User blog:08dravennew/Biscale

The Biscale is a system used to determine an verse's magnitude compared to two other benchmark verses. Its syntax is defined as $$\beta^a_b(c)$$, where a is the upper boundary of the scale, b is the lower boundary of the scale, and c is the object being compared.

It works on a system of infinite interpolation; it will constantly evaluate midpoints until a result is reached.

"Mathematical" definition
For a defined $$\beta^a_b(c) = x$$ and $$\beta^a_b(d) = y$$, $$\beta^a_b(e) = \frac{x+y}{2}$$ if "c" is indirectly/directly contained by "e", "e" is directly/indirectly contained by "d", and "e" is the least isolated verse under the previous two conditions from "c" and "d" (determined by the maximum of the isolation from "e" to "c" and from "e" to "d").

Also, $$\beta^a_b(a) = 1$$, and $$\beta^a_b(b) = 0$$.

This can be extrapolated to values lower than 0 or higher than 1, using algebra to find roots.

Biscalar classes
Two lower bound benchmarks are used in the Biscalar Class System: Class 0 (String), and Class 1 (Universe). The object/verse/etc at the lower bound of class X is $$C_x$$.

Using extrapolation, for x > 0, the lower bound of Class x+1 is equal to the smallest possible "b" of $$\beta^{C_x}_{C_0}(b) = 2$$.

Else, the lower bound of Class x-1 is equal to the smallest possible "b" of $$\beta^{C_1}_{C_x}(b) = -1$$.

Hierarchies
A hierarchy using this method can be found at User blog:08dravennew/ TOH using Biscalar Classes.

Examples
Let's try and find $$\beta^{Metaverse}_{Universe}(x) = 0.5$$.

As an axiom, $$\beta^{Metaverse}_{Universe}({Metaverse}) = 1$$, and $$\beta^{Metaverse}_{Universe}({Universe}) = 0$$.

However, if we now try to find $$\beta^{Metaverse}_{Universe}(x) = 0.5$$, then it gets harder.

The most isolated verse relative to the Metaverse and Universe that is also "inbetween" the two in containment needse to be found.

If the containment hierarchies going between the Metaverse and Universe are traced, the following hierarchies are found:


 * Universe -> Multiverse -> Metaverse
 * Universe -> Universe Cluster -> Multiverse -> Metaverse
 * Universe -> Terminal Sphere -> Multiverse -> Metaverse

Multiverses already are connected majorly to Metaverses and Universes, while the others aren't as much.

This means that the Multiverse is the "x" in $$\beta^{Metaverse}_{Universe}(x) = 0.5$$

Other Examples

 * $$\beta^{Metaverse}_{Universe}(x) = 0.25$$ has solutions of both Universe Cluster and Terminal Sphere for x, given that both aren't really connected to the Multiverse content-wise, leading to large amounts of isolation from the Multiverse which makes the maximum isolation equivalent