Thus, we start by acknowledging that, in order to have the freedoms required to intentionally construct the hidden message that you propose is present then, in accordance with the method of construction you propose, we would have to be able to have control over each of the three digit-pairs comprising the eight right ascensions and each of the forty planetary signs independently of each other. We do not gain the necessary control if changing one of these elements effects a parallel change across a whole series of other such elements. In the latter case we would merely be exercising a single local ‘freedom’, if you like, only to shift a new ‘constraint’ across all the other affected elements.

We can reconstruct the right ascension for 1984 as a straightforward table look-up making erroneous use of the daily solar epoch for the previous year, having missed the change for 1984. Can this, you ask, not be deliberate, in order to support construction of the hidden encoding?

No. It can’t, for the very reason that such a supposed intentional shift would affect both the minutes and the seconds for 1984 and further, since the RA for 1984 is perpetuated as a baseline through six of the remaining rows, the total number of elements that would suffer an uncontrolled modification under this supposed ‘freedom’ would be fourteen. Thus, even despite the fact that the 12h error is wholly and reasonably accounted for, there would yet not be the freedoms remaining as required by your model even were we to reject this explanation.

Likewise, we find a one-day error of accounting for the year-day of the event in 1984 committed and perpetuated through six rows. The error here again affects both the minute and the seconds elements. Thus, were we to suppose that this one day anomaly were chosen intentionally to make one row produce the required freedoms according to the proposed encryption model, we would merely be subjecting ten other encoding elements to an uncontrolled and fixed shift as a result.

The same considerations apply in relation to the five sign columns. If we were to consider your additional and somewhat misguided proposal that there was some intention in the choice of which planets were selected to be referenced in the table, we find the same unwanted spill-over of the consequences of any such selection. For instance, swapping Mars out for Jupiter with the aim of obtaining a favourable sign in one row for our proposed encryption model, we have to acknowledge that we have thereby inflicted an uncontrolled shift on each of the seven remaining rows. 

The elements from which you construct your model are, in fact, not independent in the manner they would need to be.

The three remaining seconds elements in the right ascensions, even if not readily accountable for by a plausible shift in the time of the evening when these events occurred, together with two sign changes by one sign only are far from sufficient to turn an otherwise wholly fixed table into something masking the complex and intricate encryption you aim to set underneath it.

On the contrary, the analysis of ‘freedoms’, in this instance and in the analytical sense, proceeds like this.

We define a problem space, this being the figures and numbers actually drawn on the artefact. We give no consideration to what could have been set there, as the next phase will show. Upon this clearly defined and limited problem space, we impose a description of its meaning and intent. This is where all the choices and selections as to what planets to include, why certain years are selected, etc. are fixed and formalised. We then consider there being some second layer of meaning and we therefore ask, given the problem space as defined and given the meaning and intent deduced as to the purpose of the first layer, what freedoms would remain to the addition of such a further layer.

The formal analysis of freedoms in this manner is a mathematical, not a psychological one. At this point we are no longer considering why the author chose only to consider planets up to Mars, or any other such choices made prior to this point as, from our prior analysis, we have already fixed these. Our question, then, becomes “given this, what else?”

With this explained, would you still be interested in proceeding with our freedoms analysis in the correct formal manner?

I think, however, that the author’s degrees of freedom should not be calculated starting from the 44 zodiac symbols that appear in the finished table.

If we assume that the ephemeris he was using contained 12 possible celestial bodies or astrological points, then for the eight double murders he theoretically had 96 zodiac positions available to him.

This is wholly untenable. You expand the pool of data points to include a multitude that the author does not consider only to advise that you want to regard their absence as somehow pertinent to what we are left with. As with the astrological account, your second layer must start solely from what we have and not from what we don’t have also. This is the most basic of constraints and both we are both working with exactly what we are presented with.

I believe we should consider the 96 potentially available zodiac positions (12 × 8), rather than just the 40+4 symbols appearing in the final table.

After all, regardless of who the sender was, your sixteen-year-old or my Monster of Florence, it is clear that the letter and envelope required considerable preparation: ephemeris calculations, the numerical triplets, and the selection of clippings from different magazines, some apparently chosen for their specific meaning, as in the case of Monica's envelope.

It is therefore reasonable to assume that the author first planned everything and then produced the final version we are examining today.

It would have cost him virtually nothing to use a larger sheet of paper, fold it, and put it inside the envelope to complete the table. Yet he chose not to, deliberately leaving out some data.

Why? For convenience? To hide something? Or simply out of laziness?

But if it was laziness, why put so much effort into the preparation only to omit some of the table's data at the very end?

This is not proof of encryption, but I think it is more than enough reason not to regard those omissions as accidental or inevitable.

According to my hypothesis, these are precisely the kinds of choices that could have allowed him to reach the numerical or alphabetical combination he wanted.

And these choices are precisely the ones we are investigating here to see if they reflect sufficient freedoms to permit your goal. I will be arguing that they are far from being so, as I confident we shall discover.

The author deliberately chose to stop at Mars, effectively removing the bodies further to the right in the ephemeris. Every column removed means eliminating eight zodiac signs from the construction at once. In this way, he could alter the resulting values simply by deciding which planets or points to retain and where to stop.

This choice, however it might have been made—of course, it was in fact clearly made by merely taking the first three planets in order, in addition to the Sun and the Moon—does not in any way change the freedoms that you would have available under your model for the very reason that any chosen  planetary column, even including those for the various asteroids and whatever artificial satellites were up at the time, merely replaces one wholly fixed and determined column of values with some other fixed and determined column of values. Any gain, therefore, in one row would be offset by an uncontrolled loss in the each of the others. The central point that an analysis of freedoms must confront is not what values you may start out with but whether, under the second model layer you strive to introduce, you have the ability to vary them freely.

Here, you have no greater freedom whichever planets you choose. Not to mention that the actual choice is dictated solely by the author’s astrological purpose. 

There are 44 signs in the table and 24 digit pairs. That’s our data set.

I think, however, that the author’s degrees of freedom should not be calculated starting from the 44 zodiac symbols that appear in the finished table.

If we assume that the ephemeris he was using contained 12 possible celestial bodies or astrological points, then for the eight double murders he theoretically had 96 zodiac positions available to him.

This is wholly untenable. You expand the pool of data points to include a multitude that the author does not consider only to advise that you want to regard their absence as somehow pertinent to what we are left with. As with the astrological account, your second layer must start solely from what we have and not from what we don’t have also. This is the most basic of constraints and both we are both working with exactly what we are presented with.

If we assume that the ephemeris he was using contained 12 possible celestial bodies or astrological points, then for the eight double murders he theoretically had 96 zodiac positions available to him. On top of that, he added a ninth row that is not tied to any of the eight murders and therefore, at least in principle, gave him another 12 completely unconstrained positions.

So from my point of view, the starting space is not 40 + 4, but potentially 96 + 12 values from which the final table was constructed.

The author deliberately chose to stop at Mars, effectively removing the bodies further to the right in the ephemeris. Every column removed means eliminating eight zodiac signs from the construction at once. In this way, he could alter the resulting values simply by deciding which planets or points to retain and where to stop.

He then added a ninth row that is not constrained by the date of any murder, and in that row he changed the structure again by omitting the Sun.

Finally, we also have two Moon positions that appear to have been shifted by one zodiac sign from the astronomically expected values.

So, in my view, the author's freedom does not mainly consist in arbitrarily changing the 44 symbols that survive in the finished table. It lies in being able to select which columns to include, which ones to exclude, add an unconstrained row, and alter a small number of specific values.

According to my hypothesis, these are precisely the kinds of choices that could have allowed him to reach the numerical or alphabetical combination he wanted.