There is(Ǝ) – Such that (∋)

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Let me tell you about a language. But if you wish to go play instead go here. It's going to get a little abstract below.

There is a Canvas to Compose Upon<br>The canvas is a square with the largest circle that has a radius of ρ.<br>There are Vectors of Time<br>Ǝ a raven ∋ the vector of hours.<br>Ǝ a crow ∋ the vector of minutes.<br>Ǝ a mag-pi ∋ the vector of seconds.<br>Ǝ an origin ∋ a vector of zero.<br>The Vectors can form:<br>Scalars<br>Where the vectors become a single number.<br>./ρ² – the normalized dot product of two vectors<br>||˙||/ρ – the normalized magnitude<br>→/ρ – the normalized horizontal component<br>↑/ρ – the normalized vertical component<br>(All scalars are normalized by ρ (the canvas radius) )<br>And once you have scalars, they can form new scalars too: sum, subtract, multiply, divide.<br>⊞ Add<br>− Subtract<br>⊠ Multiply<br>⊡ Divide<br>Modified Vectors<br>Vectors can be added, subtracted, rotated and multiplied

Vectors and Modified vectors have a horizontal and vertical component just like a point or location.<br>Glyphs<br>Make things visible. They take in vectors and output to the canvas. The moon, sun, and star are at the vector's coordinates and the line connects two vectors.<br>Each glyph can be tuned.

Habitats<br>Add composition and can take vector inputs.<br>Habitats paint the canvas — not just a point.<br>grass<br>trees<br>a nebula<br>a meta-trace<br>an egg<br>a focus (a porthole)<br>moss<br>Vector inputs will change how they move just a little bit.<br>Tuning ◍<br>Parameters can change how the whole composition breathes.<br>cycles per day — how many times the clock wraps in 24 hours<br>hours per cycle — the base for the raven's loop<br>default breath depth and speed — the resting rhythm everything inherits<br>default stroke weights for lines and shapes<br>a theme — ambiance, mono, contrast, cividis, tri, botanical<br>a backdrop color, a default line color, a default shape color<br>frame rate<br>Composition<br>Compose a clock using all of the types of pieces and connecting them.<br>Go to https://te-st.ing and make a clock for yourself, then export it to save.

How?<br>I am currently in a 6-week batch at the Recurse Center. I wanted to make a language that produced clocks for "Impossible Day." After drafting a prototype, I refined the idea a little and made a second prototype.<br>It starts with types<br>There are vectors, modified vectors, scalars, scalar modifiers, glyphs, and habitats.<br>the shape<br>There some main components to the tool:<br>A Loom holds the composition — nodes, arrows, and globals.Types are represented as nodes.<br>You can bring a node from the palette to the Loom.<br>Nodes can connect with arrows.

A Weave compiles the composition into a p5 sketch inside a preview iframe. Every change in the Loom re-weaves the clock in the preview

Each Clock can be downloaded as a standalone HTML file.<br>the pieces<br>Svelte 5 — runes, snippets, event attributes.<br>TypeScript with svelte-check and ESLint.<br>Vite for dev and build.<br>Svelte Flow for the node-graph (Loom)<br>p5.js for the rendered clock on the canvasInline into the exported HTML so the file is self-contained — open it offline, drop it on a slash page (maybe /clock would be nice on a blog - hint hint)

localStorage for autosave, undo history, positions, and some preferences.<br>Everything in your browser.<br>choices<br>The editor is wordless (mostly) Sigils on the buttons, hand-drawn icons on the nodes, minimal clutter. Only the header actions keep their labels. Tool tips are toggled on and off (after feedback from IndieWeb meet)<br>The clock is procedural The nodes in the palette and the on-canvas node bodies use symbols or hand-drawn PNGs. But the exported clock paints everything from p5 primitives with randomness.<br>One source of truth for time. A dayFraction function in the woven sketch returns where we are in the day, and every bird's angle derives from it. Change cyclesPerDay or hoursPerCycle and the clock re-paces.<br>Debug mode is visual Toggle ⌖ and the debug mode turns on. A slider appears that scrubs through the whole day. Selected nodes highlight in this mode.<br>Canvas The empty-canvas has some example clocks after some feedback from the IndieWeb. Layers panel is drafted, but still getting worked.<br>the names<br>The header sigils Ǝ and ∋ read as there exists / such that — the editing side and the rendering side. The "Loom" holds the threads; the "Weave" turns them into something you can see ( ∋ such that).

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Welcome to the 252nd Carnival of Mathematics! This post brings together submissions and other posts from the mathy web. Thanks all for participating.

Let's start with the number: 252

* Divisors: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

unedited human writing before bed

Origin

In the beginning there was a point.

...And the beginning was but a period in which time was noted by a wisp of this existence

that was in the aether of light

in which the point existed

– without form, coordinates, or dimension,

this point

Thanks to Sam Graf for...