PEB line 12 and 14

John Bjarne Grover

I here discuss three famous examples of simultaneous discoveries from the history of mathematics for the theory that these are encoded mirror-symmetrically into the millenial span of the blue metre of my 'POLAKK English Bloggi' line 14. I follow up with some considerations on a similar function for line 12.

The theoretic basis

In the years 1997-2008 I wrote 16 books of poetry collected in the socalled 'The Endmorgan Quartet' = 'TEQ', a work of 16 books with 1719 poems wherein each and every line is annotated with date of writing. It is written successively from beginning to end with only a few exceptional lines scrambled. Each book constitutes a study of a certain particular function of time - and the work in total constitutes a theory on the compositionality of time. The poet climbs the mount of poetic enlightenment which is reached in the last poem. These 11 years of writing of TEQ was poetry chemically free of any formal constraints. The only cue to the progress of the poetic lines was in the inner poetic articulation - and the poet's aim was to forward the poetic lines of a quality of 'divine revelation', that is, a level 4 and not a level 2 articulation. In the following 10 years I wrote the way down again - in the form of metric poetry - what I called a blue, a red, a yellow and a white metre. The blue - called 'POLAKK English Bloggi' = 'PEB' written in 2008-2010 consists of 365 'sonnets' (14-line poems with sonnet line-end rhymes) plus a leapyear poem. It is a 'transform' of TEQ in the sense that line 1 in all the 365 sonnets interprets book (poetic function) 1 of TEQ, line 2 is book 2 etc. The net result of this is that the PEB can be used to date texts: Take a text written in, say, 1850, and compute offset as (2009-1850) * 0,366 = 58,194 = #59 - that means that if you divide the 1850 text into 366 equal parts, then you can align this series 1-366 with the poems of PEB starting from #59 for part 1 up to #366 for part 307 followed by the poems #1-58 for parts 308-366 - and this will be the optimal semantic correlation (as far as the meaning of the correlating parts is concerned) between the two series of texts, as is the dating principle. Conversely, if you have a text which you know not when it was written, you can divide it into 366 equal parts and search for the optimal correlation with the PEB - and the text can be dated by the offset. I have tested a good number of texts and the theory is thoroughly confirmed.

See this article for a study of line 4.

See this article for a study of line 6 - a theory on its formal properties.

See this article for a study of line 1.

Lines 1, 4 and 6 adhere to different principles of interpretation of the assumed compositionality of time.

In this article I study some properties of lines 12 and 14 - corresponding to TEQ books 12 and 14. This TEQ book 14 is particularly interesting since it provides for a theory of distributional semantics which seems to land on a mirror-symmetric distribution of semantic and phonological logic.

See this article towards the end of its first part - search for 'Book 14' for a very brief outline of the basic principle of this distributional semantics. In the example of poem #161 of book 14, "the clocks would open for the documentation" when somebody is "aufzuwaken/aufzuwuken": This is a very strong semantic theory - which can be made even stronger by using not only poem #161 but also the other two intervals. (I have tried many dozen examples and at least the weaker form of the theory is very well confirmed). The semantically based logic of human cognition (a logic based on the meaning of words) is well known since at least Aristotle - but the phonologically based logic I have detected on basis of the poems in the mirror point to this distibutional semantics (in the example of the article it is in poem 208-161 = #47) is probably new and could be a major breakthrough in logical theory. The present article contributes to that logic by examples. These examples suggest that both line 12 for 'divine apparitions' and line 14 for 'simultaneous discoveries' in mathematics will exhibit a distribuion of mirror-symmetric kind as they apply on the span of a millenium - corresponding to semantics in the one point and phonology in the mirror point across the blue-metre millenium. These examples will suggest an interpretation of a possibly important aspect of what the phonological logic in question could be about. I start with line 14 which is the most obvious and clear instantiation of this logic and follow up with some examples from line 12 which seem to exhibit not so clear but nevertheless quite important aspects of the same logic - and point eventually to some corollaries for the history of religion as far as the dogma of christian resurrection is concerned.

Line 14

The full interpretational span of this line is as yet not clear but the example is the phenomenon of simultaneous discoveries in the exact science of mathematics. The three examples of socalled 'priority disputes' which I discuss here are among the most well known from the history of mathematics. I refer to my lecture in the theory of science for details on the three examples I discuss here.

Example 1: Bolyai and Lobachevsky: The transylvanian János Bolyai and the russian Nikolai Ivanovitch Lobachevsky made the discovery of non-euclidean geometry around the same time. Bolyai's theory was published as an appendix to a work of his father in 1832, but it is said that the theory was completed in 1829. Lobatchevsky is said to have published on non-euclidean geometry in russian since 1829-30 but various factors made it remain largely undiscovered in the west. Gauss was a friend of Bolyai's father and had been in contact with Lobatchevsky, as tells the story, and there were rumours that Gauss had leaked details from Bolyai's early work to Lobatchevsky who thereby came to publish first. However that be, if 1832 is set as year of publication of the discovery, the formula I have established for line 14 starts from the year of writing of PEB at 2009: (2009-1832) * 0,366 = 64,782 = PEB #65 with its line 14 - which I compare with the name of the discoverer:

had not been in store
János     Bolyai

The mirror poem to #65 is 367-65 = #302 with line 14:

my finger's stripper
m       ai finger's stripper
Nikolai Ivanovi tch Loba - chevsky

The surplus material in the name is this:

ikol   vitch     chevsky
Carl Friedrich Gauss

for which reason the name of Gauss seems to have integrated into the name of Lobatchevsky - and hence the rumour that Gauss had brought the material from Bolyai on the other side of the 'rainbow' constituted by the millenial span of the blue-metre PEB - as goes this 'phonological logic' here.

Example 2: Grassmann and Hamilton: Hermann Günther Grassmann in Stettin discovered his 'Ausdehnungslehre' and William Rowan Hamilton in Dublin discovered his 'quaternions' at about the same time - in 1843. See my lecture in the theory of science for details. Computing line 14 for this year: (2009-1843) * 0,366 = 60,756 = poem #61 - with its line 14:

and very smilingly greets my 'buongiorno'
and very smil ingly greets my 'buongiorno'
Her-is-mail ingli Gritsma n buotgiorn
Hermann Ginti Grassmann bridgehead
POLAKK english             bloggi

The mirror poem is 367-61 = poem #306 with its line 14:

we have a sip of tea.
wi hav e sip ov ti.
wil am re himovtin

It seems that some phonological material must be transferred from #61 to #306 for making this last name complete - notably some nasal. In fact if one transfers from 'here is mail for you' in 61 with a 'bridgehead' annotated, one can complete the name of William Rowan Hamilton - who reportedly got the idea to his groundbreaking quaternions in a 'flash of genius' at a bridgehead in Dublin while he was out walking - and he immediately inscribed the solution into a stone wall there.

It is typical of the story that Grassmann never got a chair at a university. There was probably a good reason for his 'Ausdehnungslehre' - it spread quickly down to Dublin, for example. A good luck the recipient Hamilton was gentleman enough to call his discovery 'qua turn-ians'. One guesses that the relation between these two (similar) discoveries is the factual format of the metaphysical theory which forms the basis for my fundamental theorem of linguistics - telling that '2 and only 2 items can be the same across different realities' - from which the form of the human language faculty probably can be derived.

'POLAKK English Bloggi' is a name with probably many reasons - one of them is easily spotted here - inside the mechanism of a phonological logic.

Example 3: Newton and Leibniz: Isaac Newton and Gottfried Wilhelm Leibniz discovered the infinitesimal calculus around the same time, around 1670-80. If one puts the year to 1682 the line 14 seems to provide for the two names quite well: (2009-1682) * 0,366 = 119,682 = #120 with line 14:

oneself the distance
oan self the distens
    Isaa c       Nitens

Mirror poem is #247 with its line 14:

exploring Egypt's boats
iksplor iN idjipts bouts
gitflor wilfrid lai bnits

By studying the details in the phonology, one can probably reconstruct the history.

Line 14 is a derivation from TEQ book 14 with its distributional semantics which opens for two sorts of logic: One based on semantics and one on phonology (in the mirror point on the rainbow from poem 1 to poem 207). One observes how this will apply to the phenomenon of line 14 in PEB: There will - by the mirror principle - be what corresponds to a semantic reading of Newton or Grassmann and a study of the phonological relation between the line and its mirror line relative to the names will be telling of the details of the history. Grassmann and Hamilton at the bridgehead, or Bolyai and Lobatchevsky with Gauss between, tell quite well the details in the following story. Are there any similar data available for Newton and Leibniz - such as that apple that fell on Newton's head when he discovered the law of gravity? I would guess that there is an apple in the mirror line - unless it simple is that 'mail-for-you falling into the bridgehead'.

Howard Eves' "An introduction to the history of mathematics" tell on Newton on p.397 that he as a boy made a toy gristmill that ground wheat to flour and had a mouse serving as motive power. He also made a wooden clock that worked by water - and for reasons of his clever inventiveness his schooling was extended (a career in farming, like his father who died before he was born, had first been planned). This extended schooling could have been comparable to Grassmann's 'Ausdehnung' and reached Leibniz thereby, so to speak:

exploring Egypt's boats
iksplor iN idjipts bouts
git   flor   wil   frid   lai   bnits
grist-flour millwheat toy mouse

It can perhaps be conjectured on basis of this that 1682 is a good guess for the discovery (or at least publication into the formal representation of the collective historic consciousness) of the infinitesimal calculus.

Conclusion is that the name is an important factor for the indexation in the blue metre as a formal logic for the collective historic consciousness. Could be, therefore, the examples I have studied for line 6 can be taken seriously after all. What is interesting is that the mathematical discoveries seem to be mirror-symmetrically distributed on the millenial span - in the same way as the semantic and phonological logic in the distributional semantics of function 14 = book 14 in TEQ. It is this phonological logic (in the span of collective historic consciousness) that applies to the form of names - as is the natural guess here.

This means that a study of the history of mathematics can lead to some cues for the construction of the phonological logic.

Line 12

TEQ book 12 seems to be about divine revelation. For its relevance for these semiotics studies, see also this article with its comments on 'Meaning qua divine revelation'. In the following example the idea would be that 'divine revelation' in line 12 entails an element of 'semantics' - for which reason the viewpoint of the visionaries that observe the divine revelations would be somewhat phonological - that is, expectedly, their names or other indexes.

Example 1: The Madonna of Knock - the apparition lasted for 2 hours in outdoor rain and showed the Madonna next to her husband Josef and John the evangelist, and an altar with a lamb on it - this was observed by Mary Beirne and Mary McLoughlin in 1879. I apply the same form of computation for finding the line 12 as for line 14: (2009-1879) * 0,366 = 47.6 = #48 which has line 12:

Glass, fork, knife, spoon from the supper
from supper knife forkglassspoon
Mary Beirne Mary McLoughlin

Mirror poem to this is 367-48 = #319 with line 12:

This is what I thought was the third
Josef altare John Mary Jesus/Lamb

Hence the observers and the observed are mirror-symmetric in this revelation - seen from the viewpoint of the names of the visionaries.

Example 2: The Madonna of Fatima - was observed by the three visionary children Giacinta, Francesco and Lucia in Fatima, Cova da Iria in 1917: (2009-1917) * 0,366 = PEB 33,7 = PEB #34 with line 12:

It's Wittgenstein with his pensive look,
its wi-tgentain withis pens ivluk
        Giacinta, Francesco, Lucia

Mirror poem is 367-34 = #333 with line 12

Among the tourists in tunics and sari
emongtheto ristsintun iksensari
a Madonna of Fatima, Cova da Iria

Could be the name of Francesco is the one in most need of revision - the Madonna said that Giacinta would go right to heaven while it was possible that Francesco, who also would go to heaven, would come to need to do much prayer for getting there.

Example 3: The Madonna of Paris 1830 - Catherine Labouré met the Madonna in the Chapel of Rue du Bac in Paris - a very lively apparition it was which even allowed her to put her folded hands on the knees of the sitting Madonna. She was shown the 'Miraculous Medal' which turned around. (2009-1830) * 0,366 = 65,5 = #66 with line 12:

Pray, pray, exhort and
    Labrei   Catherine

Mirror poem = #301 with line 12:

A sudden fit
A Rue du Bac
A Madonna

Here an extra 'P' (the knee?) can be lifted over from #66. The Madonna was seated in an armchair - could be the expression 'armchair philosopher' (cp. #66 - and Grassmann) derives from this story. Whether it was the factual Madonna from Heaven or only the caretaker's wife is not essential for the epistemological value - I myself could tell stories of what happened after I had been to this chapel.

Example 4: The Madonna of Lourdes, Hautes-Pyrénnées, France, 1858 - Bernadette Soubirous met the Madonna several times in a grotto. (2009-1858) * 0,366 = 55,266 = PEB #56 with line 12:

takes down from bathroom wall
Lourdes, Hautes Pyrénnées, France

Mirror poemn is 367-56 = #311:

A silhouette, all black, he is
    bernadette   soubirous

The order is turned - with the name of the visionary in the mirror part. Could be the reason for the grotto? The Madonna was partly in a grotto also in the next. If the grotto is the 'bathroom' of PEB #56, there is a clear semantic interpretation present.

Example 5: The Madonna of Laus, France, 1664 - Benoite Rencurel met the Madonna in 1664: (2009-1664) * 0,366 = 126,27 = #127 with line 12:

when do I wept
  ben   oite renc-urel

Mirror poem is 367-127 = #240 - a more difficult - line 12:

Their feet are heavy, and their minds are, too
Dauphine   Vallée de Kiln   Parfume de Laus ???
wept - Saint Maurice - panis cibarius etc

The story of Rencurel has many defining indexes and includes several movements for meeting the Madonna. If movements by walking causing 'heavy feet' on basis of worries = 'heavy minds' is the story, then the reference is highly 'semantical'. This example is not immediately transparent - even if the name of the visionary seems easy to recognize.

Example 6: The Madonna of Guadalupe, Tepeyac Hill, Mexico City 1531 - Juan Diego & uncle (Juan Bernardino) in a story of the uncle's disease and sudden healing ending in the imprint of Madonna's icon inside the cloak of Juan. (2009-1531) * 0,366 = 174,948 = PEB #175:

and the waves with their ups and their downs
  Mexico City,   Guadalupe, hill     Tepeyac

Mirror poem is 367-175 = #192:

These digits of a girl
juan diego & uncle

Here the place indexes seem obscure but the name of the visionary seems quite clear - but it is in the mirror point - and indeed the most sensational aspect of the story is in the imprint of the Madonna's icon inside the cloak - like inside a grotto.

A window?

The discussion of three simultaneous discoveries in mathematics showed that they distribute mirror-symmetrically across the series of PEB 1-366. The example with Newton and the gristmill was very suggestive - enough to raise the question: Would there be an apple falling in or on his head somewhere - a mythos element which is of very strong force relative to Newton? It is perhaps found in a 'window' that arises from computing the mirror symmetries in both halves of the 1-366: When Newton's name is in #120 and Leibniz and gristmill in #247, one finds the two other points by 184-120 = #64 and 367-64 = #303 - here by line 14: #303 = all suddenly, #64 = It's 5022 Firenze. Could be these conspire on 'falls the apple in his head' - but it is the only convincing example I have found. For Bolyai and Lobachevsky the two new line 14 cases are: #119 = by Sanguinor & Simble, #248 = in regional cassettes. For Grassmann and Hamilton, the two new line 14 cases would be #244 = when he says: 'But I don't have small', #123 = the compilation of the martyrs of the kirk.

The resurrection dogma

The conclusiom to these examples is that the systematic semantic-phonological relation between the point and the mirror point seems to be most acuts in line 14 and less acute in line 12 - and one can postulate that it gets more opaque the further down in the lines one comes. For line 4 it seems that the principle is not the mirror point but a coordinate system around an origo that makes the names of the governments in France, England, Belgium and Spain distribute on line 4 in poems with 90, 180 and 270 degrees turn in the circle of 366 poems.

However that be, one can guess that line 12 still is quite close to line 14 in many respects - which means that the point and its mirror point in the millenial span are closely related epistemologically.

The 'origo' of my book is in its year of writing which is 2009 with millenial cycles - which suggests that the year 9 will be the turning point around the time of Christ. If Jesus were, say, 34 years at the age of his death and following resurrection, and if year 9 is the turning point, the other end of the millenial mirror will be 16 BC (or 1984 in the present era) - and hence it could be the year of birth of Mary the mother of Jesus who then would be 16 at the time of his birth. This will make for the catholic conception of a close and systematic union of the two - by the idea that the knowledge is locked down in the coffin at year 34 and the resurrection takes place very soon thereafter in the other end of the 'blue' millenium - that is in year 16 BC with the announcement by Gabriel of the birth of Jesus - which means that the resurrection means a 'simultaneous discovery' a la Bolyai and Lobatchevsky with names on the millenial scale. It is of course possible also that Gabriel arrived at the time of Mary's puberty - in which case Jesus would have been a little younger at the time of his death.

The interesting corollary to this theory is that it sheds some light on the controversy of protestantism (such as anglicanism) and catholicism in the sense of a possible 'fear of catholic secularization' nourished by protestantism when they saw this 'lid of scientific scholarship' rising in the idea that the resurrection of Jesus could have come to mean not much more more than a skeleton format of the birth of his mother Mary - in the sense that if history in a very general sense of it repeats itself within a cycle of 1000 years - and if religious matters seem to appear also in the mirror fields of this cycle, a Madonna apparition (as in a mirror) could be taken to mean her birth in history and as such be 'the same' as the resurrection of her son Jesus. Could be 'transubstantiation' of flesh could be needed.

It could have been this idea which sparked the alarm and gave rise to protestantism who did not want to see the resurrection reduced to a mere shadow or reflection in a mirror. Protestantism would then hide behind reflections on the opposite of what they really meant - that catholicism was too shrouded in mysticism and fragrant smoke and therefore M.Luther threw his ink bottle after the shadow of Satan and turned to a study of the scriptures instead.

Modern terrorism could be an attempt to get the shadows down to earth.

If the protestant problem is that the secularization consists in true eternity being converted into an asymp-totic approximation via a chain of millenia, the liquidation of Jesus - who had come out from the grotto of the 'Weib' or womb of Mary - would find its erroneous interpretation in the idea of a 'wipe-out' strategy (such as the holocaust) for demonstrating the failure (qua secularization) of the blue-metre philosophy. However, it may well be that this trick consists in a transubstantiation contained in a 'chain of liquidation' - that is, the joints of the chain (like nails in the palms of Jesus) turned apparently liquid. It may have been this trick which Adam and Eve tried with the apple in paradise - a 'failure' that was. (Jesus conceived of himself as the vine and the disciples as the grapes - but these grapes would then not form a chain). Ideas of a 'Black Sea Loop' (a chain of liquidation running from the Van See in Turkey around the Black Sea towards Paris - the eastern arm of the european swastika) would then find its rationale in the protestant wish to demonstrate the failure of catholic 'secularization' via the blue metre - that is, to prove that application of the blue metre logic means the same as a throw-out from paradise. However, it is easy to see that this is but the reaction to new knowledge - a reaction which could have been prompted by the fear of seeing the hopes of resurrection reduced to a mere asymptotic approximation.

The opening of the 'lid' with some resurrection theory thereon could have come to constitute the format of related political theories.

Humans are often fragile as far as truth is concerned, and it may perhaps be a relevant question whether non-euclidean geometry was sufficiently attractive for the mathematically concerned around 1830 to call for Lobachevsky as the one and only 'simultaneous discoverer' along with Bolyai. Lobachevsky, who was recognized only after his death as the co-founder of the new mathematics along with Bolyai, was rector at the mathematical faculty of Kazan when Ilja Uljanow, the father of Lenin, studied there. If 'resurrection in the flesh' is the story, then the mythos of Transylvania and Dracula and all that could have its origin there.

It should not be necessary to get St.Peter's Cathedral in the Vatican 'down to earth'. A war against Italy should not be necessary.


The examples discussed here suggest that there exists a logic of not only semantic but also phonological form in the collective historic consciousness with a memory span of 1000 years. One can guess from the examples that the exactitude gets more and more acute the closer one comes to line 14.

But this would mean that History would have reserved the discovery and understanding of a new field of mathematics to persons with suitable indexes and geographic locations. This of course have imposed very strong and 'biased' constraints onto the development of human knowledge history - and on the development of knowledge generally.

It is this binding to the progress of history confined in the blue metre which now - with these discoveries in the field of the blue metre - can be dissolved and the progress of knowledge can speed up without this 'confinement' control. It is not necessary to make confinements in catholic Italy for the development of, say, anglophonic interpretations.

The finite metres are measures on the limitations contained in the human semiotic contitution when bridging from one reality to the other. The blue metre (being a formal and hence limited aspect of knowledge) is likely to postulate the theory that the human constitution interprets the bridge from one reality to the other in terms of a millenial span - such that the interlocking or cogwheeling of two realities with each other makes for a co-occurrence of similarities every 1000 years - that is, this is how the human constitution measures out the sameness of the two realities - interpreted also by Jesus in his double-role of God and human being in the same body - and hence also his divine posthuman existence being 'the same' as the birth of his earthen mother - in the blue metre. History is likely to be a function of such an aspect of the human constitution.

How was it possible to write the PEB - with such apparently amazing precision in the phonology of the lines? That was possible after the poet had climbed the mount of poetic enlightenment in the 11 years of writing (1997-2008) of the non-metric TEQ. It is mystic poetry.

The poet adds the comment that even if some or most of the poems in the PEB could look a little 'strange' compared with normal poetry, that should not be a reason for labelling it 'not goodenough' for publication. There is much scholarly study that can be done on basis of it and therefore the book should be published.

A pity the poet is still subjected to much apparent 'monkey business', not the least apparently from the public advertisement business of Vienna, in particular on background of the value for the developmental potential for the society contained in the study of line 1. The value of the poet's work should of course be in the form of serious study, not for enhancing sales or for political control, which also means that the poet's work should be published. It is interesting to observe that 'monkey business' concerned with line 1 could be a counterpoint to the 'monkey business' of line 14 - and that is when it should be possible to get the phenomenon under control in a positive sense of it. The poet hopes to get back some poetry notebooks that disappeared in the summer 2019. It is important to understand that the problems can be solved by way of the poetry - and that the poetry notebooks must not be conceived as words in the grotto of the Madonna from the angel Gabriel for a new millenium.

The PEB does not mean a secularization or reduction of religious mystic knowledge - I would say it is rather the opposite.


Eves, H.: "An introduction to the history of mathematics". Harcourt, Brace, Jovanovich 1992.

© John Bjarne Grover
On the web 23 november 2019