/an introduction to toy theory

sketch: when considering sets with warped elements or those having similar components with unramified locales, the easiest way to perform any pertinent analysis is with a toy theory. Doing so simplifies both locally and globally melodic scales. We introduce the theory of toys as a new tool for mathematics with clopen properties.

/UUe [automata]

"I have a magic jukebox." - 🧑🏿lnq

Inventor: 🧑🏿Link Starbureiy | License: UUelcome
UUe® (aka 🧑🏿lnq's jukebox) :== client for stew choreography^{^}. In streaming The Origamic Symphony🎶, it auctions + dispenses^@ stews.^~ ^^ Stereotype:=sequence+print. @@ A function of fugue extensibility. ~~ server actions

UUe is a kind of abstract cell. This [26-brane] automaton is an organic development from attempting to prove Q♭, a deep math 🧩puzzle* rooted in random walks. Two (2) genera abstractions are: a kernel for mathematical modeling (of auction theory applied to twistorspaces), and a method of compliance.** An over-simplified explanation of the problem is: if you take a really long (but finite) tape and split it into some countable number of smaller branes, how does that effect the computability of the tape itself?

/// +UUe was originally an acronym for 'United Under economy',later changed to 'united under Egglepple'. It no longer is an acronym; it's just 'UUe' (pronounced like "whee"). However, both 'United Under economy' and/or 'united under Egglepple' are still applicable.
+UUe - a mathematical model - qualifies as a jukebox by its rotisserie, with internal operations similar to those of a cell. Realization of its utility happens via the Stewdio.
+Because u-u economics mandates that clientele in the (u-u) scheme is part of a supply chain, UUe functions like a vending machine.
+lnq is the (official) mascot of UUe. This is "🧑🏿lnq's Jukebox".
+In gameplay, UUe is the house🏠.

united under Egglepple™| united under Egglepple is the unofficial (yet formal) name for UUe. This is the kernel orchestrating u-u economics - systematic configuration* of the payload by auctioning^% fibor(s) from the portfolio: [SSS = (micro) through UUU = (macro)], which leverages stewc taxation.%% A necessitation of compliance. This is to say that the whole of Egglepple (particularly the nuts) is 'statistically united'; a parimutuel system is extensible and potentially twistable (u,u).

Server operations are shelled using tokenage* for auctioning and gameplay.** Kernel development is an organic reaction to gameplay. Ludologically, this conversely implies that all disjoint games are variant. Put another way, yesegalo and 🍄meshroom are self-synthetic. (see UUelcome, u-u economics, .uue, UUe interface, Juke Lemma, patch, Pink program, braine🧠🗂, Quantumquotient, DUCC🦆, #recital, Stewdio)
/// It was originally a trust that has since morphed into something much more sophisticated; a shift similar to Egglepple being re-appropriated into the the jukebox.

dependencies

parsing

storage

catalysis

Function map: UUe ↔ UUelcome → Pajamas

/The Egglepple Company

The Egglepple Company (or just Egglepple) is the pseudonym given to what is now known as Egglepple (kindergarten). It was an incorporated^@ business entity in various states throughout the United States of America prior to its deprecation, reorganization, and later inclusion into 🧑🏿lnq.@@ Reference: Ohio Secretary of State's Office

Historically, Egglepple was the very first establishment to be a standalone/independent recreational mathematics+ enterprise (+:=contract-based, sometimes ghostwriting for academe from 10/2000 - 02/2001 (also of interest The Stewart Ellis Company - Gobotech, Link Starbury Network, #305)
/// pm:=pure mathematics, am:=applied mathematics. (see Funshine/Toonlight)

"Egglepple" is the middle name of 🧑🏿Link Egglepple Starbureiy, after whom the company is called, and by whom the entity was created. It spawned from the unincorporated/unorganized Egglepple portfolio (for toy [🧩puzzle] design, circa 1991).
/// Nowadays, the 'company' portion is assumed to be my roster (of characters/personalities +gallery) and the yots.

I attended The Ohio State University foremost to gain access to its aero facilities and research laboratories (I worked in aero/astro at HCGL-R1). As a student, I 'dabbled'; never settling on a major/minor. Back then, I put in my time roving the halls of the mathematics, physics/astronomy, and chemistry departments, as well. I was fairly new in that world ("publish or perish") and really wasn't familiar with LaTeX (I still don't like it -- tmi: I am notoriously bad with grasping foreign languages, and as more of a visual person, reading modern mathematical notation - of which Latin & Greek is the foundation - was a weak suit for me. Sometimes I felt like and have been called an idiot for not bothering to master the syntax because "real" mathematicians seem to rely on it, but my rationale is that the world is operating entirely on holograms, algorithms, music to some extent, and genetic code, not formulae, and so mathematical modeling [mathmod] is my preferred method for ideation. This forced me to get along by creating my own style to communicate with my peers.) and that publishing scheme back then (the departments certainly didn't make it easy for non-staff to be resourceful with the system), so I did what I did best when it came to visual expression, I drew stuff up/wrote stuff down on napkins (yes, at times with wax crayons🖍️ or colored pencils✏️). The astronomy department was awesome in the regard that they treated people who came through their doors respectfully. The math department, however, was the total opposite. There was so much ego (mine included) polluting the building that it was almost laughable, yet frustrating. [-- Mathematicians can be a pompous bunch who struggle for trivial results, and their demeanor reflects that. --] Anyway, there would be these 'challenge' problems/help requests from the community (ie. intra-departmental) often posted on bulletins, offering modest bounties💵 (very short-term contracts) for their solutions. The opportunist in me would peel these from the boards, take them home, and come back shortly thereafter with my answer(s) written on (paperclipped🖇️) napkins. In addition to being a technician in the engineering building, I remember just vagabonding off of those purses (yes, I was a 'bounty hunter') for periods at a time (sometimes in conjunction with all-levels math tutoring/coaching gigs). I guess that - in addition to responding to Michio Kaku's earlier proposition - was me (being the person responsible for) turning math into my version of a sport (, and thus, solidifying my interest in ctfs🏁).

/Egglepple [directory]

Creator: 🧑🏿Link Starbureiy

[pronunciation "/url/"]

Egglepple® :== 🧑🏿lnq's portfolio^*. ** As in porting from one directory of the 🍃leaf (recto) to the other directory (verso) of some function space. On the basis of quoting, fault tolerance increases with each proof and is infinite when completely solved (/totally sequenced).

Statistically, it is the animorphic (ie. to STU^{^n}) tape of leaf🍃 definitions (literally "🥚egg leaf🍃 ↔ epp leaf🍃"), and subjectively^{^} the cellspace (SMALL∪BIG ⊂ Stewniverse) spooling both ends of any generic 26-measure signal; but, mathemusically, the minor and major scales. ^^ Egglepple is what we are imaging (by stewcing/vending its calculus, STU, via gameplay. To make a Humpty Dumpty allusion, we break up the brane into finite pieces, only to put it back together again continuously.).

In terms of cell structure [:= 🔋polarized membrane] - Egglepple represents automata (ie. totality of circuitry between the cell membrane), itself an automaton (UUelcome). Ludologically, its kindergarten describes aspects of the braneworld.

"Egglepple is the ultimate puzzle🧩. It's like playing 26-dimensional ♟️chess in a spreadsheet." - 🧑🏿lnq
/// Egglepple is a portfolio of puzzles🏁, itself a puzzle🧩.

(Not to be confused with The Egglepple Company. See The Origamic Symphony🎶, koala8, "Egglepple, everywhere!", 📓Egglepple: Unfolded, 🎞️Egglepple: The Mathemagical World, Joey Koala🐨, Puwun, Stewniverse, yoyo, UUelcome, 🔋e:e statistics, quantumquotient, UUhistlegrass, stewc, STU, united under Egglepple, UUe, 🧑🏿lnq's Starting Five, 🧑🏿lnq's walk, 🧑🏿lnq's motif, 🧑🏿lnq nomenclature, mathemusic, Egghead/🥚Eggheads, #Egglepple@30)
/// +Joey Koala is the official mascot and Puwun the unofficial mascot of Egglepple.
+"Egglepple" was invented and coined by 🧑🏿Link Starbureiy.🤓 The word is also part of his name (...he wanted a name history would remember when he "had created the greatest portfolio of all-time").😉 (see 🧑🏿lnq nomenclature)
+To phonetically distinguish it from the name itself, the kindergarten/portfolio aspect of Egglepple is pronounced like 'egg·ul·epp·ul' (cf. the old 'Peggy from Margaret' conundrum).
+For those wondering why Egglepple has such a juvenile presentation, it's because the portfolio was founded/created when I was a little kid, and I intentionally never bothered maturing it in that regard (hence, the kindergarten). It was at this founding point that I pretty much committed to living full-time in my own world.
+The color scheme for the 'E-g-g-l-e-p-p-l-e' logo is a nod to the original team colors for the Miami Dolphins 🐬 🏈football franchise of the National Football League (NFL). The Miami Dolpins are the only team with aquatic (cf. Pisces♓) representation.

I kickstarted this on my twelfth birthday. Having somebody who believes in you can take you farther, and there's no convincing me otherwise. As the story goes, my sixth grade teacher, Mr. Woodring (without a doubt the best school teacher🍎 ever), picked me up from my house on my birthday and showed me around Washington, D.C. that evening. On the way home, he encouraged me to save my work (some of my doddles) in hopes of one day having something to present to the world that I could be proud of. That is the gist of how the portfolio came to be. Back in my elementary school days, I took a keen interest in puzzling🧩 (generally solving them, along with maze designs of my own imagination), which likely stemmed from both being an avid 🎮video gamer and personal mathematical curiosities. Each activity helped me to get 'lost' (a personality thing of mine, and something every kid needs in their development). Pronounced "earl", the word/name "Egglepple" itself didn't come about (I made it up) until the end of the century, although most of the other elements of the portfolio were already in place by then.

Function map: preimage ← Egglepple → image ⇔ UUelcome

/toy

toy :== an object subject to gameplay. Technically, it is a functor* that a player can use to induce a payoff or proof. ** Some loadable or printable kernel module in the context of UUelcome. (see Starbureiy Toy, game, play, yots, puzzle🧩, cassette🧱, lnq🧑🏿)
/// +I personally like to say that toys are jukebox add-ons/extensions for playback.
+My hobby/habbit is to create and assume the identity of a toy to advance character play in some game(s). These identities (as alter egos - or rather, altered states of my singular ego, which in certain cases populate the phantom orchestra) are usually (more often than not) ephemeral.

/flageolet pencil✏️

Inventor: 🧑🏿Link Starbureiy
flageolet pencil✏️ (or just pencil✏️, or krayon) :== a finite n-dimensional cell^~ that is subject to rhetorical arrangement (ie. variation).~~ Which can propagate like a cellular automaton. Thus, a pencil✏️ is quantum by proxy*.** Ludologically, a pencil✏️ is a toy; mathematically, a pencil✏️ would be an element on the number line. It is a metric generator (musically: metronome or counter); equivalent in most instances to a hash, stew, residue, or brane declension (eg. 0-brane). Normally, flageolet pencils✏️ are not colored. (see colored pencil✏️, leaf, Stewniverse)
/// The twenty-six varieties stem from the fact that The Origamic Symphony🎶 spans 26 measures in relation to STU.

Flageolet pencils✏️ lay the foundation of stew choreography; they are intonation points in cheironomy, and can be used to draw tape and/or establish melodies+grooves. Pencils✏️ may concatenate or split among themselves (this is called interaction).

Flageolet pencils✏️ are the motifs of string (à la "integration-by-parts"). There are twenty-six (26) different varieties of pencil(s)✏️. When measured, each pencil is worth some integer [1-26] multiple of one-hundred (100) ¢ents🪙.
Function map: pencil✏️ ↔ RONALD (Mathilda)

/krayon

krayon (also known as 🧑🏿lnq's finger) :== a colloquy (for any number of) 🧑🏿lnq's personal choice of flageolet pencil✏️ (conductional in a stewc field).
/// The spelling with a 'k' is of my recipe. It's actually (or would be) 'crayon🖍' (like the wax-based stylus), a favorite tool of mine used throughout my career for painting.

The krayon hosts a complete copy^@ [latest build] of UUelcome, and is, defaultly, an organic membrane utensil wrapping 🧑🏿lnq's yoyo finger, as his jointed digitus secundus* [with an end serving as the ornamenter].@@ Coded only to me, the impresario. ** Any finger (usually aside from the pollex) should suffice.

When called, it undocks/peels from the hand allowing it to transform (unroll) into a bow [+joey]. 🧑🏿lnq may (characteristically) also choose to wear the (dislodged) krayon held behind an ear. (see yoyo, 🧠brainbrane, Stewdio, UUelcome Matte, Koala Krayon, Pajamas, 🧑🏿lnq's bubblegum, cassette, k-mode. Compare baton)

/puzzle🧩

puzzle🧩 :== an object or objective lending itself to ludological inference [preimage→image] (ie. all puzzles beg to be solved*; a solved puzzle is in itself considered a goal).** Decrypted and/or encrypted. Someone who composes/solves puzzles may be referred to as a puzzler.

Stewcing-wise, our puzzles are ctf🏁-styled asymmetric rondos in a three (3)-act continuum: bug-bid-bounty = arithmetic+algebra(curvature)+analysis(logarithm). (see puzzle script, Puzzle Punk, gameshow, Egglepple, crypto)
/// Mathemusical translation: intonation, melody, and measure.

/nut

nut (or ball) :== an endpoint of a loopstring➿. String only have two (2) endpoints, hence, only two nuts.

Each nut is either a start or stop identifier (leaf).*** The two nuts of Q♯🎶 are minor scale and major scale, connected by stews. As an arbitrary ordered pair [egg,epp], they may be referred to as abscissa and ordinate (u-u).
/// Balls are pseudo-theoretical (abstract) objects that only exist as placement functions. There is no 'ball', so-to-speak, just a representation of an endpoint (dot). However, in gameplay, a ball can be a toy (eg. ctf flag🏁, see zero-bubble). Likewise, macroeconomically, a ball would be lyric (triangulated data point). Also, in energy🔋 speak, nuts are representative of electrodes [anion (-) and cation (+)].

Mathematically, it's called a 'ball' (and sometimes 'dot') because as the string folds upon itself, the endpoints (a metric space) coordinate ("connecting the dots") into a loop➰, and the overall structure usually assumes a shape that is similar to some ovoid with boundary (cf. compact blob) in stereo. (see Egglepple, ballet🩰, Funshine/Toonlight)

/Starbureiy Toy

On behalf of 🧑🏿Link Egglepple Starbureiy, the Starbureiy Toy, also noted as "The Starbureiy" or just "The Toy" - named in honor of stewcing's pioneer, 🧑🏿Link Starbureiy - :== a hypothetical individual award [denoted as: 'the championship'🏆] given seasonally in accordance with BOT to UUelcome's winning team [denoted as: 'champion'🥇]. (see treble, +list)
/// +A minor locution would be to say that "so-and-so is the 'next' Starbureiy".
+If presented as a tangible 🏆trophy, the toy is a (stereo) printout of the UUelcome Hut.