in order to test the possibility of a deliberate secondary construction

This has been completed now. See above.

In other words, how can we exclude the possibility that what we are interpreting as a one-day error was instead an intentional choice by the compositor to move certain values where he wanted them?

This can be ruled out on nothing more than the fact that the one-day error, clearly identified as such, is propagated equally across all of the extrapolated rows, adding precisely 24/365.242 to each. There are no independent freedoms arising from this as all such rows are merely shifted according to the same rule, equal in all instances. Thus, you could perhaps force one row into some sought value but the consequences would be that all the other rows would be merely altered in some manner that is out of the compositor’s control. It is the propagation here that allows us to deduce, with certainty, that the one-day shift is a result of a counting error and not by intention, since it is not capable of producing the independent shifts that would be required to bring each row separately into some preferred arrangement.

This should be clear. If not, imagine having one row precisely as you want it for your proposal. Next, choose something other than a one-day shift and implement this to get a further row to a result you seek. Only, in doing so you have now lost what you had for the first row. There are no operational freedoms to be gained from a single shift that propagates. Being unable to effect any value operationally, we are left with unintentionality. That is, an error or slip, merely, in counting.

The same with your erroneous considerations around what you saw as offering freedoms through selecting which planets are chosen to construct the right-hand side of the table. Choose a planet just to get one row into line, and all the others are thereby corrupted, since the column values are again not independent but fixed.

Understanding this, at the very least, will get you closer to a correct understanding.

I wonder whether, when trying to establish what freedoms were actually available to the compositor, we should distinguish between values that are independently determined by the astronomical data and values that only become “fixed” after introducing errors needed to reproduce the values in the artefact.

The case I am most interested in is the +1 day.

If I have followed the development of the model correctly, the +1 day is first noticed because the discrepancy in the 1974 row corresponds almost exactly to one day of mean solar RA motion. It is then introduced into the calculation, and we find that it also improves the fit of the other rows considerably. Afterwards, the error is located in the day-number of the 1984 baseline, because that would be the most logical place from which a single error could propagate.

But if we do not yet have an independent reconstruction of the specific calculation error that would produce exactly that +1 day, can we really regard the values obtained after applying this correction as completely “fixed” for the purpose of analysing the freedoms?

In other words, how can we exclude the possibility that what we are interpreting as a one-day error was instead an intentional choice by the compositor to move certain values where he wanted them?

I am not saying that this was necessarily the case. I am only wondering whether, in order to test the possibility of a deliberate secondary construction, it might be useful to compare the results at different levels:

1. the correct astronomical values;

2. the values produced by the model before introducing errors inferred from comparison with the artefact;

3. the final values after applying those proposed errors.

Otherwise, I wonder whether there is a risk of treating as constraints some of the very differences that we should perhaps be testing as possible freedoms.

This, and the prior analysis of freedoms above, transfers directly onto the further reduction of both results to 51, removing ‘Z’.

D L X H E A U Z

and:

T I S C D A,

having also freely added in an ‘L’, supposing the ‘72’ to not have any fixed meaning under the astrological model.

B G T I S C D A J.

Again, the compositor was afforded no freedoms to be able to select any of ‘B’, ‘G’ or ‘J’ at the ends.

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

whereupon, after elimination, we are left with:

J D X H E A U G Z B

Thus, even under this best-case scenario, we can retain freedom only for the single ‘D’ which arose as Δ2 from the 1968 row.

Neither of the ‘J’, ‘G’ nor ‘B’ could be inserted into the ends of the original sequence by intention.

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