Re: McCoy's grasp of error analysis is totally absent.


On 4/11/06 5:44 PM, in article
1144791855.084634.62590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx, "mccoy@xxxxxxxxxx"
<mccoy@xxxxxxxxxx> wrote:


r norman wrote:
On 10 Apr 2006 13:55:16 -0700, mccoy@xxxxxxxxxx wrote:


Interestingly enough I mention specifics in proving my case. I
mentioned adequate triangulation and how surveyers use triangulation to
determine distances. Now you claim that the tools used for surveying
aren't the same used for astronomers. No doubt you don't put tripods
into outer space, but the method hasn't changed. Triangulation is the
only way that you can determine real distances, especially with
distances that are far. Anything else is speculation. You assertion
of "ignorance" on my part falls apart when you fail to provide reason
for that claim.


You seem not to believe anything until you are told at least 4817
times and we seem to have told you only 3943 times so far.

Let me make things absolutely clear and simple, mathematically and
experimentally. Let B be the baseline and theta be the angle of
parallax. Let D be the distance to the distant object. Then simple
trigonometry says that (1/2)B/D = tan(theta/2). For very small
angles, of the magnitude we are talking about well under 1 degree,
then tan(x) = x to an approximately more than good enough provided you
measure it in radians, not degrees. If you don't like the
approximation, use the full unaproximated analysis which reaches the
identical conclusion.

Then, to an excellent approximation, D = B/theta. And, if you
understood anything at all about error analysis, you would realize
that the percent error in D is the percent error in B plus the percent
error in theta. If you do the proper error analysis not using the
approximation tan(x) = x, you get essentially the same result.

If you are a surveyor and want to measure a distance of 1000 feet
accurate to 0.1 foot, then the error in measuring your baseline and
the error in measuring the angle must be less than 0.01%. So if your
baseline is 100 feet, you must know it to 0.01 foot or less than 1/8
of an inch. If the angle is approximately 6 degrees (1000 foot
distance and 100 foot baseline), then you must measure it to better
than .0006 degrees or better than 2 arc seconds. You might possibly
get the baseline that accurate using surveying tools, but you will
never get the angle that accurate using traditional surveying tools.
That is why the surveyors say you need large baselines and,
equivalently, large angles to do triangulation "accurately".

It's interesting to not the reason surveyers know as much as they do
regarding accuracy and triagulation is because they can actually drive
their car to the site that they are measuring. Hence the methods have
been verified. This is not so with astronomy. Let's continue.



Astronomers have a very different problem.

The biggest problem is that they do not know how far stars are. They
have constructed scenarios as to how they could achieve rough
estimates, but those estimates are based on empty assumptions.

They can easily measure
angles to a fraction of an arc second and they don't need 0.01%
accuracy.

Interestingly enough nobody around here wants to put forth the distance
of a light year. Compare that to the pitiful distance of the Earth's
orbit from one side to the other and you have error seemingly
compounded.


In fact an estimate of distance that is only 1% accurate,
even 10% accurate is quite sufficient for most purposes. Hence, the
rules for astronomers are very different. If you measure angles to
0.05 arc second and need 1% accuracy, than you can measure the
distance of a star up to 5 arc second parallax . That is a distance
better know as 5 Parsec which corresponds to about 16 light years.
If you only need 10% accuracy, you can measure distances out to 160
light years. Frankly I don't know how accurate the angular measurement
is, other people have told you and you could look it up in the back
posts here. But that is what the analysis tells you.

The problem is you can't even estimate what is 10% accuracy. Say that
astronomers have been assuming that a star was 4.4 light years away
when in fact it was 10 light years away. How could this happened?

First of all, has it? I doubt it. If it has not, then your example is
meaningless.

Now if you have a real example, then please put it forward. I would be
interested in the analysis and how it was mishandled and eventually
reconciled.

In any case, you are wrong. We have some very accurate instruments, much
more so than even 25 years ago. So (thinking offhand here) we have very good
accuracy for up to a hundred plus light years. But what about stars after
that?

The wonderful thing about physics is that it is consistent. We can do some
very, very good statistical analysis on the stars that we can measure, and
we can apply what we know about the stars up close to the stars far away.

For example, we know that the color/composition of a star and its heat and
brightness are all related. We can measure the color *very accurately*, and
so know heat and brightness. The apparent brightness we see compared to the
actual brightness we infer when we measure color provides us with a nice
little ratio -- a kind of triangulation, if you like. We can thank Isaac
Newton for part of it. He described the relationship between distance and
apparent brightness in his Optics. Wasn't that nice of a creationist
scientist to provide us with?

Is it reliable? Only if the laws of physics are reliable, and I should
suppose that if God made them, they ought to be. Do we know the distance
*exactly*? Of course not. There are always error bars, reflecting
measurement margins of error and what we know about the close stars.

I suppose it is possible that all of the close stars are anomalous outliers
which do not say anything about the Main Sequence stars that populate the
universe. In that case, we have a bum rap and our estimates are off more
than we think they are. But we have pretty good stats on the closer ones,
and they don't seem to have anomalous characteristics, given what we have
been able to learn about stellar mechanics.

Then again, we not only see individual stars out there. We see whole
galaxies, huge immense things that often take up no more pixels than closer
stars do.

With galaxies, we need to do a bit of work -- but they often provide us with
some nice shortcuts, depending upon their orientation to us. If one of their
axes are orthogonal to our line of sight, we have a vertical axis we can do
regular trig with *if* we can get a feel of how big the galaxy is.

We know something about the distribution of stars in our own neighborhood.
We are rather spread out, being in the Sagittarius arm of the Milky Way. But
how big is a galaxy? If we were to judge by the vast number of stars in the
Milky Way and use our own local spread as a measure, we would be far too
large. The estimate for our own Milky Way is that we are about 100,000 light
years across and 30,000 light years in thickness. We aren't likely to get
any better estimate for a long while, and we can't know whether we are 10%
or 20% or more off. After all, the galaxy doesn't have a sharp edge to it,
so the size depends on where you place the edge.

But given that (we are really a very mediocre galaxy as far as size is
concerned), we can play a bit. The Hubble Ultra Deep Field is a picture made
by staring at the same spot for 3 months. The image is 3 arc minutes square,
and contains over 10,000 galaxies! What about a galaxy that shows the major
axis orthogonal to us that is 1-arc second in length? If we say that the
galaxy is, say, but 50,000 light-years across, the galaxy is about 10
billion light-years away. With simple trig.

Shoot, if you want to get miserly, you could perhaps assert the galaxy was
only 5000 light-years across, for a 1-bly distance. But that would be pretty
miserly, considering what we know about galaxies.

And even with One billion light years, that blows a 6000-year-old creation
out of the water. Unless God is using the stars to deceive us.

Well, the supposed triangulation attempt was made (and one wonders as
to why it was attempted in the first place), and based on the 10% rate
of acceptance the figure of 4.4 light years is generated. The fact is,
you can't determine accuracy rates unless you can actually measure the
actual rate. At least that's how accuracy rates are calculated based
on surveying techniques! What's the difference between some astronomers
and surveyers? Surveyers prove their work and some astronomers keep on
guessing.

Better than guessing. And certainly the errors they make are less
egregiously bad than your own, seeing that you want to make judgments about
things you know practically nothing about.



That is, it tells you if you had the slightest grasp of error
analysis.

Incidentally, as so many other people have told you, astronomers do
NOT measure parallax by measuring the angle at which their telescopes
are pointing but by measuring the apparent shift in position of nearby
stars with respect to much more distant "fixed" stars.

You haven't figured it out yet. The fact be told is that these are
complete guesses. One assumption based upon another.

Well, if you consider the assumption that the laws of physics really are
laws to be invalid, you might have a point. We do assume that the
consistency we see here on earth applies elsewhere in the universe.

So yes, one assumption based upon another, as all science is. The medicine
you take, by the way, is based upon the same kind of assumptions. Yet you
pop your pills without a second thought.

There isn't much
information that can be conveyed by shifting position of stars. It
becomes even particularly harder when you can't even place your self in
that space. On earth everything has geographical relatedness. In space
information content is sparse.

Say what?

Well, maybe. There is -- or was a point to that before the last century. But
when we figured out the distance from the earth to the sun (triangulation
using the earth and the transits of Venus) we suddenly had the geographical
relatedness we needed.

It does take time and observation to put everything into place. When you
operate with such dated and limited knowledge, you forget that there is ever
so much more going on than you imagine. We have a lot more data than you
know of.

I'd be nice if we could draw a permanent
grid across the universe. If this is done automatically then all we
have to do is measure the squares in our solar system and you can
measure anything that is in view (almost I suppose). But in reality
there is just too much empty space inbetween us and the stars. And, to
be sure, that's the only thing that astronomers really know.

To be sure, you *don't* know what astronomers really know. You simply have
no idea.

And I imagine that if we had that nice permanent grid, you would insist that
we couldn't know it was consistent unless we had measured each piece,
especially if it conflicted with your interpretation of Scripture.

John, truth isn't measured by what makes sense to *you*. And knowledge is
not measured by your lack of it. You are no expert in astronomy, yet you
presume to tell astronomers what they really know and what they don't? You
presume to tell them why they don't know, when they have faced these
problems and figured them out?

I agree that astronomers haven't figured everything out. They don't know the
distance to every star (they haven't tried every one they have cataloged,
BTW). But they *are* working hard on the issues, and they aren't afraid to
confront the issues, the anomalous data, the things unknown. They don't
expect to know everything. You shouldn't expect them to. Then again, you
shouldn't have the temerity to make judgments about things you are ignorant
of.

As a Christian, I ask you to back off on this one. Even major creationists
admit that there are stars billions of light years away. You can't win on
this one. All you can do by keeping on is to demonstrate that you base your
faith on silly things.

Regards,

Raymond E. Griffith


JM


.

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