SNEEFT COEIL and the Catalan number

John Bjarne Grover

The article discusses a principled nexus between natural language and mathematical number.


I have defined the fundamental theorem of linguistics like this: "Two and only two items can be the same across two different realities". The theorem tells how the human psyche attains its shape in such a way that two items from two different realities can be conceived as one and the same even if they are quite different: If a stone in one reality shall be conceived by the human psyche as the same as an umbrella in another reality, the human psyche has to be quite special and biased for making that identity. The theory goes that this is what gives the human psyche its innate language faculty including its capacity for symbols. The human spirit makes for the identity of two different things and reduces these in the act of creation to one material being - while the surplus, the difference which is ignored thereby, goes into the constitution of the soul or semiotic meaning generally. This tells why the human soul attaches to the human body.

The fundamental theorem is what can open for an information technology to communiate with remote intelligences: For transcending the speed of light, the information will have to go through a metaphysical reality prior to the constitution of light (or signals generally). This metaphysical reality can be modelled by way of a reversal of the spirit's act of creation - when matter is reversed by bifurcation into two different and primordial realities - wherein the two original metaphysical elements can be put in relation to other metaphysical elements for a reconstitution of new matter 'ex nihilo' - which can be carriers of information.

Although this bifurcation resembles quantum theory, it is likely to be different via the semiotic connection.

SNEEFT COEIL is my book of poetry in 8 chapters (142 poems) studying the synchronic dimension in signification. It is in german language and adds to the diachronic study 'Der Dornenstrauch'. I have now discovered that it contains the material suggesting a potential role for the socalled 'Catalan constant' for the border between metaphysical and physical reality - for the mystic nexus between language, logic and mathematics. It was on 12 august 2019 that I found it - following a hint from a nice white cat. It is possible that the observation has some value. I tell the story here.

The first principle

There are 8 chapters in the book - each chapter being concerned with various aspects of human signification. Chapter 7 is called "20 Gedichte - in September und Oktober" and is about the poetic constitution of mathematical number - or the human-semiotic interpretation of numerality generally. There are 20 enumerated poems in this chapter and it seems that these constitute a running poetic definition of the real numbers from 0 to 20. Poem 11 is a simple illustration of the meaning of '11'. More advanced is the constant e = 2,718281... which is found about 0,718281... into poem 3 - that is up to line 11.492 of the 16-liner, approximately half way into line 12. Lines 10-11-12 are these:

Dann fiel ich auf den Bodenstein
und rief es wie ihr alle fielt
dass jeder Gott war ewig mein.

Now I wanted to look up some other mathematical constants to see if they had an interesting echo in my book and I searched in Rottmann's Formelsammlung - and there I came across Catalan's constant G which is the integral from 0 to 1 of the arctan x divided with x. This constant is

G = 0,9159655941772190150546035...

This number is said to be either irrational or transcendental and it is probably an infinite series of decimals. The computations seem to be going on for the time being and in mid july this year (a month ago that is) one had come to more than 600 billion decimals and still not found the end. It goes and goes like a clock that never comes to the door.

I was looking at this number when I suddenly discovered that its numeral decimal symbols seemed to contain the title to the 7th chapter: 'Gedichte in September und Oktober' - if the number 20 is seen in the initial 0 and the comma. That was interesting! I then noticed that the continuation of the number seemed to be the start of poem 1. 'Allein ist niemand':

20 GE
915 965 594
dichte in Sep
177 219
tem ber
015 054 603 5
und Oct boe r
1 4 932 38...
1.Allein ist

But this poem 1 is where I also would find the constant itself hidden 0,9159655941772190150546035... through this poem. I started to map text onto digits and found that the constant itself would be in the poem at 0,915965 * 16 lines = line 14,655, which is the form "Der Mensch wenn er ist" - with potential ambiguity of temporality and conditionality in 'wenn'. Aligning the poem with the decimals I found that the corresponding digits in the long number were the quasi palindromic sequence

75532307 6 85653357
75335658 6 70323557 = mirrored

Hence even the words can be turned around:

[d]er mensch wenn er ist
tsir ennew schnem re[d]
(says a new schneeft red)

Ah, here is the SNEEFT COEIL - the book's title.

Including the initial zero but not the comma, the number of digits from beginning of the number to the end of this self-referential fragment is 333 digits. Recursively applying itself in this point.

The theory is confirmed by computing the same point in all the other 7 chapters in the book - for example, the mirror point in chapter 2 ('Die Steine') is 'in Tirol' - which is close to SNEEFT COEIL.

It is the chapter 3 which gives the proof - the last poem corresponds in mirror symmetry to the first poem in chapter 7 - and when it has 9 lines (title included) one computes 0,915965 from the end upwards and comes to the title line:

Schnee der dunkle 2-3'E

0,915965 * 9 lines = line 8,24 computed from the end = 2-3'E

But now there is the palindromy of the self-reference of the Catalan constant:

[d]er mensch
tsir ennew

dunkle 2-3'E
wenn er ist
schnem re[d]
Schnee der


2307 6 85653357
2307 6

This seems to constitute a tentative proof that SNEEFT COEIL is concerned with the Catalan constant.

What does it mean? It means - by the poetic principle of my chapter 7 on the semiotics of numerality - that Catalan's constant is an infinite number that contains in itself (in its sequence of symbols) the semiotic definition of all numbers. Or, rather, itself is just that SNEEFT COEIL.

a = 0,75532307685653357
b = 0,75335658670323557
G = 0,915965594177219

sqrt (a * G ) = 0,83177518049570343295029956851028
sqrt (b * G ) = 0,8306917078958660049156861185062
G * G = 0,838992969716425849237578573961

Adjusting the end of 'b' by the formula 2-3'E into a new number

c = 0,76848869401681550965402837819589

makes for the identity with G*G.

This means that it can be a variant of Cantor's diagonal.

The conclusion is likely to be that the Catalan constant is about the relation between matter and soul when the spirit reduces two metaphysical items to one - by my fundamental theorem of linguistics.

The second principle

Chapter 8 is a little special and can be considered 'one level up'. In vol.4 of my collected works, I have studied the possibility of detecting the phenomenon of divine or poetic revelation in a text - as a technical term for finding a higher level of knowledge. If a metaphysical logic for communication with the universe is to be established, it must be based on empirical evidence or reflex from the metaphysical reality to try and find the logic that conducts the 'transcendent reasoning' there beyond. Briefly, a metaphysical logic can quickly be made and be used for constructing a transcendent information technology to which the development of the society adheres and conforms, but since we cannot wait 5 millions years for the answer from remote intelligences via signals we have to take a chance that the transcendent logic is right: The answer looks meaningful and says that indeed they eat sausages even on Andromeda, but we cannot find out whether this is an answer generated by our own redundancies of thought or if they really eat sausages. If after 300 years it turns out to be based on faulty logic, the whole development must down - and that means war and destruction. It is possible that this is what war is - and that such transcendent logics are constructed continuously by the human society. The only solution found so far is by the parametre of faith - that is what religion is for - and the 20th century tried to establish a concept of 'arbitrarity in signification' to handle this problem - in the hope of finding a quasi mechanical procedure for finding the 'higher logic'. My vol.4 studies one particular aspect of this - in the corollary from my fundamental theorem of linguistics, which has three main corollaries:

1) 2 realities can be reduced to 1 in the human psyche
2) Logical order and semantic assignment are thereby one and the same
3) Synchrony and diachrony is methodologically the same

It is from these three corollaries that I could study the phenomenon of 2 and only 2 diachronic occurrences of words in a text - on the assumption that diachrony is the same as synchrony. By a logical order of the words that occur twice and only twice, I list these words in alphabetic order and study them relative to works on metric aspects. My poetic work is divided in two different types: 1) The non-metric 'The Endmorgan Quartet' of 1719 poems written exclusively by inner poetic articulations (the work of an inspired poet, that is), and 2) the metric work on blue, red, yellow and white metres. For 1) the essential question is where these inner poetic articulations come from: If they are a case of divine revelation, technically speaking, they can form the empirical basis for the development of a metaphysical logic, but if they come from mass media propaganda from the secret intelligence services. the resulting logic is likely to be of sausage type and the society built thereon will have to be demolished later, leading to much panic and problems of thinking clearly and logically. The question is therefore of vital importance. Vol.4 is a study of the degree to which vol.2 = TEQ can be used for such an empirical basis. The example is from the article 'Fatima and the fundamental theorem of linguistics', the following scheme where the lefthand column is from the alphabetically ordered list of words that occur twice and only twice in book 14 of TEQ while the righthand columns is from the 'white metre', the book 'Stillhetens åndedrag':








Savonarolas tanke

Mennesker reiser i rom.
Jeg sitter og hviler blant dem
og jeg grubler og tenker på om
jeg noensinne har gått frem.

Fuglene reiser i tid
som byggekunstenes hjem.
Savonarola var i
tanken som tenkte dem.

Husene tett i tett
bak løvverkets grønne skur
skildrer mitt synske vett.
Tiden ligger på lur.

Dette landskapet skygger sitt grønt
og hang med hodene tyngre,
forteller om det du nettopp har skjønt        
at når vi kom frem var vi yngre.

Dette landskapet henger sitt brunt
som dreier sitt hode om.
Rovfuglen kaster sitt legeme rundt
mellom det hvite skum.

Savonarola's thought

Humans travel in space.
I sit and rest among them
and I ponder and think if though
I have ever progressed.

The birds travel in time
as the home of the art of building.
Savonarola was in
the thought that thought them.

The houses tightly and tightly
behind the foliage's green shed
describe my clairvoyant intelligence.
The time lies in ambush.

This landscape shadows its green
and hung with its heads heavier,
tells of what you have just understood
that when we arrived we were younger.

This landscape hangs its brown
which turns its head around.
The bird of prey throws its body around
inbetween the white foam.

It is because the fundamental theorem tells that logical order and semantic assignment are one and the same thing that one can take the lines of 'Stillhetens åndedrag' in the righthand columns as definitions of the entries of double-words in the lefthand column. What is 'step'? It is when 'humans travel in space'.

Now 'SNEEFT COEIL' contains approximately 1823 lines in chapters 1-7 which are aligned against the 1823 double-words of TEQ books 6-12 and against 1823 event elements that I recorded in Oslo in 1995: There were 163 events in the street outside my home and these contain a total of 1823 event elements. Chapter 8 contains 163 lines which run in parallel with the 163 events - this is why chapter 8 can be seen to be a 'level up' compared with the chapters 1-7 which are in parallel with the 1823 event elements. Vol.4 contains a list of the 166 double-words of TEQ book 5 - and a list of the original order of writing of the 163 lines in chapter 8.

Chapter 7 finds the Catalan number at 0,915... through poem 1: This chapter 7 contains 20 poems - 16 of these have 16 lines and 4 have only 12 lines. That makes for 304 lines. Poem 1 in chapter 8 has 16 lines. To compute the correlate in chapter 8 with its total of 163 lines takes it to

((0,915965 * 16) * 163/304 = line 7,858 in poem 1 of chapter 8.

That is line 8 "du freundlichst war nah". It is the grammatical error which attracts interest: Duden prescribes 'du freundlich warst nah' while I wrote 'du freundlichst war nah'.

Since this chapter has lines correlating with events numbers of 1995, the corresponding event to line 7,858 in chapter 8 is then event 8 which has 29 elements: Multiplying 29 with the constant G takes it to element 26,5 = element 27 which is #331:

du mit diesen            

und weißt und





- The yellow car stands as I pass,
and then it drives past and in front
of me. I walk behind it.

- Car parked by Sofie's restaurant,
to the left in the street: MØKK is
written with a finger on its dirty
driver seat window

This is just before #332 which tells of 'weißt und treut' and the writing of 'muck' on a dirty car window = white and black. The list of 1823 elements is mirror symmetric and one looks up 330-331-332 counted from the end - which is in event 121 - corresponding to line 121 in chapter 8:

nachfragend wie ein Kind.


EVENT (121)
- As I am about to pass the boundary, I see a woman coming down Glükstad's gate towards me.

Man gibt es zu dem Präsident 1493 author 331 - Nothing in the significant stretch of thee street, but four people in Krumgata outside the dentist mechanic's workshop: A man, a woman, an older woman, all visible, and the speech of a child.
Begnadigung zu sehen 1494 authority 330 - As I step onto the stairs, I turn my headd and look down the street, and catch a glimpse of the child.

Returning to the list of double-words from TEQ book 5, the entry #121 (corresponding to this event #121) on this list is the word 'says', while the list containing the original order of writing of the lines of chapter 8 (against the eventual order) in SNEEFT COEIL tells that line #121 is written as #118 and line #125 is written as #121: These lines 121 and 125 are lines 6 and 10 in poem 8:

Line 6 = ist in diesem Leben letzt (originally written as #118)
Line 10 = ...sechzehn wechselt mit sechzig... (originally written as #121)

Now returning to the list of double-words in TEQ book 5, assuming, as suggests line 10, that 60 interchanges with 16, I found that on this list entry 16 = 'call' and entry 60 = 'identical'. But this is just what the spirit does when it - according to the fundamental theorem of linguistics - identifies two items from two different realities as one and the same - which then is considered material body - it 'calls identical' - while the difference between them is relegated to the constitution of soul or semiotic 'meaning'.

(Some unfortunate politics has made the mistake of believing that the call for the identical means replacing a person with an engineered copy - and presents this as 'heaven on earth'. That is a very deplorable mistake).

Now the sum of this comes to be 'says call identical' - or simply 'says a new SNEEFT COEIL' - the words for the self-.referential Catalan number of chapter 7. It thereby suggests that a SNEEFT COEIL can be understood as that item from one reality which the spirit recognizes as the same as one from another reality.

The third principle

This chapter is called 'Die Verwandlung (Unter vier Wänden)'. It contains 16 poems which are assigned to national characteristics of the languages of 16 european countries. The example is the hungarian language with its code word 'hymen'. See also this file on the Beachy Head cliff fall for the estonian example. It is probable that some 'national parametre' in natural language exists and that this somehow regulates the interface between subjective and collective memory and cognition.

My guess is that the chapter 'Die Verwandlung' is about the change that takes place when the Metaphysics of 2 and only 2 (by the fundamental theorem) turns into History with 3 or more - for the distributional semantics of TEQ book 14. In contrast, 2 and only 2 is the semantics established by recognition of 2 metaphysical items as one - which gives shape to the human psyche and is something else than categorization and classification. When only 2, one can draw one and only one straight line through it - when 3 one can draw one and only one circle through them. These are contained in the lapis philosophorum which I made in 2014:

The lapis was found in the drainhole of the kitchen sink. Die Verwandlung is the turn from 2 on the lefthand side of the diagonal - the man and the woman - and the third on the righthand side of it. It is the boy who pulls the wagon with the man on it. Both male and female archetypes cross the street - and in the dogs paradox inbetween ('My mention e Anna') the dogs dig a hole which comes to contain water, probably coming from the rope that goes under the fence from the tree

. The mystery is that the water is the light. It comes from the tree = the triangle under the man on the lapis, it crosses the fence = the diagonal and goes into the space. It is the zigzag form of egyptian hieroglyphs - crossing the diagonal along the lower line of the square - which tells that the water is below the eyes of the man:

Could be this paradox is the squaring of the circle.


If you fold the stone along the mid line, the righthand side of the square, you will get a sort of squared circle - and the boy will share views (and woman) with the man. If you fold the word COEIL over along the word SNEEFT, you get something resembling the CHRIST with a JESUS on the crossover.

The diagonal is the rope with which the boy pulls the wagon across the street. The square is the curbstone into which the wagon slams - as if the wheel of the wagon suddenly turned square - before it lifts itself up by magic force contradicting even the law of gravitation. That is because the square is a little higher up than the circle. It is a LIFTED COEIL.

Hence the curbstone is the squaring of the circle. The man on the wagon does not say anything - but he gave me a friendly look in return for me waiting for him to cross.

The first thing one sees when meeting the man-on-wagon is when one spots in the corner of the eye the boy lifting a finger on the other side of the street - to catch your attention. In the moment when one turns the head to look what it is, he starts running across the street with the wagon after him in a rope. This finger could be the erection in the square - approximately on the position of the golden ratio in the vertical dimension. That ratio is 0,618: Computing this for the first poem in chapter 6 one finds

in meinen Fenster-Rahmen hinein
als gleitet die Vision von meinen Au[gen]

while the same position in chapter 7 is

Das Essen ist das schnelle Licht.
Das Trinken ist der We[in].

This tells why the faculty of vision is the water - or the wine. It is installed in christian holy communion.

The catalan number is believed to be transcendental or irrational - that is (probably) a matter of definition by cantorian diagonals of notation. In the present case the 'transcendence' or 'irrationality' can be said to emerge from notation issues by the comparison of the alphabetic script with the decimal notation of the catalan number: If it were to be notated with 26-imal notation of the latin alphabet, it would not resemble my poem at all - not the least because it would be much shorter or 'denser'. Hence the paradox which can be recognized as 'transcendence' or 'irrationality'. This proof is 'poetic' and 'intuitive' more than strictly formalistic - it is based on the fact that the 20 poems in my chapter 7 run through the poetic-semiotic definitions of the numbers in natural language from 0 to 20 and that is when the isomorphy with the decimal notation occurs. But what is so holy about decimal notation? It is the 10 fingers of the working hand and the 1000 years of the blue metre - which defines the interface between collective historic and subjective consciousness - that is, precisely where the 'national' parametre of language must be situated. But that is just where the chapter 6 is.

I notice also that by decimal notation there are 333 digits from the beginning to the end of the self-referential string in the Catalan number, including the comma as a third it goes thrice up to 1000 = 10*10*10. That is perhaps something.

The number 'π' is also proven to be transcendental, and the natural logarithm base 'e' likewise. The 'π' is in the circle while the 'e' is in the lapis philosophorum itself.

The fourth principle

Chapter 5 contains 32 poems, the double of the more usual 16. I multiply the Catalan number with 2 and get 1,83193 from which I subtract the first poem 1 - that leaves 0,83193 which is multiplied with the 12 lines of poem 2 - for nearly 10. It is 9,98... but since the chapter is called 'Ich ginge aus zu Breleon' it can count as 10 when seen through the berylls. This line 10 = "'Wie heilig ist Judas doch auch!'" which looks like a cantorian diagonal.

The cantorian diagonal is based on the possibility of proving that an adjectival quality can be negated and from this conclude that the negative of the adjectival quality exists. If the set is countable, then so-and-so, but since so-and-so does not obtain, it follows that the set has the quality uncountable - that is, that 'bigger than normal infinity' exists. Like letting a drop of red into the infinite green ocean and from this conclude that 'the ocean is no longer green - hence it is red'. But this is all and only about the epistemological status of the adjective ('countable'). It can perhaps be argued that "der Mensch wenn er ist", with temporal-conditional ambiguity, is a hallmark of adjectivism - which likewise can be recognized as the same as the status of being witness. But that is just Judas - the very Witness of dubious quality.

What goes out to these Breleons is the light that goes out from the eyes. Or it is the faculty of vision that goes out into the eyes.

Chapter 4 likewise has 32 poems and is the mirror to chapter 5. I compute in the same way (G*2)-1 = 0,83193 times the 8 lines of poem 2 = line 6,66 = 'Wirkichkeit lebt' in line 7. That is the story of the witness and the constitution of the human reality. Computing the same from the end takes it to the line 'am hinten ist es schnell' - which is an easy reading of 'wenn er ist der schneM'. Cp. also the form 'Schnee der dunkle 2-3'E' from chapter 3.

Chapter 1 is about the 'Wahrnehmungen'.

Summary of the four principles

1) G = 0,915... ... G...
2) Call identical on higher level: G = 0,915......G...?
3) Squared circle = unsolvable by euclidean tools        
4) Holy Judas! = cantorian diagonal
= recursion
= recursion
= transcendental/irrational
= transcendental/irrational

This suggests that (e.g.) the Catalan constant as a 'transcendental number' (determined by Cantor-diagonal method) could be the secret nexus between language and mathematical number.

General considerations

The Catalan complex described here tells of the semiotic nexus between language and number. That the number may be transcendental means that it exists and is not algebraic - that means it cannot be written as a polynomial with rational coefficients. The proof that such numbers exist is the normal symbol manipulation style of a cantorian diagonal: If all such polynomials can be listed, then one takes the diagonal which is not in the list - hence transcendental numbers exist - is the logic.

But isnt this somewhat nonsense? The logic would be based on the idea that number is the same as a series of symbols - but then one finds a number that cannot be squeezed into these series of symbols and therefore cannot be written down. But doesnt that rather mean that 'a series of symbols' is not a goodenough definition of number? Modern mathematics is perhaps much the art of moving symbols around on paper.

It seems to be about a paradox based on the involvement of perception on the border between matter and soul - the very borderline between the 'call identical' turning into matter and the surplus soul or semiotic meaning. The present study suggests that the ratio between matter and soul in this sense of it is the Catalan number - and that this number also tells of the border between number and natural language: It is a number which cannot really decide if it is a number or only an obscurely written language.

It is likely that the cantorian diagonal tells of this border more than strictly speaking any bizarre uncountable sets - that is, that a transfinite number tells of the soul rather than the countable numbers which can be represented on visible paper. Then the diagonal makes sense - as on the lapis philosophorum. My fundamental theorem of linguistics tells that different realities exist - and that is what the cantorian diagonal tries to tell as well: Some numbers can be ordered in this reality but not all, and those which cannot be ordered belong to another reality. It means that numbers exist which cannot be written on material paper.

It is probable that conditional entropies can be used for describing the affinities between realities.


The story can be said to be 'if you could explain it' = 'om du kunne forklare det' = 'wenn Sie es erklären könnten'. This is 'der Mensch wenn er ist' = when the psyche is turned into stone - which can be folded to the squaring of the circle.

PS It can perhaps be considered trivialities that these observations on the parallel of my poems with the number of Catalan obtain for decimal notation and german language. Or maybe it is not so uninteresting?

Added on 18 august 2019: As is seen from the article, my poetry can come to lead to a new information technology which even can come to allow for communication with remote intelligences. But that is only because of my poetry. Could somebody please help me get my rucksack with the poetic notebooks back? It is particularly worrying if it has been stolen by political interests for abuse in the upcoming election. There could be international interests more than only local independent ones who use terror. Simon Walther Hauge (who died in 1980) once told me that he had travelled 'on the thumb' to Copenhagen for finding a violin teacher in his youth. He was a good violinist but worked as a farmer because, as he said, he was 'too bound to the earth' to be a professional violinist. Notebooks are in the news. I forgot the rucksack in a church on 3 august 2019 and when I came back a good hour later it was gone. Jeffrey Epstein died a week later, for whatever reason. .

The author thanks the friendly white cat who gave me the cue to this discovery

© John Bjarne Grover
On the web 15 august 2019
Last updated 18 august 2019