AUTHOR'S POSTING: ERRORS IN MY 1999 STATISTICS PAPER

THIS POSTING WAS MADE TO THE ANOMALIES WEBSITE ON MARCH 24, 2003

My name is Mary Anne Weaver, and I wrote the statistics paper, "INVESTIGATION INTO THE ENTERPRISE MISSION'S PROPOSITION THAT THE 19.5 AND 33.0 DEGREE STAR ALIGNMENTS CONSTITUTE A PATTERN."

Recently, a friend of mine contacted me and informed me that there is a "heated discussion" regarding this statistics paper on this BBS.

I debated with myself about whether or not to post something to this BBS. I dropped out of such discussions long ago because of moving on to other research projects and other topics of greater interest to me than statistics and probability as applied to Hoagland's "RAT" (Ritual Alignment Theory). I also became VERY tired of the whole subject because of having spent thousands of laborious hours on that paper, making thousands of RedShift observations, figuring out the appropriate methodology to accurately investigate the RAT situation, checking and re-checking the math and the equations, etc., etc.

The other reason I dropped out of such discussions is that too many people were disturbed and distressed by the very idea of doing a statistics and probability analysis of a topic that explored possible connections between star alignments and NASA launches. I found that too often, even professionals didn't stop to analyze what I had done mathematically, so they did not offer constructive, well-thought-out or useful criticism, but rather stooped to saying things like were said on this BBS regarding me and my work: i.e., that my paper is either a "bad joke or the product of a deluded mind." (Readers of this BBS may recognize this as a sentiment expressed by Sol, my fellow UW alumnus who apparently has a doctorate in Statistics.)

Whether I deserve criticism from statistics experts like Sol or not, is not the point. The key issue is, can the people who discuss this and who have valid points about the math I do in the paper -- and the arguments I present -- maintain an impartial view of the analysis? If so, then it's possible to have interesting and productive discussions. Otherwise, I have found from personal experience, that the presence of bias prevents people from evaluating the merits of any idea; and discussions resort to an exchange of scorn and insults.

In retrospect (hindsight is always 20/20) I can see that I DID make some mistakes in my statistics paper. For reasons I mention later, it is my opinion that this does not invalidate my work entirely; but it does make the "odds against random" less than what I quote in my paper. I will go into those points later. I know that someone like "Sol" could and most likely does have useful feedback to offer. (Though for the record, I don't want to hear from Sol, himself. I hope this does not offend anyone; and I mean no insult toward Sol. I simply have found it useless to "get" helpful input from people with such a strong bias against me or my work.)

Everyone who is truly involved in advancing the field of science knows that human beings are flawed; therefore, feedback on the weak points of a theory or a paper such as mine, is essential and helpful. I only wish I'd known someone like Sol at the time I published the paper. I did have it reviewed by a man who performed statistics and probability studies (though he did not have a PhD in Statistics, nor was he a prof), and he thought that my study was well done. That is the sort of feedback I got from most people who were knowledgeable on the topic. Unfortunately, they didn't catch the errors I will speak to you about later on in this posting.

Now, I am going to share with this group, a little bit about the history of my statistics study.

When I did the study, I was intrigued by RCH's RAT. I wanted to find out if there was anything to it. So, I started out by investigating a star alignment model that had equal tolerances for all angles. I tried a model that was +-0.5 degrees around each angle of interest (zero, 19.5, 33.0, and the meridian), and then one that was +-0.25 degrees around each angle. I found that the 0.5 degree tolerance model didn't beat the odds by much. However, the +-0.25 model beat the odds more significantly. I felt that there might be something to it, but that perhaps the "same tolerances for all angles" model wasn't sufficient to explore all the synchronicities I was seeing in the data.

In my paper, I think I do mention the fact that I did investigate a "consistent tolerance" model in my statistics paper; but I don't recall that I went into it in great detail. (It's been a long time and I only took a cursory look at my paper before writing this; mainly because I don't have time to read and go over the whole thing at the moment!) I don't remember writing much, if anything, about my first "consistent angle tolerance" model; except I believe I wrote in my paper, that I did evaluate a model such as that.

Because I saw that there was something "to" the RCH RAT, and yet the "consistent angle tolerance" model wasn't accounting for all the tetrahedral numbers in the data, I designed another model that could and did account for the presence of tetrahedral numbers in the launch data, as well as the "ritual angles" that RCH believed were important. I know that some people argue that this was unfair or inconsistent with RCH's model. I can understand people's objection to this, except that in research, it's often useful to explore what the data suggests might REALLY be happening, not just what the researcher thinks "should" happen.

In researching a connection between launches and star alignments, where there is no known mechanism that could explain it, there is nothing that implies that all angle tolerances should or even would, be the same for all star alignment angles. No one knows why synchronicities such as these appear in the first place; it could just be the result of natural processes and not the RCH RAT that causes it. Even so, because I was testing the RCH RAT, I did not "arbitrarily" assign different spatial windows to the angles: I was constrained by RCH's theories that there is a larger correspondence of tetrahedral numbers in the RAT scenario; and I designed the model to take the presence of tetrahedral numbers into account -- as well as the standard "19.5" and "33" angles. No one knows what the pattern really should look like; if it is a pattern with "equal angle tolerances" or not.

But in all fairness, I do understand the objections to that model I analyze in my paper. It might seem as though I was just "arbitrarily" assigning tolerances to make the odds high. I do explain in my paper, more about this rationale and why I used it; so I won't reiterate it here.

My hypothesis at the time was that the second model, IF it was valid, should work on for the launch data I had, but also other events pertaining to NASA missions. When I found that this pattern also was present in the "Apollo astronaut activities" I was then documenting, I was astounded, because of how unlikely it was for the same pattern to show up in yet another set of data. That is why I thought I might be on the right track with the second model, and why I ended up using it in my final paper. I also planned on doing another analysis to see if my second model was valid or if a "standard tolerance" model was better to use for analyzing these star alignment synchronicities.

Naturally, when you adjust a model to find synchronicities in data, it's going to show up as large "odds against random" because the model has been designed to do just that -- catch the appearance of certain numbers in the data. My designing the second model was not a random process -- I designed it to better account for the presence of tetrahedral numbers as well as tetrahedral star alignments in a set of data, and that's exactly what my second model did. But, that is also why my second model needed to be tested on a second set of "unrelated" data (ideally, a different set of launches, and not just Apollo mission events the way I did in my paper), to see whether or not these synchronicities would also occur for OTHER NASA launches.

I deeply regret that I was too burned out at the time I completed my paper, to explore how my model may have worked on other launch times for other missions, such as the Space Shuttle missions. Plus, I wanted to keep it consistent; I didn't want to do only some of the Mars missions for example; like I did with Apollo, I felt if I did one type of NASA mission (like those to Mars), I should do the entire set. I just didn't have the energy or ambition to do that by the time I'd finished my paper, which I had originally planned to be the first in a SERIES of investigations; not the one and only investigation I did!

Out of curiosity but not as a formal study (I was not interested in putting more effort into a statistical study after all that work), I did try my model out on other launch data. And truly, that's the test that matters -- does a model that is developed on the basis of findings in one instance -- work in other instances? Unfortunately, I found that the model I develop and analyze in my paper didn't produce the same stunning results as with Apollo. It's probably safe to say that my model does reveal the presence of an unusual amount of order and synchronicity with regard to tetrahedral star alignments and numbers in the APOLLO program. But, it's not safe to conclude that I've proven the RCH RAT or that the model I developed shows the same pattern in all NASA launches. So -- even though I did get good results for the model I tried and the data I had, BECAUSE of the fact that there was a lot of tetrahedral numbers in the data -- I can see now that this may only be true for that particular set of data that I examined, or perhaps just for various facets of the Apollo program. (It's always possible that if I'd analyzed enough Space Shuttle launches, a pattern would have emerged. But, that is unknown at this point.)

Ideally, I should do another study that examines this, so that people know that the model I developed on the basis of what I saw in the Apollo and pre-Apollo launch data, might not work for other NASA launch data. However, this will depend on my available time. This doesn't stop someone else from doing that sort of study, though. I clearly define the parameters of my model and why I use those specific angle tolerances; so it's easy to test it out.

Therefore, using my methodology, the RCH RAT model has not been numerically proven, and my model may not stand up to the test of other launch data; at least the other NASA launch data I looked at.

With that, let me address some simple points. I am only directing my replies to the commentary I read, so when I am quoting someone's posting I will simply place their comments in quotes and not mention their name(s).

First quote:

"1) The statistics are flawed because they fail to take into account that space launches are far from random events. Yet they try to assign odds and probability as if they were. If you want to get your probe or your manned craft to a particular target in space you have VERY specific launch windows. The "analysis" that has been presented of the RAT (Ritual Alignment Theory) fails to account for that."

Actually, my paper and myself DO take into account that space launches are "far from random." But, I do assert that if there is no connection of NASA launches with the stars based on celestial mechanics (since NASA launches are NOT planned according to the position of the stars over Earth or the Moon, to my knowledge) -- THERE IS NO PHYSICAL CONNECTION and therefore the data might as well be random with respect to star positions over Earth or the Moon. It doesn't matter that launches themselves aren't random -- I didn't compute the probability against "random chance" that space launches would spontaneously and randomly launch themselves and get to where they are going in some sort of random fashion. Therefore, I do not claim nor state that space launches are the result of random processes, anywhere in my paper.

Also, I didn't investigate the notion that the rotation of the Earth is "random" and randomly speeds up or slows down, stops, flips on its axis, etc. That's because everyone knows that the motion of the Earth is very predictable from day to day and year to year, and is anything BUT random. What I investigated was the probability of a connection between launches and star alignments; a totally different matter, since the two are supposedly completely unrelated. And that which is completely unrelated, SHOULD have a statistical distribution that is reflects that lack of connection.

If it were not possible to examine whether there is a connection between seemingly unrelated "non-random" events, insurance companies would never hire probability and statistics experts to find connections between events such as automobile accidents and intoxication (which is not a random process, either -- unless one can claim that people walk into bars by some sort of random process, and somehow end up drinking alcohol "by accident"). In such studies, there is no NEED for someone's choice to drink alcohol, to be a random process. The whole point of such a study is to determine if there is a non-random CONNECTION between drinking and auto accidents; not whether either of those two events are randomly generated.

Probability and statistics examine connections between random or non-random events, by making a series of observations and then analyzing the results. The events do not have to be randomly generated; but a lot of the time, probability studies are done to demonstrate the possibility of connections between events that previously had no obvious or demonstrable connections and are not the result of random processes; another such example is the connection between smoking and cancer, which was also revealed by statistics studies.

So in my opinion, my analysis would have been flawed if I HAD assumed that there was a connection between launch windows and the position of stars over Cape Canaveral and similar sites. I don't assume there ISN'T a natural or explicable connection for the synchronicities in the Apollo data. I only conclude based on the probabilities, that there seems to be some sort of connection or non-random process at work, because the probabilities I do get indicate how unlikely it is to have THAT many tetrahedral numbers and alignments in a set of data.

Therefore, based on what we know of the factors that govern NASA launches and celestial mechanics, it is reasonable to model them AS IF they are random WITH RESPECT TO the position of stars as viewed from the surface of the Earth or Moon (depending on which "ritual site" of Hoagland's one is looking at), because of this lack of a demonstrable or reasonable connection between launches and star positions.

For the record, I am not defending the RAT theory; but rather, explaining my methodology. I will say more on this point later on in this posting.

Quote #2:

"No, I didn't say that NASA's launch and landing events were connected to the 19.5s, 33s and the stars.... I said that the launches and landings for that matter are not random. The rotation of the earth on its axis is not random, the perceived movement of the stars based on that is not random. There is no reasonable expectation of an even distribution...."

Yes; it is POSSIBLE that there might not be an even distribution, since space launches aren't random processes. However, the position of the stars change constantly relative to terrestrial horizons, minute by minute in the case of Earth, and in a way that is not related to the planning of NASA missions. For example, there was no demonstrable connection between smoking and cancer prior to the statistical studies that showed that; yet smoking is NOT a random process. In the same way, NASA missions aren't planned with the position of the stars in mind (again, to my knowledge); and celestial mechanics do not tend to produce repetitious star alignment synchronicities. NASA missions are planned according to where the positions of destinations of interest, such as the Moon, are with respect to Earth; and that is dependent on celestial mechanics, not the position of stars over terrestrial horizons. Apollo "prep" missions, such as the Gemini missions, didn't require the Moon to be close to Earth, and were often determined by launch conditions such as what the weather was like on a given day, and where they wanted a satellite or other observation equipment deployed, the sorts of tests they needed to finish (such as docking maneuvers), etc.

But for the sake of argument, suppose there is a mechanism that creates a "non-random" statistical distribution of star alignment data, with respect to NASA launch times. (Because the position of stars over Earth's horizons change in just a FEW minutes' time, it's not likely that such a bias would occur -- especially since many of these missions weren't even concerned with making it to the Moon; the Apollo prep missions I examine (such as Gemini missions) only needed to make it into orbit. But just for the sake of argument, again, let's say it's possible and there is some sort of hidden connection between launch times and star positions, based on some esoteric or unknown celestial mechanics fluke; or something else entirely.)

If there is such a bias, celestial mechanics being what they are -- the bias in any one direction would not last long, because orbits of planets and such do not "synch up" in that precise or repetitious a manner. For example, the orbit and rotation of the Moon is not an even multiple of Earth days (which would tie the Moon in with the positions of the stars over points on Earth at any given time -- and that is not the case).

So in that scenario, because the bias is always changing over time, one need not necessarily expect an uneven distribution biased IN FAVOR OF the RAT, like the one I found. Unless you DO claim there is just that sort of connection and demonstrate it mathematically (and the only justification for that would be celestial mechanics), such a bias wouldn't be the expected result. Also, given celestial mechanics and the differing position of the stars over the Moon OR Earth during launch windows, then at any given time in history, such a bias could just as easily happen against the RAT; meaning fewer RAT hits than one would expect in a truly random situation. If humanity started the space program in 1000 AD for example, launch windows would "synch up" differently with respect to star positions, than they do in the 1950's or 1960's AD. That's why I say -- there is no basis for assuming a connection between star alignments and space launches; and why they might as well be considered "random" with respect to star alignments over horizons. If when you launch a space program has nothing to do with star alignments, from a celestial mechanics point of view (which is the main one that matters for launch windows) -- there is no connection; therefore, given enough samples of launches, the star alignments should appear as random or near-random distributions; reflecting that lack of connection.

It may interest you to note that another statistical study on the RAT was done; except with the Mars mission data. I don't recall the gentleman's name; but he did a study which used the same equations I did; only he focused on the Mars missions. I did not read his paper, because by that time I was tired of this whole subject. But, he did inform me that he did not find statistically relevant synchronicities; i.e., he did not find an adherence to the RAT pattern, the way I did with the data I used. So, there is another indication that the RCH RAT may not be possible to prove numerically, because star alignments such as RCH observes are too common; and that those interested in figuring out how to examine the RCH RAT numerically, may have to include different factors in addition to star alignments or use a different model than I did. (And it may be found that there is no numerical basis for the RCH RAT.)

Quote #3:

"I welcome Hoagland commissioning a proper study and hope that he does this some day. I'm not going to get into this in any great detail, but here's just a few objections to the Weaver study: * In comparing her "random" control studies to actual space mission test events, she uses a higher sampling frequency for the control data and then proceeds to compare the statistical outcomes of the two groups .... * She does not document how her "random" control samples were generated. No program source code is presented for inspection and no reference to the algorithm and its imposed constraints are offered...."

Well, I thought that including the large amounts of data on star positions during launches and so forth would be sufficient. But I can see that in the case of a formal study, having everything "out there" would be essential for peer review. And if I were part of a research team, all of my data and even my computer programs, would have been presented in just that manner, for just that reason. But, I was presenting my paper to the public; and I was rather worried that I had overdone it as it was. I did not expect everyone to read through all my star alignment data, let alone (for example) photocopied RedShift2 notebook entries for my thousands of RedShift observations.

I will note here that it is EASY to compute the "transit time" of any and every star that passes through a spatial window on the Earth or Moon, without using any software to make such observations. The rotations of the Earth and Moon, that "create" star transit times through such spatial windows, is simple to model. All you need is the boundaries of the spatial window and the position of the star. Then, via trigonometry and by knowing the speed of rotation of the Earth or Moon, you can figure out just how many minutes it takes (and it's not many, if you're talking about Earth), for the star to transit this spatial window. You can do this for every star of interest -- Regulus, Sirius, and each of the three belt stars -- and you also do that for the spatial windows you want to look at (33 degrees above and below both horizons; the meridian; etc.). And, when you're done adding them all together; in the case of Earth, you divide by 24 hours. This gives you the EXACT percentage of time that stars transit spatial windows, for the location of interest. (And that percentage of time, folks, IS the probability that a star of interest "can" or "will" be found in the appropriate spatial "window" -- because of the laws of physics; NOT because of the samples I took or did not take, of star motions.)

Therefore, I did not NEED to make all the observations I did for the year 1969 and the years 1958 thru 1978. The laws of motion and of physics, are very specific and don't need to be "proven" by my random samples. I didn't take the random samples to "prove" anything. I made those samples to ground my work in empirical observation; which is just my way of double-checking my calculations and work, and making sure the foundation for the rest of my calculations is a solid one. And, my samples only verified what ever first-year college student of Physics knows -- the Earth turns at a specific rate; and therefore, objects in the heavens "appear" to traverse the sky at a constant rate that is predictable; thus, the probability of "finding" a star of interest in a specific spatial window can be calculated from those equations; not only from a set of random observations of star positions.

That's why the "roulette model" works in this instance. It's simply a re-stating of the laws of physics; in this case, applied to rotation. If precession on Earth or the Moon made much difference in star transit times, that could be taken into account as well; but it is a very small factor in the case of the Moon, and virtually zero in the case of the Earth -- because I do not take samples of star positions over hundreds or thousands of years, where precession would change the orientation of the Earth to make an appreciable difference in a star's transit time through a spatial window.

I did these calculations on star motion, prior to making any RedShift2 observations. Of course, I got values that matched the probability values I got when I took my random samples of 1969 and 1958 thru 1978. And, that's just what one would expect to see, if the laws of physics apply to this situation and if my random number generator was truly random! So, that's one check of my random number generator! However, at the time, I wished I could have provided more samples, just because it would have made the case even more solid.

If I did share my random-number generating software with you, you'd find it very simplistic and uninteresting, if effective. It's written in "C" for DOS. It uses a standard random number generator provided by the "C" language, that computes a different random number in a specific range of interest; and the seed number for the random number generator is based on the computer clock at the time the program is run; plus I included other factors to make sure that the seed number varied considerably every time I ran the program.

I designed this simple C program to produce 20 sets of random dates each time I executed the code. Each date listing consisted of the following sets of numbers: 1) a random number from 0 through 23 (24 hour clock), 2) another random number representing minutes of time, from 0 to 59; 4) another random number representing a day of the year from 0 to 365, which I then converted into a day (0 to 364 if the year was not leap year); and finally 5) a year, randomly selected from the year range of 1958 thru 1978; and this feature was disabled for the year 1969.

By requiring the random number generator to separately generate an integer value in the ranges I specified, i.e. for a year, day, hour, and minute of time, I could ensure that the dates and times would approximate random.

I generated my random samples by running that simplistic but effective "C for DOS" program to generate a set of 20 random "sample" years, days and times of the day. I then jotted down these 20 sample dates/times in a notebook. After that I would begin the grueling process of using RedShift2, to look up all those random times and observe every single star position (of stars I was interested in), write it down, and so on. Then, I counted all of the times that a star fell into one of the "spatial windows" defined in my model (the parameters of which I clearly define in my paper), added them up, and divided by the total to get the probability of stars traversing, by pure random chance, my particular RAT model spatial windows. I did this until I had 100 sample dates and times, for a total of 2500 RedShift2 observations per sample (2500 for the year 1969, and 2500 for the years 1958 to 1978). The reason for so many samples for only 100 dates/times is that there were 5 sites, times 5 stars, for 100 generated dates/times -- and 5 x 5 = 25, and 25 x 100 = 2500.

In terms of your argument about sampling frequency, I'm not sure how that applies in this case. Stars do not change positions much over thousands of years; some stars only change positions by mere arc minutes over THOUSANDS of years (and I speak here of their positions relative to one another and NOT relative to the Earth's horizons and so on).

An observer on Earth is sitting on a spinning ball, which as stated earlier is like an ideal roulette wheel, except it's a roulette wheel that keeps spinning and spinning at a constant rate and doesn't EVER stop or change speed (at least, not appreciably).

Again for the sake of argument, let's say that you had such an ideal roulette wheel in your home. Then suppose that you painted one arrow pointing from its center outward, on its surface, and then set this ideal roulette wheel to spinning again. Unlike a "real" roulette wheel, this wheel continually spins and spins at a constant speed, and never stops. The speed of rotation of this ideal roulette wheel is constant over time -- just as is the Earth's rotation.

Just for kicks, you decide to do a statistical study of where this "pointer" is over time. Never mind that you can easily compute the probability of the arrow pointing at 19.5 or 33 degrees (within a specified error tolerance) a certain part of the time, just using the laws of physics as applied to rotation.

Next, at random times chosen by a computer program, you take one photograph of this spinning wheel. In each photograph, you note the position of the painted "pointer" on the wheel's surface and where it is pointing at. You are interested in finding out how much of the time the pointer "points" to 19.5 and 33 degrees, within a certain but specific "error" tolerance.

1. You do one probability study of where the painted "pointer" on the wheel is positioned, over the course of one year, taking thousands of pictures over the course of that year -- all at random times.

2. Then you do another study of where the painted "pointer" on the wheel points to, over the course of decades, showing up at random times just as before. But now, the intervals between pictures are more widely spaced because you are spreading out your thousands of observations, over the course of decades and not just one year.

Naturally, you'd find that it wouldn't matter if you took thousands of sample photos of where the pointer was at random times during one year, or thousands of photos spread out over many decades. The sampling rate in such a case is irrelevant for determining the probability of how often the arrow points to 19.5 or 33 degrees, as long as the roulette wheel makes enough rotations during the time interval that you took your samples. (I.e., suppose the wheel completed only one and 1/6 rotations during all that time. Then, the pointer would repeat 1/6th of its cycle, etc., which would change the distribution away from random, since you took more pictures of one part of the wheel's cycle than another.)

In the case of this ideal roulette wheel that constantly spins, if the times you select are truly random, and the speed of the roulette wheel is constant over time, AND if you take enough samples -- then the pointer would still point to a specific location or locations, only so much of the time -- and this would be true regardless of which "sampling rate" was used.

That is the situation with Earth, within the relatively short span of human life. As far as we humans and the tolerances of MY model's approximation of RCH's RAT are concerned, the Earth is just like an "ideal" roulette wheel, because even precession doesn't affect transit time of the stars appreciably. In my section on the "roulette wheel" approximation that I use in my work, I noted that the difference in probability created by differing star transit times due to the Moon's precession for example, is negligible. With the Earth, there was no difference that made any difference, because precession (within the span of a few decades) produces such tiny differences in star transit times that it isn't even noticeable over the course of 20 years.

Nevertheless, to be strictly accurate, the next person who does such a study should do thousands of observations for the surface of the Moon, for EACH YEAR. RedShift2 is not the best tool for doing that. (I'll explain later.) But currently as in the past, I am not aware of a "freeware" program in C or any other language, that would allow a programmer such as myself to modify the code to run thousands of randomly generated times for stars over the MOON's surface. There are plenty of software packages that do that for Earth, naturally.

I suggest that anyone that is concerned about this issue do the sampling themselves, and see what happens. But if you want to compare it with my study, use the same tolerances as I do and use similar date ranges, or the results would not be comparable.

Quote #4:

"* Her use of angular tolerances is inconsistent and is not in agreement with the proposed model being tested."

The problem with someone using my statistics analysis to prove all of RCH's work is, that as RCH himself admits, he doesn't use consistent tolerances. So it's not possible to "test" all of the alignments he claims to be non-random. In my paper, I do not state or claim that I am proving all of RCH's RAT work; only that I made a model which APPROXIMATES his, and got specific results, which I report on in my paper.

I explained why I chose the model I use in my statistics paper; so I will not reiterate that. I wish now I'd have taken the extra effort and written up more information about that "consistent tolerance" model I investigated; it would have made it clearer (at least to some people), how I came up with the second model and why I investigated the data using that second model. Because the other "same tolerance for all angles" model beat the odds, I could see there was something there; and that's why I investigated further.

Those who are interested in the parameters and spatial tolerances I used, and the reasons for them, are welcome to consult my paper. You will find though, that I am very consistent with the model I chose to examine. Are the two models I chose to examine in my paper, comprehensive of RCH's entire RAT theory? No, because of time and efficiency I felt it best to make the model simpler and less comprehensive. And I chose to publish "model #2" because it was the most interesting -- and I developed it, as I said, to test the occurrences of tetrahedral numbers in addition to the angles of interest.

Quote #5:

"* She claims that the program RedShift was used because "it uses NASA data and observations to ascertain star positions at any given date and time". This is incorrect as the program uses the European Space Agency's Hipparcos catalog. Any serious investigation would have utilized the same source data that NASA planners were alleged to have used in their mission planning rather than satellite derived data that was unavailable at the time in question...."

You are right about NASA using different sources to ascertain star positions in the 1950's and 1960's. But it would be good to consider the following. Even if I was mistaken as to the source data for RedShift2, I doubt it would make any difference to my analysis if I had used the data available to NASA at that time instead of RedShift2 (provided I was able to obtain a copy of what the NASA engineers used for their computations). The reason, as I stated earlier, is that when it comes to star positions, there is VERY little change in their spatial positions with respect to time. Also, human technology was sufficient up to that point in the 1950's when NASA started the space program, to accurately measure AND predict the position of stars with great precision. It's measuring the position of moving bodies such as planets, that was harder to do with precision back then.

Why didn't I use that sort of data? Well, for one thing, I was not being paid for this analysis, and as it was I lost thousands of dollars every month for cutting back on my work schedule so I could complete the statistics paper. It's the last time I want to devote myself to a project like that, because it really takes way too much time (and time is money for most of us). And because of the above situation being true (i.e., star observation capabilities being quite accurate in the 1950's, albeit less automated or satellite-precise) -- I didn't deem it necessary.

Also, I knew that a lot of non-technical people would read my paper. Most people wouldn't or couldn't use those sorts of "by hand" mathematical methods to check my work. RedShift2, or any RedShift program for that matter, is easy to use and allows a lot of other people to easily confirm my observations.

It would be ironic if RedShift2 were proven to be inaccurate for TTM ("to the minute") positions of stars. I'm not saying that this is true; for all I know, RedShift2 is very accurate in this respect -- I know that the designers of RedShift certainly seem dedicated to accuracy (I've corresponded with one of them and can attest to that). I only say this now because, after having dealt with a number of astronomy software packages, I can see that even the most well-intentioned programmers can be off in their programming code or their calculations. It's possible that RedShift2 could have small inaccuracies like this; which would also throw off the results of my study, since my second model relies on TTM positions of stars as well as the typical RCH RAT alignments of 0, 19.5, and 33 degrees.

The main reason RedShift2 was used, aside from its accuracy rating, is that not all of the observations I had to make were based on Earth. I don't know of any "freeware" that computes the positions of the stars over the surface of a specific location on the Moon, and I wouldn't want to try and write such a piece of software myself. I could do it, but I simply don't want to invest the time. Therefore, a program is needed that will make observations of star positions over the surface of the Moon, and Mars too for that matter, if the RAT theory is to be tested in a totally automated manner as would be best. Otherwise, any random number generator and a program like RedShift is fine to use, if overly labor intensive for someone like myself, since a lot of notebook entries have to be made and then looked over and counted by hand (which I did many times over, to make sure they were all counted correctly -- thus, part of the reason that paper was so labor-intensive).

Quote #6:

".... In any case, RedShift is highly unsuited to this kind of work as it lacks a programming interface to the numerical integration engine and requires manually entering hundreds of control and test events making the study extremely labor intensive (Weaver even bemoaned this fact herself). This is not the way to engage in serious numerical analysis: the claimants should develop appropriate test software and make the source code available for comment and verification purposes."

As I said before, I could make the software available, but I don't think it would help much. What interest is there in evaluating a fairly standard, effective and simplistic "C" language random number generator? I could see the value in it, if you thought that the random number generator was somehow in error; or if the laws of motion regarding the Earth or Moon created unpredictable irregularities in star transit times. Since the results I obtained from my random dates/times samples confirmed celestial mechanics equations -- equations that are already very straightforward (after all, the Earth turns at an essentially fixed rate every day and has been doing it for a very long time) -- I don't think it was in error.

I do not intend to make light of your objection. Certainly, such a study would be ideal if one had the time and resources to do it that way. But in this case, confirming my work isn't hard. All such a study would do is confirm, like my own data did, that the Earth turns at a fixed rate and therefore, stars spend exactly so much time in spatial "windows." Also, the Earth not only turns at a constant rate, it turns at what might as well be deemed as a fixed position in space with respect to the stars (because precession is too slight to make a difference to star transit times), during the span of a human lifetime or a few decades. The Earth's orbit is not large enough for parallax to be a significant factor in star positions; which means that, as far as we're concerned on Earth, stars always rise and set in the same places every day, every year (even though during some times of the year, we can't see them during daylight hours, stars still rise and set in the same places every day of every year, and take the same amount of time, every day of every year, to traverse a specific spatial window).

I mainly took those thousands of observations (which only translates into a hundred samples for each case I did!), to confirm what I had done with my equations of motion and make my work all the more solid and grounded in empirical observation.

-- END OF QUOTES SECTION --

I am now going to mention errors that my paper contains. These errors are probably obvious to statistics profs and others who specialize in statistics, which I do not. That's probably why I did not catch it; aside from the fact that it's much harder to spot logic or math errors in your own work -- that's why it's so important to have it checked! (Which I did; but apparently, not by the right people.)

One mistake I made was to mix the Apollo astronaut events in with the launch data. I didn't do this at first; but later in the paper, I multiply it in to show how unlikely it was that my second model would work on Apollo astronaut events such as the date and time of course changes of Apollo spacecraft, as well as the launch data. I do think the "star alignments" for launch times is interesting and holds together because launches are a specific group of data points that can reasonably be said to belong to the same "set."

But, the other events I looked at, such as dates and times of "course corrections" or "space walks" made by Apollo astronauts, is not conclusive. To be consistent, I really needed to look at other events too. And in that case, where do you draw the line? Should I also have looked at when the astronauts ate breakfast? Should I also have looked at the times that Houston controllers held meetings to discuss course changes? So, I think I'd have been better to just have stuck with launch and landing times, and left it at that.

It isn't good statistical practice to mix one set of data with another, because it can produce erroneous and meaningless results. For example, I was examining the connection between launch times and star alignments in my paper; not between spacecraft course corrections and star alignments. Therefore, it wasn't appropriate of me to "mix" other events into that analysis. I could claim, "I am analyzing the connection of all Apollo astronaut events, including launches, and star alignments." But then, where would I draw the line? When the astronauts ate breakfast is also an astronaut event; even though the time they ate is probably not documented, as are the times they went on "space walks" or made course corrections.

I do find the amount of correspondence with Apollo astronaut events, such as course corrections, which ARE documented -- and the RAT theory -- to be interesting; and the fact that these documented events such as course changes actually corresponded to my model, was absolutely amazing because it was so unlikely. And it does mean that there are an unusual number of synchronicities in the timing of Apollo mission activities. But if you actually wish to CONCLUDE something about that level of synchronicity -- other than "Wow! Isn't that interesting and unlikely!" -- then, only "course corrections" should be looked at as one grouping, or only landing times, or only launch times, etc. Otherwise, the question must be asked -- "are you looking at the connection of star alignments with astronaut events, or with launch times? And if you are making the connection between astronaut events and star alignments, then why stop at course corrections and docking maneuvers?"

Those of you who are calculus majors, not just statistics experts, could also have caught this next error already. When I say in my paper, something to the effect that "the probability of up to this many alignments occurring are _____", I in fact use a probability equation that is used to calculate the probability of EXACTLY THAT MANY alignments, NOT "up to and including that many". Unless the math takes into account the probability of, for example, more RCH RAT hits occurring than what actually did occur, I am calculating the probability of EXACTLY the amount that occurred. I thought I had taken that into account; but I had not and the mistake is glaringly obvious once it's pointed out. Needless to say, I didn't realize this at the time I published my paper. The error was pointed out to me in January of 2000, and I sent the fellow a thank-you email after I realized my mistake.

That one mistake alone would probably send statistics profs (or PhD's like Sol) into fits, because it's an obvious error to someone who works with statistics and probability all the time. I did study the principles of statistics and probability again prior to writing the paper; I made sure I was well-grounded in those basics, and double-checked my work. I had my work reviewed by another person who was knowledgeable in statistics and probability theory, to assure myself of this. Why my associate who does statistics and probability analyses, didn't catch my mistake when I had him review my paper -- I don't know. Perhaps he, like many busy professionals, just didn't have the time to look it over in depth.

Anyway, the effect that this error would theoretically have on the rest of the paper is to diminish the "odds against random chance" -- not necessarily eliminate them. There is no way of knowing if this totally demolishes my conclusion about a pattern in the data or not, but I don't think it does. I will explain why in case some of you are interested.

If my paper were rewritten using the appropriate equation, that takes into account the probabilities of "more" RCH RAT hits happening than what actually happened, we'd have an equation that looks like this:

Where: P(hits) = probability of RCH RAT hits that actually happened, then:

P(up_to_that_number_of_hits) = P(hits) + P(hits+1) + P(hits+2) + P(hits+3) + . . . P(every_data_point_is_a_hit)

From my paper, it can be seen how small and unlikely P(hits) is. And, P(hits+1) is much smaller than P(hits); likewise, P(hits+2) is many times smaller than P(hits+1), and so on. Therefore, I still think the "odds against chance" would be significant, because although the other probabilities are additive (and therefore make it MORE likely that "so many" RCH RAT alignments could occur), they are so small that I think the P(up_to_that_number_of_hits) probability value would be close in value to P(hits). Which is also why the "odds against random chance" values would still be significant.

However, IMO it's best -- if anyone wants to take up where the paper left off, or rewrite it -- to not include the Apollo astronaut mission event data such as course correction timing; except to note that the timing of the documented Apollo astronaut events seem to follow the same pattern as the launches I examined, and that this degree of correspondence between the two sets of data is highly improbable.

I can only say this regarding the data that I looked at and worked with, of course. According to my source, the other statistical analysis of the Mars missions didn't turn up what mine did. And later on, as I mentioned earlier, I examined other data such as some of the Space Shuttle launch data, and didn't find the same adherence to RAT as the Apollo data showed. I don't say that proves anything, one way or another. But it does imply that it's premature to conclude that my study does prove the RCH RAT.

I've not wanted to make this correction to my paper and then republish; as I've said, that paper was a royal pain to finish and rewriting it is not something I'd undertake lightly. But it does bother me, to let errors perpetuate themselves without correcting them. So perhaps I can make the time to correct my mistakes and republish, someday.

So I don't think I've proven RCH's entire ritual star alignment theory, nor do I believe RCH's "NASA" Egyptian ritual theory is the only explanation for the "odds against random chance" being significant or indicative of non-random occurrences. I don't think anyone could prove his entire theory, at least the "star alignment" synchronicities part of it, without analyzing more data or coming up with a more comprehensive model. I do allow for the fact that RCH could be right; but I don't think it's proven. After doing more research of my own into the phenomena of synchronous events, I do believe that it's possible for a lot of seemingly "non-random" events to come together, without necessarily requiring that something such as RCH's Egyptian ritual scenario be behind this "star alignment" phenomena. That's why I'm not a RAT fan. I'm not against RCH's theories, but I also allow for the fact that he might not be correct or there might be another explanation for the star alignment phenomena, based on other research I've done on my own time that suggests just that.

We all live and learn, and so it is even with researchers. I only wish I'd known someone with a PhD in statistics, to help me spot the statistics errors I did make in the paper, before I published! Even so, I worked hard to lay a good foundation for probability analysis as applied to star alignments; and I think my paper succeeds in that area, with the exception of that probability equation I used -- which unfortunately, undermines all the "odds against chance" results. (I do believe that the control data worked out well because I didn't use a probability equation in that instance; I simply expected -- due to my own use of motion equations, and my own observations -- to see a specific number of "hits" in a random situation, and that's exactly what the data showed). Still, as I said, were I to use that equation and rewrite my paper, I would no doubt find that the "odds against chance" would still be significant enough to reveal that synchronicities were present. I will not go so far as to say that RAT was responsible for the synchronicities, because I don't think anyone knows that for sure at this point.

I think this covers the latest news about my paper.

I wish I could promise that I will answer all inquiries or continue to post on the BBS. My time is valuable, and I can't promise that I will be able to continue this sort of discussion about my paper. Feel free to send me emails if you have questions. If I can't answer them due to lack of time I will say so. I'll do what I can to answer questions or objections; and if I don't have the time, I'll let you all know.

Thank you all for your interest. I can be reached at the email address astro_hist@dcemail.com.

All the best,

Mary Anne