Showing posts with label knottheory. Show all posts
Showing posts with label knottheory. Show all posts

+tangle

+braid

+link

A link is a non-intersecting collection of knots. (not to be confused with lnq, see also hyperlink)

Note (+): Likewise, we can describe a knot as a link with one (1) component.

+knot

A knot is a closed string as a link with one (1) component. It can also be defined as a tangled string in Euclidean space (R3).

+hypocurrency

Hypocurrency is tokenage held* by a merchant (think 'cache' or 'cash'๐Ÿ’ต). (compare hypercurrency, see also hyperlink)Not in circulation.

+fibor

A unique cluster of datapoints known as fibor, is a totally twisted ||f(u,u)=0|| loopstring definition (word) subject to bifurcation* (ie. a meter signature). This is Egglepple's tertiary (stereo) structure. Fibor^ functions as the basic component of twist economics; threaded to form some image. As part of the endgame๐Ÿ, we care mainly for the ludological aspect(s) of juking (topology, rhetoric, mechanics, etc.), as they relate to cybernetics.There are two (2) classes of fibor: MONEY and bubblegum. Each fibor is its own unique brane. (see also minor, major, fibor bundle, fibor mutation, font)

Notes (+): +Mathematically, fibors are trivial zeroes (compared to fonts which are non-trivial zeroes).

+Fibor is the 'print' (or tuning) stage. This would be the total algorithm input assigned from stew choreography. Gameplay-wise, jukers should aim to get here as quickly as possible.

+For purposes of imaging, the l-string may be a simple topological schematic, serving to illustrate some animation directive.

+Just to reiterate, our primary interests are not in figuring out the science (eg. chemistry, biology, physics, etc.) behind the folding (chemical bonding, dipole moments, things of this nature are left to such experts). We are chiefly concerned with "writing a playbook", so to speak, that will enable anyone to generate algorithms (plays) for configuring polymorphisms and coordinating meshes.

+We must be careful with our vocabulary. Yes, fibor is stringy, but it is not a requirement that it be physical, per se. It just necessarily assumes the properties (namely that it can vibrate in multiple dimensions) of strings as it propagates into worldspace. In this case, we are concerned strictly with string dynamics (incorporating the landscape vacua philosophy). However, fibor - in the mold of stew choreography - is open/closed in some arbitrary volume, whence it is attached to a dynamical mem(brane). Oddly, however, there exists a method to start at the Planck length, and work our way up to normalization with g-folding.


Function map: minormajorfiborfibor bundle

+fruut

Fruut are a class of transformers sourced from EGP, and translated into the main geometrical primitives: rectangle, circle, and triangle. For identification purposes, we like to say that each shape corresponds to a 'fruit'; respectively: blueberry (alpha helix), banana๐ŸŒ (beta sheet), and lime๐Ÿ‹ (gamma delta) [colloquialized as 'bag']. The fruut are part of the Stewdio's kit (complementing the flageolet) for transcoding (the parameters of) twistor fields so as to establish both intonation+melody/groove of The Origamic Symphony.
TOS
In time signatorial mode, fruut are the tools used for folding stews to derive (arrive at) a fibor.

It is assumed that the shapes are true (ie. two-dimensional) by default, and can occupy higher dimensions of uuater (world volume).

Notes (+): +It is prerequisite that mathematics begin with primitive notions. Hence, when postulating, we start at some angle and navigate from there.

+Geometric primitives are called such because they are the building blocks for other forms and shapes.

+The melody is a secondary actor in stew choreography (ie. essential for closing๐Ÿ”’ an l-string generated from its walk).

+Rule of thumb: fruut is for folding, and the flageolet is a metronome for pencil generation.

+ellis

ellis (encrypted leaf-leaf integer statistic) is a class of genetic algorithms for performing random walks. ellis guides stew choreography. This is the Pink program's.

Notes (+): + In simplest terms, loop-erasure is a methodology for not repeating/replicating common walks (recorded as unique resource addresses); a most important checkpoint for obtaining a 0b. The sole purpose for loop-erasure is to ensure that stew choreography is as fast as possible. Needless to say, this intrinsically frees-up compute cycles, thereby increasing folding speeds.

+ To complete the program, ellis - together with earl - comprises the protocol.

+loop

Mathematically, a loop is a closed๐Ÿ”’ string. Ludologically, a loop is a simple infinite walk; such that it encloses leaves (reading frames) on a loopstring. In both cases, a loop is continuous with either no nuts, or has homologically conjoined endpoints.

Note (+): For sake of stew choreography, a loop is just a completed walk that has become unavailable for recycling.

+¢ent

mathemusical cent Mathemusically, a ¢ent is a ratio* of two (2) (close) frequencies. For the ratio (a:b) to remain constant over the frequency spectrum, the frequency range encompassed by a ¢ent must be proportional to those frequencies. Scaled๐ŸŽš, an equally tempered semitone spans 100 ¢ents (a dollar) by definition.Made from stew choreography.

According to The Origamic Symphony, an octave^ - the unit of frequency level when the base logarithm = [font size × font weight] - spans twenty-six (26) semitones (intervals/measures), and therefore, 2600 ¢ents. Because raising a frequency by one (1) ¢ent is equivalent to multiplying this constant ¢ent value, and 2600 ¢ents doubles a frequency, the ratio of frequencies one ¢ent apart is calculated as the 2600th root of 2 (~ 1.00026663).The interval between the first and second harmonics of the harmonics series. (see also ¢ent formula, juke tax, MONEY, meshroom, Double U economics)
TOS

Note (+): Economically, the ¢ent (cachecredit) is the rudimentary Double U currency object (used to measure/determine the size of twistor space). Reward function-wise, ¢ents are transacted in the twist economy as the negotiable instrument [standard currency].

+twistor

In a folding scenario, the twistor (u,u) is a complex transform* of EGP solved from stew choreography.Defined by a tight (≤ handicap) walk.

Twistors are derivatives of unique plays embedded in twistor space that are hedged from tablature. Statistically, twistors act as complexity catalysts and can have negative (vacuum) or non-negative (bubble) potential.

Let (u,u) be any two (2) leaves sequenced for juking. A twistor is an operator that associates a jukeable dyad (egg,epp) in a field which is coded to eventually become a zero-bubble. Twistors are measured with ¢ent values that are typically small (ie. frets).

Note (+): All twistors are assumed to be fit. We juke (hedge) in order to identify those folds which are ideal/most fit.



Function map: stew choreographytwistor

+twistor space

Ludologically, twistor space or "slot" is a complex configuration space (eg. geotop) of solutions to the twistor identity ||f(u,u)=0||. Because a fibor is encoded to close๐Ÿ”’ its loopstring the exact same way every time (ascertained from the uniqueness property), there must exist an acoustic bound in place enforcing these conformations (bubble or vacuum); without such a field, the fibor (as measured in ¢ents) would not bifurcate (into MONEY or bubblegum) as a function of symmetry-breaking.

Notes (+): +We assume that each twistor field is unique to some fibor. Essentially, this is a mapped spinor. The 'spin' (an object's spinning metric signature) here is identifiable with the quantum fields of arbitrary spin.

+Everything in twistor space is dyadic (u,u).


Twistor space' complexity is curvilinear (T)*.More accurately, sesquilinear. (see also handicap, jukespace)