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

This is nearly the text of footnote 382, which precises

Actually the nautilus is quoted too in

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 8

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

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 8

^{th }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.

(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

became

255 x 1280

with the appropriate result

326,400.

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 463

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 463

^{rd}digit. This means the sequence 466 appears ending on the 466^{th}digit. It has been done such calculations with Pi, notably showing the sequence 360 appears ending on the 360^{th}digit.
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