If I apply all possible Caesar shifts to the triplets after converting them using an A=0 system, some interesting combinations begin to emerge and seem to recur across different years. In a few cases, similar sequences or structures appear despite starting from different triplets. I don’t know whether this has any real significance or whether it is simply a natural consequence of the transformations, but I think it is still worth keeping in mind.

Sorry about the odd formatting there, if you’re getting it also. Again, as an image:

Posted by: @lendor-77

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In a few cases, similar sequences or structures appear despite starting from different triplets. I don’t know whether this has any real significance or whether it is simply a natural consequence of the transformations, but I think it is still worth keeping in mind.

This recurrence is happening because in two of the cases—1968 and October 1981—the difference between the first and second numbers and that between the second and third, each taken modulo 26 where required, are the same, namely:

10 (–9) 01 (+3 + 26 + 26) 56

14 (–9) 05 (+3 + 26) 34.

There is nothing particularly special about this occurring. What it produces is the same repeating cycle, just out of step with each other by 14 – 10 = 4.

Posted by: @shaqmeister

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There is nothing particularly special about this occurring. What it produces is the same repeating cycle, just out of step with each other by 14 – 10 = 4.

Another way of noting the same is to take the two RAs and reproduce them with each of their three components reduced modulo 26, where required. This brings them to:

10 01 04
14 05 08

after which we can see readily that the second row, per digit pair, is derived from the first by adding 04 three times.

The value of the ‘Zodaic’ ephemeris, namely:

is that it illustrates immediately what the sender of the Vagheggi letter was attempting to emphasise in respect of Il Mostro’s attacks.

Unless we are applying pre-judgement and effectively begging the question, then the Zodiac ephemeris should function as a randomised control to what we have from Il Mostro. And we do, indeed, see this clearly. Even with only the four events, we effectively lose all of the tendency towards higher degrees of concentration of signs. That is, except in the last row, partly, but this is only brought about by the fact that the Moon happened to be close to new. And neither do we find our celestial bodies confined in the main to the domiciles of the Sun through Mars, as we now find all of Capricorn, Aquarius and Pisces occupied.

Posted by: @lendor-77

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If I apply all possible Caesar shifts to the triplets after converting them using an A=0 system, some interesting combinations begin to emerge …

So I’ve made several attempts to apply this, your favoured method, to the numbers given in the Vagheggi table—for example, summing the three numbers in each RA, applying a modulo 26 and then running through the corresponding Caesar shifts—and I’m not finding anything at all that stands out to me. Taking this along with my analysis of the general aim and purpose of what the table appears to be conveying, I do not get any sense that there is anything deeply cryptic that is hidden here. I have reached the point of feeling that I am caught in the proverbial act of “looking for a black cat in a dark room that isn’t there.” 🤣

I found this article at the end of my own researches and feel that I can broadly agree with what is there deduced as to what it is we actually have in the Vagheggi table: Il Mostro di Firenze Addendum 2: sulla lettera a Paolo Vagheggi. (Not so much the “motivation” part, though.)

All the same, I wish you happy hunting and better luck than I have had. 👍

Maybe some of your thoughts, and this conversation in general, have helped me find something! I can’t say yet whether it’s really the solution to the problem, but at least it’s a solution that finally feels right to me and that I’m genuinely happy with. Hopefully I’ll manage to write it down today or tomorrow!

In the meanwhile, it seems worthwhile to offer a reconstruction as to how the sender of the Vagheggi letter may have easily gone about constructing the table of Right Ascensions and signs, requiring nothing more than access to contemporary ephemerides and astrological tables and the application of only some basic degree of skill in interpolation. The purpose, here, is to demonstrate that there is no requirement that he or she possessed overly specialised knowledge or was called upon to perform complex calculations involving spherical trigonometry or any other such horrors.

The calculation I shall reconstruct shall be the one that is most readily demonstrated, although this is not with the intention to hide that there are real problems in accounting for evident errors in the compiler’s handling of data for the most part. We shall also be making use of contemporarily available data sources without any claim that these were the precise ones originally accessed. However, as the data themselves are not such as should show variation across alternative presentations, we can be largely confident that the same results would be attained whatever the specific sources used.

The line in the table for 1984 reads: 

8 34 59 84 LEO LEO VIR LEO SCO

The interpretation of the table as a whole, as discussed already, informs us that the context for this entry is the 1984 double killing of Claudio Stefanacci and Pia Rontini on July 29 near Vicchio, in the Metropolitan City of Florence, Tuscany. We would then be looking for the first three numbers on the left to correspond to the Right Ascension of the Sun on, or around, the time of the killing. For this, we have the reports of witnesses placing the sound of gunshots around 21:45 hrs CEST. We will then, first of all, see how an ephemeris may have been consulted and used to determine the Sun’s RA in the first instance and, for this, we will turn to the Bureau des Longitudes, Éphémérides astronomiques 1984 (Paris: Gauthier-Villars, 1983) and the specific Sun tables for July, which are as here:

Now, 29 July 1984 at 21:45 CEST equates to 19:45 UT on the same date. We therefore need to undertake a straightforward interpolation of the RAs given for the 29 and 30 July 1984 at 0h UT, over which period the Sun’s RA changes from 08h 33m 43s to 08h 37m 38s. This amounts to an increase of RA by 3m 55s, or 235s, per day. We next determine that 19:45 UT corresponds to 19.75h past 0h UT on the 29th, which is a duration of 19.75/24 = 0.8229167day. We then need merely to add 0.8229167 × 235 = 193.385s of RA to the RA for the 29th at 0h UT, which gives 8h 36m 56.4s.

But this, clearly, does not give us the 8h 34m 59s we had been expecting!

Now, here, we can diagnose the influence of an easy-to-make error. Let us suppose that the author had confused his morning and evening times in his calculations and, instead of 21:45 CEST had used instead 09:45 CEST, equating to 07:45 UT. That deduction of 12 hours then accounts for a reduction of the RA by 0.5 × 235 = 117.5s or 1m 57.5s and, deducting this from our initially determined 8h 36m 56.4s gives us 8h 34m 58.9s, which rounds up precisely to the value we see in table.

From this, it is thus evident how the Right Ascension for the Sun at the event time of the double killing on the evening of 29 July 1984 could have been readily obtained from conventional astronomical tables albeit, in this instance, involving a clearly deducible and understandable error.

The path to which constellations the five celestial bodies were in at the time of the event in Vicchio (whether taken correctly, or including the 12h timing error), would have required access merely to the kind of astrological almanac that would have been readily available over newsagent counters across Europe. Such almanacs would have produced some such simple table as the following, which itself is taken from the 1983 edition of The American Ephemeris for the 20th Century (Michelsen, N. F., 1983):

Simply tracing back up the columns from the row for the 29 July 1984, we can immediately see that the Sun was in Leo, the Moon in Leo, Mercury in Virgo, Venus in Leo and Mars in Scorpio.

Again, this is precisely what we find documented against the 1984 entry in original artefact, which one line, at least, we have now been able to readily and plausibly account for.

Posted by: @shaqmeister

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From this, it is thus evident how the Right Ascension for the Sun at the event time of the double killing on the evening of 29 July 1984 could have been readily obtained from conventional astronomical tables albeit, in this instance, involving a clearly deducible and understandable error.

On further study it would appear that our identified 12h error here, although still very much present and demanding of explanation, may actually derive from a more plausible source. From the table of the Solar RAs that we had taken our start from, we can see the daily epoch clearly stated as being 0hUT. Prior to 1984, however, the same ephemerides were constructed using noon (12hUT) as the daily epoch. A person, therefore, ingrained in the old format would make just such a 12h error if it were simply the case that they had not registered the change. This feels like a much more plausible explanation than grounding the error in some unlikely mixup between times am and pm.