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. 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.
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.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
Besides, the absence of certain data points must affect all hypotheses equally and thus can play no role in deducing whether any two can coexist simultaneously.
There are 44 signs in the table and 24 digit pairs. That’s our data set.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
Let start off correctly. Of the 3 digit pairs starting the 1984 row which, in your model, if any would you wish to consider you have freedom over? That is, which are not already fixed by some criteria already existing under the astrological accounting?
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
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.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
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.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
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.
This is all interesting, but it is not how one defines ‘freedoms’ in the analytic sense. You appear, from what you are asking for here, to be using the term in the every day sense, something like the ‘freedom to chose’. I am beginning to get a sense of how it is you are able to remain optimistic in the face of contrary evidence.
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?
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
As it happens, even without risking getting lost in discussions around the details we can, in fact, undertake a qualitative analysis in the following manner, the conclusion from which is nonetheless clear and unequivocal.
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.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
On the zodiac signs, I understand your point: choosing a different column does not mean having eight independent freedoms, because that choice changes all eight rows at the same time.
However, in my view, this does not necessarily rule out an intentional construction. The author may not have been choosing individual signs, but rather the combination of columns as a whole, precisely because that combination produced the overall sequence he wanted.
As for the numerical triplets, I think the issue is even more interesting and less clearly defined.
Those values do not directly match geographical coordinates, sidereal times, or solar Right Ascension values obtained in a unique way without further assumptions. Your reconstruction based on Right Ascension is certainly interesting and, in several cases, produces results that are very close or virtually exact, but in order to reach the final values we still have to introduce a number of assumptions: the one-day error, the 12h/0h ephemeris reference, specific interpolation choices, the selected time, and, in the case of 1983, a particular procedure.
There are also still small discrepancies in some of the rows.
For this reason, it seems to me that the real question about degrees of freedom, at least for the numerical part, is: how uniquely determined is the final value produced by the model?
If, starting from the same astronomical data, more than one plausible value can be obtained depending on the chosen time, interpolation method, rounding, or other assumptions, then there may also be a certain degree of freedom available to the author there.
in order to reach the final values we still have to introduce a number of assumptions: the one-day error, the 12h/0h ephemeris reference, specific interpolation choices, the selected time, and, in the case of 1983, a particular procedure.
There are no assumptions here. The presence of each of these factors has been deduced from the evidence of the construction of the table.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
There are also still small discrepancies in some of the rows.
For this reason, it seems to me that the real question about degrees of freedom, at least for the numerical part, is: how uniquely determined is the final value produced by the model?
The analytical model of the astrological construction of the table does not have to get to ultimate precision for it to still negate the possibility of there being sufficient freedoms for your additional layer. The idea that this has to be the case evidences a persisting lack of full understanding of analytical freedoms. I can’t see I am able to make any further progress in helping you towards this end.
There are NO sidereal times here.
All the best to you.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
However, in my view, this does not necessarily rule out an intentional construction. The author may not have been choosing individual signs, but rather the combination of columns as a whole, precisely because that combination produced the overall sequence he wanted.
This is where the correct analysis of freedoms comes in. To say the author “chose … the combination of columns as a whole, precisely because that combination produced the overall sequence he wanted” is simply to say that “the combination he [allegedly] wanted” appeared “coincidentally,” which is the same as to say that he had no control over whether “what he [apparently] wanted” appeared or not. I would hope by now this would have become clear.
Equally, it should be apparent to you that such a columnar choice, when the elements of each column are internally fixed, cannot help with any freedoms required of a method that produces sums and differences along rows. You are merely trying to expunge some of the total coincidence due to the appearance of what you attribute in your model through randomly handing it over to the astrological model that has been sufficiently analysed to all but it’s final details.
The analysis I had given in the last post you replied to is correctly undertaken and its conclusion is sound.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
One final point. When we talk about how closely the deduced model for the astrological layer concords with the actual artefact table, we have to be clear about how we are evaluating this. Having your mind fixed on the left-most triads as being mere numbers to be added or combined it is easy for you to miss the mathematical order of such components. You would take something like the triad for 1968 and see this as ‘10’ followed by ‘01’ followed by ‘56’. Thus, when the deduced model produces ‘10’, ‘01’ and ‘43’ you would see the last of the three as being “in error,” or “out by,” 56 – 43 = 13, which seems significant. The reality is, however, that the triad actually comprises three terms of a single number of hours written in base 60 form, such that the three correspond to:
10 → 10h; 01 → 0.0167h; 56 → 0.0156h; 43 → 0.0119h.
Thus, the “error” in the last element actually corresponds to a mere 0.0037 in the value’s units, which is of an order easily comparable to that attributable to some or other intermediary rounding, a 0.04% “error,” if indeed it is an error at all.
Don’t forget that some single value had to be chosen for the actual local time of the murder event in each case and, since we are not advised as to what specific time the compositor used, we should not be demanding that it might be precisely the same time we would choose. The order of the residual errors sits precisely in the range of a slight adjustment in times only on each given day.
The deduced model is all but a precisely matched one across all rows barring the anomalous 1983 row, which can be separately accounted for.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
The solar Right Ascension for 19:45 UT on 09 July 1984 is obtained by table look-up using an ephemeris for 1984 whilst mistakenly applying the 12h UT daily epoch from the ephemeris for the previous year, 1983, which had just changed to using 0h UT as the new standard. This fixes 08 54 39 at the start of the 1984 row. This likewise fixes Δ1 and Δ2 as 26 and 25, corresponding to ‘A’ and ‘Z’ respectively for this row.
The solar Right Ascension for 22:00 UT on 08 September 1985 is obtained from that for 1984 through incrementation by the motion of the mean sun corresponding to the time interval between the two events plus one day. This fixes 11 12 06 at the start of the 1985 row which, in turn, fixes Δ1 and Δ2 as 1 and 6, corresponding to ‘B’ and ‘G’ respectively for this row.
The solar Right Ascension for 22:45 UT on 22 October 1981 is obtained from that for 1984 through decrement by the motion of the mean sun corresponding to the time interval between the two events plus one day. This fixes 14 05 34 at the start of the Oct. 1981 row which, in turn, fixes Δ1 and Δ2 as 9 and 29, corresponding to ‘J’ and ‘D’ respectively for this row.
The solar Right Ascension for 22:00 UT on 14 September 1974 is obtained from that for 1984 through decrement by the motion of the mean sun corresponding to the time interval between the two events plus one day. This fixes 11 34 27 at the start of the 1974 row which, in turn, fixes Δ1 and Δ2 as 23 and 7, corresponding to ‘X’ and ‘H’ respectively for this row.
The solar Right Ascension for 21 August 1968 is obtained up to minute precision from that for 1984 through decrement by the motion of the mean sun corresponding to the time interval between 22:45 UT on this date and the 1984 baseline plus one day. This fixes 10 01 at the start of the 1968 row which, in turn, fixes Δ1 as 9, corresponding to ‘J’.
The solar Right Ascension for 06 June 1981 is obtained up to minute precision from that for 1984 through decrement by the motion of the mean sun corresponding to the time interval between 22:00 UT on this date and the 1984 baseline plus one day. This fixes 05 01 at the start of the June 1981 row which, in turn, fixes Δ1 as 4, corresponding to ‘E’.
The solar Right Ascension for 19 June 1982 is obtained up to minute precision from that for 1984 through decrement by the motion of the mean sun corresponding to the time interval between 21:45 UT on this date and the 1984 baseline plus one day. This fixes 05 51 at the start of the 1982 row which, in turn, fixes Δ1 as 46, corresponding to ‘U’.
Thus, of the complete sequence derived from the deltas preceding row by row we can ascribe potential freedoms only to those not marked as strikethrough below:
J D X H E A J D U E D G A Z B G
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)