliting" beat (part of learning who to be is learning who nobody else wants to be), I feel it is upon me to inform you that the hiliter tool in @CleanShot is mind-bendingly good: it auto lines up with text in screenshots & remains editable 🤯

pixel text is as valid a text as character-encoded text: the substrates have different tradeoffs, but as readers we just want affordance-parity & better tools!

this feels like exactly the kind of thing for which @jondotbo once coined the phrase "materials R&D for digital paper"!

btw, that screenshot is from this lovely tribute to birds

it inspired me to pay attention to birds around me, like how the top of these tall proud trees is bent from being perch to tiny birds

https://x.com/moultano/status/1911938304246964414

Back to hiliting news, have you seen @david_perell's Writing Examples? The site is only 6 months old but already wide-ranging & worth a deep dive.

Choice quotes are drenched with layers of annotation to pinpoint the how of remarkable writing. I feel far less of a weirdo for my intense hiliting!

https://x.com/david_perell/status/1841875983676162124

let's wrap up with past hiliting tweets:

from 2023 a visualization of how I hilite, by the Principle of MOST Surprise 

(remembering, as @yukihiro_matz once clarified: it's the principle of most MY surprise) 

https://x.com/elzr/status/1617945515710349312

a high-res composites of book hilites (a book map!🗺️📖) from 2020

(I should do this for many more books! I finally have the gear for it & friends have wanted to train an AI to hilite this way)

https://x.com/elzr/status/1340778243444633602

finally, this tweet from 2019 chronicles my slow realization that my hilites are a "destructuring" (as @jondotbo describes it) of the 1D-linearity of text strings (a la @karpathy) to color, to outlines & to 2D space (as in my syntactic spacings)

https://x.com/elzr/status/1112037124805582848

Text hiliting news

While area is easily approximated by squares, length resists being defined out of simpler parts!

A diagonal isn't just right-angle steps, no matter how tiny. An ever finer staircase converges to the area of the triangle, but NOT to its perimeter —a foundational fractal paradox.

It's unexpected because the method of exhaustion does calculate the perimeter of a circle out of simpler shapes: infinitesimal diagonals approximate the length of a curve, a keystone of calculus from Greek antiquity.

But this method breaks down for diagonals themselves!

In a geometric space, the "easier" concept of 1D length turns out to be "harder" than 2D area. It is the paradoxical genius of the Pythagorean theorem that it uses area to define length, building down the simple from the complex.

This is all very related to Weyl's tile argument that in a discrete universe the Pythagorean theorem doesn't apply.

Though here you're not counting steps as square sides, the squares are distance atoms, so the diagonal of our triangle has leg length (vs × 2 or √2).

Weyl's 1949 argument is simple yet obscure. It seems to be of serious interest to philosophers & physicists more than mathematicians. https://en.wikipedia.org/wiki/Weyl%27s_tile_argument

Of the precious few to ever tweet about it, there's of course @prathyvsh, referencing a fun thread on this meme:

https://twitter.com/prathyvsh/status/1594768105309237249

I gather from this comment https://twitter.com/PeterSaveliev/status/1662109644431433732 by @PeterSaveliev that this recent thread seems to be a key to this whole discussion, but I'm still trying to figure out the math.

https://twitter.com/gabrielpeyre/status/1661960353809580034?s=20

See also years of discussion in the Math StackExchange where the most upvoted question calls it the staircase paradox https://math.stackexchange.com/questions/12906/the-staircase-paradox-or-why-pi-ne4

> The problem is it doesn't approach in a "smooth" way.

> By splitting the path you essentially create lots of little triangles.

Finally, you can read the unrolled version of this thread here: https://typefully.com/elzr/Ztw5QAC

The Pythagorean paradox

The main avatars of 💻desktop computing are the slanted arrow cursor & the flashing-line caret.

Let's talk lyrically about each style of embodiment: the pointerfeel of the cursor & the keyfeel of the caret.

🦅The cursor is an eagle soaring above content, changing shape to match its hovered "prey", ready to swoop down with a click. It moves continuously & untrammeled across the entire screen.

🖱️To be a cursor, your hand gloves a pointing device: a mouse or track-pad/ball/point.

👣♟️The caret is a footsoldier at the vanguard of text entry, your man on the ground adapting to the terrain of content & its bounds. It steps, discretely, by letters, lines or cells (also by words or to the edges of lines & paras).

⌨️To be a caret, your fingers play arrow keys.

Cursor & caret are great friends, specially in laptop configurations where the hands scarecely travel between them. The eagle cursor swoops in to rescue the caret & plonks it close to where it's needed, in LOTR fashion.

🐴 The far, far rarer "dials" are a bit like horses, they can gingerly pace stepwise but will gallop at a moments notice, though only in one dimension.

My thumbs still remember how fun it was to glide through menus on the iPod's clickwheel.

The joystick is a marvelous shapeshifter: a one-finger pointer that's also easy to chunk into arrows for occasional menus.

It's fluidity & compactness shines in modern game controllers, where you usually have two: one for moving you avatar, another for adjusting the 3D camera.

Modern infinite canvases sadly lack the keyfeel navigation of carets!

But that OG infinite canvas, the spreadsheet, achieves thru cells an exquisite keyfeel: more predictable than word processors & hacked by advanced users with "landmark handles" (cc @DKedmey & @AJNandi).

In @figma you almost get a caret! You move thru layers by their stack order with (⇧)Tab, out & into groups with (⇧)Enter, and thru frames by their "row" order with (⇧)N.

But, as @brianjoseff points out, to rely on this you must construct & maintain your space obsessively.

What made a tool like 2006 Dasher so radical (and radicalizing) was that it allowed us to navigate the letter-space of written language by pointer. We had only ever known it through keyfeel! Dashing was a damburst for both abled & disabled.

https://twitter.com/disconcision/status/1579973825596645376

Maybe you think this thread strange but what's strange to me is how rarely we pay attention to matters of digital phenomenology. That's a fancy word but really it's just "feel-ology", attending to how interactions feel.

Inspired by @maxkriegers & @rsnous: https://twitter.com/maxkriegers/status/1345574975974027265

https://twitter.com/maxkriegers/status/1345574975974027265

Ultimately, what I want is "software criticism" like @sheonhan proposes: https://www.wired.com/story/software-criticism/

Not assessments of the whole of tech, of which we have plenty. Focused interrogations of single works that show us how to see, a "rough blend of product review & lit crit".

.@craigmod does fantastic software criticism, like when he rhapsodized about iPad's 2020 cursor https://www.wired.com/story/ipad-trackpad-cursor/

Upon finding unexpected joy in a trackpad's indirect manipulation: "The cursor lives in the same virtual space as the interface in a way our finger never can."

You can read the unrolled version of this thread here: https://typefully.com/elzr/bsx2P3T

Cursor pointerfeel & caret keyfeel

Here's a really weird way to visualize business inspired by @prathyvsh & @nbashaw:

Imagine a constellation of dots as the latent capabilities in an economy.

Producers like companies are sets that actualize capabilities by offering their services.

The (Σ) union of all companies is the actual productive capacity of an economy.

While the area of an economy, its total number of actual capabilities, is in direct relation to company (Δ) differentiation, the unique capabilities each producer offers.

Besides being business jargon, that's also kinda like the fundamental theorem of finite calculus! 🤯

https://twitter.com/prathyvsh/status/1597693380548448257

Why do economies expand? That is, why do companies differentiate? Because by doing so, they become links in the value-chains of capabilities that get consumers what they want.

The less replaceable links get to capture more of the value.

https://twitter.com/elzr/status/1262135059496284160

This is almost a rewrite of the bolt of lightning that was reading this trippy thread. 🤯

https://twitter.com/prathyvsh/status/1624588347736981504

Visualizing business

The recusive, binary structures at the root of modern math.
Visualized to show their unity-in-diversity.

This builds on this recent, unexpectedly viral diagram. I'm adding to the parallelism the structures of set theory, combinatorics & order theory: the Venn diagram, Pascal's triangle & Hasse diagram.

Also being more explicit about the duality in computation between code & data.

https://twitter.com/elzr/status/1622022572530606083

For friends who'd like to see me 🫳🤌🫴🙌 emoting & gesturing excitedly about abstractions, I recorded this 12min screencast unfurling this new diagram. cc @jamescham, @dela3499, @maxkriegers https://www.loom.com/share/afca55c3ce9845c9b4796fdce906dc5e

These "recursive, binary structures" — are they in the room with us right now? (They've surely been with me this past week! 🤣)

https://twitter.com/stevekrouse/status/1444281751682142214

I integrated Pascal's triangle thanks to @prathyvsh's many kind prompts 😅 (combinatorics is still very foreign to me):

https://twitter.com/prathyvsh/status/1622027820431183872

Instead of the more common sums in Pascal's triangle, I preserve the binary "vertices" to make it match with the other diagrams.

Their stacking makes very clear the connection with the Galton board —how combinatorics gives rise to probability! Left diagram by @AlanZucconi.

Seeing the pebbles falling down the Galton board makes me remember this visualization of luck that's been a sort of lucky charm itself since it periodically resurfaces:

https://twitter.com/elzr/status/1381105950602461189

My visual investigation into logical fundamentals can be traced back to this 2019 tweet, where I come up with a tetragram to represent logic gates visually (iconically, as Peirce would say), then build up additive circuits!

https://twitter.com/elzr/status/1169409893197111296

Back then, deep in the comments (with @prathyvsh, in an exchange that would start our friendship) we ended up with Venn-like diagrams too:

https://twitter.com/elzr/status/1171641749057495041

I was also led to Euler diagrams and how they match with trees & Hasse diagrams in this beautiful & clear thread on lattices by @prathyush (often it's only until he makes a graphic thread that I can finally grok his references ;)

Going Venn instead of Euler was a hard choice! 💔

https://twitter.com/prathyvsh/status/1476974452705480712

Key inspirations for including Venn diagrams were the layouts by Russell Johnston (1987) & Stephen H. Cullinae (2007) http://finitegeometry.org/sc/16/venn.html as well as the many ones found across logical articles in Wikipedia, like Greg Bard's (2007) https://en.wikipedia.org/wiki/Logical_connective

Back to the head diagram. Notice the 2-arity of all the structures. Binary seems the simplest, but nature may speak more natively in higher-arities, as @stephen_wolfram & @getjonwithit point in @wolframphysics.

We need @TheTedNelson in our math to hyper-ify all the things!

https://twitter.com/elzr/status/1622022587277799424

Would also like to recommend here the fantastic work Mark Jeffery is doing at the @lasttheory_ project (videos, podcast, newsletter). He has several great tutorials on arity & this  explanation of why hypergraphs by @getjonwithit recently blew me away. 🤯

https://twitter.com/lasttheory_/status/1606055527141646339

Spivak's Calculus has an appendix on how you can build up the ordered pair from sets.

"Abstract nonsense," said my teacher when I mentioned it excitedly. Spivak too frames it as if pesky construction-ism is just to assuage nerves about abstraction.

But it's also just beautiful!

And having many alternative constructions of abstractions can be of world-historic importance!

It wasn't until logic gates & boolean operators that we really figured out how to instantiate abstractions physically, dynamically, as computers.

https://twitter.com/elzr/status/1615057520585842688

Anyway, what I'm really trying here is to "sensualize abstractions" (to mangle Hamilton's 1858 phrase), to share with you the aesthetic chills I feel at the convergence we find as we discover new bedrock for the formal science of math.

It's like the Swift quote Spivak has as epigraph to an epilogue constructing the ℝeals. Below modern math's rarefied heights, we're also building & discovering its foundation —and always will, for it's 🐢foundations all the way down, as @DavidDeutschOxf coulda but never said ;)

Let's end with a visual joke: Here's another kind of binary tree, in the red/black styling I'm using ( which @gwern calls rubrication: https://gwern.net/red ).

PS: There are non-binary Easter eggs in the original comic! (2 & 4 but seemingly no 3).

https://twitter.com/turnoff_us/status/781662589965172740

You can read the unrolled version of this thread here: https://typefully.com/elzr/Pi8RzS2

The recursive, binary structures at the root of math

A fundamental link between logic, computation & geometry is that every truth table is also a binary tree and also a cube.

Notice also the duality between seeing the grid or the crosses, the edges or the nodes, the branches or the leaves.

This is also the duality between code & data. https://twitter.com/elzr/status/1371732525106790402


Computation is so twined with duality, this inverse is true: you can go from propagating, bi-stable perception to computation —as @MarkChangizi found out back in 2008, creating optical-illusion circuits.

See https://www.changizi.com/uploads/8/3/4/4/83445868/viscomp.pdf & https://www.humanfactorylab.com/uploads/8/3/4/4/83445868/changizi_eyecomputer_presspiece.pdf


I've long been playing with these ideas but the 3-way connection of table/tree/cube finally became clear from doing this personality-space explorer & the discussion about it with @prathyvsh: https://twitter.com/elzr/status/1621624447286509568

The higher-arity project points the way forward to a radical extension beyond the binary of the fundamentals of logic, computation & geometry!  https://twitter.com/ZapataCarratala/status/1616072117291974658


Table, tree & cube - Logic, computation & geometry

Explore the Myers-Briggs personality space through your MBTI result!

I loaded the explorer with just a sample of 6 of @HeidiPriebe1's  hundreds of 2014-2017 articles on MBTI for @ThoughtCatalog. They're a goldmine! Her writing is playful, with heart & insight. https://thoughtcatalog.com/heidi-priebe/

Here's what's going on: The 16 types of MBTI are usually presented as a table but playing with representations took me to nested quadrants & a hypercube graph.

Playing with hypercube perspectives, took me to a shape-free graph, with 4-edges per node as its defining quality.

Fun starts when we pick a node (say, YOUR personality type) and then stretch the graph along the edge-DISTANCE to you.

Here's that same strestretch-tiletched graph but now, instead of balls as nodes, we have tiny grids that highlight the edge change:

🗺️ This strange notion of distance between personalities allows you to stumble on new ways to think about yourself & others:

Who are your adjacent selves, 1 step away? Who's your opposite self, your antipode? How does the world look like to others?

You can play with this tool right now: It's just a Google Sheet. Go to this link to make your own copy to play with 👉🏼 https://docs.google.com/spreadsheets/d/176fwoj8LbHhKSb6oFsX7zzxztitPkPDbgmKsxcQQ36s/copy

Notice how strange a spreadsheet this is! I think you could do something like it in @shishirmehrotra's @coda_hq but making it in @NotionHQ would just be painful.

I'm using sheet's value rule, their time-less/spaceful nature, & array spilling. See more at: https://twitter.com/elzr/status/1610084298501271554

Would be fun if visual theorizers like @thekenwilber, @vgr,  @tiagoforte, @balajis, @kevinkwok, @eugenewei, @packyGM, @benthompson, @ystrickler, @tegmark, @Alex_Danco experimented with 2x2x2x2 hypercubes to play with the distance between their concepts, methods & scenarios.

2D 4x4s "achieved the status of intellectual farce," @vgr wrote in a classic 2009 essay. Yet they're still indispensable: 1D/Δ too limiting, 3D overwhelms our visual processing.

But 4D, starting at 2x2x2x2=16, can introduce Hamming-distance for concepts! https://www.ribbonfarm.com/2009/04/20/how-to-draw-and-judge-quadrant-diagrams/

I was inspired by @gordonbrander dream of: "More tarot than flash cards. Tarot for thought." https://subconscious.substack.com/p/second-subconscious

This explorer is a bit like what Brander calls oracles (geists inside Subconscious). Like  @brianeno's 1975 Oblique Strategies or @jesseschell's deck of lenses.

Notice the stance! Asking whether an oracle is truly "scientific" or "magical" or "aware" is besides the point —of course not! These tools dare YOU to create meaning. They prompt YOU with their procedurally-generated creativity.

There's a long tradition of 🃏 card-based oracles & games. The (shuffled) deck is the latent space & your hand the prompt.

Personality tests (from the Big Five to @BuzzFeed  quizzes) as a proposed personality space, with your answers as prompt, the initial vector of exploration.

Or consider the TRIZ matrix, a database of known solutions able to overcome contradictions. A space of principles that you explore through a vector of contradiction (feature you want to improve × feature you want to preserve). https://twitter.com/worrydream/status/1614087776194166784

Of course there's also the I-Ching, the ancient Chinese divination text. But I know too little about it yet to say anything other that I once made a visualization for logic gates that many remark looks a lot like the I-Ching hexagrams: https://twitter.com/elzr/status/1169409893197111296

I like how @HowardxBloom defends oracles as vital identity-boosters & aids-to-choice for our constant identity crises & decision panics. He urges us not to look down on them but to make better aids for making up our minds.

Finally, see @slatestarcodex's defense of personality types as a handy vocabulary: https://slatestarcodex.com/2014/05/27/on-types-of-typologies/

"MBTI is trying to separate... continuous personality space into discrete and easy-to-think-about terms suitable for human processing."

OK, end of rant. To wrap up, this is a toy explorer of MBTI as a personality space. Should be fun, might be useful. Try it now! 👉🏼
https://docs.google.com/spreadsheets/d/176fwoj8LbHhKSb6oFsX7zzxztitPkPDbgmKsxcQQ36s/copy

You can read the unrolled version of this thread here: https://typefully.com/elzr/XzXLV4z