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Possible New Double-Pulsar With Low Mass Errors



 
 
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  #11  
Old November 18th 14, 07:11 PM posted to sci.astro.research
David Staup[_2_]
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Default 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  
Old November 19th 14, 09:09 AM posted to sci.astro.research
Craig Markwardt[_2_]
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Default 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  
Old November 20th 14, 07:26 PM posted to sci.astro.research
Robert L. Oldershaw
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Default 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  
Old November 20th 14, 07:27 PM posted to sci.astro.research
Jonathan Thornburg [remove -animal to reply][_3_]
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Default 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  
Old November 21st 14, 11:36 AM posted to sci.astro.research
Craig Markwardt[_2_]
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Default 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  
Old November 21st 14, 05:18 PM posted to sci.astro.research
Robert L. Oldershaw
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Default 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  
Old November 25th 14, 09:41 AM posted to sci.astro.research
Robert L. Oldershaw
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Default 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  
Old December 4th 14, 08:22 AM posted to sci.astro.research
Robert L. Oldershaw
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Default 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  
Old December 5th 14, 04:54 PM posted to sci.astro.research
Craig Markwardt[_2_]
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Default 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  
Old December 14th 14, 10:29 AM posted to sci.astro.research
Robert L. Oldershaw
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Default 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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