RECURSIVITISM.
Version of Monday 21 October 2019.
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Typographical convention: When a word is being introduced in running text, or when it being discussed as a symbol and not for its meaning, it is generally underscored. The more common practice throughout literature is to use italics for this purpose, but the conventions of mathematical notation, which must be employed here, complicate the matter. Italics are used for other customary purposes when no confusion will result. By contrast, terms introduced in tables receive no special treatment.


§1. People often observe our universe and deem it complicated and intricate beyond human understanding. They ask an obvious question:

"How did the universe get created?"
☞ To answer this, many religions posit a deity of great (perhaps infinite) intelligence and power; sometimes multiple deities. Implicit in this context are two assumptions:
  • the universe has not always existed, thereby necessitating a creative event for it to come into being;
  • the universe could not have created itself.
☞ Skeptics might counter as follows: If the complexity of the universe requires a creator, then surely that creator is no less complex than the universe it created. Hence the creator must need a higher-level creator.

The skeptic's response is made more pungent if the religion insists that the universe is of irreducible complexity. Certainly difficult to explain is how a creator who is not irreducibly complex could create something that is irreducibly complex.

☞ A frequently-heard religious rebuttal to this point is that the first-level creator has always existed — or perhaps it self-created — and therefore it requires no higher-level creator.
☞ At this stage, however, the skeptics will likely contest that if the creator can have always existed, why must we dismiss the possibility that the universe has always existed?
… and the debate will continue back and forth without end.

Such exchanges, although they have occurred countless times, have arguably never led to a solid resolution of the matter; if they had, the participants would have discontinued re-enacting this script, moving on to other issues.

There is a second concern: If the purpose of the mortal life is to prepare us for some sort of afterlife, then what might be the purpose of the afterlife?

Fortunately, the religion known as RECURSIVITISM provides a comprehensive and fully satisfying answer to these and a wealth of other age-old conundra.


§2. Here is an introductory over-simplification:

• The universe was created by God.
• God was created by Über-god.
• Über-god was created by Über-über-god.
• Über-über-god was created by Über-über-über-god.
continuing without bound

Superscripts provide a convenient generalized notation for many divine terms. Examples:

nouns adjectives
capitalized when substantivized
superscriptnon-superscriptsuperscriptnon-superscript
Über0godGod all1mightyalmighty
Über1godÜber-god all2mightyall-almighty
Über2godÜber-über-god all3mightyall-all-almighty
Über3godÜber-über-über-god all4mightyall-all-all-almighty
continuing without bound

Comments:

• An italicized n is often used as a generic superscript, and its value would ordinarily be a nonnegative integer.
• If a superscript equals 0, both the superscript and the affected portion of the word (which is usually a prefix or a suffix) can be omitted. Hence Über0god → God.
• If a superscript equals 1, it can be omitted; optional is to insert a hyphen for clarity. Hence Über1god → Über-god.
• Superscripts are sometimes off by one: Überngod is alln+1mighty. (This is not a bug, but rather a design feature.)
• Analogous to allnmighty are the terms omninpotent and omninscient.
• In general, one can say that Überngod was created by Übern+1god.
• By infrapolation, ordinary mortals might be designated Über−1gods who are all0mighty.

It now becomes clear why the founding documents of RECURSIVITISM are sometimes called the "Holy Superscriptures". (Informal motto: "RECURSIVITISM is super!")

Expansive as this theology may seem thus far, what we have seen so far is only a glimpse into a single chain of command; far greater breadth awaits the true believer. It turns out that there are multiple gods on every level.


§3. The reader may be familiar with the multiverse theory in science, which says that every universe that can exist does exist. This leads to infinitely many universes, which meshes perfectly with RECURSIVITISM. Every universe has its own God, at the Über0god level to be specific.

Here is the general structure of the hierarchy:

 
Each mortal is responsible to one God.
Beyond that:
 
Eachreports to anWho supervises
GodÜber-god10 Gods
Über-godÜber2god 10 Über-gods
Über2godÜber3god 10 Über2gods
Über3godÜber4god 10 Über3gods
ÜberngodÜbern+1god10 Überngods

This is how creations are structured:

 
Each God created Its own universe, which contains everything.
Beyond that:
 
EachcreatedEach of Whom createdaggregation
Über-godten GodsIts own universe Ten universes combine into a
decaverse (101verse)
which contains
every-everything (every2thing).
Über2godten Über-godsIts own decaverse Ten decaverses combine into a
hectoverse (102verse)
which contains
every-every-everything (every3thing).
Über3godten Über2godsIts own hectoverse Ten hectoverses combine into a
kiloverse (103verse)
which contains
every4thing.
Übern+1godten ÜberngodsIts own 10nverse Ten 10nverses combine into a
10n+1verse
which contains
everyn+2thing.

This gives rise to a RECURSIVITIST catchphrase: "What hath Übern+1god wrought? Ten Überngods.".

Naturally, each Überngod governs what it created:

Eachdirectly governsindirectly governs
God 1 universe
Über-god 1 decaverse10 universes
Über2god 1 hectoverse10 decaverses
100 universes
Über3god 1 kiloverse10 hectoverses
100 decaverses
1000 universes
continuing without bound

When precise terminology is needed:

the study of a(n)is athe components of which are
Godtheologydoctrines
Über-godmeta-theologypara-doctrines
Über2godmeta2theologypara2doctrines
Über3godmeta3theologypara3doctrines
Überngodmetantheologyparandoctrines


§4. When worshiping, mortals might offer prayers in the form of invocations and benedictions to their God.

Some mortals skip up within the chain of command, with wor2shipful (or worship-ful2) in2vocations and bene2dictions directly to their Über1god; or more generally, worn+1shipful (or worship-fuln+1) inn+1vocations and benen+1dictions directly to their Überngod.

(Although most RECURSIVITISM superscripts are attached to prefixes, they can also be attached to suffixes, as seen here, in which case a hyphen makes it easier to see exactly what part of the word is superscribed.)

Some Recursivitists are concerned that, when m > n, if they pray directly to an Übermgod, an Überngod Who has been bypassed in the chain of command might become displeased; so these believers limit themselves to wor1shipful in1vocations and bene1dictions to their Über0god. These Recursivitists also fear that an Übermgod might become perturbed when receiving an orison that could have been handled at a lower level, by an Überngod.


Some groups of adherents see an obligation to promote RECURSIVITISM; they are uniform in holding that it is desirable for each believer to spread the "good news" about their own Über0god through a process called ev1angelism.

On the other hand, there is disagreement about whether they ought to evn+1angelize about an Überngod when n ≥ 1. This matter is parallel to the matter discussed previously; Recursivitists who object to skipping Überngods in the chain of command will usually object to evnangelization for n > 1. By contrast, Recursivitists who find skipping acceptable generally see no problem with evnangelization for all n ≥ 1.

The expression "good news" can be inflected:

deity superscript non-superscript
Über0god bett-er0 news good news
Über1god bett-er1 news better news
Über2god bett-er2 news bett-er-er
Über3god bett-er3 news bett-er-er-er
continuing without bound


§5. Two sides of an important characteristic are transscendence and cisscendence, in the aggregate scandence. (The spellings are explained in §5A below.)

A God is transscendent relative to a mortal; an Übern+1god is transscendent relative to an Überngod. More broadly, an Übern+mgod is transmscendent relative to an Überngod. Finally, an Überngod is transn+1scendent relative to a mortal.

Cisscendence is the opposite of transscendence; specifically, cisnscendence is the same as transnscendence. Hence, a mortal is cisscendent relative to a God; an Überngod is cis1scendent relative to an Übern+1god, and so forth.


§5A. The documents of RECURSIVITISM, at least in the English language, spell transscend and its inflections with two esses rather than one. This reflects that the word comes from Latin trans scando, in which the two esses were ultimately contracted into one. Additionally, this clarifies the structure of the word when a superscript is inserted, as trans3scend.

As cis- is the opposite of trans-, the same considerations apply to cisscend, although Latin cis scando has scarce classical precedent.

It must be noted that Latin often changes the first vowel of a word when a prefix is added; that is why (in standard English spelling) we have transcend and not transcand. Familiar examples of how the Latin vowel change survives into English are the pairs tangent-contingent; apt-inept.


§6. RECURSIVITISM demonstrates that it is a genuine religion by wanting money. Upholding the finest tradition of capitalism, it is a multi-level marketing scheme. Here is the schedule of explicit payments:

• Each mortal pays ten percent of their income to their God.
• Each God pays ten percent of Its income to Its supervising Über-god.
• Each Über-god pays ten percent of Its income to Its supervising Über2god.
• Each Über2god pays ten percent of Its income to Its supervising Über3god.
• Each Überngod pays ten percent of Its income to Its supervising Übern+1god.

The following calculations reveal the net throughput of the explicit payments; these are not additional payments:

• Each mortal pays 9 percent of their income to their God.
• Each mortal pays 0.9 percent of their income to their Über-god.
• Each mortal pays 0.09 percent of their income to their Über2god.
• Each mortal pays 0.009 percent of their income to their Über3god.
• Each mortal pays 9 × 10n percent of their income to their Überngod.

The money that a mortal pays to their God is called an offering, which word is an assimilation of the word that would be obfering. The portion of the offering that goes to their Über-god would be called an oboffering, of which term the likely superscript forms are ob2fering, of2fering, or ob1offering, according to taste. In the general case, the portion that goes to their Überngod is an obn+1fering, of n+1fering, or obnoffering. A synonym of the gerund obnfering is the noun obnlation (from Latin fero, ferre, tuli, latum).

All of the superscripts mentioned so far are from a mortal's point of view, but Überngods reckon things differently. For instance, when a mortal (i.e. an Über−1god) makes a donation, the portion that reaches their Über5god is what the mortal calls a ob6fering. As the funds are passed up the line, their Über2god would by contrast call that same portion an ob3fering.


§7. Some additional vocabulary is helpful in describing what happens after a mortal dies. Here are some destinations a soul might visit:

superscriptnon-superscriptsupervised by a(n)   superscriptnon-superscriptsupervised by a(n)
ultra0heavenheavenGod   infra0hellhellSatan
ultra1heavenultra-heavenÜber1god infra1hell infra-hellUnter1satan
ultra2heavenultra-ultra-heavenÜber2god infra2hellinfra-infra-hellUnter2satan
ultra3heavenultra-ultra-ultra-heavenÜber3god infra3hellinfra-infra-infra-hellUnter3satan
continuing without bound

Contrast that Über has an umlaut, Unter does not.

As suggested by the table above, there is a one-to-one correspondence between ultranheavens and infranhells; and between Überngods and Unternsatans.

The table below introduces the afterlives and their durations:

superscriptnon-superscriptsuperscriptnon-superscript
after0lifemortal life hyper−1eternityfinite time
after1lifeafterlife hyper0eternityeternity
after2lifeafter-afterlife hyper1eternityhyper-eternity
after3lifeafter-after-afterlife hyper2eternityhyper-hyper-eternity
continuing without bound

There are two equivalent families of adjectives, as below.

superscriptnon-superscript
hyper0eternaleternal-er0eternal
hyper1eternaleternal-er1eternal-er
hyper2eternaleternal-er2eternal-er-er
hyper3eternaleternal-er3eternal-er-er-er
continuing without bound

The purpose of the mortal life is to prepare the soul for the after1life. The purpose of any afternlife is to prepare the soul for the aftern+1life.

A hyperneternity lasts for a inn+1finite amount of time. On the other hand, the duration of mortal life is finite (in0finite). These inn+1finities need a more precise description; they are based on the sequence of aleph numbers, each an infinity that is "larger" than the previous.

alephdurationeternity
0 in1finite timehyper0eternity
1 in2finite timehyper1eternity
2 in3finite timehyper2eternity
3 in4finite timehyper3eternity
n inn+1finite timehyperneternity

The aleph numbers lead to an uncomfortable source of schism within RECURSIVITISM. (What genuine religion does not have a schism?) The disagreement parallels the continuum hypothesis, and in theological terms may be explained thus:

For any non-negative integer n, there is an Überngod. Recursivitist theologians are divided as to whether the limitation of integrality can (or must) be lifted. If that is done, there could be an Überxgod for any real number x. Each Überxgod would report to an Überx+1god, and other constructions follow similarly.

Unsettled is what, if anything, the relationship between an Überxgod and an Überygod might be if xy is not an integer.

Radical Recursivitist theologians have proposed a further extension to superscripts that are complex numbers, but research in that area is still at the earliest in its nascence. Another notion of yet-resolved meaning uses superscripts that are ordered tuples of numbers, such as Über(3,6,4)god.


§8. The overwhelming view within RECURSIVITISM is the Decimalist, meaning that:

Decimalism forms the basis of this report, but some Recursivitists prefer a different number. The Dozenists, for instance, hold that each Übern+1god supervises twelve Überngods, and all payments are one-twelfth of income.

Variegationalists go further, using different numbers for different purposes. For instance, an Übern+1god might supervise nine Überngods, but payments would be one-eleventh of income. As a more elaborate example, some Fibonacciïsts say this:

Also, payments vary at each level within Fibonacciïsm.

Beyond that, there has been proposed a structure where, for instance, a committee of 3 Übern+1gods would supervise a group of 19 Überngods. No Überngod would report to any single Übern+1god, and no Übern+1god would be the sole immediate supervisor of any Überngod.


§9. Every religion has rules and regulations, and RECURSIVITISM is no different. On the one hand, there are infinitely many commandments; on the other hand, each God has issued only one commandment, helping to simplify things:

Each God requires the mortals in its universe to obey the sole commandment (com1mandment) that It has issued … …which is to obey the com-commandment (com2mandment) issued by its Über1god.
Each Über1god requires the Gods in its decaverse to enforce the sole com2mandment that It has issued … …which is to obey the com3mandment issued by its Über2god.
Each Über2god requires the Über1gods in its hectoverse to enforce the sole com3mandment that It has issued … …which is to obey the com4mandment issued by its Über3god.
Each Übern+1god requires the Überngods in its 10n+1verse to enforce the sole comn+2mandment that It has issued … …which is to obey the comn+3mandment issued by its Übern+2god.

Rigorous orthographers might apply superscription to the verbs, as "Each Überngod ren+1quires …".

A mortal is not required to obey any commandment from outside their own chain of command.

An open question is this: A mortal's violation of the commandment given by their God is termed a transgression. Should such a trans1gression of their Über0god's com1mandment also be regarded, by transitivity, as a trans2gression of their Über1god's com2mandment?

Obedience to a commandment, the opposite of transgression, is of course called cisgression. This would suggest the notational identity transngression = cisngression.


§10. This section explains how a soul can move around. Unfortunately, there is a schism on this matter, with the respective advocates being labeled multidurationalists and unidurationalists. They disgree on whether a soul might experience an afternlife of a particular duration more than once.

According to either group, a mortal at the end of their earthly life goes to heaven if their God deems their behavior satisfactory according to Its com1mandment as described in §9 above; hell otherwise. Beyond that, they differ, as follows.

At the end of a soul's eternal afterlife, their Über1god evaluates the soul's compliance to Its com2mandment:

situationmultidurationalismunidurationalism
A soul in heaven who has behaved poorly is demoted to … … hell, to begin another eternal afterlife. … infra-hell, to begin a hyper-eternal after-afterlife.
A soul in hell who has behaved well is promoted to … … heaven, to begin another eternal afterlife. … ultra-heaven, to begin a hyper-eternal after-afterlife.
A soul in hell who has behaved poorly is demoted to … … infra-hell, to begin a hyper-eternal after-afterlife.
A soul in heaven who has behaved well is promoted to … … ultra-heaven, to begin a hyper-eternal after-afterlife.

At the end of a soul's hyper-eternal after-afterlife, their Über2god evaluates the soul's compliance to Its com3mandment:

situationmultidurationalismunidurationalism
A soul in ultra-heaven who has behaved poorly is demoted to … … infra-hell, to begin another hyper-eternal after-afterlife. … infra2hell, to begin a hyper2eternal after3life.
A soul in infra-hell who has behaved well is promoted to … … ultra-heaven, to begin another hyper-eternal after-afterlife. … ultra2heaven, to begin a hyper2eternal after3life.
A soul in infra-hell who has behaved poorly is demoted to … … infra2hell, to begin a hyper2eternal after3life.
A soul in ultra-heaven who has behaved well is promoted to … … ultra2heaven, to begin a hyper2eternal after3life.

At the end of a soul's hyperneternal aftern+1life, their Übern+1god evaluates the soul's compliance to Its comn+2mandment:

situationmultidurationalismunidurationalism
A soul in ultranheaven who has behaved poorly is demoted to … … infranhell, to begin another hyperneternal aftern+1life. … infran+1hell, to begin a hypern+1eternal aftern+2life.
A soul in infranhell who has behaved well is promoted to … … ultranheaven, to begin another hyperneternal aftern+1life. … ultran+1heaven, to begin a hypern+1eternal aftern+2life.
A soul in infranhell who has behaved poorly is demoted to … … infran+1hell, to begin a hypern+1eternal aftern+2life.
A soul in ultranheaven who has behaved well is promoted to … … ultran+1heaven, to begin a hypern+1eternal aftern+2life.

According to the multidurationalists, a soul whose behavior is erratic might bounce several times between a heaven and a hell of the same duration. Unidurationalists by contrast say that each time a soul moves, it enters an eternaller afterlife. However, both factions agree that a soul never moves from a longer afterlife to a shorter, and certainly never returns to mortal life.

A summary:

current
location
next location
according to
multidurationalists
next location
according to
unidurationalists
satisfactory
behavior
unsatisfactory
behavior
satisfactory
behavior
unsatisfactory
behavior
mortal life heavenhell heavenhell
heaven ultra-heavenhell ultra-heaveninfra-hell
hellheaveninfra-hell
ultra-heaven ultra2heaveninfra-hell ultra2heaveninfra2hell
ultra-hell ultra-heaveninfra2hell
ultra2heaven ultra3heaveninfra2hell ultra3heaveninfra3hell
ultra2hell ultra2heaveninfra3hell
ultranheaven ultran+1heaveninfranhell ultran+1heaveninfran+1hell
ultranhell ultranheaveninfran+1hell


§11. Some branches of RECURSIVITISM might have a hierarchical structure:

• A bishop would supervise a priest, an archbishop supervise a bishop, and an archn+1bishop supervise an archnbishop.
• As the office of a bishop is called an episcopate, the office of an archnbishop would be an epin+1scopate.
• For districts, there are two plausible systems of nomenclature:
  • In the first, the district that a bishop supervises would termed a diocese, with an archnbishop over an archndiocese.
  • In the second, an archdiocese would instead be called a dia-diocese. The equivalent to an archndiocese would be written diandiocese, except that some writers might prefer dian+1ocese or din+1ocese.

The full prefix (from Greek) is dia-, but the letter a is dropped when dia- is attached to a word beginning with a vowel. An analogy to oboffering emerges, where again a prefix is changed according to what it is attached to. To make the orthographic parallel explicit:

prefix never changed obn+1fering dian+1ocese
prefix always changed ofn+1fering din+1ocese
prefix sometimes changed obnoffering diandiocese

Some other branches of RECURSIVITISM might be organized as autonomous congregations, with no hierarchy. If several congregations elect to form an association, it might be called a con2gregation; with an association of con2gregations termed a con3gregation, et sequens.

Some congregations might choose to have officals called deacons, holding the position of the diaconate. Superscription of these terms is etymologically justified, if the need arises: deancon and dianconate. Terms for similar positions are elder, eld-ern.

Etymological purists might point out that the word congregation in its usual sense is redundant, as it is based on Latin grex which itself means group, specifically flock. Hence a rigorous definition of congregation would be a group of groups. It is not clear whether Recursivitists will adopt this interpretation.


§12. Already noted are several points of disagreement among Recursivitists; more will surely develop in the coming years. For that reason, some taxonomical vocabulary ought to be provided. What follows is an example of its use.

Suppose Recursivitist group A splits into groups B and C. At some later point, B splits into D and E, and C splits into F and G. This chart summarizes the divisions:

A
 
B  C
   
D  E  F  G

Then it can be said:

these groupsare
B and Cse1parated
D and E
F and G
B and Fse2parated
B and G
C and D
C and E
D and Fse3parated
D and G
E and F
E and G

Senparation is not here defined between a group and any of its ancestors. Matters will become complicated if two groups decide to merge.


§13. How was the information in this document obtained?

• About the Gods and Satans: from revelations delivered to prophets.
• About the Über-gods and Unter-satans: from re2velations delivered to pro2phets.
• About the Über2gods and Unter2satans: from re3velations delivered to pro3phets.
• About the Überngods and Unternsatans: from ren+1velations delivered to pron+1phets.

A pron+1phet is also a pronphet, with ren+1velations similarly subsumptive. However, a pronphet is not necessarily a pron+1phet.


Recent research has hinted that RECURSIVITISM might be merely one of a family of religions under the umbrella term RE2CURSIVITISM. It is anticipated that information about the Überübergods in that family would come from rerevelations delivered to proprophets. The syntax of numerical supersuperscripts has yet to be disdisclosed.

One might further suppose that proproprophets would furnish rererevelations about the Überüberübergods of RE3CURSIVITISM, if such a thing exists.


§14. Miscellaneous notes on the terminology and orthography:

• There is no restriction on translating the documents of RECURSIVITISM into any language that will foster understanding. Diagrams are also acceptable, as are audio and video recordings.

• Variations in the use of hyphens are not regarded as heretical. This is because languages differ in their use of that mark of punctuation, and because within any one language authors exhibit diverse practice. Hence no rigorous policy will be promulgated.

Afterlife is a widely-used word, so this report inserts no hyphen. By contrast, Über-god is hyphenated because Übergod is scarcely attested (although the German equivalent Übergott does enjoy some currency).

• Contrast that infra-infra-infra-hell would be very difficult to figure out without hyphens (infrainfrainfrahell), while the hyphenless everyeveryeverything is moderately readable.

• Orthographical alternatives to eternal-er-er are eternalerer and eternallerrer.

• Some authors might prefer to use two capitals: Über-God. In a font that does not support umlauts, Ueber-God can be written.

• The interjection OMG! is often seen in electronic communications. For stronger effect, it can be extended into OMÜG!, OMÜ2G!, and OMÜ3G!; although something like OMÜÜÜG! might have greater visual impact.

• The use of small capitals in RECURSIVITISM is comparable to their use in LORD in some religious texts. This document writes RECURSIVITIST when it is an adjective for RECURSIVITISM; but Recursivitist when it is a noun referring to a follower. Some scribes will non-heterodoxically differ.

• From the extensive use of superscripts naturally arises the question of whether subscripts might have value; but no purpose for them is yet known. Superscripts that contain subscripts (Über53god) or the reverse (Über53god) do have potential to convey great theological subtlety.


In a typographical context that does not support superscripts or subscripts, square brackets with slashes are an alternative:

• A superscript is preceded by [/ and followed by ]
• A subscript is preceded by [\ and followed by ]

For example, Über[/n+1]god = Übern+1god. Also, nesting is supported:

• pro[/pro[/pro]]phets = proproprophets
• Über[/5[\3]]god = Über53god
• Über[\5[/3]]god = Über53god

Parentheses may be helpful for clarity when the superscript or subscript is a fraction, as might be required in some advanced developments of RECURSIVITISM:

• Über[/(37)]god = Über(37)god


Being the one and only true, all-embracing, and perfect religion (as all religions are), RECURSIVITISM has garnered its share of misguided detractors, who in their disappointing parodies characterize it as woo, woo-woo or woo2, woo3, et sequens to reflect the discouraging magnitude of the ill-aimed disdain arising from their regrettable ignorance. Devout and loyal defenders sometimes respond in kind by writing woo with a negative superscript, as woo−3. Other insensitive disparagements employed by the naysayers are pre2posterous, ab4surd, ortho−3dox, and convoluted.

Because of the meaning of the prefix de-, it may not be appropriate to write denfender to denote an especially vigorous defender; the same with denvout. To replace those words, the terms subn+1porter = supn+1porter = subnsupporter and faith-fuln+1 are valid, with the obvious meanings.


A few denigrators go so far as to deprecate this very document as overnwrought, grieving its manuscribing pronphet inn−1immensely.