A definitive test of discrete scale (relativity, numerology)

Martin Hardcastle wrote in news:mt2.0-
:

In article ,
eric gisse wrote:
Irritating perl bug: The value of $residual is going to be negative a
significant portion of the time, but squaring the negative quantity
triggers some sort of overflow/insanity. Might need to do some
reporting/squashing after this.

Not in the perl I use! (I did test the script I posted...) That would
be a very serious and basic bug if it were really present!

Yeah. That's what was throwing me.


I think you are mistaking the operator ^ for the operator ** (see my
code). ^ in perl is not 'raise to power' but 'bitwise xor'. ** is the
exponentiation operator.

That'll do it. Major bug, but easily fixed.

This is what happens when you use too many devices and languages that
use different symbols for the same things.


Now, you don't want just the regular chi-squared value. That isn't
useful. What is wanted is the reduced chi-squared value, which is chi-
squared divided by the number of degrees of freedom

Not so. The reduced chi^2 is a useful way of telling at first glance
whether there is something wrong with a model: a reduced chi^2 much
greater than 1 indicates a problem. However, the reduced chi^2 doesn't
tell you everything that you want to know, quantitatively -- a reduced
chi^2 of 2 for 2 degrees of freedom is very much less interesting than
a reduced chi^2 of 2 for several thousand degrees of freedom. So in
fact the standard thing to do is use the chi^2 value itself and
calculate (or look up) the critical value for a given number of
degrees of freedom. You can do the equivalent thing for a reduced
chi^2, so it's not a big deal, but chi^2/d.o.f. is what people quote
in the astrostatistics literature, so it's what I used.

I'm somewhat confused as what you said reinforces my point. The reduced
chi squared, in my understanding, takes into account the differences in
degrees of freedom.

As for the calculation, I see two different things going on:

In Taylor, the gamma integral is done over the reduced chi squared to
infinity, while in my 31st edition CRC the same integral is done from 0
to chi squared. I wonder if I'm just confused or there's not a standard
in the literature.

But as you say this is all (or should be) the same thing, so I am not
abundantly concerned.


For this, the hypothesis is a binning of 0.145 solar masses. This
requires figuring out the amount of bins, and can't be done beforehand
because the data set covers a wide range of masses with a wider range
of
confidence.

Now this may be a point of contention, but I argue the degrees of
freedom is not the amount ouf stars themselves but rather the amount
of
bins of 0.145 M_sun required to cover the mass range. This is actually
more generous to the testing, given that more degrees of freedom makes
it more likely that the hypothesis is true. Turns out to not matter
much, since the answer is "zero" for meaningful chunks of the data.

I don't think this is right. The degrees of freedom is the number of
data points, minus the number of free parameters of the model (none in
this case): see e.g.
http://en.wikipedia.org/wiki/Chi-square_statistic.

I saw that, and was in fact the first thing I looked at before I
remembered "I have books on this stuff! Books that cost me money!"


So I don't think
your numbers are correct (in particular, it would seem very bizarre
if, as you suggest, including stars with larger errors caused the
model to be ruled out more stringently...

Well, I was running through the calculations with the exponentiation
done incorrectly the whole time. Either way, I do not get an answer
distinguishable from computational zero until I reduce the sample size
to like ten stars which is bad regardless.

The calculated probability for 185 stars (the 1%-or-better sample) is
indistinguishable from zero after fixing that and using both the number
of bins as well as the number of stars themselves as degrees of freedom.

in fact, if you include all
the stars with huge errors *and* calculate the chi^2 correctly, you
should find an acceptable fit, but that's only because you'd be
diluting the stars that can actually constrain the model with the many
more that can't).

True, but the hypothesis is so wrong that the calculated probability is
computationally equal to zero until I work with a sample size on the
order of 10 stars.

The reason I argue that more degrees of freedom is more generous is that
it becomes more mathematically possible that the chi squared vs reduced
chi squared comparison does not reject the hypothesis being tested.

Take a chi squared of 10, for example.

Ten degrees of freedom vs one degree of freedom. Which one gives a
result that is more likely?

You can see this in a chi squared integral table, because as you
increase the degrees of freedom the probability goes up.

Or going by actual data:

The chi squared of the 1% set is 2460,

If I use the bins of 0.145 M_sun as the degrees of freedom, I have 25
degrees of freedom. Reduced chi squared is 98.4

If I use the actual amount of stars, I have 185 degrees of freedom.
Reduced chi squared is 13.3.



However, the key point is that this test can be done, and, when it's
done with stars with accurately measured masses, it is inconsistent
with the proposed model at a very high confidence level, as I said
earlier.

Martin

Yep.

On Sep 18, 6:34*pm, Martin Hardcastle
wrote:

So, again, the data are not telling you what you would like them to
tell you. It took me about ten minutes to find the data you referred
to, get them into the right format, modify and run my code, and do the
modifications needed to run it again on the sums of the masses.
Testing models, when they make quantitative predictions, is easy, and
it's a skill that any would-be-modeller ought to learn. The half-hour
or so I've spent on this today is enough for me, though.
---------------------------------------------------------------------------

When you get refreshed, maybe you could put in a half hour or so on
white dwarf masses.

No one seems to want to talk about the Tremblay et al SDSS white dwarf
mass function.

This is odd since it is a large, recent sample, and is carefully
analysed.

It also has clear and statistically significant peaks at DSR's
predicted values.

Why is everyone ignoring this piece of information? (He asks
rhetorically).

RLO
http://www3.amherst.edu/~rloldershaw

On Sep 18, 6:02*pm, Martin Hardcastle
wrote:

However, the key point is that this test can be done, and, when it's
done with stars with accurately measured masses, it is inconsistent
with the proposed model at a very high confidence level, as I said
earlier.
--------------------------------------------------------------

There is something that should be borne in mind: the Sandage - de
Vaucouleurs dust-up.

If you will recall, the two protagonists battled long and hard over
the value of the Hubble constant. Sandage insisted upon 50 km/sec/
Mpc, while de Vaucouleurs insisted upon 100 km/sec/Mpc. The battle
raged on for many years.

Both camps had the same observational data to work with.
Both camps had the same statistical methods to work with.
Both camps included the best astrophysicists of the time.
Both camps insisted that they were obviously right.
Both camps insisted that the other side was wrong.

If things can be unambiguoulsy decided with some data and some
statistical analysis,
HOW CAN THIS BE POSSIBLE?!?

There is a very important lesson here about a very common problem in
physics: often wrong - never in doubt.

Who was right? NEITHER, apparently. We now think that H ~ 70 km/sec/
Mpc.

Bottom lines: Be careful about what you say you can rule out.
And be very careful about what you say you are SURE is right.

Sorry for the EMPHASIS (perhaps I miss PH).

RLO
http://www3.amherst.edu/~rloldershaw

"Robert L. Oldershaw" wrote in news:mt2.0-
:

On Sep 18, 6:02*pm, Martin Hardcastle
wrote:

However, the key point is that this test can be done, and, when it's
done with stars with accurately measured masses, it is inconsistent
with the proposed model at a very high confidence level, as I said
earlier.
--------------------------------------------------------------

There is something that should be borne in mind: the Sandage - de
Vaucouleurs dust-up.

If you will recall, the two protagonists battled long and hard over
the value of the Hubble constant. Sandage insisted upon 50 km/sec/
Mpc, while de Vaucouleurs insisted upon 100 km/sec/Mpc. The battle
raged on for many years.

Both camps had the same observational data to work with.
Both camps had the same statistical methods to work with.
Both camps included the best astrophysicists of the time.
Both camps insisted that they were obviously right.
Both camps insisted that the other side was wrong.

If things can be unambiguoulsy decided with some data and some
statistical analysis,
HOW CAN THIS BE POSSIBLE?!?

Models differ.
Fundamental disagreement over fundamental physics and assumptions.
Insufficient data.
Systematic errors in measurements.

I have no idea how many of the above were true for the kerfuffle over
the Hubble constant, nor do I care because it is completely irrelevant
to the topic at hand.


There is a very important lesson here about a very common problem in
physics: often wrong - never in doubt.

Who was right? NEITHER, apparently. We now think that H ~ 70
km/sec/
Mpc.

An answer that is now verified through several independent methods, all
with high quality data.


Bottom lines: Be careful about what you say you can rule out.
And be very careful about what you say you are SURE is right.

Your theory has been ruled out at a confidence level so high that the
chance you are right is computationally equal to zero.

You have been going on and on about this on USENET since 1995:

http://groups.google.com/group/sci.a...9046a4e1ba66c?
dmode=source

And apparently actually got an ApJ editor in a moment of weakness, so
there's a publication in 1987 about it too.

In a few hours of work using data published more than a decade ago, your
theory was excluded.

Are you going to move on?


Sorry for the EMPHASIS (perhaps I miss PH).

RLO
http://www3.amherst.edu/~rloldershaw

"Robert L. Oldershaw" wrote in
:

On Sep 18, 6:34*pm, Martin Hardcastle
wrote:

So, again, the data are not telling you what you would like them to
tell you. It took me about ten minutes to find the data you referred
to, get them into the right format, modify and run my code, and do
the modifications needed to run it again on the sums of the masses.
Testing models, when they make quantitative predictions, is easy, and
it's a skill that any would-be-modeller ought to learn. The half-hour
or so I've spent on this today is enough for me, though.
----------------------------------------------------------------------
-
----

When you get refreshed, maybe you could put in a half hour or so on
white dwarf masses.

What a ballsy request.

The programming for handling large data samples of star masses has been
written out and explained by me, and further refined by Martin.

I spent a few minutes debating with myself whether to bother because I
knew the result would be some combination of you blatantly ignoring the
result that discredits your theory and a request for more analysis to be
done, previous results be damned.

Boy I wasn't even close, was I?


No one seems to want to talk about the Tremblay et al SDSS white dwarf
mass function.

It might have something to do with you having performed literally no
effort on your own.

I have news for you: there is no serious intere


This is odd since it is a large, recent sample, and is carefully
analysed.

True, yet completely irrelevant.


It also has clear and statistically significant peaks at DSR's
predicted values.

Really, Robert? How do you define 'statistically significant'?

Have you done any analysis of the stars themselves to see if they match
your predictions?

You could, because the programming is RIGHT THERE FOR YOU.

Will you? Probably not. Feel free to use your reflexive disagreement
with me as an engine for doing something useful for yourself, though.

Are you being consistent with your atomic scale numerology?

Nope. You want to claim that white dwarfs obey a mass distribution
similar to atoms, but completely neglect the fact that the stellar mass
distribution completely disagrees with you.

Plus, there are plenty of stars in the neighborhood of 0.73 M_sun which
further discredits your theory.

Given the existence of 100+ solar mass stars, your numerology predicts
600 atomic mass nuceli. Or inverting the argument, your numerology
predicts a lack of stars above 15 solar masses or so because there are
no stable nuclei past Z ~ 100.


Why is everyone ignoring this piece of information? (He asks
rhetorically).

Probably because nobody cares. Or maybe because people are willing to
put in about as much effort as you, which is to say 'none at all'.

I have arguably worked harder on this subject than you have in the last
decade.

* Your notions of dark matter composition and distribution? Completely
wrong. I was the one who gave you the literature on microlensing
searches, which was ignored.

No, saying "Hawkins" three times fast doesn't make 15 years of
microlensing surveys go away.

* Stellar mass distribution? Completely wrong. You've already moved on
to completely ignoring how wrong you are about this, and it didn't even
take 24 hours.

You've put literally zero effort into doing this yourself, and you've
had decades. The data set I used was published in 1999. You have no
excuses.

* Eclipsing binary system mass distribution? Completely wrong. Martin
did the analysis for you, which you are free to repeat yourself given
the available framework. But you won't, and we both know that.

The most recent data is from 2010, but since you missed stuff from 1999
I am not surprised you missed that.

* Planet mass distribution? You've made literally zero effort in testing
that one despite being given the data, and I'm not doing it for you.

Guess we'll never know on that one...

Oh wait, yes we will.

http://groups.google.com/group/sci.a...568058f29d8ea?
dmode=source

I generally interpret "complete ignoring of technical points" on
research newsgroups as evidence for the person I'm responding to having
no argument.

So much for numerology on planetary mass distributions.

Given all the failures and didn't-even-try's above, do you really have
to ask why another block of data you think is interesting is being
ignored?

I will promise you this however: If you ever get another journal of note
to publish your claims after this, I'll be sure to get a refutation
published.

The science is in, and your theory is wrong. Will you be the scientist
you claim to be and move on to something new, or adopt crank behaviors
like ignoring data that disagrees with you?

Choose carefully, as this is an archived medium.


RLO
http://www3.amherst.edu/~rloldershaw

On Sep 19, 3:59*am, eric gisse wrote:

Who was right? NEITHER, apparently. *We now think that H ~ 70
km/sec/
Mpc.

An answer that is now verified through several independent methods, all
with high quality data.
------------------------------------------------------------------------------------

Perhaps someone will offer a primer on how the recently postulated
acceleration of the Huble Bubble might affect the value of H and the
concept of uniform expansion.

Both Sandage and de Vaucouleurs argued that their "answer [was] now
verified through several independent methods, all with high quality
data."

Don't people understand?

There are Platonic over-simplified mathematical models of reality,
i.e., pseudo-reality.

And then there is the physical reality of the real world, i.e.,
reality.

If you assert that the former model is an absolute and unchangeable
version of the latter, you commit a cardinal sin, from the scientific
point of view.

RLO
Discrete Scale Realtivity

On Sep 18, 6:34*pm, Martin Hardcastle
wrote:

earlier posting for the individual stars with errors less than 0.145
solar masses: chi^2 of 16085 for 172 degrees of freedom, null

If I add up the two components and take only the systems where the
combined error on mass is less than 0.145 solar masses, I get a chi^2

-----------------------------------------------------------------------------------------------

How can you possibly test a "model" that predicts quantization at
0.145 solar mass when you accept data with an error of up to just
under 0.145 solar mass?

Would you not need errors of 0.01 or less?

Are systematic errors accounted for?

How much error can sin(i) and sin^3 (i) introduce into mass
calculatuons?

Thanks,
RLO

In article ,
Robert L. Oldershaw wrote:
How can you possibly test a "model" that predicts quantization at
0.145 solar mass when you accept data with an error of up to just
under 0.145 solar mass?

Easy: the chi^2 statistic does this for you. Stars with large errors
will just not contribute very much to the final sum. Any basic
statistics book will explain this. Bevington & Robinson is one I've
recommended to students in the past.

(If we restrict ourselves to systems where the magnitudes of the
errors are very small, the result is actually much, much worse for
your model, because all the systems where we don't actually know
enough to say much are excluded, leaving all the systems which simply don't
fit. Run the code, make a different cut, see for yourself.)

Are systematic errors accounted for?

You tell me what systematic errors are present, I'll tell you whether
they're accounted for. As you'll see if you look at the paper, the
authors have gone to some trouble to determine and correct for
systematic errors in the fitting.

How much error can sin(i) and sin^3 (i) introduce into mass
calculatuons?

They're *eclipsing* binaries, as again the paper makes clear. So,
virtually none; and what there is is accounted for in the errors in
mass used in the chi^2 calculation.

This is the database *you* suggested I run the test on: the paper is a
good piece of work, standard in its field, and clearly provides the
'definitive test' you wanted: I have done a test that any competent
undergraduate could do and the result is completely inconsistent with
your expectations: several of us have also provided you with the tools
you need to do the same test yourself, so you don't really have any
excuse to call bias. When the best available data conclusively rule
out a model, a good scientist thinks again. I think that's all I need
to say on the subject.

Martin
--
School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK
Please replace the xxx.xxx.xxx in the header with herts.ac.uk to mail me

On Sep 19, 5:43*pm, Martin Hardcastle
wrote:

This is the database *you* suggested I run the test on: the paper is a
good piece of work, standard in its field, and clearly provides the
'definitive test' you wanted: I have done a test that any competent
undergraduate could do and the result is completely inconsistent with
your expectations: several of us have also provided you with the tools
you need to do the same test yourself, so you don't really have any
excuse to call bias. When the best available data conclusively rule
out a model, a good scientist thinks again. I think that's all I need
to say on the subject.
-----------------------------------------------------------------------------------

Sincere thanks for your efforts on this sample, which I do not
dispute. This sample does not manifest the predicted quantization.

However, we know that the number of stars with masses below 1.00 solar
mass and with errors at the 0.01 solar mass level is still quite small
in this sample. So I am nowhere near ready to give up yet.

I have much less faith in the arguments you use to summarily dismiss a
whole paradigm on the basis of one dubious sample, having seen this
kind of reasoning falsifed over and over again throughout the history
of science. You know: disproving evolution because it could be
mathematically "proven" that the Sun was less than a million years
old; or proving mathematicaly that H had to be 100 +/- 10 km/sec/Mpc
while simultaneously proving it had to be 50 +/- 5 km/sec/Mpc.

If white dwarf samples are consistent with discrete masses, or at
least show evidence for preferred masses, what do you say then?

RLO
http://www3.amherst.edu/~rloldershaw

On Sep 19, 5:04*pm, "Robert L. Oldershaw"
wrote:

And then there is the physical reality of the real world, i.e.,
reality.
-------------------------------------------------------------------------

Here is an interesting system - a pulsar/star binary, published in
NATURE IN 2010.

http://arxiv.org/abs/1010.5788

Pulsar mass is 1.97 +/- 0.04 solar mass
Star mass is 0.500 +/- 0.006 solar mass

Total mass = 2.470 solar mass

Predicted DSR peak at 17 times 0.145 solar mass = 2.465 solar mass.

[2.470 - 2.465/2.470] times 100 = 0.2% error = 99.8% agreement.

RLO
http://www3.amherst.edu/~rloldershaw