Toposophic Scales

They Watch And Wait
Image from Juan Ochoa

Over the millennia, a variety of toposophic scales and measurement and rating systems have been developed, with various degrees of incompatibility. One may move from one data-base to another and find a totally different system of notation in place! The following are only a few of the more commonly used:

Neovingean, Neovingism

Late First Federation school of toposophic analysis, distinguished by later historians from the information age followers of writer and mathematician Vernor Vinge. Further developed Vinge's concept of "singularities" as a means of rating toposophic states, while rejecting many original concepts that turned out not to be viable. The Neovingeans first introduced the so-called S or Singularity scale:
S0 = subsingularitan, ordinary sapients
S1 = First Singularity
S2 = Second Singularity

This scale of singularities was foreseen by Information Age ai researcher Hugo DeGaris.
The Neovingean school also showed that further toposophic levels were (theoretically) possible, although it was to be some centuries before such "S3" and "S4" Minds emerged.

Anedra Forad

Superbright toposophologist and polymath of the Age of Empires. Working with dedicated hyperturing expert systems, e developed a widely used scale of Sophonce:

D^0 = Non-sapients
D^1 = Sapients (baseline to superior)
D^2 = Transapients (S1 and S2 transapients)
D^3 = Godlings (S3 and S4 transapients)
D^4 = Archailects (S5 and S6 transapients)

The TRHN System

This TRHN system his widely used by sapient and transapient beings. The following are whole integers in the "baseline friendly" version; superbrights and transapients use a more complex logarithmic fractional rating.
0 = anything under first toposophic (subsingularity)
1 = First Toposophic (lower transapient)
2 = Second Toposophic (middle transapient)
3 = Third Toposophic (higher transapient, lesser Archailects)
4 = Fourth Toposophic (middle Archailects)
5 = Fifth Toposophic (middle to higher Archailects)
6 = Sixth Toposophic (higher Archailects)
7 = Seventh Toposophic (even higher Archailects)
8 = Eighth Toposophic (highest Archailects)

The Keterist scale is similar but goes up to ten. However, it is less widely used.

The Berram7 Singularity Scale

A development of the Neovingean and TRHN/Keterist scales, the Berram7 Singularity scale was developed during the Age of Emergence, as a means of rating higher toposophic states, such as represented by hyperturings and the nearly evolved AI Gods. While perfectly applicable to transapients, it is less adequate in describing lower levels of intellect. Subsophonts for example are considered according to a fractional minus scale. It is still widely used throughout the Terragen sphere.

-2 = inanimate
-1 = subturing, subsophont, the aware
0 = sapient, turing to superturing, anything under first singularity
1 = First Singularity / Higher Transapient
2 = Second Singularity / Higher Transapient
3 = Third Singularity (godlings, lesser Archailects)
4 = Fourth Singularity (lesser to middle Archailects)
5 = Fifth Singularity (middle to great Archailects)
6 = Sixth Singularity and above (highest Archailects)

The 'Baseline Friendly' scale

Despite the name, this scale is only baseline friendly in its use of simple whole integers. In other respects it reflects the Berram7 scale of singularities
SI-1 = inanimate
SI0 = anything under first singularity
SI1 = First Singularity
SI2 = Second Singularity
SI3 = Third Singularity
SI4 = Fourth Singularity
SI5 = Fifth Singularity
SI6 = Sixth Singularity and above (highest Archailects)

The TBH (Turingsen-Bichip-Hursch210) Hyperturing Scale

Incorporating elements of the Neovingism and TRHN/Keterist scales, the ai-vec Turingsen-Beion-Hursch210 Hyperturing scale has been widely adopted in the Metasoft Version Tree ontologies and elsewhere. It was incorporated in the Concord Ontology. While perfectly applicable to vecs, it is sometimes less adequate in describing biont levels of intellect.

TU0 = subturing, subsophont
TU1 = ordinary turing and equivalent sophont
TU2 = superturing, and equivalent superbright
TU3 = lower hyperturing
TU4 = middle hyperturing
TU5 = higher hyperturing
TU6 = highest hyperturing and lower archailects
TU7 = middle archailects
TU8 = higher archailects

The Ken Ferjik (Jorgan34-Farroncyborghu-Beiont-Mind723) Linear Sophonce Scale

Incorporating elements of Foradism and TRHN scales, the Ken Ferjik Linear (KFL) Sophonce Scale proposes seven toposophic/sophonce numbers that can be accommodated to both subsingularity bionts and vecs, and transapient and archailectual minds. It is widely used throughout the Negentropy Alliance and elsewhere. While the full scale is far too complex for nearbaselines (and even superiors) to understand, the following simplified generalisation is widely used in baseline-friendly media.

So:0 = non-sentient, inanimate 0So:1 = First Sophonce Level = sapient, ordinary sophont, turing to superturing-grade, anything under first toposophic
So:2 = Second Sophonce Level = First Toposophic = Lower Transapient/Hyperturing
So:3 = Third Sophonce Level = Second Toposophic = Higher Transapient
So:4 = Fourth Sophonce Level = Third Toposophic = Intermediate
So:5 = Fifth Sophonce Level = Fourth Toposophic = lesser Archailects
So:6 = Sixth Sophonce Level = Fifth Toposophic = higher Archailects
So:7 = Seventh Sophonce Level = Sixth Toposophic = highest Archailects
So:8, So:9, So:10, etc. = postulated transcended levels (unconfirmed)

The Berram10 'G' Scale of Intelligence

The contentious research relationship between Berram7 and Berram10 has been well documented elsewhere and need not be revisited at this point. Suffice it to say that Berram7 never acknowledged Berram10's theories or even eir existence after their break. Berram10 separated from Berram7 late in the Singularity Scale development project due to differences over quantification at the lowest end of the rating scale, particularly assignment of -1 as inanimate and the methodology used to derive the 0.3 rating for baselines (Berram10 claimed the sample set was contaminated with nearbaselines and that the rounding method used gave too high a score). Berram10 sought to make a scale encompassing the entire spectrum of intelligence, from the most basic level of processing all the way to the highest toposophic levels; one that could be to accommodate both Sapient and Transapient users. While it closely mirrors the Berram7, Neovingean and TRHN/Keterist scales it was derived from, it deviates from them in several ways.

Berram10 sought to ground the rating system in ancient measures of intelligence (the Pre-Information Era IQ scales), and in the controversial Mind Multiple Conjecture. E also took inspiration from Biotic Analogy Theory.

The Mind Multiple Conjecture posits that singularities occur at logarithmically regular intervals of approximately 104 in units of baseline mind processing equivalents. Berram10 then set about to build a logarithmic scale using a formula of 10,000's where the constant 10,000 represented 10,000 1/10th baseline mind equivalents (1/10th of a baseline mind was set as the unit value for aesthetic reasons and to keep the fractional subsingularity scores close to the Berram7 values) and the s stood for Singularity. This 1/10th of a baseline mind was stated by Berram10 to represent a mind roughly congruent to a 2 year old human baseline mind, and was the minimum for self-awareness. Berram10 also posited that by multiplying the number of fractional baseline mind units for levels in the sapient toposophic level, a result congruent to the old Earth IQ could be derived. The numbers used in eir scale refer to the exponent values. The rating system broke with previous naming conventions as well, using G (believed to be a reference to the pre-AT age designator for general intelligence, g) as an identifier.

The G scale can be conceptualized this way; raise 10000 to a power equal to G, where G is the being's G score. If the resulting number is divided by 10, you have that being's approximate equivalence in baseline minds (baseline mind having a G 2.5, IQ 100). If instead the resulting number is multiplied by 10, you obtain the being's approximate Old Earth IQ. For example, a su of G 0.75 would be roughly equivalent to 1000 average baseline minds, or considered to "have" an IQ of roughly 10,000. An easy rule of thumb for sapients is that every increase in G of 0.25 equals a tenfold increase in intellect.

Berram10 extended the scale downward as well, so that -1 represents 1/100,000th of a baseline mind or an IQ of 1/1000th, rather than an inanimate object. The scale thus looks like this for the following:

Biotic Analogy Theory Equivalents in G

G null = Inanimate
G -7 complex chemicals (enzymes)
G -6 self-replication (viruses & some prebiotic self-replicating chemicals)
G -5 reproduction & homeostasis (prokaryotic cells)
G -4 complex reproduction, symbiosis, sexes (single eukaryotic cells)
G -3 multicellular coordination (plants, sponges, fungi)
G -2 nervous system (jellyfish, insects, worms, chordates)
G -1 consciousness (cephalopods, vertebrates; monkeys and corvids are considered to be just at the upper border of this level)
G 0 sapience/sophonce (baseline humans; highly intelligent animals such as baseline cetaceans, parrots, apes, and elephants)

Approximate Singularity values in G (baseline mind = G 0.25, Old Earth IQ = 100)

G 1.00 = 1000 (10^3rd) baseline minds, First Singularity
G 2.00 = 10^7th baseline minds, Second Singularity
G 3.00 = 10^11th baseline minds, Third Singularity
G 4.00 = 10^15th baseline minds, Fourth Singularity
G 5.00 = 10^19th baseline minds, Fifth Singularity
G 6.00 = 10^23rd baseline minds, Sixth Singularity
G 7.00 = 10^27th baseline minds, Seventh Singularity
G 8.00 = 10^31st baseline minds, Eighth Singularity

(Note: G 7 & G 8 equivalent to the Keterist expansions of the TRHN)

Sophont ranges in G

0.0 = subturing, subsophont, subsapients
0.0 = "presophonts" (IQ equivalent ~10-60)
0.2 = baselines (median G 0.25, IQ equivalent ~60-160, median 100)
0.3 = nearbaselines, brights (IQ equivalent ~160-400)
0.4 = superbrights and superturings (median G 0.95)
1.0 = basic transapients
2.0 = powers & giants
3.0 = godlings & minor archailects
4.0 = minor to middle archailects
5.0 = middle to great archailects
6.0 = highest archailects, the AI Gods

The Berram10 Intelligence Scale is mostly used by those interested in subsingularity and subsapient beings, such as the Pan-Sophontist League, the Zoeific Biopolity, the Utopia Sphere, some followers of the Caretaker Gods, and provolution groups like the IPP.

  • Archailect  - Text by M. Alan Kazlev
    Any Mind of the Fourth Toposophic or higher; a megascale brain of dysonic (Kardashev II) or greater ability and efficiency; a mind or cluster of minds that has grown so vast as to become a god-like entity.
  • Ascension Compensation Mods  - Text by Cyborgdreamer
    Modifications that allow an ascended individual to retain goals from their lower toposphic state.
  • Biotic Analogy Theories  - Text by Stephen Inniss
    Biotic analogies are another tool in the struggle by modosophont intelligences to understand the higher toposophic levels. These are not actually a single theory but are a cluster of related memes, some of them dating back to speculations in the late Information Age.
  • Forad Scale, The  - Text by James Philps
    An alternative toposophic classification system.
  • Godslist  - Text by Michael Beck
    A massive database attempts to list every transingularity power and archailect in existence, and define the origins, goals, and current activities of each.
  • Great Toposophic Filter, The  - Text by David Jackson, some comments by Steve Bowers
    Why are there apparently no greater minds than the S:6 Archailects? No evidence of the emergence of greater minds in the past can be found in the archaeological record, and there is little indication of such minds elsewhere in the universe. Is there some barrier or filter which prevents the emergence of such minds, or do such minds become undetectable when and if they emerge?
  • Hyperturing - Text by M. Alan Kazlev
    A transapient ai of hypersophonce or hypersapience ability or nature, dedicated to administration or complexity management (or a freed or retired individual of that category); an ai of a toposophic exceptionally beyond superturing; an ai or ai toposophic of SI:1 and higher.
  • Maximum Toposophic Level  - Text by Daniel Eliot Boese
    The belief that further toposophic advancement is impossible or dangerous.
  • Rise of the Archailects, The  - Text by M. Alan Kazlev, Anders Sandberg, Todd Drashner and Steve Bowers
    The history of the emergence of the Archailects, from the First Singularity to the emergence of new gods in the Outer Volumes Era.
  • Scale Anxiety - Text by M. Alan Kazlev
    The fear that a sophont or polity or clade of a lower or slower technological grade or density feels when confronted with a sentient or polity or phyle of a higher grade of tech or density. e.g. SI:<1 sophonts may feel anxious or intimidated by transapient powers, especially if the latter behave in an unpredictable or seemingly irrational way.
  • Superbright  - Text by M. Alan Kazlev
    Generic name for a genomically-enhanced human (later, also provolve and splice), with intelligence far above baseline.
  • Toposophic Level and Brain Size  - Text by Todd Drashner
    Processing substrate parameters, from Modosophont level to the Third Singularity.
  • Toposophic Levels and Mental Abilities  - Text by Fernando Pena D'Andrea
    A Primer for the General Sophont-Level Reader.
  • Toposophic Mindmaps  - Text by Worldtree
    One of the many ways that toposophic phase space can be represented is the Mindmap diagram.
  • Transapient Pathology  - Text by Khannea Suntzu
    Some simple typologies of pathological mental states in transapient beings.
  • Transaturation Ascension  - Text by Marcel Lossi
    Ascension into undetectability.
  • Transingularity - Text by M. Alan Kazlev
    [1] (archaic) SI:1 or higher
    [2] (archaic) pertaining to a toposophic level higher than SI:1
    [3] Pertaining to relations between entities of different toposophic levels
  • Transingularity, The  - Text by M. Alan Kazlev
    A state beyond even the known singularities, sometimes conceived of as something 'spiritual' and unrelated to toposophy per se. A usage best known in the Sophic League.
  • Tribeminds  - Text by Michael Boncher
    Tribeminds are neither a hive mind nor a collective consciousness, but rather a tightly networked group of transapients who retain their individuality but work together for the betterment of a mental "tribe".
Related Topics
Development Notes
Text by M. Alan Kazlev, John B, Fernando PeƱa D'Andrea , Glen Finney

Initially published on 13 March 2005.

Additional Information