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.

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