Related paper: https://arxiv.org/abs/2504.12962
SESCC is also implemented as a spreadsheet:
)
-the spreadsheet will be also uploaded to this repository as a libreoffice document.
(sescc for short)
2024 Carlos Baiget Orts (cjbaiget)
https://www.youtube.com/@CarlosBaiget
sescc is a generic method for dating stellar catalogs compiled in ecliptical coordinates.
sescc finds the date of catalog by the speed/error correlation of the stars and uses an static star for frame reference.
sescc provides further proof of scientific activities in -2nd cy B.C. Meaning: knowledge of writing, fractional counting, astronomical reference systems, documentary repositories, a great deal BEFORE the 11th century. This fact contradicts THE FUNDAMENTAL AXIOM of Fomenko and Nosovsky's 'New Chronology,' rendering it irreparably flawed and requiring a comprehensive reconstruction from its foundations.
- Dating the Almagest star catalogue using proper motions: a reconsideration (https://people.sc.fsu.edu/~dduke/pmotion.pdf)
- On the Origin of the Ptolemaic Star Catalogue, parts 1 & 2 (https://adsabs.harvard.edu/full/1987JHA....18..155E) (https://adsabs.harvard.edu/full/1987JHA....18..233E)
- The enigma of Ptolemy's catalogue of stars (https://adsabs.harvard.edu/full/1992JHA....23..173S)
- The dating of Ptolemy's Star Catalogue (https://adsabs.harvard.edu/full/2002JHA....33..265D)
- Dating Ptolemy's star catalogue through proper motions: the Hipparchan epoch (https://adsabs.harvard.edu/full/2000JHA....31..115D)
- Declinations int the Almagest: accuracy, epoch, and observers (https://www.narit.or.th/files/JAHH/2014JAHHvol17/2014JAHH...17..326B.pdf)
- (1) Geometrical and statistical methods of analysis of star configurations : dating Ptolemy's Almagest (https://library.navoiy-uni.uz/files/fomenko%20a.%20t.,%20kalashnikov%20v.%20v.,%20nosovsky%20g.%20v.%20-%20geometrical%20and%20statistical%20methods%20of%20analysis%20of%20star%20configurations%20(2000)(300s).pdf)
- The New Chronology of Fomenko and Nosovskyi ends today (=2024/4/15) (https://forum.chronologia.org/viewtopic.php?t=901)
WARNING: This program downloads 1.7Gb of ephemeris from NASA in its first run. more info: https://rhodesmill.org/skyfield/planets.html
sescc was made to astronomically date Ptolemy's Almagest.
This is the sescc dating program, you can use it to SCIENTIFICALLY PROVE that the Ptolemy's Almagest was initially compiled by Hipparchus and Ptolemy in the -2nd and 2nd century C.E.
sescc can reliably date the Almagest by latitudes or longitudes, as well as any other catalog compiled in ecliptic coordinates, between -1500 and 1900 C.E.
This program requires Python, Skyfield, Numpy, Matplotlib and Panda libraries:
- https://www.python.org/
- https://rhodesmill.org/skyfield/
- https://numpy.org/
- https://matplotlib.org/
- https://pandas.pydata.org/
What on earth is "Speed / Error Signal Cross Correlation"?
Will explain with more detail soon. Briefly:
- The working set is a list of stars. Each of those stars has proper motion. The list of speeds is a discrete signal, the 'speed signal' A:
Fig 1. Example of the speed signal A of a catalog.
- For every epoch t, the difference of the stars positions in the catalog and the computed positions for that epoch defines a list of errors, that is the 'error signal' B(t).
Fig 2. Example of the set of errors signals B(t) of a catalog. Each color is the error signal associated with a candidate epoch t.
- But the speed of a star CANNOT be a source of its error in the catalog!
THEREFORE:
When a signal cross correlation between A and B(t) appears is necessarily due to B being computed for a wrong epoch t.
MEANING:
- DATE OF THE CATALOG IS THE DATE OF THE MINIMAL CROSS CORRELATION BETWEEN THE SPEED AND ERROR SIGNALS.What on earth is "Shared reference in Delta Geminorum?"
- We just don't know how accurate was the ancient astronomer determination of the (0,0) coordinate.
- We could use an almost static star near the ecliptic as a shared reference between the ancient astronomer and us, to match the ancient catalog with each of our computed ones.
- This star exists and was compiled in the catalog! It's Delta Geminorum with a combined proper motion of only 18 mas/year.
This shared reference is what allows dating the Almagest by longitudes.
Basic usage in LINUX:
pip install pandas skyfield "numpy<2.0" matplotlib
./sescc.py < catalogs/almagest.csv
./sescc.py 1 < catalogs/almagest.csv
3.Date ("New Chronology"=NC) Fomenko, Kalashnikov, Nosovsky's 'informative kernel' by latitudes (use ./sescc.py 1 for longitudes):
./sescc.py < catalogs/fkn_kernel.csv
./sescc.py < catalogs/fkn_wo_arcturus.csv
In the default setting, sescc will discard stars with mag>2.5 (brighter stars were measured first). This results in a set of 91 stars for dating the catalog. You may wonder if (as is the case with FKN method), the dating relies on a single star (see below). A set of 91 stars results in 2*10²⁰ combinations of 70 stars. To date the catalog based on a random combination, you can use the following command. A few executions are enough to verify the typical outcome.
./sescc.py 0 70 < catalogs/almagest.csv
Here's a 1000 iterations plot of this example:
And the corresponding histogram:
Repeating the same experiment with longitudes:
It seems that later astronomers frequently re-measured longitudes more often than latitudes. Probably they were interested in determining precession accurately.
To expand de working set, set a higher magnitude. Maxmag = 3 gives a working set of 157 stars. So to date the catalog from one of its 2*10⁴¹ combinations of 50 stars you can use this command:
./sescc.py 0 50 3 < catalogs/almagest.csv
"NC's informative kernel" is the WORST set of stars to date the Almagest. It consists of a selection of stars that will give a medieval date. Those stars where updated by later astronomers, Battani in 9th Cy, Regiomontanus in 15 cy.
Dissection of "New Chronology's" "informative kernel":
- Procyon, Capella: Regiomontanus (15th century)
- Arcturus: Al-Battani (9th century)
- Regulus, Spica, Vega, Antares, Asellus: Hipparchus (-2nd century)
Fomenko, Kalashnikov, Nosovsky's dating is dominated by Arcturus due its much higher relative proper motion:
"informative kernel" w/o Arcturus is dominated by Regiomontanus stars:
That's how they achieved a 10th Century date.
If this error is not admitted, it's just scientific fraud in plain sight.
If admitted, an honest explanation be explored:
NC's selection criteria looking for bright and quick stars had an implicit and lethal risk: that precisely those were most carefully tracked by later astronomers who of course noticed the error in their own times and updated the catalog.
Results indicate that this is what happened with al-Battani, who updated Arcturus in the 9th century, and Regiomontanus, who updated Procyon and Capella in the 15th. Those updates made their way into the canonical edition of the Almagest in the 15th century, by none other than Regiomontanus. Later researchers thought erroneously that the whole catalog was from Ptolemy. Detected incosistencies, attributed him a fraud.
However, the main result of SESCC is that Star positions and established chronology of the Almagest are fully coherent.
Clarifications:
- Any other consideration about any other information within the Almagest requires a separate analysis.
- SESCC results do not contradict the conclusions of the book "The Crime of Claudius Ptolemy" from R.R. Newton (1977). In fact, its a corroboration of one of the main points in it: that it contains original work from Hipparchus.
- As SESCC shows, this part is precisely the LATITUDES part of almost all the star positions.
Syntax for WINDOWS:
python sescc.py < catalogs/almagest.csv
python sescc.py 1 < catalogs/almagest.csv
etc...
Creates a catalog for any epoch, list of stars is taken from another catalog, example:
cat catalogs/fkn_kernel.csv | ./stella.py 1100 10 0 0 | ./sescc.py
This takes the list of stars detailed in 'fkn_kernel.csv' and creates a new catalog for year 1100, with 10' resolution (using the fractional system of the Almagest), with 0' of systemical error and 0' of random error.
You can feed the output to sescc.py to verify it works as expected. stella.py can also be used to prove that sescc.py doesn't date the longitudes by their magnitude. Magnitudes can be adjusted for the axial precession of any other epoch and the results will be the same.
An example of this modification is the catalog 'almagest_fake_longs.csv' where longitudes are increased by 15º (+1000 years into the future), not affecting the dating of the catalog by longitudes:
./sescc.py 1 < catalogs/almagest_fake_longs.csv
gives the same dating as:
./sescc.py 1 < catalogs/almagest.csv
$ tail -n5 catalogs/almagest_fake_longs.csv
105382;-22.17;281.17
106327;-21.17;284.0
105696;-20.83;282.0
102831;-17.0;283.83
103738;-14.83;283.83
$ tail -n5 catalogs/almagest_fake_longs.csv
105382;-22.17;296.17
106327;-21.17;299.0
105696;-20.83;297.0
102831;-17.0;298.83
103738;-14.83;298.83
Format of 'almagest.csv' (data adapted from G. J. Toomer, Ptolemy’s Almagest , (London, 1984)): Star_HIPPARCOS_ code ; Latitude in Almagest ; Longitude in Almagest; HR code; HD code; name; Almagest number
'0;' before star code means a reject, which will be ignored when loading catalog
There are just three rejects:
HIP71683 - Rigil Kentaurus
HIP69673 - Arcturus
HIP97649 - Altair
You can explore the effect of uncommenting those lines in the result.
First line must be HIP35550 (Delta Geminorum), which is a surrogate of the equinox as the reference point for any epoch, rather than the one employed by the computer, which may differ from that of the ancient astronomer.
A series of experiments derived from this dating method allow us to propose a new hypothesis about the history of the Almagest, which explains some of its most enigmatic peculiarities. Unfortunately, due to lack of time, I cannot document these investigations properly. However, I am leaving the conclusions here so they do not fall into complete oblivion in case I finally do not find the time or motivation to do so.
The strange characteristics of the Almagest's star catalog led to the hypothesis of forgery long ago. R.R. Newton proposed that Ptolemy, in a sort of scientific fraud, simply copied Hipparchus's catalog and merely adjusted the longitudes based on precession. A.T. Fomenko argues that the catalog was compiled around the 10th century and medieval reformers adjusted the longitudes a millennium into the past to support a falsified chronology.
Dating by sessc resolves the apparent inconsistency of the Almagest's star positions, while also proposing a reasonable history that explains the content that has come down to us and that has given rise to previous hypotheses. It is an interesting story among other things because, despite the unanimous opinion that Hipparchus's catalog was completely lost, sessc dating shows that this is not the case.
The solution is as follows. In the time of Hipparchus and his immediate predecessors, the first star catalog was compiled with the ambition to record stellar positions with sufficient fidelity to be compared by later astronomers. However, their measuring instruments were somewhat rudimentary and only allowed a resolution of 1/4 degree. The first novel conclusion is that the positions in the Almagest recorded in quarters of a degree belong to Hipparchus's original catalog. Since the fractions of 0 and 1/2 degree can correspond to both a system of measurement based on quarters and on sixths of a degree, in an initial analysis we can only certify Hipparchus's positions as those detailed with 1/4 or 3/4 of a degree.
The subdivisions of quarters and sixths of a degree are incompatible, and a system that uses both is incoherent. The reason is that determining a position with a fractional value of 1/4 degree, compared to the possibility of doing so at 1/6 or 2/6, implies a discriminatory capacity of 5 arc minutes (case A in the diagram). This corresponds to a subdivision of 1/12 degree, not 1/6. The system attributed to Ptolemy makes the absence of subdivisions between 2/6 and 1/2, and between 1/2 and 3/6, nonsensical (case B). This system would also create an asymmetric distribution in more than half of its subdivisions (case C). Therefore, these are two systems corresponding to two different periods: one coarser, belonging to an earlier stage of astronomy, and another more refined, corresponding to improved instrumentation. The coexistence of both systems in the same catalog is due to the fact that this catalog consists of an aggregation of different sources, which mainly, as mentioned earlier, come from two independent sets: that of latitudes and that of longitudes.
Astronomers following Ptolemy measured in sixths of a degree, and when they corrected some position, they did so using this system. Ptolemy compared his accurate positions with those vague inherited from Hipparchus and obtained an aberrant value for precession.
Fortunately for us, Ptolemy and his successors were not interested in latitudes, as they considered them perennial. They were much more interested in longitudes, to be able to accurately determine the value of precession. Accordingly, Ptolemy measured practically all the longitudes in the catalog himself, but simply copied Hipparchus's latitudes. This is why sessc dating by latitudes gives us Hipparchus's era, but by longitudes, it gives us Ptolemy's.
After that, the catalog continued to be updated and expanded over the centuries. The two main occasions when this happened were in the 9th century by al-Battani and the 15th century by Regiomontanus. For some prominent and very fast stars, like Arcturus, the change in position relative to Hipparchus was very evident in the 9th century, and their latitudinal position was corrected. This correction likely attributed to an ancient measurement error by Hipparchus, as a complete revision of latitudes was not carried out to solve the question of the existence of proper motion of the stars. However, this specific correction had disastrous repercussions when A.T. Fomenko based the dating of the entire catalog on it, under the clearly erroneous premise that it was a measurement corresponding to the original catalog of Hipparchus or Ptolemy. The latitude of other relevant stars, despite not being fast, was corrected in the 15th century by Regiomontanus.
Clearly, the Almagest catalog that has come down to us is a series of additions with a fundamental core of latitudes due to Hipparchus and another of longitudes due to Ptolemy. The latitudes corrected later were few, as it was considered of little benefit to do so. The longitudes, on the other hand, suffered few updates after Ptolemy. However, when new stars were added, since the value of the longitude implies a specific era, it was harmonized with the era it should have had in Ptolemy's time, by means of an adjustment due to precession. This is why all the longitudes in the catalog 'appear' to be from Ptolemy's era, and it also explains the vestiges of positional calculation and large errors, since many stars have the longitude that corresponds to the latitude of 300 years earlier, if not a millennium (longitude of al-Battani in the 9th century and latitude of Hipparchus in the 2nd century BC). However, this was not a fraud but an attempt by medieval astronomers to compile a coherent catalog.
Of the latitudinal positions with fractional values of 0 or 1/2, many of them belong to Hipparchus's original catalog. However, determining this requires a combinatorial approach to the problem, which can generate millions of datings of small groups, and I am not sure how viable it is. But I believe that at least for the brighter stars it is possible, and I would like to attempt this classification as soon as time allows.