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#11
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Possible New Double-Pulsar With Low Mass Errors
On 11/18/2014 4:28 AM, jacob navia wrote:
But with that we can justify ANYTHING. My point EXACTLY We don't know what we don't know until we know it. I just don't like hubris and I see an awful lot of it demonstrated here. |
#12
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Possible New Double-Pulsar With Low Mass Errors
On Friday, November 14, 2014 3:06:17 PM UTC-5, Robert L. Oldershaw wrote:
A measured mass of 145.0725 +/- 0.0001 is highly unrealistic. Such narrow error bars on such a large stellar mass are hard to imagine. ... Thanks for missing the point. The point was that you are dividing by an artificially large number to make the result look like better agreement with your quantization than there really is. I just took it to absurdity to demonstrate the point. (i.e. that a mass completely inconsistent with 0.145 Msun and yet looks like an excellent match according to your arithmetic) Also, would you prefer that I not divide by 2.61 and instead just say the error is 0.0034 solar mass? I would prefer that a real statistical test be performed. Which is what I did. A chi-square test excludes 0.145 Msun quantization with 100% confidence [**]. In terms of the actual mass of J1906+0746, I would think an accuracy of +/- 0.01 solar mass is a reasonable uncertainty to hope for at present. I see what you did there. You picked an uncertainty just large enough to be consistent with your model, but not too large compared to 0.145 that makes it completely ambiguous. Talk about wishful thinking. But the truth is that there is no quantitative rationale to the uncertainty you hope for. CM [**] Really (100-1e-27)% = 99.999999999999999999999999999% confidence. |
#13
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Possible New Double-Pulsar With Low Mass Errors
On Wednesday, November 19, 2014 3:10:47 AM UTC-5, Craig Markwardt wrote:
I would prefer that a real statistical test be performed. Which is what I did. A chi-square test excludes 0.145 Msun quantization with 100% confidence [**]. [**] Really (100-1e-27)% = 99.999999999999999999999999999% confidence. The Solar System is the most extensively studied system available and the mass estimate uncertainties are lower than for other systems. Comparing M(total,observed) = 1.99158 x 10^33 g with M(total,predicted) = 1.99184 x 10^33 g, how would you evaluate the agreement between the observed and predicted mass values? If a colleague at your institution achieved the same results with a more conventional theory, would you react the same way and give the same answer? [Mod. note: reformatted -- mjh] |
#14
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Possible New Double-Pulsar With Low Mass Errors
Robert Oldershaw wrote:
Also, would you prefer that I not divide by 2.61 and instead just say the error is 0.0034 solar mass? Let me try to describe the situation in a slightly different manner, which I hope will make the issues a bit clearer. It's convenient for purposes of exposition to use round numbers. So, imagine that we are considering whether or to what extent some quantities are quantized in multiples of 10. If we get a value of 1004 +/- 1, then it seems to me that you (Robert) arguing that we should say error = distance from 1004 +/- 1 to the nearest multiple of 10 = 3 (at the extreme ends of the error bars, i.e., 1004 +/- 1 means a range of 1003 to 1005, and 1003 is 3 away from the nearest multiple of 10) so the quantization condition is 100 * (1 - error/value) = 100 * (1 - 3/1004) = 99.7% satisfied I (and many others in this discussion) think this is a misleading way of stating the result. For example, if we use this means of stating the result, what's the *worst* (farthest-possible-from-quantized) answer one could possibly get for a value that's around 1000? The answer is an error of 5 (for a value that's exactly half-way between two multiples of 10, measured very accurately)... which by this criterion would still count as having the quantization condition 99.5% satisfied! Instead, we should consider the distance from the nearest multiple of 10, and ask whether or not this is consistent with 0 to within the error bars. (For my example, 4 +/- 1 is not consistent with 0 to within the error bars.) To characterize the error in a dimensionless fashion, we could, for example, observe that mathematically the error lies in the range 0 to 0.5*10, so if we were to divide the error by 10 we would get a dimensionless number in the range 0 to 0.5. If this is all clear, then I leave the substitution of 0.145 M_sun for "10" as an exercise for the reader. -- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" |
#15
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Possible New Double-Pulsar With Low Mass Errors
On Thursday, November 20, 2014 1:26:29 PM UTC-5, Robert L. Oldershaw wrote:
On Wednesday, November 19, 2014 3:10:47 AM UTC-5, Craig Markwardt wrote: I would prefer that a real statistical test be performed. Which is what I did. A chi-square test excludes 0.145 Msun quantization with 100% confidence [**]. ..... Comparing M(total,observed) = 1.99158 x 10^33 g with M(total,predicted) = 1.99184 x 10^33 g, how would you evaluate the agreement between the observed and predicted mass values? a) I would evaluate it with a real statistical test, using reported measurement uncertainties. b) I would evaluate it on the basis that the "predicted" mass should be a multiple of 0.145 Msun, which it is not. (1.0014 Msun / 0.145) = 6.91. CM |
#16
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Possible New Double-Pulsar With Low Mass Errors
On Thursday, November 20, 2014 1:28:21 PM UTC-5, Jonathan Thornburg [remove -animal to reply] wrote:
Let me try to describe the situation in a slightly different manner, which I hope will make the issues a bit clearer. I am not aware of any stars with a mass of 1000 solar mass, but I do see what you are saying. Let's take a more reasonable mass in the vicinity of 1.000 solar mass. The predicted multiple would be 1.015, and say the empirical mass estimate was reported as 1.080 solar mass. 1.080 - 1.015 divided by 1.015 times 100 = relative error of 6.40%, and the corresponding relative agreement of 93.6%. Surely we can recognize a large difference between 99.987% and 93.6%! Surely you do not think that I would claim that 93.6% constitutes a "hit" on one of the predicted peaks, or a near miss! So let's talk about the Solar System's total mass. Yes, I know it is only one system, but surely you know that it is not just any system and it is the one system for which we have the most accurate, as well as precise, measurements. Given the results for that system which has the most accurate total mass value, do you alter your Bayesian prior, or is it "excluded at 100%" forever with no hope of ever reviewing that summary decision? [Mod. note: reformatted -- mjh] |
#17
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Possible New Double-Pulsar With Low Mass Errors
On Friday, November 21, 2014 5:36:43 AM UTC-5, Craig Markwardt wrote:
.... Comparing M(total,observed) = 1.99158 x 10^33 g with M(total,predicted) = 1.99184 x 10^33 g, how would you evaluate the agreement between the observed and predicted mass values? a) I would evaluate it with a real statistical test, using reported measurement uncertainties. b) I would evaluate it on the basis that the "predicted" mass should be a multiple of 0.145 Msun, which it is not. (1.0014 Msun / 0.145) = 6.91. There is a mistake in your calculation. The error is that you assume that the first approximation heuristic: (n=7)(0.145 solar mass), is sufficient for the calculation of a second, i.e., more refined, approximation. This is not true. If you study the page on my website that I specifically directed people to, then you will see how to do the second approximation calculation correctly and why the theory demands this, and always has. When you understand what the theory actually predicts, then we can discuss the comparison between predicted and observed total masses. I think they are indistinguishable, given a realistic assessment of all relevant uncertainties. [Mod. note: reformatted. This newsgroup is not the place for discussion of the details of this fringe theory, so I guess this should end here -- mjh] |
#18
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Possible New Double-Pulsar With Low Mass Errors
On Friday, November 21, 2014 5:36:43 AM UTC-5, Craig Markwardt wrote:
b) I would evaluate it on the basis that the "predicted" mass should be a multiple of 0.145 Msun, which it is not. (1.0014 Msun / 0.145) = 6.91. On further analysis there are two problems with this calculation. The first is my error - another rounding off error! I used the rounded off 1.7 x 10^56 in calculating the predicted mass. When I used the original 1.73 x 10^56 the predicted mass comes out 2.02728 x 10^33 g, which is 1.0192 solar mass. The second problem is believing that predicted peaks occur at integral multiples of 0.145 solar mass, rather than approximate multiples. The correct n value for the (n)(0.145 solar mass) approximation in this calculation is 7.016, as can be looked up in any physics handbook. Here I assume that one needs to use the relative atomic mass in the calculation. So: 1.0192/0.145 = 7.029, which is not too far from 7.016 [99.8%] This messes up the nice agreement between the predicted and observed masses for the total mass of the Solar System, but they still differ by a reasonable 0.01785 solar mass. The above has reminded me that without more exact values for the empirically derived scaling constants, it is very hard to accurately compare systems on different cosmological scales, but not impossible. There are plenty of predictions that do not require 1% accuracy. |
#19
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Possible New Double-Pulsar With Low Mass Errors
On Thursday, December 4, 2014 2:23:09 AM UTC-5, Robert L. Oldershaw wrote:
This messes up the nice agreement between the predicted and observed masses for the total mass of the Solar System, but they still differ by a reasonable 0.01785 solar mass. The mass of the sun is known to about 0.0125%, so a 0.01785 solar mass deviation from expectation of the model would be a 141 sigma deviation. Statistically, the model would be excluded. Also, let's pretend that we have the basis to loosen standards and allow +/- 0.01785 solar mass deviations from the model. That covers 0.01785*2/0.145 = 25% of the total possible range of deviations. I.e. even if the theory is wrong, this error tolerance would declare "theoretical victory" 25% of the time just by random chance. No scientist I know would consider that an acceptable false positive rate. CM |
#20
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Possible New Double-Pulsar With Low Mass Errors
On Friday, December 5, 2014 10:55:04 AM UTC-5, Craig Markwardt wrote:
Also, let's pretend that we have the basis to loosen standards and allow +/- 0.01785 solar mass deviations from the model. That covers 0.01785*2/0.145 = 25% of the total possible range of deviations. I.e. even if the theory is wrong, this error tolerance would declare "theoretical victory" 25% of the time just by random chance. No scientist I know would consider that an acceptable false positive rate. Using absolute mass values, rather than the relative mass values in my 12/4 post, gives the following results. Predicted mass = 1.013374 solar mass 1.013374 sm/0.145 sm = 6.988786 Predicted - observed total mass of Solar System = 0.01203 solar mass. Sun's mass is not a constant and the self-similar scaling parameters are empirically-derived approximations. |
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