Some years ago I
published this post about document 046665 in House of Leaves (HOL), by Mark Z. Danielewski (MZD).
It shows two envelopes, and it seems they are disposed to fit into a golden rectangle (the width of a golden rectangle is its length multiplied by .618).
Just under this white golden rectangle is carefully written Even today the Kitawans view the spiral of the Nautilus pompilius as the ultimate symbol of perfection.
This is nearly the text of footnote 382, which precises the Kitawans of the South Pacific. It comes from a book in which it is stated this feeling is an unconscious perception of the properties of the golden ratio.
Johnny Truant, who studies the story of the house, has drawn a map of it on the little envelope. It seems to be a square (but it's never told what is the length of the house). A totally new feature is that the width of 32' 9 3/4" is said to be equivalent to 20 cubits.
The word cubit
never appears in the text, in which there's no hint to another standard of measurement.
Why should the House be 20 cubits wide? There is a famous place which is a cube of 20x20x20 cubits, and that's the HOLy of HOLies, the most sacred part of the House of YHWH, the Temple built by David's son, Solomon.
As says Navidson:
Jewish exegesis has seen a proof of the almightiness of God in these 20 cubits, as the Holy of Holies contains the Ark of Covenant. The Talmud asserts, “The space of the ark is not measured.” (Yoma 21a).
From each wall of the chamber to each side of the ark was 10 cubits. The ark itself measured 2½ cubits by 1½ cubits. Yet from one wall to the other measured not 22½, but exactly 20 cubits. The ark both occupied space and did not occupy space.
This was remarked on the forum, but the given link is not good now, here is another one (look for 'Space and Non-Space').
This same page links the miracle of the 20 cubits to the dream of Jacob at Bethel (meaning 'House of God'), and quotes Genesis 28,17, also given in footnote 153 of HOL:
393 3/4"/20 = X "
(393.75/20 = X ")
then X = 19.6875"
Why? As I'm French I searched how many centimeters it was. One inch is exactly 2.54 centimeters, and the conversion gives
19.6875 * 2.54 = 50.00625 cm,
so the cubit is almost exactly 50 cm, and the outside width of the house should be 1000 cm, 10 meters, or 10.00125 if Navidson's measurement was perfect, but I guess MZD could not give a better precision in order to make a cubit equal to exactly 50 cm.
Why? First this 'Why ?' after the final measure of the cubit could hint again to the House of YHWH. Hebrew is written from right to left, YHWH is often reduced to YHW which is then written 'WHY'.
Being French helped a lot for the next step, and MZD lived several years in France.
In 1985 a little abbey in Provence published the Cahier de Boscodon 4, a roneoted manuscript which the abbey claims to have sold 60,000 copies.
It's about L'art des bâtisseurs romans, 'The art of the Romanesque builders', and the golden ratio. Its main feature is that Le Corbusier borrowed his Modulor, an anthropometric scale of proportions based on the golden ratio, from an esoteric model existing at least in the Middle Age, and maybe far before, the 'quine des bâtisseurs', a set of five measures ruled by the golden ratio and the human body.
Some tables might seem accurate, with a lot of measures (in cm) that look like results of a scholarly study.
Yet is it serious that these measures have for standard the diameter of a barley grain, with a precision of one thousandth of millimeter?
Actually all numbers are imaginary, except the pied, 'foot', of 32.48 cm, which is known as 'pied de Charlemagne', but of course it was not 144 times the ligne, 'line' of .22558 cm, and the other measures multiplying this line by numbers of the Fibonacci sequence are just fake.
But this was not enough, and the monk at the origin of this, Jean Bétous, imagined the 'standard of the insiders' of .2247 cm. This leads to the five measures of the quine, paume-palme-empan-pied-coudée, 'palm-hand-span-foot-cubit'.
Another table allows to understand what was in his mind:
The measures are 20 times the golden sequence based on φ, the only sequence which is both an additive sequence and a geometric progression (the ratio of which being φ).
The middle unit, the empan, the hand-span, is exactly 20.00 cm, hundreds of years before the metric system.
This looks quite silly, yet it was taken seriously by many readers, reprinted in other books, even school manuals...
An example on this site, which gives a link to upload the Cahier de Boscodon. There is a French Wikipedia page, but it presents the theory as doubtful.
The above table starts with the palm, 20 times .382. It might be meaningful the most suggestive hint to the golden ratio in HOL is footnote 382, about the Nautilus shell. The Cahier de Boscodon also mentions this shell. It's interesting to compare this handwritten Nautilus pompilius with the one Truant (more likely MZD) wrote under a golden rectangle.
Another strong clue showing MZD's knowledge of the 'quine' is a fictitious book about the Navidson house, Concatenating Corbusier, by Aristides Quine (footnote 150). Quine is not an usual word in French for a set of five, the usual word is quinte, and the association of 'quine' and Corbusier is stronly evocative.
So the biggest unit of the quine is the coudée, the cubit, measuring 52.36 cm. If 10 meters would be exactly 50 spans of 20 cm in Boscodon system, MZD could have preferred 20 cubits of 50 cm, in order to fit the 20 cubits of the Holy of Holies.
The Cahier de Boscodon studies several historical monuments, including the Temple of Solomon:
The Holy of Holies is a square, and the other part of the Temple is a double square, the figure used to build the golden ratio, as the diagonal of a double square of width one is the square root of five.
The freedom taken with the cubit becoming 50 cm seems to show MZD does not have any respect towards the Boscodon quine, so what could all this mean?
Besides many fake claims about the golden ratio being a standard of harmony in art and nature, it's a real question of interest, and a good approach can be found on Ron Knott's site.
A friend of mine developed a tool calculating the values of words and phrases according to various systems of gematria, the most simple being ordinal gematria, from A=1 to Z=26.
As I'm interested by the golden ratio, a feature of the Gematron is to give the approximate golden sections of the input text, so
MARK Z DANIELEWSKI = 43 + 26 + 112 = 181
The output shows a big 69 after Z, it means that the total 181 has for optimal golden sharing 112-69.
The interesting thing is that the optimal golden sharing of 112 is 69-43, so the three elements of MZD's name form a 'quine', a set of five numbers belonging to an additive sequence:
1-8-9-17-26-43-69-112-181-...
This sequence is OEIS 22098 on the OEIS, On-line Encyclopedia of Integer Sequences.
I recall the fictitious book of footnote 150, Concatenating Corbusier, by Aristides Quine. Le Corbusier created his system Modulor in 1946.
It's based on the height of a man, and he hesitated about what should be the ideal measure. Although he used the metric system, and first chose 1.75 meter, 175 cm (his own height), his final choice was 183 cm, probably because it was 6 feet, 72 inches, 144 half-inches, 144 being a number of the Fibonacci sequence.
So the measures of his system could be expressed by Fibonacci numbers, and, as an only sequence was not sufficient, he created two sequences, each based on 5 main measures:
- Red sequence, 21-34-55-89-144 half inches;
- Blue sequence, 21-34-55-89-144 inches.
As he was speaking French, the measures in his book Le Modulor are approximations in the metric system, 27-43-70-113-183 cm for the Red sequence.
It's quite impressive to compare with the 'MZD quine':
This could suggest a strong ego of MZD, and actually MZD put his name by different ways in HOL. So readers found acrostics formed by the first letters of the footnotes.
There are 452 footnotes to the Navidson Record, the main part of HOL, and the first letters of the 5 first chapters are
ASOTILAiM
INITDSSMILDAAS
BDR MARKZ
DANIELEWSKI NF Z
DANIELEWSKI TNOWLFJHTTWSKYFPTMYTFSCBSNZSAnT
This is obviously not by chance, and I remark the chapters introduce cuts between MARKZ and DANIELEWSKI, then between Z and DANIELEWSKI.
There are only 2 footnotes in the last chapter:
The acrostic here is only MD, but Z can be found in the title Z (on public booksignings, MZD signs with just a Z).
The last footnote shows that all footnotes are not introduced by numbers.
All the acrostic is here. Four footnotes are empty, just lines of _. So there is 452 notes, but 448 with a possible meaning, whatever it is; these are four times 113 and 112, the 'navels' in Corbusier's and MZD's quines?
There are 26 footnotes before the beginning of the acrostic MARKZ DANIELEWSKI. Some readers proposed various anagrams, not quite convincing, but a fact is the ratio vowels/consonants (10/16) allows anagrams.
I suggest 26 is the rank of letter Z.
There are 16 letters in the author's full name, of which 6 are vowels. 6-10 and 10-16 are golden sharings of 16 and 26, simplifying in 3-5 and 5-8, consecutive terms of the Fibonacci sequence. Next term of this sequence 6-10-16-26 is 42, and there are 42 footnotes to chapter 5, the one beginning with DANIELEWSKI, so we find in the first 4 chapters
26 letters + 16 letters of the author's full name, + NFZ, and next
11 letters DANIELEWSKI + 31 letters = 42 = 26 + 16. Only 4 vowels among the 31 letters.
So the total value 181 shares following the golden ratio into 69-112. To this sharing correspond 5-11 letters, and it's astonishing that
181 centimeters convert into 5' 11" (and 1/4 inch!).
More, an additive sequence starting with 5-11-16 continues with
27-43-69-113-183, the approximations of Corbusier's quine (OEIS 22136).
This becomes quite silly. It seems obvious that Tad Z. Danielewski did not call his son Mark in order to built a gematric quine, yet MZD might have found it by himself. I feel pretty sure that the cubit of exactly 50 cm is an important clue, and the conversion of 181 cm to feet and inches could be in the same mood.
Yet coincidences do exist, and there is one concerning the Modulor and its creator. Le Corbusier chose measures that could be expressed in inches, but he gave a tribute to the metric system with two measures that are exact, 113 and 226 cm. The tool used by architects using his system is a ribbon of exactly 226 cm, graduated in centimeters and inches.
It happens that Le Corbusier's real name is
Charles-Edouard Jeanneret = 226.
There are many acrostics in HOL, and many other tricks. The 24 pages of Codes for Dummies can give an idea...
Here I try to propose new things, and I insist on the fact that footnote 35 sends to document 046665:
The I beginning footnote 35 is the I of MARKZ DANIELEWSKI, sum 181; the envelope shows the width of the house should be 20 cubits, and
TWENTY CUBITS = 107 + 74 = 181.
The Holy of Holies is called the Oracle in KJB, and here is verse 1 King,6,20:
LENGTH + BREADTH + HEIGHT = 66+58+57 = 181, and HOL can suggest
FOUR DIMENSIONS = 60 + 121 = 181.
181 in letters gives
ONE HUNDRED EIGHTY ONE = 34+74+74+34,
another kind of palindrome. The sum 216 evokes again the Holy of Holies, Qodesh haQodashim, that has another name in Hebrew, debir, דְּבִיר, a word which has the value 216 in the traditional Hebrew system.
216 is the cube of 6, 6.6.6, the debir is a cube of side 20 cubits, and the value in Hebrew of twenty cubits (181 in English), 'esrim amah, עשׂרים אמה, is 666.
I recall footnote 35 using the I of MARKZDANIELEWSKI, and 181+35=216.
Le Corbusier first thought of an average height of 175 cm for the man Modulor. This placed the navel at 108 cm, and the arm raised at 216 cm.
---
If HOL is a harsch reading, what is the word for OR, Only Revolutions? Especially when you're French.
I concentrated on the acrostics of the 45 sections in the two narratives. The Gématron reveals an ideal golden cut after 7 words and 27 letters:
SAM AND HAILEY AND SAM AND HAILEY = 243
AND SAM AND HAILEY AND = 150
Looking further, this comes from 2 golden blocks:
AND-AND-AND = 57, 3 words and 9 letters;
SAM-HAILEY = 97, 2 words and 9 letters.
This allows to build:
AND-AND-AND: 3 words, 9 letters, value 57;
SAM-HAILEY: 2 words, 9 letters, value 93;
SAM-HAILEY AND-AND-AND: 5 words, 18 letters, value 150;
SAM-HAILEY AND-AND-AND SAM-HAILEY: 7 words, 27 letters, value 243;
SAM-HAILEY AND-AND-AND SAM-HAILEY AND-AND-AND SAM-HAILEY,
a rearrangement of the 12 words and 45 letters of the whole acrostic, value 393.
The two blocks could build an infinite golden sequence. If it's not true with the actual acrostic, two other steps might occur, adding 7 words, then 12:
SAM AND HAILEY AND SAM AND HAILEY = 243
AND SAM AND HAILEY AND SAM AND HAILEY AND SAM AND HAILEY = 393
The two blocks system leads to
3-2-5-7-12 words, the beginning of sequence OEIS 1060;
57-93-150-243-393 for the values of these words, that correspond to 3 times
19-31-50-81-131, the continuation of
3-2-5-7-12 (3 is there the term 0 of sequence OEIS 1060);
45 letters for the whole acrostic, and 45 is the sum of the first five terms of this sequence, 2-5-7-12-19.
I notice 45 is too the value of DANIEL.
The golden cut for the actual acrostic is after 27 letters, corresponding to 216 pages. I recall it's the Hebrew gematria of debir, Holy of Holies. 27/45 or 216/360 is again 3/5, the ratio of the Ark and MZD's birthday.
The arithmetic of additive sequences is addictive. If we add the number of words to their values, for example 3+57=60, we get
60-95-155-250-405, 5 times
12-19-31-50-81, still sequence OEIS 1060, and this is due to a general law of additive sequences:
5 A(n) = A(n-4) + 3 A(n+1).
The egality
SAM AND HAILEY = 33+19+60 = 112 = DANIELEWSKI
is too linked to the properties of additive sequences.
Prime additive sequences (i.e. sequences in which 2 consecutives terms have no common divisor) are linked 2 by 2. If we add a term A(n) to the term A(n+2), you obtain either a term of the conjugate sequence, either 5 times a term of the conjugate sequence.
The two most known sequences are so linked: the Lucas sequence (1-3-4-7-11-...) is conjugated with the Fibonacci sequence (1-1-2-3-5-...).
And the MZD sequence (1-8-9-17-26-...) is linked with OEIS 1060 (2-5-7-12-19-...), as 2+7=9, 5+12=19, and so on.
The egality above
SAM AND HAILEY = 33+19+60 = 112 = DANIELEWSKI
is a consequence of a general property of additive sequences:
A(n) + 3A(n+1) is a term of the conjugate sequence (here 19+3*31).
This becomes quite silly, but why 20 cubits? why Aristides Quine concatenating Corbusier? Why Viabibonacci (a character in OR)?
Is there a link between the width of the house, 393 3/4", and the value of the acrostic, 393?
Between footnote 150 (Aristides Quine) and number 150 in the acrostic quine 57-93-150-243-393?
Between the cubit of 50 cm and OEIS 1060 (19-31-50-81-131)?
The conjugate sequences (2-5-7-12-19-...) and (1-8-9-17-26-...) have interestng properties. One is linked to number five as each term of the first one is the sum of 5 consecutives terms of the Fibonacci sequence. So is the other, but with the Lucas sequence.
OEIS 1060 is known too as Evangelist sequence. It was used by composer Sofia Gubaidulina, notably in the oratorio Alleluia. From time 1:40 can be heard successive crescendos of 5-7-12-19 notes:
There are numerous examples of golden ratio in literature, claimed or not. John Barth claimed to have used it in his novels Chimera and Letters.
There are many examples too in cinema, up to 1925 and Eisenstein's Battleship Potemkin, made of five episodes, five being much associated with the golden ratio. There is an intended important event at the phi-point of each episode, and the climax of the film is at the end of the 3th one, when the red banner is hoisted on the mast. In this b&w movie, the red color was painted on the photographic film.
I cannot read OR. All I've been able to do is to check the numbers of
words of some of its 360 pages. I found each time 360, 90 in each
sector.
There is a certain logic for this number 360, the degrees of the circle, letter O, revOlutions, but could it be something else? Actually, counting the two pages with a big S and a big H, introducing the two narratives, there are 362 pages, 2 times 181, MARKZ DANIELEWSKI.
Numbers are counted as words, and each page is foliated with 2 numbers of page, so there are 181 words to read in one way, and 181 upside down.
The numbers of page add up to 361, of which middle point is 181.
The title has 15 letters centered on a O, 15th letter. On the cover of the paperback edition, little | | are inserted in this middle O, maybe showing the middle and the two readings, and maybe suggesting to add 2 to the 360° of the O...
The value of the two words are
ONLY REVOLUTIONS = 66 + 170 = 236.
Without the 3 O's, printed in another color in the first edition, we find
236 - 45 = 191.
236/191 is what French painter Sérusier called double coupe d'or, 'double golden cut'.
Because 191 is the half of 382, a term of the golden sequence
236-382-618-1000-1618 (OEIS 22367)
already seen with footnote 382 and Boscodon quine.
Shall I add that
A NOVEL = MARK Z = 69,
a number that remains unchanged upside down.
The total value of the 15+16+6 letters of the circle is
236+181+69 = 486, two times 243, the golden cut of the 45-letter acrostic, and there is an acrostic in each narrative, SAM AND HAILEY..., and HAILEY AND SAM...
45 and 191 are terms of the prime additive sequence 22095,
1-5-6-11-17-28-45-73-118-191-...
and 236 is again the result of a general law,
A(n) + A(n+3) = 2A(n+2) or 45+191 = 2*118 = 236.
As I said, additive sequences are easily driving mad, so I stop here, but there is probably much more to find.
The big envelope is a double golden rectangle.
The white rectangle using the tip of the slap is again a golden rectangle.Just under this white golden rectangle is carefully written Even today the Kitawans view the spiral of the Nautilus pompilius as the ultimate symbol of perfection.
This is nearly the text of footnote 382, which precises the Kitawans of the South Pacific. It comes from a book in which it is stated this feeling is an unconscious perception of the properties of the golden ratio.
Johnny Truant, who studies the story of the house, has drawn a map of it on the little envelope. It seems to be a square (but it's never told what is the length of the house). A totally new feature is that the width of 32' 9 3/4" is said to be equivalent to 20 cubits.
Why should the House be 20 cubits wide? There is a famous place which is a cube of 20x20x20 cubits, and that's the HOLy of HOLies, the most sacred part of the House of YHWH, the Temple built by David's son, Solomon.
As says Navidson:
Our house is not a house of God, the house is God.On page 333 of HOL is “The Hol[ ]y Tape”.
Jewish exegesis has seen a proof of the almightiness of God in these 20 cubits, as the Holy of Holies contains the Ark of Covenant. The Talmud asserts, “The space of the ark is not measured.” (Yoma 21a).
This was remarked on the forum, but the given link is not good now, here is another one (look for 'Space and Non-Space').
This same page links the miracle of the 20 cubits to the dream of Jacob at Bethel (meaning 'House of God'), and quotes Genesis 28,17, also given in footnote 153 of HOL:
“How dreadful is this place! this is none other but the house of God, and this is the gate of heaven.”
When Mark is represented by the only initial M., letters ARK are hidden... It has been noted that the Ark, 2½ cubits by 1½ cubits, has a ratio of 3/5, near a golden rectangle. Mark is born on a 3/5.
It might be a hint to the Ark of covenant in footnote 82, page 77, in which Truant speaks about cats on the prowl:
Noah’s ark is mentioned in footnote 134, in which it's suggested as the antithesis of labyrinth, and in footnote 249, with the statement there's no Noah’s ark in the Navidson labyrinth.
The little envelope shows too Johnny calculating the cubit in inches, starting with 32' 9 3/4"= 393 3/4".
It might be a hint to the Ark of covenant in footnote 82, page 77, in which Truant speaks about cats on the prowl:
a covenant of light, ark for the instant,Footnote 166 mentions Raiders of the Lost Ark.
Noah’s ark is mentioned in footnote 134, in which it's suggested as the antithesis of labyrinth, and in footnote 249, with the statement there's no Noah’s ark in the Navidson labyrinth.
The little envelope shows too Johnny calculating the cubit in inches, starting with 32' 9 3/4"= 393 3/4".
(393.75/20 = X ")
then X = 19.6875"
Why? As I'm French I searched how many centimeters it was. One inch is exactly 2.54 centimeters, and the conversion gives
19.6875 * 2.54 = 50.00625 cm,
so the cubit is almost exactly 50 cm, and the outside width of the house should be 1000 cm, 10 meters, or 10.00125 if Navidson's measurement was perfect, but I guess MZD could not give a better precision in order to make a cubit equal to exactly 50 cm.
Being French helped a lot for the next step, and MZD lived several years in France.
In 1985 a little abbey in Provence published the Cahier de Boscodon 4, a roneoted manuscript which the abbey claims to have sold 60,000 copies.
It's about L'art des bâtisseurs romans, 'The art of the Romanesque builders', and the golden ratio. Its main feature is that Le Corbusier borrowed his Modulor, an anthropometric scale of proportions based on the golden ratio, from an esoteric model existing at least in the Middle Age, and maybe far before, the 'quine des bâtisseurs', a set of five measures ruled by the golden ratio and the human body.
Some tables might seem accurate, with a lot of measures (in cm) that look like results of a scholarly study.
Yet is it serious that these measures have for standard the diameter of a barley grain, with a precision of one thousandth of millimeter?
Actually all numbers are imaginary, except the pied, 'foot', of 32.48 cm, which is known as 'pied de Charlemagne', but of course it was not 144 times the ligne, 'line' of .22558 cm, and the other measures multiplying this line by numbers of the Fibonacci sequence are just fake.
But this was not enough, and the monk at the origin of this, Jean Bétous, imagined the 'standard of the insiders' of .2247 cm. This leads to the five measures of the quine, paume-palme-empan-pied-coudée, 'palm-hand-span-foot-cubit'.
Another table allows to understand what was in his mind:
The measures are 20 times the golden sequence based on φ, the only sequence which is both an additive sequence and a geometric progression (the ratio of which being φ).
The middle unit, the empan, the hand-span, is exactly 20.00 cm, hundreds of years before the metric system.
This looks quite silly, yet it was taken seriously by many readers, reprinted in other books, even school manuals...
An example on this site, which gives a link to upload the Cahier de Boscodon. There is a French Wikipedia page, but it presents the theory as doubtful.
The above table starts with the palm, 20 times .382. It might be meaningful the most suggestive hint to the golden ratio in HOL is footnote 382, about the Nautilus shell. The Cahier de Boscodon also mentions this shell. It's interesting to compare this handwritten Nautilus pompilius with the one Truant (more likely MZD) wrote under a golden rectangle.
Another strong clue showing MZD's knowledge of the 'quine' is a fictitious book about the Navidson house, Concatenating Corbusier, by Aristides Quine (footnote 150). Quine is not an usual word in French for a set of five, the usual word is quinte, and the association of 'quine' and Corbusier is stronly evocative.
So the biggest unit of the quine is the coudée, the cubit, measuring 52.36 cm. If 10 meters would be exactly 50 spans of 20 cm in Boscodon system, MZD could have preferred 20 cubits of 50 cm, in order to fit the 20 cubits of the Holy of Holies.
The Cahier de Boscodon studies several historical monuments, including the Temple of Solomon:
The Holy of Holies is a square, and the other part of the Temple is a double square, the figure used to build the golden ratio, as the diagonal of a double square of width one is the square root of five.
The freedom taken with the cubit becoming 50 cm seems to show MZD does not have any respect towards the Boscodon quine, so what could all this mean?
Besides many fake claims about the golden ratio being a standard of harmony in art and nature, it's a real question of interest, and a good approach can be found on Ron Knott's site.
A friend of mine developed a tool calculating the values of words and phrases according to various systems of gematria, the most simple being ordinal gematria, from A=1 to Z=26.
As I'm interested by the golden ratio, a feature of the Gematron is to give the approximate golden sections of the input text, so
MARK Z DANIELEWSKI = 43 + 26 + 112 = 181
The output shows a big 69 after Z, it means that the total 181 has for optimal golden sharing 112-69.
The interesting thing is that the optimal golden sharing of 112 is 69-43, so the three elements of MZD's name form a 'quine', a set of five numbers belonging to an additive sequence:
1-8-9-17-26-43-69-112-181-...
This sequence is OEIS 22098 on the OEIS, On-line Encyclopedia of Integer Sequences.
I recall the fictitious book of footnote 150, Concatenating Corbusier, by Aristides Quine. Le Corbusier created his system Modulor in 1946.
It's based on the height of a man, and he hesitated about what should be the ideal measure. Although he used the metric system, and first chose 1.75 meter, 175 cm (his own height), his final choice was 183 cm, probably because it was 6 feet, 72 inches, 144 half-inches, 144 being a number of the Fibonacci sequence.
So the measures of his system could be expressed by Fibonacci numbers, and, as an only sequence was not sufficient, he created two sequences, each based on 5 main measures:
- Red sequence, 21-34-55-89-144 half inches;
- Blue sequence, 21-34-55-89-144 inches.
As he was speaking French, the measures in his book Le Modulor are approximations in the metric system, 27-43-70-113-183 cm for the Red sequence.
It's quite impressive to compare with the 'MZD quine':
MARKZDANIELEWSKI = 181 183
DANIELEWSKI = 112 113
MARKZ = 69 70
MARK = 43 43
Z = 26 27
DANIELEWSKI = 112 113
MARKZ = 69 70
MARK = 43 43
Z = 26 27
This could suggest a strong ego of MZD, and actually MZD put his name by different ways in HOL. So readers found acrostics formed by the first letters of the footnotes.
There are 452 footnotes to the Navidson Record, the main part of HOL, and the first letters of the 5 first chapters are
ASOTILAiM
INITDSSMILDAAS
BDR MARKZ
DANIELEWSKI NF Z
DANIELEWSKI TNOWLFJHTTWSKYFPTMYTFSCBSNZSAnT
This is obviously not by chance, and I remark the chapters introduce cuts between MARKZ and DANIELEWSKI, then between Z and DANIELEWSKI.
There are only 2 footnotes in the last chapter:
427 Massel Laughton's “Comb and Brush” in Z, v. xiii, n. 4, 1994, p. 501.
Δ Daphne Kaplan's The Courage to Withstand (Hopewell, NJ, Ecco Press, 1996), p. iii.
The last footnote shows that all footnotes are not introduced by numbers.
All the acrostic is here. Four footnotes are empty, just lines of _. So there is 452 notes, but 448 with a possible meaning, whatever it is; these are four times 113 and 112, the 'navels' in Corbusier's and MZD's quines?
There are 26 footnotes before the beginning of the acrostic MARKZ DANIELEWSKI. Some readers proposed various anagrams, not quite convincing, but a fact is the ratio vowels/consonants (10/16) allows anagrams.
I suggest 26 is the rank of letter Z.
There are 16 letters in the author's full name, of which 6 are vowels. 6-10 and 10-16 are golden sharings of 16 and 26, simplifying in 3-5 and 5-8, consecutive terms of the Fibonacci sequence. Next term of this sequence 6-10-16-26 is 42, and there are 42 footnotes to chapter 5, the one beginning with DANIELEWSKI, so we find in the first 4 chapters
26 letters + 16 letters of the author's full name, + NFZ, and next
11 letters DANIELEWSKI + 31 letters = 42 = 26 + 16. Only 4 vowels among the 31 letters.
So the total value 181 shares following the golden ratio into 69-112. To this sharing correspond 5-11 letters, and it's astonishing that
181 centimeters convert into 5' 11" (and 1/4 inch!).
More, an additive sequence starting with 5-11-16 continues with
27-43-69-113-183, the approximations of Corbusier's quine (OEIS 22136).
This becomes quite silly. It seems obvious that Tad Z. Danielewski did not call his son Mark in order to built a gematric quine, yet MZD might have found it by himself. I feel pretty sure that the cubit of exactly 50 cm is an important clue, and the conversion of 181 cm to feet and inches could be in the same mood.
Yet coincidences do exist, and there is one concerning the Modulor and its creator. Le Corbusier chose measures that could be expressed in inches, but he gave a tribute to the metric system with two measures that are exact, 113 and 226 cm. The tool used by architects using his system is a ribbon of exactly 226 cm, graduated in centimeters and inches.It happens that Le Corbusier's real name is
Charles-Edouard Jeanneret = 226.
There are many acrostics in HOL, and many other tricks. The 24 pages of Codes for Dummies can give an idea...
Here I try to propose new things, and I insist on the fact that footnote 35 sends to document 046665:
35 In Appendix II-A, Mr Truant provides a sketch of this floor plan on the back of an envelope.This document is followed by 081512, which obviously must be understood 8-15-12, H-O-L, so the rank of letters is important to MZD, and maybe their sum, here 35.
The I beginning footnote 35 is the I of MARKZ DANIELEWSKI, sum 181; the envelope shows the width of the house should be 20 cubits, and
TWENTY CUBITS = 107 + 74 = 181.
The Holy of Holies is called the Oracle in KJB, and here is verse 1 King,6,20:
And the oracle in the forepart was twenty cubits in length, and twenty cubits in breadth, and twenty cubits in the height thereof.We have also
LENGTH + BREADTH + HEIGHT = 66+58+57 = 181, and HOL can suggest
FOUR DIMENSIONS = 60 + 121 = 181.
181 in letters gives
ONE HUNDRED EIGHTY ONE = 34+74+74+34,
another kind of palindrome. The sum 216 evokes again the Holy of Holies, Qodesh haQodashim, that has another name in Hebrew, debir, דְּבִיר, a word which has the value 216 in the traditional Hebrew system.
216 is the cube of 6, 6.6.6, the debir is a cube of side 20 cubits, and the value in Hebrew of twenty cubits (181 in English), 'esrim amah, עשׂרים אמה, is 666.
I recall footnote 35 using the I of MARKZDANIELEWSKI, and 181+35=216.
Le Corbusier first thought of an average height of 175 cm for the man Modulor. This placed the navel at 108 cm, and the arm raised at 216 cm.---
If HOL is a harsch reading, what is the word for OR, Only Revolutions? Especially when you're French.
I concentrated on the acrostics of the 45 sections in the two narratives. The Gématron reveals an ideal golden cut after 7 words and 27 letters:
SAM AND HAILEY AND SAM AND HAILEY = 243
AND SAM AND HAILEY AND = 150
Looking further, this comes from 2 golden blocks:
AND-AND-AND = 57, 3 words and 9 letters;
SAM-HAILEY = 97, 2 words and 9 letters.
This allows to build:
AND-AND-AND: 3 words, 9 letters, value 57;
SAM-HAILEY: 2 words, 9 letters, value 93;
SAM-HAILEY AND-AND-AND: 5 words, 18 letters, value 150;
SAM-HAILEY AND-AND-AND SAM-HAILEY: 7 words, 27 letters, value 243;
SAM-HAILEY AND-AND-AND SAM-HAILEY AND-AND-AND SAM-HAILEY,
a rearrangement of the 12 words and 45 letters of the whole acrostic, value 393.
The two blocks could build an infinite golden sequence. If it's not true with the actual acrostic, two other steps might occur, adding 7 words, then 12:
SAM AND HAILEY AND SAM AND HAILEY = 243
AND SAM AND HAILEY AND SAM AND HAILEY AND SAM AND HAILEY = 393
The two blocks system leads to
3-2-5-7-12 words, the beginning of sequence OEIS 1060;
57-93-150-243-393 for the values of these words, that correspond to 3 times
19-31-50-81-131, the continuation of
3-2-5-7-12 (3 is there the term 0 of sequence OEIS 1060);
45 letters for the whole acrostic, and 45 is the sum of the first five terms of this sequence, 2-5-7-12-19.
I notice 45 is too the value of DANIEL.
The golden cut for the actual acrostic is after 27 letters, corresponding to 216 pages. I recall it's the Hebrew gematria of debir, Holy of Holies. 27/45 or 216/360 is again 3/5, the ratio of the Ark and MZD's birthday.
The arithmetic of additive sequences is addictive. If we add the number of words to their values, for example 3+57=60, we get
60-95-155-250-405, 5 times
12-19-31-50-81, still sequence OEIS 1060, and this is due to a general law of additive sequences:
5 A(n) = A(n-4) + 3 A(n+1).
The egality
SAM AND HAILEY = 33+19+60 = 112 = DANIELEWSKI
is too linked to the properties of additive sequences.
Prime additive sequences (i.e. sequences in which 2 consecutives terms have no common divisor) are linked 2 by 2. If we add a term A(n) to the term A(n+2), you obtain either a term of the conjugate sequence, either 5 times a term of the conjugate sequence.
The two most known sequences are so linked: the Lucas sequence (1-3-4-7-11-...) is conjugated with the Fibonacci sequence (1-1-2-3-5-...).
And the MZD sequence (1-8-9-17-26-...) is linked with OEIS 1060 (2-5-7-12-19-...), as 2+7=9, 5+12=19, and so on.
The egality above
SAM AND HAILEY = 33+19+60 = 112 = DANIELEWSKI
is a consequence of a general property of additive sequences:
A(n) + 3A(n+1) is a term of the conjugate sequence (here 19+3*31).
This becomes quite silly, but why 20 cubits? why Aristides Quine concatenating Corbusier? Why Viabibonacci (a character in OR)?
Is there a link between the width of the house, 393 3/4", and the value of the acrostic, 393?
Between footnote 150 (Aristides Quine) and number 150 in the acrostic quine 57-93-150-243-393?
Between the cubit of 50 cm and OEIS 1060 (19-31-50-81-131)?
The conjugate sequences (2-5-7-12-19-...) and (1-8-9-17-26-...) have interestng properties. One is linked to number five as each term of the first one is the sum of 5 consecutives terms of the Fibonacci sequence. So is the other, but with the Lucas sequence.
OEIS 1060 is known too as Evangelist sequence. It was used by composer Sofia Gubaidulina, notably in the oratorio Alleluia. From time 1:40 can be heard successive crescendos of 5-7-12-19 notes:
There are numerous examples of golden ratio in literature, claimed or not. John Barth claimed to have used it in his novels Chimera and Letters.
I cannot read OR. All I've been able to do is to check the numbers of
words of some of its 360 pages. I found each time 360, 90 in each
sector. There is a certain logic for this number 360, the degrees of the circle, letter O, revOlutions, but could it be something else? Actually, counting the two pages with a big S and a big H, introducing the two narratives, there are 362 pages, 2 times 181, MARKZ DANIELEWSKI.
Numbers are counted as words, and each page is foliated with 2 numbers of page, so there are 181 words to read in one way, and 181 upside down.
The numbers of page add up to 361, of which middle point is 181.
The title has 15 letters centered on a O, 15th letter. On the cover of the paperback edition, little | | are inserted in this middle O, maybe showing the middle and the two readings, and maybe suggesting to add 2 to the 360° of the O...
The value of the two words are
Without the 3 O's, printed in another color in the first edition, we find
236 - 45 = 191.
236/191 is what French painter Sérusier called double coupe d'or, 'double golden cut'.
Because 191 is the half of 382, a term of the golden sequence
236-382-618-1000-1618 (OEIS 22367)
already seen with footnote 382 and Boscodon quine.
Shall I add that
A NOVEL = MARK Z = 69,
a number that remains unchanged upside down.
The total value of the 15+16+6 letters of the circle is
236+181+69 = 486, two times 243, the golden cut of the 45-letter acrostic, and there is an acrostic in each narrative, SAM AND HAILEY..., and HAILEY AND SAM...
45 and 191 are terms of the prime additive sequence 22095,
1-5-6-11-17-28-45-73-118-191-...
and 236 is again the result of a general law,
A(n) + A(n+3) = 2A(n+2) or 45+191 = 2*118 = 236.
As I said, additive sequences are easily driving mad, so I stop here, but there is probably much more to find.
