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Liber VII vs. Liber CCXX - An experiment with numbers


threefold31
(@threefold31)
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Dwtw

This post is in response to a comment in the Fill/Kill thread which I was not able to adequately address at the time, and my response didn’t properly belong there anyway, as it would have created an unnecessary tangent.

JG made a discovery about a geometric relationship in Liber CCXX between the number of characters in the Book, and the gematria of the entire third chapter. It is essentially this:

There are 23,112 alpha-numeric characters in the text of Liber CCXX, (excluding the verse numbers, and all the punctuation; including the textual numerals 418, 718, etc, and the letters of Thelema and Tzaddi).

As it happens, 23112 is the area of a right triangle whose integer legs are of the length 214 and 216.

(214 x 216) / 2 = 92,452

By the Pythagorean Theorem, we can then calculate the square of the length of the hypotenuse by determining the sum of the squares of the two legs.

214^2 = 45,796
216^2 = 46,656
sum =  92,452 = 304.059^2

The square of the hypotenuse is 92,452, which is precisely equal to the Trigrammaton Gematria value of the entire third chapter of Liber CCXX, viz.
(The English words = 88,884) + (The textual numeral 718) + (The sum of all the verse numbers = 2850). Grand total is 92,452.

What is remarkable about this result is that there is no ‘tweaking’. The numbers are exact. The area of the square of the hypotenuse equals the gematria of Chapter 3 in its entirety, without exceptions. The area of the right triangle is precisely the number of characters used to write the text of CCXX, also without exceptions.

For those who think that fiddling around with numbers will always allow you to get the result you desire, this can be true to some extent, but it is not in evidence in this case. A simple experiment will show how difficult this result is to obtain.

We can make a fair comparison with another Holy Book, Liber Liberi vel Lapidis Lazuli, sub figura VII, also written by Crowley, and of practically the same length as Liber CCXX.

Liber VII has 23,052 alphanumeric characters. We will have to leave out the 16 (?) sigils in the text, as these have no comparable occurrence in Liber CCXX. We are also not including the verse numbers, since we didn't count those in CCXX either. The total number of characters is only 60 less than in Liber CCXX, so the two books are almost identical in length.

Following the criterion already established, 23,052 must be the area of a right triangle. This is done easily enough, using the numbers closest to the square root of 23,052:

(204 x 226) / 2 = 23,052

Again, we use the Pythagorean Theorem:
204^2 = 41616
226^2 = 51076
sum = 92,692 = 304.453^2

As we might expect, the right triangle has a similar area (it is only 240 larger than the one for CCXX), and the hypotenuse is almost the same length as well. So now we simply need to find a section of Liber VII whose gematria, including the verse numbers, sums to 92,692, and we will have matched the result from CCXX. This should be a piece of cake. After all, we’re just fiddling with numbers, and in a book this large, surely we will get the gematria result we are after.

Now admittedly, Liber VII has 7 chapters, not three, so I will loosen the constraints a little - we should be able to find an exact gematria result that includes about a third of the Book, and starts at the beginning of a chapter, and preferably concludes at the end of another chapter. But even stopping at the end of a complete verse would be acceptable in this case, or at least a full sentence.

Here are the results, simplified to keep this short. I will identify the beginning and ending points of a gematria string in Liber VII that totals 92692:

Starting with the Prologue of the Unborn to verse 3:33, in the middle of a word
Starting with Chapter 1 to verse 3:42, in the middle of a word
Starting with Chapter 2  to verse 4:26, in the middle of a word
Starting with Chapter 3 to verse 5:2, at the numeral 2.
Starting with Chapter 4 to verse 6:15, in the middle of a word
Starting with Chapter 5 to verse 7:33, in the middle of a word
Starting with Chapter 6 to the end of the Book, the gematria is far too small.

We very nearly had a hit there. Chapters 3 and 4 came within a few hundred of the total, but required the first verse of the next chapter, and the numeral of the next verse, to get to the desired total. So, that’s a near-miss, but a miss nonetheless.

All the other instances do not even end with whole words, let alone whole sentences, verses or chapters. In all cases, they overshoot the total somewhere in the middle of a word whose value is large enough to put them over the target value.

So, in summary, the attempt to duplicate in Liber VII what was found so beautifully and simply in Liber CCXX, is a complete failure. It simply can’t be done.

It may be possible, if one started at the head of every single verse, to find a string that ends with another complete verse. But I don’t have the software or time to check that. And I seriously doubt it is possible. The larger the gematria result you are looking for, the less likely you are to find an exact hit. There will be plenty of instances where a word equals 56, far less of words that equal 220. There will be plenty of verses in the hundreds or thousands, but far less of any specific number; and in most cases, a number won’t be represented at all. Any reasonably close study of the Torah will prove that in no time. Or look in 777, and see how the gematria equivalents get fewer and fewer as the numbers grow larger.

We had six chances to replicate the results from CCXX in LIber VII, and none of them succeeded. Only one even came close. But that is exactly what one would expect if the number strings were random - that there was no deliberately encoded pattern. I have no idea how to go about calculating the odds, but the chances of getting a string of roughly 7700 characters to have a gematria of precisely 92,452 must be astronomical. And the characters have to make whole words in English, not just nonsense letters, or partial phrases.

So this geometric result in Liber CCXX sets a benchmark. Scoff at gematria if you will, but duplicate these results before you laugh too heartily at the idea. Until counterexamples can be shown that prove this result is simply due to chance, we have to accept it as a tenable theory that the words in Liber CCXX were deliberately encoded. And this is precisely why this result was germane to the topic of Fill vs. Kill, because it goes to show that Chapter Three, and by extension, the whole of CCXX, is specifically written with a cryptological component. Changing a letter destroys that cryptogram.

What is amusing about the attitude of skeptics who claim that one can fiddle with numbers long enough and get the result that they want, is that they’re right! Of course you can. But if that’s the case, then why wouldn’t you think that Aiwass was capable of doing it? Or even Crowley himself. Which would then go to prove the very point they think they’re disproving.

With a computer and a target value, I could eventually concoct a text that would satisfy the parameters of this experiment. But it would take some doing, that’s for sure. And in the end, it would prove the point again - that making this kind of gematria happen is the result of deliberate design.

The other question that was raised was this: what does such a result tell us about the text? Well, aside from the obvious conclusion that it is encrypted, perhaps the legs of the CCXX triangle can give us a clue:

214 = it is revealed by Aiwass
216 = the threefold book of Law

Litlluw
RLG


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jamie barter
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Bravo!  So you have found a way round the kill me/ fill me dilemma, too! (cf John Griffths).  Such creativity!!  “Where there’s a will there’s a way” - Good luck!

DownTown (doing the bossanova),
Norma N. Joy Conquest


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Azidonis
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I think it's pretty remarkable, myself.

The scenario would be different had the TEG been twisted, or even invented, in order to get the set of values in question. But it wasn't. RLG, I know you've been working on the TEQ for many years, and it is well established overall. That this discovery of JG weaves in so nicely with the TEQ that has already long since been established, and with no alterations, is a testament to the wonderful symmetry that exists in both The Book of the Law, and the TEQ.


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obscurus
(@obscuruspaintus)
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"We very nearly had a hit there."
A word here, a letter there.....who knows? Having never seen the original as received, one has to wonder?
I'm thinking of a word...and it begins with "f".


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jamie barter
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"jamie barter" wrote:
Bravo!  So you have found a way round the kill me/ fill me dilemma, too! (cf John Griffths).  Such creativity!!  “Where there’s a will there’s a way” - Good luck!

DownTown (doing the bossanova),
Norma N. Joy Conquest

To be precise, my cf. referred to Azoneris in the “Correspondences between Crowley’s pre-1904 works and Liber AL” thread – although both John Griffiths and abn53 are also no doubt willing their way forward & onwards…

“Forget all your troubles, forget all you cares & go…” (= that Friday feeling),
N. Joy


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Los
 Los
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"threefold31" wrote:
What is remarkable about this result is that there is no ‘tweaking’.

Except for the decisions to exclude verse numbers and punctuation, while including textual numerals and the letters of Thelema and tzaddi, along with the arbitrary decision to use a right triangle and the Pythagorean theorem.

For those who think that fiddling around with numbers will always allow you to get the result you desire, this can be true to some extent, but it is not in evidence in this case.

Sure it is. In this example, if you had added up the characters and you didn’t get results that seemed interesting, you could have done the calculations again, this time including verse numbers or excluding textual numerals until you got results that “fit” something that looked "amazing." Or you could have tried a different shape or different mathematical formula. Or you could have gotten one of the other chapters to add up to the hypotenuse. Or lots of different ways of fiddling. Just keep going until something looks "amazing."

So, in summary, the attempt to duplicate in Liber VII what was found so beautifully and simply in Liber CCXX, is a complete failure. It simply can’t be done.

Well, obviously, the exact same number game won’t work for different texts, but I’ll bet someone can find some number game of some sort that works for VII and looks "amazing."

What is amusing about the attitude of skeptics who claim that one can fiddle with numbers long enough and get the result that they want, is that they’re right! Of course you can. But if that’s the case, then why wouldn’t you think that Aiwass was capable of doing it? Or even Crowley himself. Which would then go to prove the very point they think they’re disproving.

The point is that it’s not an example of ookity-spookity magic, which is the unspoken implication behind all of these claims of “amazing” gematria results.

The implication is that these “amazing” results point to the preterhuman nature of the author of the Book. If you’re willing to say that such gematria results don’t point to any such claim, and could very well be coincidence or the act of an everyday human being constructing a number puzzle, then you and I are in complete agreement on that point.


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threefold31
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"Los" wrote:
"threefold31" wrote:
What is remarkable about this result is that there is no ‘tweaking’.

Except for the decisions to exclude verse numbers and punctuation, while including textual numerals and the letters of Thelema and tzaddi, along with the arbitrary decision to use a right triangle and the Pythagorean theorem.

Dwtw

It is not a 'tweak' to include all the alphanumeric characters of the text. A 'tweak' would be more along the lines of excluding words or verses or using partial chapters to make the point.

"Los" wrote:
"threefold31" wrote:
For those who think that fiddling around with numbers will always allow you to get the result you desire, this can be true to some extent, but it is not in evidence in this case.

Sure it is. In this example, if you had added up the characters and you didn’t get results that seemed interesting, you could have done the calculations again, this time including verse numbers or excluding textual numerals until you got results that “fit” something that looked "amazing." Or you could have tried a different shape or different mathematical formula. Or you could have gotten one of the other chapters to add up to the hypotenuse. Or lots of different ways of fiddling. Just keep going until something looks "amazing."

Yes, one could have done such a thing. but it was not done here. Spare me the hypotheticals, and look at the actual results. There was no need to 'keep on going' when the simple answer was in plain sight. This experiment was not about all the ways one can parse a text through qabalistic exegesis. It is about a very specific result, and the attempt to replicate it.

"Los" wrote:
"threefold31" wrote:
So, in summary, the attempt to duplicate in Liber VII what was found so beautifully and simply in Liber CCXX, is a complete failure. It simply can’t be done.

Well, obviously, the exact same number game won’t work for different texts, but I’ll bet someone can find some number game of some sort that works for VII and looks "amazing."

May be. But it won't be this particular 'number game', the point of which is to refute the idea that such a 'number game' is so easy to do, when in fact it is not.

"Los" wrote:
"threefold31" wrote:
What is amusing about the attitude of skeptics who claim that one can fiddle with numbers long enough and get the result that they want, is that they’re right! Of course you can. But if that’s the case, then why wouldn’t you think that Aiwass was capable of doing it? Or even Crowley himself. Which would then go to prove the very point they think they’re disproving.

The point is that it’s not an example of ookity-spookity magic, which is the unspoken implication behind all of these claims of “amazing” gematria results.

The claim was not unspoken; I said it quite openly. The text is encoded. The odds against a chance occurrence of this nature are too high to think otherwise, in the absence of evidence to the contrary - none of which you're providing.

"Los" wrote:
The implication is that these “amazing” results point to the preterhuman nature of the author of the Book. If you’re willing to say that such gematria results don’t point to any such claim, and could very well be coincidence or the act of an everyday human being constructing a number puzzle, then you and I are in complete agreement on that point.

Well, no, I'm not willing to claim any such thing, so you and I are not in agreement at all. The encoding of the text is not a coincidence, as far as the present evidence allows us to conclude. The only human being who could have encoded the text was Crowley himself, and there is no evidence that he did so. Yes, he could have done it, with a lot of work and a good calculator. And if he did, it was a fine job indeed. But that would still prove the point that there was an intelligence behind this document.

Your personal opinions aside, the way to disprove the encoding of the document is to provide another one that is also encoded purely by chance. In all my years of studying the qabalah and discussing this online, I've yet to see someone provide such evidence.

Litlluw
RLG


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(@jg)
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I do not want to get into the logic of deciphering literal numerical ciphers right yet.  I sketched out a thread yesterday which touches upon a lot of the issues raised by Crowley's remark at the opening of his commentaries on AL that the "numerical system of cipher" is necessary ( my emphasis ) to prove "to the student that the Author of the Book is possessed of knowledge beyond any yet acquired by man"

When I am happy with the form of the sketch I will post it.  For now I add another little experiment, this time not using the base three values of the Trigrams which correspond to the letters Crowley assigned to them, but rather their ordinal values.  Admittedly, there appears to be a greater rationale for using the Trigram values, not only due to the richness of their global results, but from the simple fact that both the letters as a Class B assignment, and the Trigrams as Class A, already exist a priori, whereas AC never did, to the best of my knowledge, assign ordinal values to the letters.  After all, one could assign any number of sets of values - say - 1 to 10 to 100 to 800 -  along the lines of the Greek and Hebrew numbering of the letters of their respective alphabets, and other progressions.  However, one might read, as I did, many years ago, the "order & value" of II 55 as "order x value" in the manuscript - that is - the order ( of the alphabet in Trigrammaton ) is the x or unknown values of the letters.  Working from this principle here is an example using ordinal values of the letters which parallels in the measure the global sum of AL III using the Trigram values of Trigrammaton.

However, in this case let us sum AL II - all its verse numbers, words, and numbers, and we discover it equals the sum of 1 to 450 where using Greek isopsephia 450 = Νυ - the first word of the chapter just summed.  Further, the letters of the verse which follows AL II, the first verse of the third chapter

Abrahadabra!  the reward of Ra-Hoor-Khut = 450

It is also notable that by this method Abrahadabra = 146 and it is the first word of the 146th verse of the Book.  Obviously then verses 67 to 146 of the book equal counting all words, numbers, and verse numbers, the sum of 1 to 451 where 451 is the sum of verse 146 when its verse number is included.  These are the verses which are numbered in the manuscript.  The difficulty of determing a "best fit" gematria - and if I have not made it clear - I think the "minimum" classical values do the trick - is further borne out by the fact if we take the letters of Trigrammaton 0-25 instead of 1-26 verse 146 equals 418 the value of the first word of the verse using the classical values.  "Who shall determine the value?"  Whatever value anyone may place upon the above result, it actually is mathematically beautiful and elegant.  Can one say anything else without jumping the gun?

John


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