All I know about it so far is what Robert Sungenis has quoted him as saying:
Anatomy of a Smear Campaign
Anatomy of a Smear Campaign
Includes on p. 13 this quote:
Keating: Sungenis writes: "Karl Keating knows nothing about dynamics or coordinate transforms. All he knows is what he has been taught by the science textbooks in high school." This is an interesing example of fantasizing, since Sungenis knows full well what I have written in reply to him before about my educational background. I'll repeat that here, so you can judge whether his characterization of me in the preceding paragraph is correct. Of course I had some science in high school‐‐didn't we all?‐‐but that wasn't where my science education ended. My undergraduate work was done at the San Diego campus of the University of California. At the time it had three constituent colleges. I was resident and registered in Revelle College, which was the science school. It boasted half a dozen Nobel Prize laureates. With MIT and CalTech, UCSD was one of the three top schools for math in the country. I was a math major. It was a requirement to take a lot of hard science courses, particularly physics. One such course was directly on point regarding Sungenis's hobbyhorse, geocentrism. The course was a mathematical investigation of the Ptolemaic theory and the geocentric theories that flowed from it. We used the actual ancient data and worked through complex equations to see whether, with ever finer data, the geocentric theory "saved the appearances." (The answer was No.)
My own reaction, previous to reading Sungenis' reply (I am even shutting down so as not to peek) is the following:
How would working through complex equations ever possibly be able to solve that question?
Why formulate a question like "does the geocentric theory save the appearances" at all? Geocentrism is not ONE theory, it is ANY theory which saves the appearance of Earth being still by means of accepting this as a fact in itself.
The reason would perhaps be to confuse Geocentrism with Ptolemaic system.
Saying that accepting excentrics as centres for perfect circles (if we abstract the near perfect circular movement per day) which obviously do not have earth as its centre will not save the appearances as well as accepting elliptical near perfect cirles will. And the one focus for any major body except Earth (still), Sun and Moon (Earth or wobbling point close to centre of Earth, inside it for Moon, in one focus of elliptic near perfect cirle), will have Sun in one focus of elliptic near perfect circle. But not a point not the Sun as centre of real perfect circle.
If we understand "aphelium of Earth" as "apogaeum of Sun"* and "perihelium of Earth" as "perigaeum of Sun", the Sun will move around Earth variously at distances like 152 097 701 km and 147 098 074 km and any between them.
152 097 701
147 098 074
004 999 627
km difference between perigee and apogee
365.25 approx year in days
182.625 approx half year in days
So on any day between apogee and perigee we will have sun moving around (4 999 657 km : 182.625 days = ) 27 376 km** closer or further off per day, which is at any day insignificant to the total radius of the daily movement. Hence Aristotle's empiric statement that all heavenly bodies move in perfect circles. Which was just NEARLY right.
But getting back to the forms of the non-daily movements, they are not perfect circles. Even around excentrics. In that detail Ptolemy is wrong. However, other systems of Geocentrism - historical or new - are not built around that assumption. So, if we integrate data given by Heliocentrics like Kepler (elliptic orbits) and by refined observations (Mercury not behaving according to the laws of planetary movements predicted by Kepler, hence Mercury's irregularity), along with Tycho Brahe's major identification of Sun (or rather a wobbling point close to its centre, perhaps) as moving excentric centre and Galileo's identification of smaller objects having Jupiter for immediate centre, I cannot for my life see how the equations of Keating at San Diego campus could possibly rule out, optically or geometrically, Geocentrism.
What I can very easily see, however, is that if he puts in a physical or mechanical assumption of causes being limited to, for actual movements, inertia of mass and graviational attraction of other mass, and, for apparent movements, parallactic appearances plus gravitational bending of light, yes, then he will get difficulties in supporting Geocentrism. But those will not be the difficulties of saving the appearances, but rather of saving the current explanations.
If you now go to Stephen Tempier, you will not find "angels move heavenly bodies" on the index of condemned notions.
En lengua romance en Antimodernism y de mis caminaciones : Index in stephani tempier condempnationes
And if you go to St Thomas Aquinas commenting on Job, you will find him affirming it:
[In eodem bloggo] : Terra et Astra secundum Aquinatem in Commentario de Hiob capite xxxviij
[in quo et datur uinculum in situm de corpore thomistico]
Which will involve the disappearance of that kind of difficulty. Pretty immediately - unless you think St Thomas was wrong, unless you think it has been validly demonstrated that angelic movers must be excluded. I for one do not, and more importantly, I have St Thomas on my side. As well as - even more importantly than that - the book of Job, the book of Baruch, the Canticle of the Three Young Men in the Furnace.
My own studies were not scientific. My main subject (I never took a licence, but in this subject I intruded to postgraduate level) was ... Latin. In Lund, South Sweden, with lots of Brigittine studies and with a Tertiary Dominican for one of the Latin teachers (now professor, the "Docent"), that meant an emphasis on Medieval Latin. What I learned to do at University was reading St Thomas.
Any further problems or questions, Mr. Keating?
Hans Georg Lundahl
Nanterre University Library
St John the Baptist's Vigil
* Taken from current version of:
La Wikipédie française : Terre
** Unless I got a Roman Numeral wrong in the answer. Divisions ideally use Arabic numerals for dividend and divisor with its multiplication table up to V, then Roman Numerals for answer.