What we DO have is a group of highly qualified observers and analysts conducting research by applying the specific skills of their training to a problem and then reporting the results.
And yet they were only able to obtain 1 result despite having several attempts to do so. Probably because what they were trained to do, and what they were experienced at doing, was tracking rockets, whose launch time and location were known in advance.
Let me repeat that. They had several objects, on more than one occasion, and only managed to triangulate one object on one occasion.
Highly skilled experts indeed.
Actually, given that they were dealing with something they hadn't had to deal with before, and had no advanced warning of when or where they would appear I think they did well to get one triangulation, but according to your "trained, experienced expert" contention they should probably have got far more triangulations.
If you contend those results to be somehow unreliable, then you directly deny the skills of those observers and analysts to do the job they were trained for. I am sure the military would be startled to learn from you that all their expensive training is useless. That the observers and analysts they employ can not be relied upon to do their jobs.
I don't deny their skills, but they were doing something that they
weren't trained to do. Finding and triangulating an object they had no advanced warning of and no prior positional data for was outside their original remit.
No. it is a nonsense argument you propose. Simply, unless we have solid evidence that the observers and analysts can not be relied upon to have done their job - then mere speculation that they might have not done their job is pure irrationality in the face of evidence to the contrary.
I seriously doubt that they ever failed to track and triangulate a rocket, but then, that's what they were experts at doing. However, they only got one hit out of several attempts at tracking and triangulating a UFO, but then that's
not what they were experts at, so I can't blame them.
Oh but you DO! You speculate that the mathematician’s reported statistics cannot be relied upon because we have no accompanying error estimate. But that fact alone does not make the statistics unreliable - because we can think of many legitimate reasons why the mathematicians might not have included such an estimate in their summary report.
Try a class in reading comprehension. I say that we don't
know if it can be relied on, because we have no access to anything other than a final figure with no error. It could be a small error, it could be a large error, but we
don't know.
Moreover, you directly stated that they might have “unknowingly” supplied an inaccurate figure! But that is mere speculation and in the face of evidence to the contrary (their acknowledged expertise) it is not a speculation that should be given any currency.
It's a possibility, a hypothesis if you will, and since you are so insistent that all hypotheses are equal, you should be willing to consider it.
But you have not shown Dr. Maccabees calculations to be in error, you have merely cited another figure different to his and have NOT shown how you arrived at that figure. ANY mathematician knows that you have to provide a “proof” of your calculations to show their accuracy. I have no way of knowing whether you or he was accurate. All I know is that Dr. Macabbee has the qualifications, and he is the expert, I would therefore trust his calculations over your unproven ones – UNLESS you can show me he was in error… but of course you have NOT done that.
Okay, if you need me to do it explicitly, I will.
Dr. Maccabee says
The focal length of the typical telescope was 60 cm. One may assume that the 35 mm film used had an image size resolution, determined by the average film grain size, of 0.001 cm (0.01 mm or 10 microns), or less (if high resolution film was used the grain size could be as small as about 5 microns). Assuming 0.001 cm resolution at the film plane, the angular resolution was on the order of 0.001 cm/60 cm = 1.6 x 10^-5 radians = 0.0009 degrees which is about 3 arc-second resolution (1 arc-sec = 0.00028 deg). When this distance is projected to 150,000 ft it corresponds to about 2 1/2 ft.
0.001/60 is actually 1.666 x 10^-5 radiansrec radians, which corresponds to 9.549 x 10^-4 degrees which is 3.4377 arcseconds.
So far, not so good for Dr. Maccabee.
If an angular resolution of 3 arcseconds gives 2.5 ft at 150,000 ft distance, then 3.4377 arcseconds gives 2.8975 ft, which means that the 12 pixels he gives actually reduces to 10.354, but we'll round up at this point for ease of calculation, and call it 10.5.
Okay, so Dr. Maccabee then goes on to state that
An object 30 ft in diameter would have 12 of these resolution elements across its width, and about 140 such elements over the whole image area (if roughly round)
Well, if the object is round then the number of pixels can be found by simply calculating the area of a circle of diameter 12. That's pi*r^2. Now r is 6 (that's half of 12) which gives us a total pixel area of.....113.097, but let's be generous and call it 115. Still nowhere near the 140 that Dr. Maccabee finds. Of course, if we assume that the object is square then we get a total pixel area of 140, much closer to the 140 Dr. Maccabee gets, but obviously ridiculous, since the report says the object was round, and I'm sure Dr. Maccabee wouldn't have missed that.
Ah, but as I showed above, the actual diameter of the image is more like 10.5 pixels, not 12, and that gives us a total pixel area of.....86.59 pixels. Hmmmm, it appears that Dr. Maccabee is off by almost a factor of two!
I would think you might be a little more circumspect given what I have just stated above. That and the fact that abuse is the “lowest” form of argument reserved for bullies.
This is a more detailed analysis than I did previously, and I did get one number slightly wrong the first time, but feel free to do the calculations yourself. Dr. Maccabee gets them wrong. I addressed this, you responded to that, and then claimed that I hadn't, and couldn't show that I had. I had, and showed where, so you were either lying by ommission, i.e. you hadn't checked to see if I had, or you were aware that I had which makes your statement that I hadn't a blatant lie.
Merely stating that Dr. Maccabee was in error does NOT make him in error. You have to SHOW HOW he was in error. Do you get it yet?
Yes, I do get it, and have shown precisely how his maths is in error. Do you get it yet?
Here is the way I see the mathematician’s working:
Azimuth and elevation angles from one location combined with an azimuth angle from another location are sufficient to accomplish a triangulation. To see this, imagine that the azimuth angles from two locations are measured. Of course the baseline azimuth between cameras and the distance between cameras is known. From each camera location, as plotted on a map, imagine extending a line along the measured azimuth direction. The lines from the two cameras meet at a ground-level intersection point. This point is directly below the objects. Now imagine extending a line upward from the intersection point. One of the cameras also has measured the elevation angle from its location. Imagine drawing a "slanted" line upward from that camera location. Eventually the slanted line from that camera location will intersect the vertical line from the ground-level intersection point thereby forming a right triangle. The altitude of this upper intersection point is the altitude of the objects. Of course, the "mathematical reduction unit" knew this and reported the results of the triangulation (30 ft diameter, 150,000 ft, etc.)
I am well aware of how triangulation works, and the above is not a bad summary. Unfortunately it
doesn't address the problem I was pointing out.
Dr. Maccabee states that at 150,000 ft an object of 30ft diameter has an image diameter of 12 pixels. But the object is at an
altitude of 150,000ft,
not at a distance from the camera of 150,000 ft. Since we know from the report that the object was not directly overhead any of the cameras, so it
must be
more than 150,000ft (~28 miles) from the camera, which makes its angular size on the film smaller. If it's 20 miles (~100,000ft) downrange from the camera then the distance from the object to the camera is about 185,000ft. That makes the angular size about 80% of the size at 150,000 ft. That then translates to a total pixel size of about 70.
Half the value Dr. Maccabee gives.
Do you refute that this methodology could have produced an accurate statistic?
Not in the least. Of course, I'm perfectly aware that that's how triangulation works. That wasn't the issue. Not even close to the issue.
So you are contending that these expertly trained observers, using the equipment they were trained to use, were merely sloppy in their use of that equipment? One of the MOST basic functionality of their equipment (time measurement) they could not get right?
No, I'm saying that they were used to having points of reference in their film, i.e. rocket launch time, engine shut down time, which could be used to confirm the time.
Filming UFOs means that those points of reference are missing.
Oh yes it is! You directly imply that at the very least!
No. I'm not saying that they were sloppy, just that they were using the equipment in a way they weren't used to using it, as evidenced by the lack of good data they got. One hit in several attempts.
But to them it does NOT matter WHAT the “object” is that they are observing, exactly the same procedural protocol is observed in the operation of the equipment. NOTHING changes in that protocol merely because the “object” is different. You obviously have no idea about how technical equipment is actually used in these circumstances.
So how come they didn't get a larger number of reliable triangulations. By your argument they should have got it right every time. But they didn't. Why do you think that is?
Oh come on…these people were used to tracking rockets into orbit with precision accuracy and you contend that “high speed” is something they could not handle. Really Wollery!
Not the issue, not even close. A small error in
timing leads to a large error in position, if an object is moving fast. That's all. I'm sure they knew how to track something moving fast, particularly if they knew in advance the direction it should be moving in.
You're the one claiming that they
couldn't possibly have got it wrong, and yet they did, on several occasions.
Almost every time. In fact, only once did they get it right, but unlike you would like to make people think, I don't blame them for that, because they weren't trained or experienced in tracking UFOs. They were trained and experienced in tracking rockets.
You keep arguing that these guys were infallible, but the report itself shows that they actually had great difficulty getting a triangulation on the UFOs.
