At the end of the movie Pi, by Darren Aronofsky (shot in 1997, aired in 1998), Max Cohen is sitting on a bench, a young girl friend comes to see him, and she starts to play the game they used to play together.
- How about 255 times 183?
  But Max can't now answer faster than the calculator, and the girl has to answer herself:
- 46665.
  She tries another question:
- How about 748 divided by 238?
  Max keeps silent, she insists:
- What's the answer?
  And these are the last words of the movie.
  Well the answer is 3.14..., a hint to the title of the movie.

  I only know of another work ending with a number which is too a code for its title. It's House of Leaves (HOL), a novel published by Mark Z. Danielewski (MZD) in 2000, but MZD already put on line the main part of it, the Navidson record, in 1997. He put it off in 1999 when he signed a publishing contract.
  The published book was given several new parts, or appendices, notably Appendix II-A, Sketches and polaroids, which consists of four numeroted documents. The last one, page 572 of the original edition, #081512, consists of 30 polaroids allegedly showing the Navidson House, but it seems they are all different houses.
  Anyhow the important thing is probably the number of the document, to be read,
08-15-12, i.e. the ranks of letters H-O-L, House of Leaves.
  On the recto side of the leaf of the book, page 571, there is document #046665.

  So I only know of two works ending with a number which is a code for the title of the work, and in both works the key number is preceded by another number, and this number is 46665 in both works.
  When I discovered that in 2007 I could hardly think it might be undeliberate, although I'm used to huge coincidences. I shared it on a MZD forum, but this didn't help much, until I learnt that the forum was hosted by a domain created in September 1999 by MZD. He had then a postal address, PO Box 46665 at PO 90046 in West Hollywood.
  I first thought that meant number 46665 was so important for MZD that he chose it for his PO Box, until I realized he couldn't have chosen the whole of it, as the first digits 46 are the prefix for PO 90046. He just could choose a free box when opening it, so this 46665 seems to have nothing to do with Aronofsky's one.
  As document #046665 consists of two postal envelopes with sketches on them, I guess MZD gave it the number he saw every day on his mail.

  So the two 46665 just before the number coding for the title of the work seem a coincidence, and the coincidences are not over.
  It has to be thought too that Pi and HOL are the first official works of young authors, born in 1969 and 1966. Both became cult works.
  If Aronofsky's Pi deals a lot with numbers, it doesn't carry any hidden message, at least that's my opinion. The director introduces in it many tricks showing his skill, one of them is to give the image the aspect ratio of a golden rectangle, 1.618:1 (IMDb is wrong giving 1.66:1). That's probably the only movie using this ratio.

  HOL is a very intricated book, and it's quite difficult for me to read it as I'm French. Yet being French might be helpful as MZD lived some years in France while working on HOL, I'll come to it in a while.
  Document #046665 gives informations that cannot be found in the text, and these informations seem to deal with the golden ratio. The slap of the big envelope was used to draw a tight labyrinth, with a great white rectangle left.
  It looks like the length of this rectangle is the golden section of the length of the slap, and the rectangle is a golden rectangle. It's not quite perfect as it's a hand drawing, and the slap is not orthogonal, and the photo might add distorsions, yet the superposition with a screenshot of Pi speaks for itself.
  I chose the scene with the girl saying 46665...

   Now let's build a golden rectangle starting from the bottom of the big envelope, and using its width. The heigth fits almost exactly with the top of the little envelope (which is not exactly parallel to the big one).
  The vertical half of this golden rectangle, the red line, fits almost exactly with the top of the big envelope. That means the vertical half of the envelope, passing by the tip of the slap, is also almost exactly a golden rectangle. Painters using the golden ratio appreciate much this format (called 'double golden cut' by French painter Sérusier).
  I drew too in yellow the golden rectangle using the tip of the slap.

  Just under the 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.
  Actually the nautilus is quoted too in Pi, when Max talks about the golden ratio and the golden spiral: Pythagoras loved this shape, for he found it in nature - a nautilus shell, rams' horns, whirlpools, tornadoes...
  Well this is not a nautilus Max is looking at, and his statements don't reflect Aronofsky's mind. Aronofsky seems to have picked up here and there doubtful esoteric stuff, and he introduces in it evident mistakes showing the credit he gives to it. That even goes to the decimals of Pi in the opening sequence which are wrong after the 8th one. This book studies the math mistakes in the movie.
  Actually, the spiral of the nautilus is not a classic golden spiral, as it is detailed here, but it's one of the most common things often associated with the golden ratio.

  It's now time to come to the main features of the works. HOL deals with Will Navidson's house. After an incident, Navidson discovers his house is one quarter of an inch wider when measured on the inside than measured on the outside. Then the house continues to grow inside, while the outside width remains the same, 32' 9 3/4". Then corridors and staircases (spiral staircases which are the occasion to quote the nautilus) appear and disappear, and people get lost while trying to explore them...

  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.
  The little envelope shows too Johnny calculating the cubit in inches, starting with 32' 9 3/4"= 393 3/4".
393 3/4"/20 = X "
(393.75/20 = X ")
then X = 19.6875"
  One inch is exactly 2.54 centimeters, and the conversion gives
19.6875 x 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 cm 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 should be the width measured in cubits, and why should a cubit be exactly 50.00 cm? This echoes to something that can hardly be known out of France, where was published in 1985 L'art des bâtisseurs romans, or Cahier de Boscodon n° 4, of which the editor claims 60,000 sells.

  There is too the alleged golden spiral of the Nautilus pompilius in this book... 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', made of five units of measurement ruled by the golden ratio and the human body.
  Although the author, a monk of a Provence abbey, doesn't give any shadow of an evidence of his claims, the book has been so well received that its assertions were reprinted in many other books, including school manuals.
 Yet the whole thing seems quite doubtful, as the five units are, expressed in centimeters, 20 times the powers of Phi, the golden ratio (1.618):
  The middle unit, the 'empan', the hand-span, is exactly 20.00 cm, hundreds of years before the metric system.
  The biggest unit is the 'coudée', the cubit, measuring 52.36 cm. If 10 meters would be exactly 50 spans of 20 cm in this system, I'll try to explain why MZD could have preferred 20 cubits of 50 cm.
  There is a strong clue showing his knowledge of the 'quine' with an imaginary book about the Navidson house, Concatenating Le Corbusier, by Aristides Quine (footnote 150).

  It has now to be thought that 20 cubits is known to have been the width of Solomon's Temple, and especially of its most sacred part, the HOLy of HOLies, which was 20 cubits in length, breadth, and height.
  Several clues might support the idea Navidson's house has much to do with Solomon's Temple:
- Solomon was David's son, which looks much like Navidson, an unknown surname;
- the Temple is known as the House of YHWH;
- Navidson's house is at the corner of Ash Tree Lane and Succoth, a Jewish word which first refers to the Feast of Tabernacles, the first of the Three Pilgrimage Festivals on which the Israelites were commanded to perform a pilgrimage to the Temple.

  To be honest, there are many, too many clues, in HOL, suggesting many other leads.

  Now the Holy of Holies is expressly mentioned in Pi. Max Cohen has found a 216-digit number that makes him becoming a target for yuppies, who want to use it at Wall Street, and for Hassidim, who state the number is the divine key to meet God.
  Max is kidnapped by the Hassidim, and lead to an old Rabbi who tells him every year the Great Priest of Israel entered the Holy of Holies and called God with a 216-letter word, which has been forgotten. Max successes to escape, and has to withdraw the number from his brain with a power drill...
  Actually there is an important sequence of 216 letters in the Hebrew Bible, the three verses of Exodus 14,19-21, each one being 72 letters long. Jewish mystic used it to build 72 names of angels.
  It has to be said that the Holy of Holies, Qodesh haQodashim, has another name in Hebrew, debir, דְּבִיר, a word which has the value 216 in the traditional Hebrew system.
  The name 'Max Cohen' probably refers to Great Priest, Cohen haGadol, Pontifex Maximus...

  The French adaptations of HOL and Pi bring surprises.
  The name of the alleged author of document #046665, Johnny Truant, could not be kept in France, where a truand is a 'hoodlum', so the translator made him Johnny Errand. Asked about it, he replied this had nothing to do with ERRAND anagram of DARREN, Aronofsky's first name.

  Anyhow, a French spectator of Pi cannot think of HOL as there is no 46665 in the French dubbing.
  For some unknown reason, the multiplication
255 x 183
255 x 1280
with the appropriate result
  The quite strange thing is that 1280 is one of the two remaining documents in the Annex II-A, #175079 and #001280. This 1280 is also drawings on an envelope, while 175079 uses sheets of a notebook.

  The strangeness is even bigger, as the final scene of Pi echoes to one of its first scenes (time 2:10), in which little Jenna plays too with Max in the staircases (!) of their building.
  From the script Jenna had to say
What's 322 times 491?
but she was shot saying
What's 322 times 481?
  Max answers the correct question, 158,102. The wrong 481 is corrected in 491 in the English subtitles, as well as in other foreign subtitles, but as far as I know 255 x 183 has not been changed in other dubbings.

  The combination of mistakes and changes in Jenna's multiplications echoes to her divisions. In the first scene the multiplication is followed by the division
73 divided by 22?
  Max answers 3.318...
then continues 1, 8, 1, 8, 1, 8... on each stair of the staircases he is going down.
  This division has the same decimals as 7/22, the inverse of 22/7, well-known approximation of Pi. The final fivision 748/238 simplifies to 22/7, and it came to me it could be 'phinal', as the difference 748-238 equates to 510, which is the Greek value of φι, the name of the Greek letter Phi which is the symbol of the golden ratio.

  I apologize for my bad English that doesn't allow me to translate all I've seen around this 46665. There is much more on my French blog.
  Just one thing I want to add, without elaborating. The sequence 046665 appears quite soon among Phi decimals, starting on the 463rd digit. This means the sequence 466 appears ending on the 466th digit. It has been done such calculations with Pi, notably showing the sequence 360 appears ending on the 360th digit.


DNE ratio

  My first post exposed the severe heart attack Jung suffered in Feb 44. He was several weeks between life and death, and probably owed his survival to Swiss greatest heart specialist, Theodor Haemmerli, called Dr H. in Memories, Dreams, Reflections (MDR).
  Jung had visions during his illness, and an experience in which we recognize now a NDE. The testimony he gives in MDR might be the first NDE case fully published.
  Jung flew away high up in space, seeing far below the earth, bathed in a gloriously blue light. Then he saw a tremendous dark block of stone, floating in space; a temple was there, and he knew he would receive inside all the answers to all his questions, but before he could enter the temple he met Dr H., delegated from the earth to tell him there was a protest against his going away. He had to return.
  The moment Jung heard that, the vision ceased, and he was profoundly disappointed.
  I have shortened the report. Jung couldn't know in 44 a basic NDE case, where the subject meets on the other side dead members of his family, telling him the time is not yet come, but he was surprised to have met Dr H., a living person, in the other world:
I felt violent resistance to my doctor because he had brought me back to life. At the same time, I was worried about him. "His life is in danger, for heaven's sake! He has appeared to me in his primal form! When anybody attains this form it means he is going to die, for already he belongs to the 'greater company'!"
Suddenly the terrifying thought came to me that Dr H. would have to die in my stead.
  He tried to warn him, but the doctor didn't care, taking Jung's visions as pure delirium. Maybe Dr H. was wrong, as
I was his last patient. On 4 April 1944 - I still remember the exact date - I was allowed to sit up on the edge of my bed for the first time since the beginning of my illness, and on this same day Dr H. took to his bed and did not leave it again. Soon afterward he died of septicemia.
(MDR, Visions)
    Soon afterward might be unappropriate, as Haemmerli died on June 30, 87 days later (I found this date in a list of Swiss physicians, its URL is now invalid, here is another source). This was misunderstood by most biographers who didn't check this fact, which increases the strangeness of the case as June 30 might be the very day when Jung left the hospital (end of June or beginning of July).

  I found a few days ago that this June 30, 44 is too the birthdate of Raymond Moody, the one who revealed the NDE phenomenon, with his Life after Life in 1975.
  This book was a revolution. Jung's case was not unique, but the people who lived such an experience were reluctant to share it, for obvious reasons. The progresses of medicine allowed more and more people to come back from clinical death, often with a strange story to tell...
   Moody was the one who collected about 150 of these stories, and his book helped thousands of other people to share their experience.

  Moody's later researches led him to believe in reincarnation, and to state he personally had nine past-lives.
  I do not know the hour of Haemmerli's death; I found there that Moody was born at 8 PM in Georgia, which with the time difference would anyway be after the death of his Swiss colleague.
  It looks then incredible that the man who showed the reality of the NDE phenomenon was born a few hours after someone involved in what is probably  the most famous historical NDE case, someone who maybe died because he was skeptical about it.
  One could imagine Haemmerli's thoughts before his death, such as: Shit! this Jung was right. If I had a chance to live another life, I'll try my best to study this strange phenomenon.

  In 1975 Moody only knew recent NDE cases, but his next book, Reflections on Life after Life, gives in 1977 some historical cases, such as Jung's one, briefly:
Also interesting is the fact that the renowned psychiatrist Carl Gustav Jung had a near-death experience; he describes it in the section intitled Visions in the book Memories, Dreams, and Reflections.

  I came to a new interest in NDE's after a reading which mentioned the work of one of Moody's main followers, Kenneth Ring.
  While Moody only studied about 150 cases, Ring made a questionnaire that he sent to thousands of experiencers, and he published his results in Life at Death (1980), trying to approach the typical NDE, following the percentages obtained from his questionnaire:
  He subdivided the NDE on a five-stage continuum. The subdivisions were:
1) - Peace (60 %)
2) - Body separation (37 %)
3) - Entering darkness (23 %)
4) - Seeing the light (16 %)
5) - Entering the light (10 %)

  I already read that long ago, but since that time I became acquainted with the Golden Ratio, and now I recognize in these numbers 60-37-23-16-10 something that looks like a golden sequence. Starting with 60, successive divisions by 1.618 (the Golden Ratio) give, in rounded numbers:
60  - 37 - 23 - 14 - 9
  The last two numbers don't fit the percentages as perfectly as the first ones; it might be argued that the low percentages have not the same accuracy as the higher ones, but anyhow the similarity is striking.
  I notice that 60 % is near the golden section of 100 %, and here is the golden sequence starting with 100, still in round numbers:
100 - 62 - 38 - 24 - 15 - 9

  I'm afraid I cannot say if this similarity is a mere coincidence or if some mathematical correlation could explain it (notably Zipf's law). Some other studies about NDE's do not reflect exactly this first scientific approach.
  Many false claims run about the golden ratio, yet it can appear in some mathematical processes, just because it's an important algebric number. I'm rather interested in cases where there is absolutely no reason for its presence, and yet it's there. My previous post was about the first maps of Philadelphia (Phi or φ symbolizes the Golden Ratio), a rectangle of 8 x 21 blocks in which Center Square (now Town Hall) is not at all in the center but divides these numbers in 3-5-8-13, that any reader of Da Vinci Code identifies today with the Fibonacci Sequence. 
  I shared it here because I saw a parallel with Jung's experience in 1944; I gave some hints and planned to work it up, but I failed to do it, for it was a big job.

  I had a kind of NDE when I was about 19, around 1969. It was rather an altered state of consciousness as I was not at all in a near-death situation, but it had many points in common with a NDE, although I obviously didn't know such a phenomenon existed. Actually it troubled me a lot, and I kept it for myself during so many years that I was not sure then of what exactly happened.
  My favorite writer was Phil Dick, and I was puzzled to find in A Scanner Darkly (1977) the report of an experience which looked much like mine. It was attributed to a fictitious character, Tony Amsterdam, but I learnt later that it happened to himself.
  So Tony or Phil had the feeling he met God during this experience, and he saw too a doorway with pleasing proportions, leading maybe to God's world, but he just admired the door and didn't think of going through it. He worried then all his life that he would never have such another chance.
  In my experience I felt like Phil that the molecules of my mind ran very fast across the universe, until it slowed down to some rest, facing what might have been God's throne. Then I heard a sentence in an unknown language, but I could understand its meaning: I am not what people believe I am.
  Then I got back into normality, and tried to find the previous state again. I had the vision of a narrow street, of a house in this street, of its door...

  This disturbed me a lot as I was an unbeliever, having got rid of the Christian education I was raised in. So I mostly did as the experience didn't happen, until I found in my third reading of A Scanner Darkly how much Tony's experience looked like mine. It was so far away that I felt unable to remember if I ever thought of what was behind my door.
  This experience is present too in the books of the so-called Divine Trilogy, as well as in the Exegesis, and in the three novels Dick precises that the doorway was a Golden Rectangle. It seems that in his mind the Golden Ratio and the Fibonacci Sequence are privileged accesses to the other world; in The Divine Invasion, Zina and Emmanuel discuss about this doorway to Heaven:
The ratio, she said to Herb Asher, is that used in playing cards: three to five. 
  5/3 is the first Fibonacci fraction (1.666) giving a valuable approximation of Phi (1.618), but it's quite amazing that, according to the usual numerology from A=1 to Z=26,
PHIL / DICK = 45/27 = 5/3
so Phil Dick might be a doorway for those who didn't live such an experience;-)

  Later I found the case of Jung in 1944, in which there is too a doorway leading to a sacred place, but Haemmerli forbids Jung to get in. I calculated, using the same way as above,
HAEMMERLI / JUNG = 84/52 = 21/13 ≈ Phi
as 13 and 21 are two successive Fibo numbers.
Jung's report of his 1944 visions might have been the first NDE case depicted. Jung and Haemmerli met in the other world, the world of death, and both came back. In our Western tradition, what might seem the nearest could be the cases of Enoch and Elijah, the only two characters of the Old Testament that didn't die, and were raised directly to Heaven. In the Hebrew alphabet, using the traditional gematria, these two people have the same values as Haemmerli and Jung in our modern alphabet:
- חנוך (Enoch) = 84
- אליהו (Elijah) = 52

  Another disturbing echo is given by the only dates known for the 44 events:
- from Feb 11, Jung's accident, to 4/4/44, there are 53 days;
- from 4/4/44 to Jun 30, Haemmerli's death, there are 87 days.
  53-87 is the golden repartition of the sum 140
חםה 'hama (sun) = 53
- לבנה levana (moon) = 87
  Jung chiseled Sun and Moon on the Bollingen stone he engraved as a commemoration of his 44 recover.
I develop more echoes on this topic of the forum Unus Mundus.

  I'm not trying to make any theory about a link between NDE's and Golden Ratio, I just point to these echoes which might be another trick of the Trickster. In chapter two of Synchronicity, Jung accounts of an astrological experiment he imagined to give an experimental proof of the phenomenon. A first batch showed a strong correlation between the sun-moon aspects of married people and the traditional astrological correspondence, but another batch didn't confirm the first results, and that led Jung to state the first results were a synchronicity, showing the phenomenon existed, but beyond any hope of a scientific analysis.

  I don't feel I have to justify what made me calculate the values of the man who found the five stages of NDE's, with the percentages 60-37-23-16-10 :
That's a golden name, and so is the usual diminutive
KEN RING = 30/48 = 5/8
The same ratio 8/5 (Fibonacci) appears for the last two stages of his typical NDE, 16-10.

  I read long ago MDR, but in this rich book I didn't notice peculiarly the day 4/4/44. I saw its schematism much later in the book Les raisons de l'irrationnel (1976, but already published in 1970 with the title Plaidoyer pour l'extraordinaire), by Paul Misraki, a French composer who gave in the 30's the best known hits of Ray Ventura's orchestra, such as Tout va très bien, madame la marquise.
  I calculated
PAUL MISRAKI = 50/80 = 5/8,
a golden name, with the same Fibonacci ratio as Ken Ring.

  In a footnote of this book, Misraki stated there was common points between the experience of Jung in 44 and another case he held from a relative. It might have been the first connection published between NDE's, but such connections were known before in the medical world, and Moody's enquiry started in 1965 when he heard about two similar cases.
  Actually Misraki was the French translater of Moody's first books, published in France in 77 and 78.

  There is too a diminutive for Moody,
RAY MOODY = 44/72
and that's again a golden name.
  For the two diminutives,
MOODY-RING / RAY-KEN = 120/74 = 60/37, the percentages obtained by Ring for the first two stages of the typical NDE.
  In order to appreciate the probability for someone to have a golden name, I studied several lists of real names. My more important batches were two lists of 3700 actresses and 2700 actors found on the web, and both give exactly the same odds, 1 against 34.
  This is just to give an idea, as I do not try to prove anything.

   Moody and Ring were two of the five founders of IANDS, the first organization devoted to the study of NDE's. John Audette is generally considered as its main creator. It's again a golden name
  So, including all the forms of their names, 3 of these 5 founders have golden names, and another harmony appears between the 5 complete names:
JOHN AUDETTE = 47+76 = 123
KENNETH RING = 77+48 = 125
RAYMOND MOODY = 90+72 = 162
These are the ones with golden possibilities, giving the sum 123+125+162 = 410
The other two are
MICHAEL SABOM = 51+50 = 101
BRUCE GREYSON = 49+103 = 152
and 101+152 = 253 is the golden section of 410

  Joel Schumacher made in 1990 a movie about NDE's, Flatliners. Five medical students investigate the phenomenon, putting themselves in clinical death state. Another set of five, but only four of them actually experience NDE's. Here David Labraccio (Kevin Bacon) is reanimated by his friends, and it's again a golden name, 40/64 = 5/8, the same fraction encountered with Ken Ring = 30/48 and Paul Misraki = 50/80.
 There is also a golden harmony between the 4  experiencers, whose names are:
Nelson Wright    =  79  85
Rachel Mannus   =  47  82
David Labraccio =  40  64
Joe Hurley         =   30  89
       totals         = 196 320 = 4 (49 80)
  First names have for average value 49, second names 80, and 49-80 is the golden repartition of 129.
  It can be noted too that they form a Jungian quaternion, 3 men and 1 woman, this woman having the value 129, average value of the group.

 To give an example of how it is a big job to give an account of my golden researches, I recently tried to collect all the coincidences involving together numbers 13 and 21, and I soon came over 80 cases.


Philadelphia Exphiriment

This isn't directly connected now with Jung, as it would be too long to explain how Jung is related to the Golden Ratio, what I intended to develop in my next series of posts, on next 4/4.
Yet it has to do with quaternity, as I came to learn that Philadelphia was once the biggest city in America, the first one built on a rectangular plan. It was first conceived around a quincux of five squares , a central square which was planned to become the administrative center of the city, and four squares originally named Northeast, Northwest, Southeast and Southwest.
I found this 1682 map, when it was founded by William Penn on Oct 27: I was struck by a dissymmetry : Center Square looked right in the middle of East-West, but not at all in the middle of North-South, and the disposition of the four squares underlined this dissymmetry.
Maybe there was an obvious reason for this: the founders already thought the city might get extended, and some swamps prevented it to grow south (at least that was what they thought then), so Center Square was the hopeful center of a bigger city.
This book gives details: the city was organized around two big streets 100 feet broad, High Street (near the middle of the city) between the two rivers, Broad Street North-South, crossing High St right in its middle.
Center Square was 10 acres, and the four other squares were 8 acres each. There were 22 streets besides Broad Street, each side a Front Street and 10 streets numbered from 1st to 10th, 50 feet broad each, and 8 streets besides High St, 3 North and 5 South, which were named with trees, from Vine St North to Cedar St South.
8 blocks distributed in 3+5, that’s three numbers of the Fibonacci Sequence, and I was amazed cause I already associated Philadelphia with that sequence, I'll explain later how.
My curiosity led me to this site, giving many Philadelphia maps, and several 18th Century maps show a city of 21 x 8 blocks, as this French 1764 map: All these maps show 8 streets West of Broad St, 13 East, so Center Square is not at all central, and 8-13-21 belong too to the Fibonacci sequence (1-1-2-3-5-8-13-21-34...).
It's quite unlikely anyone could have planned this, as Fibonacci numbers were in the 18th century far from their actual popularity, and the strangest thing is that this perfect Fibo scheme appeared in two steps, first the repartition 3-5 from North to South, then the repartition 8-13 from East to West.
Actually the grid 9x22 shown on several maps was more a project than a real city, although the streets were probably traced on the ground, but Old City first developed on the Delaware side, and the State House was built there, far from Penn's Center Square which does not appear on this 1777 map.
Yet this grid was then used for the city extension, and it's quite clear on this 1842 map: Center Square is now Penn Square, and there are 8 streets West of Broad Street, named from (Schuykill) Front St (which is too 1st St) to 8th St, and 13 streets East of Broad Street, named from (Delaware) Front St (which is too 1st St) to 13th St.
The Fibo scheme goes on with a third step, as there are now 13 main streets crossing Broad St, apart of High St, 5 streets North of it, and 8 streets South.
It's possible to get it a little bigger with a click on the map, but I suggest to do this on the next map, in the beginning of the 20th century, where the 21+13 important streets appear more clearly, and it's necessary to get it on another window, as there are many important details: The 8 and 13 streets were renamed from Delaware Front St, still Front st or 1st St, to 22nd St for Schuylkill Front St. There is no 14th Street, which is Broad St. High St is now Market.
At least William Penn's wishes were remembered, and on Penn's Square was built the new City Hall, which was designed originally to be the world's tallest building, but by the time it was completed, in 1901, it had already been surpassed by several other places.
The ratio of two successive numbers in the Fibonacci sequence converges on Phi, the Golden Ratio, 1.618... So I applied PhiMatrix, a tool developed by Gary Meisner, webmaster of a Phi dedicated site.
I applied the grid on the historic city, between the two front streets and between Vine St and Cedar St, now South St. The validity of the results depends on the rightness of the map, and GoogleEarth will roughly confirm them.
Not surprising the main Phi lines (thin blue) follow Broad St, quite near the middle, and Market St, rather at the limit of the North sidewalk, but this little imperfection has a strange consequence. I marked with a yellow cross the intersection of these two lines, falling on City Hall which is not a symmetrical building. Quite near the 'Phi center' arises the tall 548 ft tower, with William Penn's statue on top of it.
I marked another interesting intersection: East of Broad St we have a kind of 13 x 13 blocks square, and the Phi lines in this square follow nearly the middles of the streets corresponding to the 8-5 Fibo cut, Walnut St and 6th St, crossing right between Washington Square and Independance Hall Square. It's funny thinking the Founding Fathers probably stepped many times this crossroad, between what were in 1776 State House and South East Square.
A 'Phi eye' sees something in the four Squares, which are now far from being symmetrical to Broad St, and I used again PhiMatrix to show a golden rectangle (transparent blue) which superposes roughly to the rectangle between the four external corners. GoogleEarth will show this rectangle might have been more precisely a golden one.
Here is another use of PhiMatrix on the same map, with thicker lines (click to enlarge).

Now I'll try to explain how I came to associate Philadelphia with Phi and Fibonacci. Many people learnt about these with the best selling Da Vinci Code, which begins with an enigma associating an anagram of Leonardo Da Vinci (O draconian devil) with the disordered first numbers of Fibonacci sequence (13-3-2-21-1-1-8-5), to be rightly ordered to get the code of a safe.
I was amazed because I knew a 1932 crime novel, The Greek Coffin Mystery, by Ellery Queen, dealing with the robbery of a Da Vinci painting, as well as offering a Fibo pattern.
The novel presents a strange table, with 34 chapters divided in two books, giving in acrostics the title in 21 letters, and BY ELLERY QUEEN in 13 letters.
This was the only Queen novel with such a trick, and some clues might show the Fibo pattern was intended, as
- the association with Greece, where the Golden Ratio was discovered over 2000 years ago (after that Da Vinci is the most famous artist associated with the Golden Ratio).
- 'coffin' is a Greek word, kophinos, κόφινος, written with a Phi, φ, and the Fibo cut 13-8 of the title would fall on that Phi, THEGREEKCOFFI - NMYSTERY.
- this novel is the 4th of a series of 9 with titles Nation-Noun-Mystery; these nine novels totalize 233 chapters, 13th Fibo.
- I noticed very soon there was 3 Mysteries before that very special one, and 5 after, long before I paid attention to the 3 streets North of High St, and to the 5 streets South, on the old Philadelphia map.

Queen gave up the pattern Nation-Noun-Mystery with his 10th novel, Halfway House (1936). A man is discovered dead in a house near Trenton, and there are found a brandnew car and an old one, rich clothes and poor clothes... He used this house to change identity, spending a part of the week in Philadelphia, with his young wife Lucy, aged 31, and the other part in New York with his other wife, older rich heiress Jessica, 49.
I came to find that, if not geographically, Trenton was, using gematria (A=1, B=2, and so on), exactly halfway between
and NEW YORK = 111
as TRENTON = 106 (101+5 or 111-5)
This tool allows to check it up.
The two syllables of NEW YORK = 42/69 are in a fair golden ratio, so I came to study the four syllables of Phi-la-del-phia, where first one Phi might stand for the Golden Ratio, 1.618… Next syllables give successive numbers in the Fibo sequence:
LA = 13
DEL = 21
PHIA = 34
So it's easy to understand how much I was struck when I found there were 34 streets besides the two main streets of Philadelphia, divided in 21+13.
Of course the name Philadelphia came from the Antiquity and had nothing to do with such calculations, and the name Phi for the Golden Ratio was given in the beginning of the 20th century.

The particular 13-21-34 Fibo numbers allow an unique arithmetical curiosity. When using the common rounded value 1.618 for Phi, we have
1.618 x 13 = 21.034
which could be written too
Phi x LA = DEL. PHIA

I'm not sure Queen knew about that, yet his work is full of most subtle tricks, sometimes revealed, sometimes left to the reader's sagacity.
Among the revealed that might concern this case, there is a woman named Lia Mason, which turns out to be an anagram of Mona Lisa, in Ten Days' Wonder (1948).
The alphabet rank of a letter is important in several books, and in A Fine and Private Place (1971), a man changes his name in order to get a more suitable gematria.

About gematria, I found that
WILLIAM / PENN = 79/49 = 1.612...
This is a fair golden ratio between integers, as 79/Phi = 48.8..., and 49xPhi = 79.2... A study of lists of real names shows there's about 1% of such 'golden names'.

I already spoke of Queen's wit about Easter dates in Quaternity, I have something here in English about maths in his most personal novel, The Golden Summer (my longer French study involves the golden number and Fibonacci).

So we have seen Philly in the centuries 17-18-19-20, how is she today?
GoogleEarth gives a good idea, and allows precise measurements.
Here's the GoogleMap I studied, it can be enlarged with a click on it:I'll first invite to check my measurements on GoogleEarth.
I began with finding the original perimeter (in red) of the historic city. It's not easy in the North as a good part of Vine Street left place to a large expressway, yet a part of old Vine Street remains in the East, allowing an extrapolation towards West.
In yellow Broad Street and Market Street.
Of course the measurements today can't be exactly what they were when the city started, as the streets were enlarged, anyhow I don't try to prove anything, I just explore this strange case of a city accidentally built on a Fibo pattern.
So from East Front Street to West Front Street (now 22nd St) I find 9734 ft, trying to start from the buildings. Golden section of 9734 is 6016, and from Front St to the middle line of Broad St I find 6055 ft.
From South St to old Vine St I found 5275 ft (quite near a mile). The Golden section of it is 3260, and I found 3200 ft to the middle line of Market St.
In both cases the Phi lines fall in these main axes, which are now broader than 100 ft. Placing the points of measurements in the middle of the peripheral streets would make the Phi Center about coinciding with the tower of the City Hall, and William Penn's statue.

The title of this post is inspired by the movie Philadelphia Experiment, but there's too a movie titled Philadelphia, by Jonathan Demme (1993), which I had the curiosity to watch again. It's about 115' long on the DVD, forgetting last 5' of full credits, and these 115' show a fair golden ratio between the two main parts, the exposure of the case, a gay lawyer fired from his firm cause he's infected with AIDS, and the trial which is held in City Hall.
Between these two parts there is a long aerian travelling above the City Hall, first showing William Penn's statue.
This reminded me of Queen's Halfway House, which is divided in five parts, the middle one being The Trial. This case is judged in Trenton, but the opening Milton's quote might be meaningful:
Eye me, blest Providence, and square my trial
To my proportion'd strength.

Gary Meisner, the developer of PhiMatrix, writes 5 'phive', as it's a key number to 'Phi Guys', for Phi depends on the square root of 5, for the 5th 'Phibo' is 5....
This leads me to my most astonishing measurement. It's difficult to measure the rectangle between the external corners of the four squares, as the two North squares have been modified, especially Logan Square. Yet it's possible to have an idea of their North limit by extrapolating what is left of the old Vine St, and I found a height of 3752 ft, which is very near the golden section of the length 6082 ft, 3758.
Yet this is quite virtual, and it's more sure to take the measurement between the centers of Washington Square and Rittenhouse Square, materialized by a fountain and by a hexagonal cabin. While just trying to get the most exact measurement between the two centers of these centers, I found 5555 ft.
5555 is a strange number by itself, and it factorizes in 101 x 55, 101 which is the gematria of PHILADELPHIA, 55 which is the 10th Fibonacci number, and the gematria of DEL-PHIA = 21+34.
The golden section of 5555 is 3433, and the 5555 ft line crosses the middle line of Broad Street at 3441 ft.

To come back to Jung, the discovery of the pattern 4-1 in his life around the 4/4/44 led me to think about the numbers 4444, 1111, and 5555. This is why I began this blog with five posts posted at 11:11 on 4/4, 2010. I was too lazy to write anything else within a year, so I waited last 4/4 to do the same trick.
I feel now a bit obliged to give some hints about Jung and the golden ratio, what I first didn't intend to do. I have a long practice of gematria, in several alphabets. When I learnt the name of the doctor that saved Jung in 44, and maybe died in his stead, I noticed the following
HAEMMERLI / JUNG = 84/52 = 21/13 ≈ Phi
as 13 and 21 are two successive Fibo numbers.
Jung's report of his 1944 visions might have been the first NDE case reported. Jung and Haemmerli met in the other world, the world of death, and both came back. In our Western tradition, what might seem the nearest could be the cases of Enoch and Elijah, the only two characters of the Old Testament that didn't die, and were raised directly to Heaven. In the Hebrew alphabet, using the traditional gematria, these two people have the same values as Haemmerli and Jung in our modern alphabet:
- חנוך (Enoch) = 84
- אליהו (Elijah) = 52
When I found a few days after the 136th anniversary of Jung's birth (84+52) this incredible story of Philadelphia built on a Fibo pattern, notably 21 x 13, I thought it had a relation with Jung, in one way or another, and that I had to share it here.

William Penn had the rare privilege to become a Honorary Citizen of the United States. This was done by Presidential Proclamation 5284.

PS - Sep, 19: I quoted higher the use of Fibonacci Sequence in Da Vinci Code, and I just discovered that one of John Langdon's best ambigrams concerns Philadelphia. Dan Brown's character Robert Langdon owes his name to this artist.


1: Books of the Week

Jung's life turned on 4/4/44, and this Tuesday belonged to the Holy Week from Apr 2, 1944, Palm Sunday, to Apr 9, Easter Sunday (red letter day on this calendar).

This Holy Week could be a very special one, as Jewish Easter (Pessah, Passover) fell this year 1944 on 4/8, a Saturday, as it seems to have been the case in the original Passion. This peculiarity helped to date the Crucifixion on April 7, 30, a date which was long granted for good. It seems now English sources like better April 3, 33, while French sources still prefer April 7, 30.

The important thing might not be reality, if there is any, but what people knew about it in their time, and April 7, 30 was for example the date given in Jesus in his time by Daniel-Rops (1945). I came to find that 1944 is the first Gregorian year when Good Friday falls on April 7 and Pessah on 8, as in 30 CE, and this will not come back before 2479. There might have been Julian years (from 326 to 1582) that would fit, but Julian calendar was wrong as soon as the 2nd century.

I discovered this while enquiring on a very strange novel, And on the Eighth Day..., written in 1964 by Ellery Queen (aka Fred Dannay), which is a parody of the Passion, set in 8 chapters titled from Sunday 2 April to Sunday 9 April, happening in 1944 in a kind of Essenian community somewhere in the Californian desert. The Teacher is killed by his people on 7th at sunset, i.e. on Christian Good Friday as well as on the very beginning of Jewish Pessah.
I've been for long interested in Easter dates in literature, notably in crime books. Two months before I found the pattern around 4/4/44 in Jung's life, I came to distinguish a special category that covers exactly a Holy Week, from Palm Sunday to Easter Sunday, because I found in July 2008 a new text following such a pattern.
I already knew of two other ones, discovered both in April 1997, in strange conditions. In even stranger conditions I came to find two more books offering the same pattern in Oct 2008, a month after my 4/4/44 discovery.

I'll give details in the next posts, now I'll try to study the set of the five texts together, and here they are, following the chronology of Easter weeks:
1889 - The Decorator by Boris Akunin (1999)
1895 - The Perfume Of The Lady In Black by Gaston Leroux (1909)
1944 - And on the Eighth Day... by Ellery Queen (1964)
1996 - Four Corners of Night by Craig Holden (1999)
2001 - 5 (2001) That's a French collection of short stories about the 5 senses, and the short Little Green Apples by Sébastien Fevry is in 8 sections from Sunday, April 8 to Sunday, April 15 (the 2001 Holy Week).
I found these five books by chance, and each finding was so incredible that I won't be surprised if these five books were the only one, at least the only ones easily available in France. Three of them are by best-selling authors (French, American and Russian), but from so different times that it's unlikely many people read them all.
Then American Craig Holden is not very known, he has no wikipedia file yet, and I don't think his work was translated in many languages. Happily it was in French.
The last book from 2001 was only published in French, in 2000 copies, and I would probably never have known of it if I didn't publish a book with the same editor.

Now these five texts show quite amazing features, notably following the pattern of their discovery, 2-1-2, 2 together in April 1997, then 1 in July 08, and 2 together in October 08.
They repeat this pattern in different ways:
- there are 2 French books, 1 Russian, 2 American.
- 2 texts (Queen and Holden) are whole independant novels, so published; Fevry's was published in a collection of short stories and Akunin's is a short novel always published with another one in Special Assignments; the other novel, by Leroux, was published either as a complete book, either as the second part of a volume including Rouletabille's first investigation, The Mystery of the Yellow Room.
- 2 (Holden and Akunin) clearly state the action is during the Holy Week, ending on Easter Sunday; 1 (Leroux) gives an allusion to Easter time, the 2 others don't give any allusion.
- 2 (Holden and Fevry) have an action contemporary with their writing, 2 (Leroux and Queen) are written slightly after the events (14 and 20 years), and 1 is written 110 years later.
- The Holy Weeks draw a kind of perfect pattern with 1944 in the middle (actually the exact average date is 1945, 1889+1895+1944+1996+2001 = 9725 = 5 x 1945 and the two extreme dates give 1889+2001 = 3890 = 2 x 1945.)

1944 and 1945 make me recall the 4-1 pattern I saw in WWII, starting from Sep 1, 1939 and ending with Aug 15, 1945, 2175 days of which 4/5ths fall exactly on D-Day.

At last the most astonishing thing is that 'my' 4th and 5th Books of the Week have 4 and 5 in their titles. I have nothing to add to this as I didn't choose anything. Of course I might have known of hundred of such 'Books of the Week', then have chosen among them five items in order to show striking patterns, but all I can say is that I only know of these five books, and that I would be grateful to anyone that could indicate me any other book.
Simple reason shouts it loud that there should be many such books, as I have only read a very low percentage of the millions of books published all over this world, yet I have a strong feeling that my case is quite against the odds.
Next posts will try to justify this feeling.

2: Leroux

In April 1997 I read The Perfume of the Lady in Black, a novel written in 1908 by Gaston Leroux. It follows The Mystery of The Yellow Room, where young journalist Joseph Rouletabille solves this 1892 mystery where the culprit was the inspector in charge of the case, most famous Fred Larsan, who was too most famous criminal Ballmeyer. He was too Rouletabille's father, and was supposed to have died then in a shipwreck...
He seems yet to have resurrected on April 7, 1895, when Mathilde Stangerson, Rouletabille's mother, calls him in urgency. She saw Larsan during her honeymoon trip! She spends her honeymoon in an old castle, on the French Riviera. A terrible week follows, as Larsan is a genius of disguise, and could be about anyone. A fight in Mathilde's room occurs in the night of the 12th, Larsan seems to have been killed by Mathilde's husband. Yet in the afternoon it's not so sure the man was really dead. And he was not, as at last Rouletabille demonstrates on the evening of the 13th that Larsan was Mathilde's husband. He waited until dark in order to discreetly evacuate Larsan to a secret prison, as nobody had to know Mathilde's infamous wedding, but Larsan suicides.

I happened to know that April 14 was Easter Sunday in 1895, as it's a prominent date in Maurice Leblanc's The Golden Triangle (1917, complete English text here), in which Patrice and his lover Coralie are caught in a deadly trap on Apr 14, 1895. Twenty years later, another Patrice and another Coralie, son and daughter of the previous ones, are led towards each other by a mysterious destiny. They repeat their parents' story so tightly that they fall in the same trap on Apr 14, 1915, and are saved in extremis by Arsène Lupin.
Patrice then learns that the mysterious destiny was run by his father, who came back from the dead in the evening of Apr 14, 1895, but found useful to be known dead in order to prepare his revenge. The father seems to have turned mad, as now he acts like an enemy, trying to kill Patrice and Coralie on Apr 14, 1915. Lupin will solve this enigma.

I found many things alike between the two books, the biggest one being the death of the father (real or not) on the same Easter day. There are other coincidences, as this striking one: in both books the hero, Rouletabille or Lupin, has found the truth, the real identity of the disguised murderer, but he delays its revelation, and this delay is the direct cause of another death, and in both stories the victim is a janitor.

Instead of the Son resurrecting on Sunday, the Father dies...
There might be several allusions in both books to this status of counter-Passion, especially in Leroux's where Larsan is again supposed dead then resurrected on Good Friday. It's quite striking that one of his alias is Salvator Russel (given in the scene adaptation of the Yellow Room Mystery): salvator, 'saver', is the meaning of Jesus, Jeshua, whose human father was Joseph, name of Salvator's son, Joseph Joséphin later known as Rouletabille.
Russel is an English equivalent of Leroux ('The Red'), so maybe Leroux identified a bit with his wicked character. Anyhow it's a strange coincidence he died on April 15, 1927, which was a Good Friday.
Some months after I brought together the two novels, from the common date April 14, 1895, I came to see a documentary about Alfred Dreyfus, where was seen the beginning of his Devil's Island diary, first sentence of which reading:
Sunday, April 14, 1895
Today I begin the diary of my sad and tragical life.
This led me to another look on both novels, and to find strong echoes with Dreyfus case. Here is the most striking one:
- Frederic Larsan, commonly called Fred, is too Public Enemy number one Ballmeyer, sounding like a Jewish name. Rouletabille planned to take him on a craft after dawn on April 13, 1895, towards the discrete place where he would be kept for the rest of his life, but Larsan suicides, and that's his corpse that his son takes on the craft and drowns in the sea.
- Alfred Dreyfus, called Fred by family and friends, was Public Enemy number one in 1895, when a plot made a traitor of him, probably because he was a Jew. He was offered the 'Way of Honor', i.e. to shoot himself, but he refused and was condemned to end his life on Devil's Island, where he would be the only prisoner. He arrived there in the afternoon of April 13, 1895, and Guyana time was about 5 hours late with French time, so it might be exactly at the same moment that the two Freds were taken on a craft to their last place...

I won't go any longer in this direction as I'm not trying to prove anything about Leroux's intentions in this novel. Somehow it has to be considered it might not be just a simple thriller.
I feel sure anyhow Leroux didn't choose the dates by chance, and several clues show he knew perfectly that April 7 when the story begins was Palm Sunday in 1895.

I'm not so sure about Leblanc, who anyhow could not allow himself to write a clearly scandalous novel in 1917; WWI was raging and there was a censorship surveying literary works.
Since I'm fascinated by the switch between Jung and his doctor on 4/4/44, I have another look at The Golden Triangle which begins in the evening of Apr 3, 1915. I keep on wondering about this:
- The wicked man of the story, Essarès, tried to kill Patrice's father on Apr 14, 1895, but the father 'resurrected' on that Easter Sunday. He became Diodokis, and was accepted as a servant by Essarès.
- Essarès succeeds in killing Diodokis on Apr 4, 1915, actually unaware it was Patrice's father, and it was another Easter Sunday! In order to escape to his enemies, Essarès then takes the place of Diodokis and arranges things so that Diodokis' corpse will be taken as himself. This switch will make the case quite tricky.

I have no trace of the exact days of my finding. The only thing made sure is that I heard on March 22, 1997, during a literary seminar, of a book giving strange insights on George Perec's work.
I bought this book, in which some insights about Leroux made me curious to read him again, and that led me to The Perfume, which starts on Apr 6, 1895 with the wedding of the Lady in Black. It was the eve of Palm Sunday, as was curiously enough March 22, 1997.