Let’s pause a moment, and remind ourselves that, for this particular attempt at reconstruction, we are trying our best to give every favour logically possible to our compositor. To this end, then, we can absolve him of all the nonsense we have encountered thus far in the following simple manner.

We can propose that it was always his intention to mask his cryptic hidden communication as deeply as possible behind the illusion of a straightforward and simply interpreted astrological construction. Of course, our analysis has shown that, in proceeding in this manner, for the most part he has had next to no freedom to reach a point that he could have intentionally sought or predicted in advance, but perhaps he didn’t need this.

Starting with the base model, using the two correct look-ups and applying the hybrid (nonsensical) model of extrapolation for the remaining six rows without overcount, he could then have applied the 12hr shift to the propagating 1984 RA, added in a one day overcount, again propagating, and then corrupted the 1983 lookup manner by switching the sign of the second term; and all this, just to jumble things up.

This, of course, as we have shown, would not have (to this point) permitted him any freedoms in terms of what he would obtain for his two alpha sequences later. To this point, together with the granted ‘freedom’ to perform summing across the sign columns, row by row, and then to choose to single out whatever he was left with under the Mars column (come one, come all), all this could have bought him was his actual starting point. To here, it’s all just obfuscation. The actual work of encoding starts now, with the two sequences:

J D X H E A J D U E D G A Z B G

and:

B G T J S D D A

Our compositor may have seen something he liked in either or both of these but, to this point, he has had no freedom enabling to select these outcomes in advance and manipulate the underlying data to set them here. ‘BG’, in the sign sequence, was either there, or it wasn’t. ‘J…BG’ was either there, in the RA sequence, or it wasn’t.

Being thus kind to our compositor, then, we shall suppose that all the data shifting up to this point has been merely to hide the scent, and that the real cryptic construction starts here.

Having got this far, we can imagine the compositor having added the undated row of signs, minus one for the Sun, with the intention of having these sum to the letter J which he can then add to the end of the second sequence to get the reciprocal ‘JGB’ at the ends of both these sequences, assuming that ‘JGB’ has some relevance to him. Note, however, that beyond the free addition of the final J he had had no ability to set the other five letters there, they were just there. That said, there is nothing wrong in supposing that he might take advantage of this freak of coincidence once it had been presented to him.

And yes, up to this point we are still dealing solely with data derived by coincidence. Aside from the addition of the extra J, according to the proposed SLoI, nothing else exists in either of the two sequences that could have been forced there.

(Note, also, that we cannot at this stage drop the ‘JGB’ from each, which would clearly be the logical point to do so, as we are then left with the single G in the first sequence which would remain after reducing duplicates in the way to follow. Dropping it later, however, removes a G that is no longer at the end, thus corrupting the whole intention here.)

Two single-shift freedoms are afforded to the second sequence, and I would have to imagine that we would justify these through the observation that we are thereby starting to get hints of something that could, with anagramming, end in ‘…DIAC’. This, then, leaves us with a sign sequence that contains no repeating letters and so, of course (???), we must achieve the same for the first sequence, even though in choosing to do so we are again merely imposing an uncontrolled remainder as our result. Still, we do precisely this and together, with our dropping of the reciprocal ‘JCB’s, our two sequences become:

D X H E A U Z

and:

T I S C D A

Again, these remainders are just what happens to be left after all the has preceded, all except the now presence of the introduced I and C.

We need something to direct us, at this point. We cannot simply continue to inflict uncontrolled alterations upon what we have and suppose that we have any direction, thereby, in choosing what it leaves to us. In terms of the SLoI, then, we can perhaps most usefully start with the word ‘ZODIAC’ and its relation to the second (sign) sequence, as partially present. Maybe we can visualise this relation usefully in this manner, emphasising the overlaps and the differences:

T S [D I A C] Z O

But, what does this incidental relationship afford us, precisely, in terms of how we are to proceed with some manner of encoding? How do we construct some parallel relationship with the first sequence such that we can realise some preconceived result? What, actually, is this preconceived result?

Well, apparently, we are driven to take the non-common letters here, T, S, Z, O, remove the Z (of course! No confirmation bias here 🤣) and sum them to get 51. And, while we are at it, let’s drop the Z from the first sequence to leave:

D X H E A U

Let’s then think about how we might wish to compare this with the scripted ‘DXHAND’ on the opposite side of the card to the astrological table. As before, we highlight the overlaps and differences as:

E U [D X H A] N D

and sum the differences, none of which (as has been shown) were under the control of the compositor, to reach:

4 + 20 + 13 + 3 = 40

Oops.

To get, again, to 51 (this being the point, evidently) we need an extra 11, which would require that our ultimate sequence be supplemented with either an ‘L’, or with two other letters summing to the equivalent of an ‘L’.

Let’s, then, continue to follow our hypothetical compositor reasoning and search for how we might introduce an L in the RA sequence.

Apparently, we take the fixed address from the envelope as “35 maggio,” none of which can be changed so, if it happens to contain the number ’35’, and if it happens to contain the Italian word for the month of ‘May’, so be it. We can still make use of both.

Now, given that we are applying a modulo 26 adjustment to our number-alphabet conversions, we can get the letter L from any of 11, 37, 63, etc. and, were we to wish to derive the L in some non-direct manner (why not), we might form it from any one of:

x – 35 = 11 | 37 | 63

which we get from any one of:

x = 46 | 72 | 98

We choose 72 as, masked as a year, it would fit cleanly into the sequence of years that we already have, and thus we can insert the row “72 may” into our table, appropriately.

But then, what have we got? Well, apparently, what we have got at this point is the freedom to take the difference between 72 and 35, that is, 37, to reduce this down modulo 26 to 11 and then avail ourselves of the freedom to insert a spurious L into our resultant RA sequence, to give us:

L E U [D X H A] N D

and thus:

11 + 4 + 20 + 13 + 3 = 51

Bingo!

And after all of this, dear friends, this is precisely why we must remain daily grateful of the fact that Occam chose absolutely not to keep his discovery secret. 😶 

Posted by: @lendor-77

↑

If, in order to reconstruct the triplets, we have to attribute several different errors to the author, some of them inferred precisely because they help reproduce the values in the artefact, then I do not think we can simply say that those numbers were completely “determined” by the astrological purpose.

The key factor in relation to the “inferred errors,” as you call them—the one which argues against your interpretation of non-determinism here—is that the errors thus identified propagate.

If it were a case that we had simply proposed that “this value is out by a, and this other value is out by b, etc.” and offered independent adjustments to realign each separately then I would be fully in agreement with you. You will notice that I have, for this very reason, avoided attributing any specific mode of error to reproduce the three instances where the RAs are out from the model to the order of seconds of RA.

Where, however, an error is identified and is able to be understood according to not only a simple explanation but, in every reasonable sense, an expected one; and where this same error is then found to be propagated across all of the relevant rows of the table, then we are finding ourselves traversing a wholly different territory altogether, and the suggestion that we have merely “introduced this error to reproduce values in the artefact” wholly breaks down. The very occurrence of propagation is confirmatory. Add to this the fact that our ‘errors’ are of the nature of simple unit of half-unit shifts and we can be certain, in conjunction with their propagation, that we have fully explained (determined!) their origin.

To follow up on this previous point, you can think about it like this. Where the propagation of errors appear in formulating the astrological purpose, the very fact of their propagation goes most of the way to aiding us in identifying them as actual errors. The propagation element, in this sense, is our friend here, and affords no real harm to the compositor as he clearly is unskilled in what he is seeking to achieve and is unaware of having erred at all.

As for our hypothetical cryptographic compositor, however, introducing, or even permitting, propagation in the construction of the table can only work counter to his aims. He would be merely tying his hand to no particular positive end. To give him the maximal freedoms to hide a second layer of intent beneath the mask of the first, he must seek in every way possible to ensure that he does not constrain his ultimately mutable data elements to be tied together in any “change one, change all” way. The idea that he would is simply preposterous.

Thus, we can argue with high probability that just the mere inclusion of propagating ‘errors’ argues, of itself, against the construction of the artefact table being for the sole purpose of facilitating development of any second layer.

Does that make sense?

Posted by: @shaqmeister

↑

Well, apparently, we are driven to take the non-common letters here, T, S, Z, O, remove the Z (of course! No confirmation bias here 🤣) and sum them to get 51. And, while we are at it, let’s drop the Z from the first sequence to leave:

D X H E A U

Let’s then think about how we might wish to compare this with the scripted ‘DXHAND’ on the opposite side of the card to the astrological table. As before, we highlight the overlaps and differences as:

E U [D X H A] N D

and sum the differences, none of which (as has been shown) were under the control of the compositor, to reach:

4 + 20 + 13 + 3 = 40

Oops.

To get, again, to 51 (this being the point, evidently) we need an extra 11, which would require that our ultimate sequence be supplemented with either an ‘L’, or with two other letters summing to the equivalent of an ‘L’.

On the 72 − 35 step, though, I think the logic is different from the way you are presenting it.

I am not starting from the result and saying, “I am missing an L, so let me find a way to produce one.”

The two numbers are already present in the artefact, and in my interpretation the MAY / MAGGIO wording acts as a bridge suggesting that they should be related to each other. It is precisely this element that leads me to think again in terms of a delta, just as in the triplets.

So the step:

72 − 35 = 37 → 11 (mod 26) = L

does not arise at the end because I need to add an L. It arises earlier, from the structure of the artefact itself and from the MAY / MAGGIO cue, which suggests making those two numbers interact through a difference.

The L is therefore the result of that operation, not the reason why the operation was chosen.

And the idea that the envelope itself might provide an operational hint has a very interesting precedent in Zodiac. On the Z340 envelope, “Please Rush to Editor” is written diagonally, and the cipher was later shown to rely on diagonal transposition.

That is why I think it is perfectly reasonable to consider MAY / MAGGIO not as part of the final message, but as an indication of how two already-present elements should be read in relation to each other.

Posted by: @shaqmeister

↑

Well, apparently, we are driven to take the non-common letters here, T, S, Z, O, remove the Z (of course! No confirmation bias here 🤣) and sum them to get 51. And, while we are at it, let’s drop the Z from the first sequence to leave:

Why separate the Z?

I think there is an important detail here. The residuals produced by the two paths are:

Z T S O

and

Z L U N E D

The two residual sequences have only one letter in common: Z.

Moreover, using A=0, both have exactly the same total value:

Z + T + S + O = 76

Z + L + U + N + E + D = 76

If we then separate the only element they have in common, namely Z = 25, both independently leave:

76 − 25 = 51

So whether we consider the result as 76, or as Z + 51, the correspondence between the two systems remains exactly the same.

That is why I do not see the separation of Z simply as “remove Z because that gives 51.” Z is already structurally distinguished because it is the only residual common to both paths, and once it is removed, both independently lead to the same value, 51.

Of course, one can still debate the meaning assigned to 51, but the arithmetic symmetry between the two groups of residuals exists independently of that interpretation.

Posted by: @shaqmeister

↑

We need something to direct us, at this point. We cannot simply continue to inflict uncontrolled alterations upon what we have and suppose that we have any direction, thereby, in choosing what it leaves to us. In terms of the SLoI, then, we can perhaps most usefully start with the word ‘ZODIAC’ and its relation to the second (sign) sequence, as partially present. Maybe we can visualise this relation usefully in this manner, emphasising the overlaps and the differences:

T S [D I A C] Z O

But, what does this incidental relationship afford us, precisely, in terms of how we are to proceed with some manner of encoding? How do we construct some parallel relationship with the first sequence such that we can realise some preconceived result? What, actually, is this preconceived result?

Why ZODIAC?

I think the context is important here.

We are not taking an arbitrary sequence of letters and comparing it arbitrarily with the word ZODIAC.

Those letters are derived directly from a table built from zodiac signs. So if we want to check whether the resulting sequence contains a second layer of meaning, ZODIAC is the most natural reference to test. In other words, the comparison comes directly from the same system that generates the letters.

On the other side, I am comparing the second sequence with DXHAND, which is not a word or reference I selected freely afterwards, but something given by the author himself.

So in both cases the comparison terms are closely connected to the material that produces the two sequences.

Of course, one could run another test using random words and ask how many of them, when compared with the two sequences, could produce residuals with the same numerical value.

But even if many random words were able to produce some numerical coincidence, there would still be another question: how many of those words would also be as closely connected to the subject and structure of the artefact as ZODIAC and DXHAND are?

For me, it is precisely this combination of semantic relevance and numerical convergence that makes the comparison interesting.

Posted by: @shaqmeister

↑

(Note, also, that we cannot at this stage drop the ‘JGB’ from each, which would clearly be the logical point to do so, as we are then left with the single G in the first sequence which would remain after reducing duplicates in the way to follow. Dropping it later, however, removes a G that is no longer at the end, thus corrupting the whole intention here.)

On this point, I think there is simply a misunderstanding about the order of operations.

The comparison between the two sequences is made before repeated letters are removed.

So it is in the original sequences that I observe the structure:

J … BG

on one side, and

BG … J

on the other.

Only after noticing this do I remove repeated letters from the triplet sequence and continue with the later comparisons. So the fact that the final G is subsequently removed during deduplication does not erase the symmetry observed at the beginning. That symmetry is what identifies JBG; it does not require the same three physical occurrences to survive every later transformation.

There is also another small symmetry that I may not have emphasized enough.

In the comparison:

TISCDA / ZODIAC

the two sequences have 4 letters in common:

D I A C

In the comparison:

DLXHEAUZ / DXHAND

we again have 4 letters in common:

D X H A

After removing those matches, the residuals are:

Z T S O

and

Z L U N E D

They have only one letter in common, Z, and the same total numerical value, 76.

Removing Z = 25 leaves 51 in both cases.

So the correspondence I am looking at does not arise only from the final number 51, but from a sequence of parallel structures between the two paths.

Posted by: @shaqmeister

↑

Two single-shift freedoms are afforded to the second sequence, and I would have to imagine that we would justify these through the observation that we are thereby starting to get hints of something that could, with anagramming, end in ‘…DIAC’. This, then, leaves us with a sign sequence that contains no repeating letters and so, of course (???), we must achieve the same for the first sequence, even though in choosing to do so we are again merely imposing an uncontrolled remainder as our result. Still, we do precisely this and together, with our dropping of the reciprocal ‘JCB’s, our two sequences….

Another point I would like to clarify concerns the two Moon modifications.

I am not introducing two lunar shifts because I need an I and a C.

Those two discrepancies are already present in the original table.

Starting from the correct astronomical data, the cumulative sum up to Mars gives:

B G T J S D D A

But in the actual table there are exactly two Moon positions that differ by one zodiac sign from the correct astronomical value.

If we simply apply those two anomalies already present in the artefact, we get:

J → I

and

D → C

therefore:

B G T I S C D A

So the interesting question is not whether those two modifications were added in order to make the solution work. They were not: they were already there.

The real question is whether they are simply accidental errors by the author, or whether they may have served an intentional purpose.

We may certainly disagree on that point, but I think it is important to keep those two issues separate.

Posted by: @shaqmeister

↑

And yes, up to this point we are still dealing solely with data derived by coincidence.

It is precisely the expression “solely with data derived by coincidence” that I disagree with.

Up to that point, we are not simply dealing with astronomical data passively producing an inevitable sequence.

The artefact itself is already the result of choices made in constructing the table: it presents the five bodies up to Mars, and it also contains two Moon positions that differ by one sign from the astronomically correct values.

I am not saying that this proves the author made those choices intentionally in order to create a second layer. That is exactly the question we are discussing.

But it does mean that I do not think BGTISCDA can simply be described as a result derived “solely from coincidence”. It is the result of the astronomical data filtered through the table as the author actually chose to present it, including its two lunar anomalies.

And this is precisely what I was trying to quantify with my test: not whether the author could freely choose every individual letter, but how much the choices available in constructing the table could increase the possibility of obtaining a useful configuration.

The test shows that this degree of choice can have a very significant effect. Whether the author exploited it intentionally is a separate question, but I do not think we can simply label the whole result as “coincidence”.

Posted by: @shaqmeister

↑

For some reason, focus turns to the Mars column alone—I would imagine we would be asked to believe that this was on account of the letters BG occurring at the top—and we select this one from al the others, so:

Why the Mars column?

I think there is a misunderstanding here.

I am not focusing on the Mars column because I happen to see BG at the top and then opportunistically choose that column.

In your table the values are cumulative. So the Mars column represents:

Sun + Moon + Mercury + Venus + Mars

which is exactly the set of five bodies that the author actually included in the original table.

So when I look at the Mars column, I am not choosing one column among many simply because it produces an interesting result. I am reconstructing the result obtained by using all and only the five columns that are actually present in the artefact.

The fact that you extended the calculation further to Jupiter, Saturn, Uranus, Neptune and Pluto is useful for exploring other possibilities, but those additional columns are not part of the original table.

For that reason, I do not think it is correct to describe the focus on the Mars column as being motivated by the appearance of BG. The primary reason is already present in the artefact itself: the table ends with Mars.