I’ve tried to go through the method you proposed more carefully and, at least in its overall structure, I think it works and has an internal consistency.

Starting from the 1984 value and applying the progression you identified, the results come extremely close to the values actually shown in the document. In some cases, the match is virtually exact.

What I still have some doubts about, however, are the adjustments needed to obtain an exact match for some of the values.

To achieve certain matches, we have to introduce specific assumptions about mistakes made by the author, such as the additional day or a misinterpretation of the reference time used in the ephemeris.

The problem, in my opinion, is that if we were simply dealing with a systematic error by the author, or with a general lack of precision in his calculations, I would expect that error to propagate in a reasonably consistent way throughout the table. But that does not seem to be what happens.

Applying the same underlying structure, some rows still leave small discrepancies that differ both in magnitude and in direction. In 1968 the predicted value differs by a few seconds in one direction, in June 1981 the discrepancy is different again, and in 1982 it even changes sign.

At the same time, other rows, particularly October 1981 and 1985, match almost exactly, while 1974 is still extremely close.

For this reason, I’m not entirely convinced that we necessarily need to “correct” every discrepancy by attributing it to a mistake by the author.

My impression, at least for now, is slightly different: the mathematical structure you identified may well be correct, but the remaining discrepancies may not necessarily be errors that need to be eliminated. They could instead be part of the construction itself, perhaps intended to produce an additional layer of interpretation, an abbreviation, or a short hidden message.

After all, this is a possibility that you yourself had already considered.

In that sense, perhaps one of the most interesting aspects of your model is not only that it is able to reconstruct a large part of the values in the table, but also that it allows us to determine quite precisely where, and by how much, the original values differ from the theoretically expected ones.

And from this point of view, I would also reconsider the famous one-day error: what if that too was intentional?

The 1983 case, however, still leaves me more doubtful. In that case, in order to arrive exactly at 11:08:02, we have to assume a different procedure from the main structure, together with a particular combination of errors made by the author. It is certainly possible, but for the moment I find it less convincing than the general relationship you identified for the other years.

I hope I have understood your method correctly.

In my interpretation, the author is not necessarily using sidereal time or right ascension as the actual method for generating the values in the table.

My impression is rather that he had access to astronomical tables, probably related to sidereal time or ephemeris data, and used their structure, terminology, and perhaps some of their values as a model for constructing the numerical triplets that appear in the letter.

In other words, the groups of three numbers may have been chosen primarily because they were suitable for hiding a coded message, while still preserving an appearance that was sufficiently “astronomical” to suggest hours, minutes and seconds, right ascension, sidereal time, or even geographical coordinates.

If this hypothesis is correct, the ambiguity would not be a flaw in the construction, but one of its intentional features.

The author may have wanted to create a structure that would lead anyone trying to interpret it to focus on the dates of the murders, the times, the ephemerides, geographical coordinates, and possible calculation errors. Every small inconsistency would then become a new problem to explain, continuously generating new hypotheses and wasting the time of anyone attempting to solve the document.

In this sense, even the apparent “errors” could serve a specific purpose: to make it plausible that a genuine astronomical calculation lies behind the table, without that calculation necessarily being the fundamental mechanism used by the author.

The astronomical structure could therefore function mainly as a cover or a false trail, while the real purpose of the numerical triplets would be to provide the values needed to construct the hidden message.

Put another way: the astronomical appearance may be the disguise of the cipher, rather than the cipher itself.

Posted by: @lendor-77

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To achieve certain matches, we have to introduce specific assumptions about mistakes made by the author, such as the additional day or a misinterpretation of the reference time used in the ephemeris.

The problem, in my opinion, is that if we were simply dealing with a systematic error by the author, or with a general lack of precision in his calculations, I would expect that error to propagate in a reasonably consistent way throughout the table.

I would not accept, either, any random error explanation introduced merely for the purposes of getting the results to match. For this reason, I leave the residuals that remain as unexplained currently. However, the two errors that you note certainly are not of this quality. Both are errors of the kind that a novice, or someone being just careless, could be (if you will) expected to make. More to the point, the two certainly do propagate consistently through all the rows excepting 1983.

A difference of one day corresponds to a mean increase in right ascension of approximately 3m 56s. Likewise, the table look-up error propagates an error of the order of 1m. Setting aside the baseline 1984 row and the undoubtedly exceptional 1983 row, three of the remaining fall precisely and three are out by only seconds.

As for the table look-up error, we can actually account for this occurring precisely as a result of the prominent ephemerides—principally the American Ephemeris and Nautical Almanac and its British counterpart, the Astronomical Ephemeris—not changing over from a 12h UT daily epoch for solar Right Ascensions to 0h UT until precisely 01 January 1984. Thus a person having used an ephemeris for 1983 would, if not paying attention, be more than likely to miss the change and use the wrong epoch for 1984, which is what we see.

As errors, neither are introduced solely for the purpose of getting the math to work but are deducible and confirmed precisely through their being consistently propagated.

Posted by: @lendor-77

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The 1983 case, however, still leaves me more doubtful. In that case, in order to arrive exactly at 11:08:02, we have to assume a different procedure from the main structure, together with a particular combination of errors made by the author.

For the 1983 RA, I would now loosen my previous suggestion somewhat and propose that the author chose to select an event time of 20:45 UT as perfectly reasonable and then, performing a table look-up and introducing the one slip of subtracting instead adding, produced the RA for this year precisely as it is given in the table.

This sits easily with the prior explanation of the 1984 epoch error as, having just used the 12h UT daily epoch for 1983, correctly, he would then have been primed to err as he did when turning to the ephemeris for the following year.

Posted by: @lendor-77

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And from this point of view, I would also reconsider the famous one-day error: what if that too was intentional?

It wouldn’t achieve anything other than to shift all of your deductions by some predetermined amount, different for each row and such that the author can have no control over.

Posted by: @lendor-77

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The astronomical structure could therefore function mainly as a cover or a false trail, while the real purpose of the numerical triplets would be to provide the values needed to construct the hidden message.

There simply are not sufficient freedoms left to permit anything approaching what you propose. The only such freedoms you could possibly argue for lie in the residuals in the seconds on three rows together with two two signs out of forty which, even then, are only held back by one sign each. There simply isn’t anything to work with here to add something of the intricacy and complexity that you propose. Not to mention, we can account for one of the sign errors in a fully analogous manner to how we can account for the baseline RA error, a slip of not following the given instructions fully.

Can you reconstruct the one-day error independently of the values in the artefact? In other words, what specific calculation would cause the author to assign the 1984 baseline a day-number exactly one day too high?

Posted by: @lendor-77

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In my interpretation, the author is not necessarily using sidereal time…

There are no sidereal times here. I cannot stress this enough.

From an early age I was looking through telescopes and consulting ephemerides to deduce where to point them to locate objects of interest. All this stuff is in my blood and not merely something I’m forcing my head around today, for this purpose.

Sidereal times are exactly what their name indicates… times. They only have relevance when associated with some event that they are the time of. You use the sidereal time columns in ephemerides to set your observatory clock and then you forget about them. Even then, you have to adjust for longitude and the different rate at which a sidereal clock runs compared to a conventional clock.

Right Ascensions tell you where the sun is. They have meaning.

Posted by: @lendor-77

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Can you reconstruct the one-day error independently of the values in the artefact? In other words, what specific calculation would cause the author to assign the 1984 baseline a day-number exactly one day too high?

It is the only place where a one day counting error could occur so as to propagate through all of the extrapolations identically, since the year day for 1984 would be calculated once and then used in all subsequent determinations of the time interval between each event and the baseline through simple addition. The first term in the sum is the time from the event to the beginning of 1984, a different duration in each case. It would not be plausible to propose an error of one day was made here six times over.

Don’t forget also, as I had explained previously, the effect is found to be correctly asymmetrical as it appears in the table, pushing the RAs for the years before 1984 further away whilst drawing that for 1985 closer to that for the baseline year. Non-additive errors would produce the same effect either side of the baseline, either drawing both in or pushing both out.

Posted by: @lendor-77

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The author may have wanted to create a structure that would lead anyone trying to interpret it to focus on the dates of the murders, the times, the ephemerides, geographical coordinates, and possible calculation errors. Every small inconsistency would then become a new problem to explain, continuously generating new hypotheses and wasting the time of anyone attempting to solve the document.

Is there not some element approaching confirmation bias here, Lendor? Under the straightforward astrological reading, what is there to be “solved?” At the end of the post this comes from you refer to one or other of either the “astronomical appearance” (sic., “astrological”) or some hidden message as being “the cipher,” but this without any consideration of the fact that there is almost certainly no “cipher” here at all. As a table, the context is easily understandable. As noted in the Trinca-Petronius expert report:

”From the interpretation of the tenth row, one could derive the date on which an astral situation analogous to the preceding ones might occur, corresponding to those in which the murders were committed.”

I have spent some considerable time attempting to deconstruct the artefact in order to gain a sense of the level of knowledge and expertise of the author, but I have certainly not been decoding anything. It is what it is and, to my satisfaction, can be shown to be such, as well as being the production of someone with very fragmented astronomical knowledge and only a rudimentary acquaintance with how to extract data from ephemerides correctly.

Contrary to the expert report, however, I remain strongly of the view that the author was, indeed, only sixteen at the time of its production, had joined an astronomy club or local observatory in 1983 or 1984 and had subsequently drifted away from astronomy into astrology.

Note also, if you are proposing that the result of your decoding is the real content of the artefact and that the astrological/forensic aspect is just a cover, then all you are achieving is to invite the same problems regarding ‘freedoms’ in reverse, this time in having the former demonstrate, as shown, its undoubted appearance of clear intent.

Posted by: @shaqmeister

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this time in having the former latter demonstrate, as shown, its undoubted appearance of clear intent.

Posted by: @shaqmeister

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At the end of the post this comes from you refer to one or other of either the “astronomical appearance” (sic., “astrological”)

The table is astrological in purpose, but astronomical in its underlying data. Sorry if I have been using the two terms somewhat imprecisely.

I think perhaps we are looking at the same table from two different perspectives, and I don’t necessarily see the two approaches as incompatible.

I don’t consider your interpretation to be wrong, although I still have some doubts about certain aspects of it. For example, I find it difficult to imagine a sixteen-year-old constructing and sending a letter like this while also managing to reproduce some of the distinctive features and nuances of the cut-out lettering used in the envelope sent to Silvia Della Monica.

What I would really like to understand is this: how could I convince you that my interpretation also starts from a valid premise, without having to “bribe” you, but by using criteria that are as scientific and analytical as possible?

In other words, what would my interpretation need to demonstrate for you to consider it seriously as a possible second layer of meaning in the table?

I’m thinking maybe an analysis of the freedoms actually available to your construction might be useful here. I’m needing to go out for a bit but perhaps you might start by proposing what digit pairings (‘##’) and which signs you would accept as under the control of the author once the astrological model is in place. Just as a starting point. There are 24 digit pairs and, if you count the prediction row, 44 signs. Which would you accept your adult author has the freedom to vary?