Thank you, Tony, for acknowledging that symmetric differencing is a form of data smoothing. Although you still have not acknowledged that
your raw unsmoothed data show an actual decrease in velocity, I guess we should thank you for not repeating your usual denial of that fact.
Symmetric differencing does generate an average about a data point and thus will smooth out noise.
Yes, and it also smooths out signal.
Using every data point by simple differencing essentially doubles the noise.
Yes, and it also improves the resolution by a factor of two (compared to symmetric differencing).
The question one needs to ask is why the average between two data points on either side of the point in question causes a higher velocity than the previous average. How did it get to be greater?
I see two possible interpretations of this question.
You might be asking what could cause the downward velocity of a collapsing structure to increase with time, in which case the answer is
gravityWP.
On the other hand, you might be asking us to explain to you why velocities calculated by balanced (symmetric) differencing aren't the same as those calculated by simple forward or backward differencing, in which case the answer is that balanced differencing is a form of data smoothing that effectively degrades the resolution of your data by a factor of two.
Both interpretations of your question leave me to wonder whether your paper's first author might have been responsible for the technical aspects of your paper, with the second author brought in to handle the religious aspects.
This is the reason for regression analysis and when charting data like this it is the trend which is significant.
Nonsense. Everyone knows the trend (average acceleration) is about 0.7g. If that 0.7g trend were the only significant issue, we wouldn't be having this conversation.
The central question of your paper, silly though it be, is whether that 0.7g average is (1) a fairly smooth acceleration, as would be expected from the smeared-out collision caused by a tilt, or (2) the smoothed-out average of a jerky, jolting acceleration, as expected by MacQueen and Szamboti.
I am sure some here will say that the measurement resolution is not sufficient to discern whether or not a jolt took place,
Yes, there are competent people here. One of them (
Dave Rogers)
has analyzed the situation correctly.
but that is a feigned argument for two reasons: First is that the trend is obviously increasing, and secondly the size of the jolt required is much higher than what could be indicated by one data point.
(Insert laughing dogs here.)
"first is that the trend is obviously increasing"
The object is being accelerated downward by gravity. No one in his right mind would expect the smoothed trend of the downward component of its velocity vector to be anything other than increasing.
"the size of the jolt required is much higher than what could be indicated by one data point."
A single data point measures position at a single point in time.
It can't show anything about velocity. To say anything at all about velocity, you have to look at two or more data points.
Even two data points can't show anything about acceleration. To say anything at all about acceleration, you have to look at three or more data points.
Finally, and most important:
Trends and averages can't show anything about the presence or absence of jolts. In this context, jolts are brief decreases in the downward component of the instantaneous acceleration vector, and cannot be estimated without estimates of the downward component of the instantaneous velocity vector.
Trends and averages say nothing about brief changes in instantaneous velocity or instantaneous acceleration.
If you look at MacQueen and Szamboti's three data points for position at times 1.5, 1.67, and 1.83 seconds,
they show a decrease in velocity: this is exactly the kind of jolt that
MacQueen and Szamboti say is missing from their data. That's an
epic fail.
The premise of the Missing Jolt paper is valid for the reasons stated above.
As I have explained above, your "reasons stated above" are laughable.
I can't just accept your claim on the basis of your technical authority, either. For at least
four months now, you have been having
obvious difficulties with grade school arithmetic.
In any case, we will be redoing the measurements with a more sophisticated system called Tracker, which is in the Open Source Physics project and is available on the Internet. I will make the results of the new data set public.
It would probably be good for some of you guys here to do some measurements yourself.
You and MacQueen made a truly extraordinary claim that's contradicted by your own raw data. It would have been a good idea for you to have realized that
before publishing
your paper instead of after.
Competent peer review would have helped.