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2014 May 31
A spreadsheet for calculating precession
My new telescope requires coordinates for the current date; I can't give it epoch 2000.0
coordinates (from reference books) the way I do the Meade telescope.
Further, I like to read old books that describe interesting celestial objects and
use coordinate systems much earlier than 2000.0.
So I've made an Excel spreadsheet the computes precession of coordinates for me.
You enter an object's coordinates and epoch in the first six columns.
The blue and pink columns then are computed for you.
There are more columns for your comments on the right.
Click here to download it and use it yourself.
It's intended for moderately experienced Excel users and is unsupported, although
naturally, I want to hear about serious flaws, if it has any.
This is not a photograph of Mars. It is a map, generated with
WinJupOS, an extremely useful software package that
can map the planets as seen from any angle, turn any photograph of
a planet into a flat map, and combine photographs taken from different
angles (of the planet's rotation) into a map or a rotating animation.
As the name suggests, WinJupOS was originally a tool for observers of Jupiter,
but it now covers all the observable planets. It has almost revolutionized
the serious study of the planets by amateur astronomers.
To make it clear that this is a map, I've left in some grid lines and a red dot
for the subsolar point. These, however, are easily turned off. You'll see that
this map corresponds to my Mars picture from May 8.
In one of the Facebook astrophotography groups, an eminent planet photographer
has sounded a warning. Apparently, some amateurs have been suspected of combining WinJupOS maps
with their own images! This makes the image look better but destroys its scientific
value and, more importantly, its honesty (unless of course you admit exactly what you did,
in which case people will say, "Why?").
This is not the same as simply using WinJupOS to rotate and combine your own images.
That is a perfectly honest and legitimate practice.
And there can even be legitimate reasons for combining photographs with map data.
The "remastered" Hatfield lunar atlas
is a fine example: lunar orbiter data were combined with Hatfield's original
photographs to add detail. The end result, of course, is presented as a map,
not a straight photograph!
In my 1999 book I included a short section on
"the ethics of retouching," thinking mainly of detail digitally "painted" into a
picture by hand. The bottom line: In science, we don't do that. The image that
people see should be derivable by algorithm from what your camera captured, with
no human intervention to add or remove features.
The caged bird sings
with fearful trill
of the things unknown
but longed for still
and his tune is heard
on the distant hill
for the caged bird
sings of freedom.
If, as I recommended yesterday, you only pin a few of your pieces of software to your
Windows 8.1 Start Screen, then at the bottom of it, you will see a persistent message
something like "15 new apps installed."
One way to get rid of this is as follows. Use the arrow-in-a-circle to get to the
All Apps screen. Go through and look for apps that are labeled "NEW" and right-click
on each of them once. (Then right-click on something else, or on blank space.)
This will deduct it from the count of new apps installed.
Be sure to scroll to the right so you see all of them.
Well, I'm all moved in to Windows 8. I copied all my files to a 64-GB jump drive,
then wiped the hard disk, partitioned it all as just one partition, and installed
Windows 8.1, then all the files and software. Whew! It was rather like moving to
a new house, but a little quicker.
Here are some further tips about Windows 8.
Use Windows 8.1, of course. It solves some user interface problems that made 8.0 hard to use.
Wiping the hard disk and reinstalling from scratch can be a good thing.
Windows Vista/7 and its software leave a lot of junk files behind full of
cached data and the like, and it's good to be rid of them.
Another way to discard a lot of useless data is, every couple of years, make
yourself a new user account, transfer the files that you need, and then
delete the old one. Much of the junk (?) is stored in user AppData space.
When you first sign in, you'll be asked to set up a Microsoft account.
For privacy reasons and for compatibility with my existing LAN, I chose not to do this.
The way to opt out is to tell it you're creating a Microsoft account, and then
bail out of the process. "Skip this step" is not an option where it ought to be.
Key point about the Start Screen: not all your software needs to be on it.
The Start Screen is for software you use regularly. There's a down-arrow in a circle;
click on that, and you'll see all the software, grouped the way the manufacturers
grouped it (roughly). You can also get to any piece of software by simply typing
its name while the Start Screen is displayed.
There's no substitute for reading Microsoft's instructions. There are some new
things to learn.
Is Windows 8 perfect? No. I am neither an uncritical admirer nor an unthinking critic
of Microsoft. They make useful products, and I use them.
I'm upgrading my Lenovo laptop to Windows 8. I wondered why only the full
edition of Windows 8 could be purchased, not an upgrade edition, and the
answer is a bit disappointing:
You can't upgrade, in the usual sense of the word. When you change to Windows 8
you lose all your installed software.
The reason, I'm guessing, is that Windows 8 has to see the software being installed
in order to register it properly on the Start Screen.
I decided to proceed, actually. I am going to format the hard disk and
install everything from scratch. It's time — I had been using this computer
long enough that it had a lot of detritus from no-longer-needed software.
I'm taking the plunge and becoming an enthusiastic user of Windows 8.1,
rather than someone who just tolerates it.
I already knew Windows 8 was better "under the hood" (internally).
As you know, what puts people off about Windows 8.1 is the Start Screen.
Instead of the fly-out Start Menu that has been with us since Windows 95,
you have a whole screen full of tiles. It looks like the screen of a smartphone.
My initial impression was that Windows 8 was trying to mix two completely
different GUI styles, complete with different kinds of graphic design.
I still think there's some clashing that needs to be overcome, but Windows 8.1
was a substantial improvement. Definitely use 8.1, not 8.0 when you
switch to Windows 8. The upgrade is free.
Here are the key insights behind my "conversion":
When people look at the Start Menu, they aren't looking at anything else.
You might as well make it big. (That was explained to me by a Microsoft
researcher a while back. The Start Screen is just the Start Menu "writ large.")
I was already using my Desktop as a Start Screen. I had a lot of icons
on the Desktop to launch particular pieces of software. But the Desktop was
also cluttered with folders and files of data I was working on. It was starting
to get too crowded.
It is absolutely necessary to arrange the Start Screen for yourself.
That's what I hadn't gotten around to doing until last night. The original layout
that Microsoft gives you is rather flaky and is designed to promote their
smartphone-style apps, most of which are of little interest to someone using a PC
for business or programming.
You can rename them, resize them, and control whether they are "live" (displaying
data such as the weather);
You can eliminate (unpin) icons entirely (to reduce clutter), and still see them
by going into "all apps" mode, which shows you all the software
on the machine;
You can find any software instantly by starting to type its name.
My arrangement has a Most Used group right at the left, followed by
several groups of related software items. I'm not enthusiastic about the
smartphone-like apps that come with Windows 8, so I've put them in a group called "Win 8"
at the far right.
Underlying all of this is the realization is that there are two things you might
do when you sit down at a computer: either launch software or launch data.
That is, you might choose a piece of software that you want to run, such as a web
browser, or you might choose a file to work on, such as a word processing document.
From now on, except for a few extremely often-used items on the taskbar,
I will be reserving the desktop for the latter.
(In fact, you can put files, folders, and web links on the Start Screen if you want to. I've done this
with a couple of things so they will be grouped with the software that they're associated with.)
It's not perfect yet. I wish each group of tiles (icons) could
be expanded or collapsed to a single icon (like a folder).
Maybe they'll provide that in the future.
Bottom line: I'm not going to refuse to learn this just because it's new.
Anyone with that attitude is too old to use a computer.
I don't plan to be that old until at least my 100th birthday.
On the evening of the 23rd I finally got my autoguider working well with the
new telescope. The result was two pictures that will probably be published
elsewhere, so I can't show them to you here just yet. But here's Mars:
That picture, of course, didn't involve autoguiding. It was done with the
same technique as all my recent Mars pictures, although I processed it a little
differently (for higher contrast). Clearly, the new telescope performs well
on planets.
Here's how the telescope is presently set up, with an ADM dovetail camera mount
and a Meade finder (which stays out of the way of the dovetail, unlike the
Celestron finder that came with the telescope).
There is going to be a second counterweight; the single 11-pound counterweight
that came with the telescope is barely enough and can
be insufficient when there is a camera on top of the telescope.
Besides, when I have two counterweights, I'll put them only half as far
down the shaft, and that should improve stability.
With heavier telescopes, Celestron uses this mount with as many as
three counterweights, so I don't think I'll be overloading it.
On the evening of May 21, I made my first attempt at photographing
things outside the Solar System through the new telescope
(8-inch EdgeHD with Canon 60Da camera body). The autoguider was not
yet set up properly, and results were of mixed quality, but here is
a single 30-second exposure of the globular cluster M13:
That was not actually very well tracked, but I downsampled it by a factor
of about 7 and it looks OK. Notice the star colors and the evidence of
dust lanes to the lower left of the center of the cluster.
Then I got the autoguider working well. Here is a stack of two
exquisitely-tracked 30-second exposures of M92:
This was downsampled somewhat, but not as much as M13.
(What I mean is, this is a smaller cluster and you are viewing it
at considerably higher magnification.)
Finally I took a picture of the Mizar multiple-star system.
The three brightest stars here are gravitationally bound; the
fourth one is not, and it has a strange story behind it
(look up "Sidus Ludovicianum"). Single 1-second exposure.
We bid farewell unexpectedly to John Reed, the jeweler who sold us our
engagement and wedding rings and later operated his own business, JWR Jewelers,
where we bought several things. The newspaper tells me he had a short bout with cancer.
We had not even heard that he was ill. He will be missed.
You may have heard on the Web that vinegar works as a weed killer.
Well, in my experience it doesn't.
However noxious Round-Up may be, the reason it exists is that simpler
chemicals don't do the job.
A point of logic and language: Franklin D. Roosevelt is reported to have
said, "Every American has a right to a job."
That sounds nice, but what does it mean?
Every right is nothing but an obligation on the part of other people.
For example, if you have a right to do something, other people have an obligation
not to interfere with it.
What about a right to receive something?
That is meaningless unless you say who is obligated to provide it.
So if "every American has a right to a job" then who is to be compelled to hire them?
Maybe all he meant is that we want an economy in which everyone can get a job;
but if so, calling it a "right" is misleading.
The 8-inch EdgeHD telescope is serving me well, and it's time for some technical notes.
Piggyback camera adapter:
The only real disappointment so far has been the
Celestron 93609 piggyback camera adapter
is made of plastic and is too flexible for anything more than a lightweight camera.
So I put an ADM dovetail camera mount on top of the telescope
instead.
As you can see in the pictures, it collides with the screws for attaching and removing the finder.
My solution was to replace them with 10-32 × 3/4-inch Phillips-head screws.
Now I need a screwdriver if I want to remove the finder, but there is plenty of room
to use the dovetail. (The finder bracket is mounted in slots and was already as far
from the dovetail as it could go.)
(Apologies for the mediocre photography, done in haste.)
[Addendum:] An even better solution, which I implemented the next day, was to
install the finder from a Meade 8-inch Schmidt-Cassegrain in place of Celestron's finder.
It fits, and the Meade 8×50 finder sits right above its mounting holes rather than being
offset a long way to the right, so it leaves room for equipment on the dovetail.
(Melody gave me this finder for Christmas 2001 and I had been using it on a smaller
telescope; I wanted to keep using it.) If you want to do this, all you actually need
is a Meade finder bracket, since Celestron's 9×50 finder fits in it.
There is probably an earlier Celestron finder bracket that fits as well.
I think the people at Celestron "outsmarted themselves"
(as Quick Draw McGraw would say)
when they introduced the new-style finder bracket. It is elegantly made and puts
the finder in what may be a more convenient position, but it interferes with
the use of a dovetail on top of the telescope.
What's the best thing about the EdgeHD? Two things, actually:
the optics and Celestron's tech support. They answer questions by e-mail within
one business day and have been very helpful.
Impostor T-adapter? As mentioned earlier, the EdgeHD focal plane is 133 mm
behind the rear flange, and it's important to get within about 1 mm of that distance,
while conventional SCTs are optimized for about 100 to 105 mm and have a large tolerance.
This implies that both the visual back and the T-adapter for the 8-inch EdgeHD are
about 28 mm longer than the versions for conventional SCTs.
Well, I have somehow gotten hold of a T-adapter that
is labeled as a Celestron 93644 EdgeHD T-Adapter
(including product number and EdgeHD color scheme)
but is actually, physically, a
conventional T-adapter 50 mm instead of 78 mm long.
What is the solution to this mystery? It was at my dealer as a secondhand item, so it may not
even have come from Celestron. Is someone faking Celestron products and getting them slightly wrong?
Did Celestron have a mistaken manufacturing run? I've written to them and expect to hear back on Monday.
MYSTERY SOLVED: I had only part of it! As shown in the picture below, it consists of two
parts, which screw apart. The upper part alone is used with the focal reducer and, as it happens,
is essentially identical to the non-EdgeHD T-adapter. The lower part is a 28-mm extension tube.
Here are pictures I took with the old (Meade LX200) 8-inch telescope on
the evening of May 11.
These are black-and-white infrared pictures.
DMK camera, infrared-pass picture, and each is
the best 1800 of 3600 video frames (roughly), processed with AutoStakkert 2,
RegiStax 6, and PixInsight.
Above each picture is the name of a prominent feature in it.
From there, you can go to a moon map and find out what you're
looking at.
Aristarchus:
Mersenius:
Schickard:
Copernicus:
Sinus Iridum:
J. Herschel:
Goldschmidt:
Kepler:
Just to clear up something that is sometimes misunderstood:
These and all pictures on this web site are covered by copyright law.
Anyone wanting to reproduce them elsewhere for any purpose must get
my permission.
The position of any star or other object in the sky is accompanied by an epoch,
or date. That is not because the stars are moving around; for practical purposes, within
our lifetimes, they aren't. It's because the earth's axis is shifting (a phenomenon
called precession) and the coordinates, right ascension and declination, are relative to the earth's rotation.
When I was young, star maps and lists of objects used epoch 1950. In the 1980s, everyone
switched to 2000. To be precise, the old epoch and the new one were called B1950.0 and J2000.0,
where B and J denote slightly different ways of defining the beginning of the year, and .0 means,
of course, that we're talking about the beginning of the year rather than some time midway
through it.
Older books used epoch 1900, 1875, or occasionally something else.
Until recently, all of this could almost be ignored, unless you were actually drawing a star map.
The reason is that precession is only one degree per 72 years, and when aiming telescopes by
coordinates, we used setting circles that were only accurate to about two degrees. From there,
we found objects "by eye."
But now we have computerized telescopes, and now (unlike 20 years ago) they are often
accurate to 0.1 degree or better. And we are now fourteen years past 2000.0.
That's enough to make a difference — 0.2 degree's worth.
It has just come to my attention that newer Celestron telescopes use what we used to call
the "epoch of current date," i.e., coordinates relative to the position of the earth's axis
right now, whenever "right now" may be. Some people call this "JNow".
Presumably, the catalogue stored in the telescope uses a standard epoch (J2000, maybe) and
converts to "JNow" on the fly. The important thing is, if I want to enter coordinates for
the telescope to go to, I need current-date coordinates, not 2000 coordinates.
I can get them from any astronomy software package (such as Stellarium) or from
this handy calculator.
In that calculator, I would specify the current
date (as this is written) as "J2014.4" since we're about 40% of the way through 2014.
This is bound to cause some confusion because we still need a standard (or at least known)
epoch for lists and charts that are going to be used for some time. But I don't advocate
standardizing on 2025 quite yet. Maybe not even 2050, when we get there... 2000 is a nice
round number. The point is, the era of epochs as we used to use them is over, now that
computers can give us current-date coordinates.
[Addendum:] It has long been traditional to compute planet, comet, and asteroid
positions for the epoch of current date. Converting to any other epoch would be
an extra step. That caused a bit of inaccuracy when people
plotted the positions on star maps without converting them to the same epoch.
There are other approaches. In ancient times and the Middle Ages (yes, there were precise
star catalogues then!), astronomers used ecliptic coordinates, which are based on the plane
of the earth's orbit around the sun, not the earth's rotation. Precession still affects
that system, but it's much simpler to calculate because only the longitude changes, not the
latitude. (This is an important clue; it shows that precession is caused by the gravitational pull of the sun.)
And for real permanence, some astronomers designate distant objects by their galactic coordinates,
i.e., relative to the plane and center of our galaxy. That is astrophysically meaningful
because the latitude and longitude tell you whether something is likely to be inside our
galaxy (and if so, whether in a thick or thin part of it). And there is no precession, so
the coordinates are permanent. Unfortunately, because they're unrelated to the movements
of the earth, galactic coordinates give you little help estimating where objects will appear in the
sky.
At an observatory, a "first light" ceremony marks the inauguration of a new telescope.
My first observing session with the EdgeHD took place on the evening of May 13,
and since we had a full moon, I did lunar and planetary imaging, even though the telescope
and mount are intended mainly for deep-sky work. The very first two pictures taken
with it are both creditable, although the air wasn't as steady as I could wish:
Each of these is a stack of hundreds of video frames, processed with
Autostakkert, RegiStax, and PixInsight. The second image shows the
ramparts of Mare Orientale, which I've photographed
much
less successfully in the past. It is my favorite lunar feature,
but we seldom get a decent view of it, and we never get a good
view of it from Earth.
Impressions of the telescope:
EdgeHD works. The image is indeed sharp from edge to edge, provided
you have the eyepiece or camera in the right focal plane.
I was using the Celestron EdgeHD 1.25-inch visual back, Celestron prism diagonal,
and a Tele Vue 32-mm Plössl eyepiece (chosen because it is of high quality
but simple and free of quirks). Ideal performance was with the eyepiece about
5 mm short of all the way in the barrel.
I think some thought needs to go into designing accessories to hold all types
of eyepieces and cameras at the right distance from the rear flange.
As Celestron explains, just like any other Schmidt-Cassegrain, this telescope
can shift its focal plane over a huge range, but with the EdgeHD design,
the corrections for coma and
field curvature only work at one particular position. It may have actually
been a mistake to use moving-mirror focusing; maybe they should have used a
rack-and-pinion focuser so the focal plane would always be in the right place
and only the eyepiece would move.
I have a 2-inch diameter diagonal and a 2-inch-diameter 40-mm eyepiece, so I bought
a (Meade) 2-inch visual back to use with this telescope, but I'm not sure I'll stick
with it. It's partly my eyes; I get along better with a smaller exit pupil.
And it's partly that neither this nor any other 8-inch Schmidt-Cassegrain telescope
is really designed to work with eyepieces that large. Now that I've experienced
EdgeHD, I am not entirely happy with situations where it doesn't work well — such
as this one, because I can't quite get the eyepiece close enough to the telescope to
use the best focal plane.
Speaking of focusing, there is surprisingly little image shift with focusing.
I had no trouble focusing and taking those high-resolution lunar and planetary
images without a Crayford focuser.
One disappointment: The current Celestron piggyback camera adapter is made
of plastic and is far too flexible to be trusted. I'm told the older
Celestron 93598 piggyback adapter, which is metal, will fit this telescope.
But I'm going to go new-style and put a dovetail
on top of the telescope. (There isn't room for the huge Losmandy
dovetail that I had on top of the Meade telescope.)
The mount worked quite well as far as I could tell; it was quiet, smooth,
and sturdy. I haven't tested tracking yet; that will be the next step.
"All-star polar alignment" works — it got me to within 0.1 degree
of the true pole.
12-volt power came from a battery; specifications say a 3.5-amp power source
is needed, but that is obviously the maximum, not the average; a two-hour session
left the battery still almost fully charged. I was not using an autoguider or
dew heater, of course.
It was a good observing session. A pleasant surprise was getting to see a
telescopic meteor go across M67.
Here's my first good Saturn picture from this season. You can see Rings A, B, and C
(but Ring C may be hard to see on your monitor depending on the brightness).
On the evening of May 11,
we had unusually steady air. I used the 8-inch Meade LX200, a 3× converter,
and a DFK color camera with UV/IR block filter. This is a stack of the best half
of about 1800 video frames. I got better results with a larger number of somewhat
underexposed frames than with half as many correctly exposed ones.
Now that my ribs have healed enough that I can use telescopes in the normal manner,
I've upgraded my astronomy setup a bit. The first change was to acquire
PixInsight software, which is a substitute for Photoshop for
scientific work, considerably cheaper than Photoshop, scientifically documented
(which means you're allowed to know exactly what's being done to your image).
I used it under a trial license back in November and got very good results.
The second upgrade is that, for the first time in 14 years, I have a new
telescope:
The main advantages that I expect, compared to my Meade LX200, are
better optics, smoother tracking, and greater portability.
The mount comes apart into components that weigh no more than 20 pounds.
Its performance is expected to be distinctly better than a 1990s
design with 14 years of wear and tear on it. (This is not to disparage
Meade at all; they make fine products. Everyone's technology has improved.)
And EdgeHD means the optical system is not the traditional Schmidt-Cassegrain —
it contains two extra lenses and is a distant derivative of the Dall-Kirkham design.
Details here.
In return for better optical performance (especially off-axis), there is a new restriction:
The field is only flat and sharp at one specific distance, 133 mm from the telescope's
rear flange. Instead of making large changes with the focuser, I will be taking care
to use eyepieces and cameras that always put the focal plane where it should be.
The eyepiece and camera adapters for the EdgeHD are slightly longer than those of
the traditional Celestron 8, although in all other mechanical respects they
are the same. Indeed, I'm going to kluge something with a Meade 2-inch-diameter
visual back so that I can use larger eyepieces.
Buying a new telescope always causes a spell of cloudy weather, and then there's
the "shakedown" process, making sure everything is assembled correctly, so it may
be several days before I have anything else to say about the new Celestron.
In the meantime I'll keep showing you lunar and planetary pictures taken with
the Meade, which I plan to keep, at least until I'm sure the Celestron has superseded
it in all respects. Then that eccentric but well-loved telescope may be for sale.
Tools of thought, #4: Viewing ideas from a safe distance
I don't know if anyone is still reading "Tools of Thought," but here's the fourth
and last installment.
A tool of thought that I find vitally important is
learning how to view ideas from a safe and respectful distance.
By that I mean knowing how to consider an idea (or theory or system) and learn from it,
even if I don't trust it or like it.
Far too many people's thinking is hobbled by their habit of judging every idea
before they quite know what it is. This is particularly the case in politics
and religion, where everything that isn't from My Side is assumed to be completely
wrong. Too many people are afraid of knowing, in any detail, what other people think.
They think it would constitute disloyalty, or danger, or something.
Let me be the first to admit that thinking for yourself is hard. But I can't do
without it. This obliges me to try to understand the thinking of people with whom
I disagree, even when I'm sure they are dead wrong about something important.
This doesn't mean there's no truth to be found, or that any idea is as good as
any other. Not at all. Mistakes are mistakes, errors are errors, and crackpots
are crackpots. But that doesn't stop me from learning from them.
All of this can be summed up as having the ability to view an idea from a distance.
Without making it my own, I can learn from it, and I ought to try to understand it.
Even if I think a theory is totally wrong (like the theory that the earth is flat),
I still want to know what goes on in the minds of its advocates. They may have noticed
something that I haven't, something that my own theory needs to address more clearly.
And when I look at Marxism or Buddhism,
for instance, I find much with which I cannot agree, but I also find people looking at
real problems intelligently. I can at least let them help me identify the problems,
even if I don't accept the solutions.
The main technical challenge is reconciling different terminology and presuppositions.
People in radically different schools of thought often say similar things in such
different ways that their positions look more different than they are — or the
important differences are concealed under a pile of differences that are only superficial.
Making rival theories commensurable (testable against each other) is part of the day-to-day
work of scientists; it is also an important part of philosophy.
On the evening of May 7, I got some rather good images of various
parts of the moon, using my infrared (DMK) camera (with IR-pass filter)
and 8-inch Meade telescope. Each is a stack of approximately the
best 1800 of 3600 video frames, processed with Autostakkert 2,
RegiStax 6, and Photoshop.
First, the lunar Alps, with a dramatic valley cutting through them,
perhaps cut by a meteor:
Next, the lunar Apennines (you'll note that lunar mountain ranges
are named after terrestrial ones that were part of the ancient Roman
world):
And here are the craters Ptolemaeus, Alphonsus, and Arzachel, with the Straight Wall at the bottom:
Finally, another view that includes the Straight Wall (Rupes Recta), which is a cliff, not a wall,
and is not perfectly straight:
On the same evening I photographed Mars. Same telescope, but with a 3× Barlow lens
to enlarge the image and a color camera (DFK). The image was de-Bayered with the FireCapture
de-Bayer utility, then processed much like the lunar images above.
Tools of thought, #3:
Recognize that words and phrases can be meaningless
Today's Tool of Thought is a very important one, but it takes a while to explain.
Please bear with me.
What I want to demonstrate is that nice-sounding words and phrases can be
meaningless even if they sound nice and seem to convey something deep.
Although this may be new to you, it is uncontroversial. There is some controversy
about what it implies (for instance, I think A. J. Ayer went too far in equating
meaningfulness with sense-perception), but the key insight is undisputed.
Before using English, I want to give you some examples using the language of
mathematical symbols. We all know that
(8 / 2) + (9 / 3)
is a formula that makes sense and evaluates to 7. Just as obviously,
) ) 8 2 / / + 9 3 ( (
is not a formula in this language; it uses the right symbols but does not
put them together in the right way. The parentheses are not paired up,
and the operators + and / are not between the numbers they operate on.
This "formula" means nothing.
Now look at this one:
(8 / 0) + (9 / 0)
Here the formula is constructed properly but is still meaningless.
The problem is that division by zero is not an operation; you can write
symbols that say to divide by zero, but you can't actually do it.
(I'm talking about ordinary high-school arithmetic; I know about NaN and Inf in
computer languages; that's not the point.)
Thus, the formula does not evaluate to a number.
One of the key insights of 20th-century philosophy of language — appreciated,
but not emphasized, by philosophers all the way back to Greek times — is that
the same thing can happen in English and other human languages.
You can construct phrases and sentences which,
although perfectly grammatical, do not mean anything.
Consider the phrases a green square and a round square.
The first is something that could easily be printed on a page or displayed
on a computer screen. The second isn't.
The problem is, nothing is, simultaneously and in the same sense,
round and square. Thus, the phrase a round square is meaningless
even though grammatical.
Of course, immediately you're imagining something that is approximately
round and approximately square — not exactly either one, but in between,
a square with rounded corners and bulging sides — and some of you are
ready to tell me that is a round square. I maintain that it is not.
What is happening is that people use language creatively, and if we hear
something that seems meaningless, we try to interpret it as an attempt
to express something that is otherwise hard to put into words. For that
purpose, you might say a round square and mean something. But you are
no longer using the words round and square with their full
original meanings. You've made a creative shift.
The question that interests philosophers is whether phrases that aren't meant
creatively — that are intended to be taken literally — are nonetheless
meaningless. Consider, for example, "Everything happens the way it was meant to be."
Do you mean the way God intended it to be? If so, you're talking theology, and we
can debate, for instance, whether He intended for people to sin. But if you aren't
referring to God or any other higher power — if you just believe in "fate" —
I will ask: How can you tell whether things happen the way they were meant to be?
Meant by whom? Who could have known it? Unless you can flesh these things out,
your sentence is meaningless.
In fact, a good test of meaningfulness is whether you or anyone else
(perhaps even an omniscient deity) could determine whether a statement is
true or not. If the answer is no, if there is no imaginable way to test
whether a statement is true, the statement is probably just a meaningless
arrangement of words.
Speaking of deities, there's a whole batch of logical conundrums that sound
like this: Could all-powerful God create a mountain so big that He could
not move it? That is, could all-powerful God set up a task that all-powerful God could not perform?
Or even, Could all-powerful God create a round square?
If you say "yes" you sound pious but it's not clear what you've said. If you
say "no" you seem to be denying the all-powerfulness of God.
The answer is that "create a round square" does not mean anything, so when
you ask, "Could God create a round square?" you are not really asking
a question. The same goes for the immovable mountain. As C. S. Lewis put it
(and I quote from memory), a meaningless series of words does not suddenly
become meaningful when you add the words "God can" at the beginning.
Related to the issue of meaninglessness are two others. First, some meaningful
phrases fail to refer to anything because they assume something that is not so.
An example is the present king of France. France does not have a king,
so no matter what you say about the present king of France, it can't be true.
(Nor, perhaps false. Some philosophers hold that it is not a statement at all.)
Second, some sentences are true by definition — they do not convey
facts — they just say what they already assume. An example is,
"All bachelors are unmarried." (Taking bachelor in the most common sense;
I'm not referring to academic degrees here.) Such a sentence may give you
information about the language, but it does not give you information about the
world around you. By definition, if a man is married, we do not call him a
bachelor. "All bachelors are unmarried" simply tells you how the word is used.
One of the main issues in philosophy for the past century has been that of identifying
philosophical doctrines that are actually either meaningless or true by definition.
Naturally, there are controversies about difficult cases. But "Everything happens
according to the laws of nature" is an example of something that may be true by
definition — whatever happens, we say that the "laws of nature" explain
it in some way — the statement gives us no information.
Now consider the old physical theory that all of space was full of a substance called "aether,"
invisible, massless, but serving as the medium of propagation of light and radio waves.
It gradually became clear that statements about aether were meaningless because aether
had no observable properties at all and there would be no way to distinguish between
a universe that had aether and one that did not.
The notion of aether was abandoned, but the
name lives on in Ethernet, a type of computer network that uses
radio waves inside a coaxial cable.
While testing the drive motor of the 8-inch Meade LX-200,
I took this picture of the globular cluster M3.
It is a stack of five 14-second exposures through a Canon 60Da
with an f/6.3 focal reducer (actually giving about f/7 in this
configuration).
The faintest stars that you see are around 16th magnitude.
Even a single 14-second exposure reached well beyond
magnitude 14. I'm impressed at what this camera and
telescope can do.
I'm plotting an upgrade to my astronomy equipment — about which you'll hear more soon —
and every so often someone at Deerlick or somewhere says to me, "You're a prominent amateur astronomer.
Why don't you have the best equipment on the field?"
Indeed, the equipment that I use is not too different from that of a serious beginner.
I have a Meade 8-inch Schmidt-Cassegrain, the most popular size and type of amateur
telescope. Why don't I have $20k worth of Astro-Physics gear, or a Meade 16-inch, or
something like that? I'd surely get better pictures. And after this many years, surely
I could afford it.
The answer is twofold. First: High-end equipment can be a lot of work to set up and use.
It works well, but when something has 5 components that each weigh 50 to 75 pounds, it's
almost beyond one person's capability to set it up and take it down. I don't want to spend
an hour building an observatory, so to speak, before I can start looking at the sky, nor an
hour taking it down when I'm ready to leave.
Second: My hobby is not simply taking good astrophotos. It's making astrophotography
easier. I get satisfaction from finding a way to take good pictures with modest
equipment, then sharing the knowledge with others. I'm wanting "bigger bangs for a buck,"
not simply "bigger bangs."
If I had simply wanted to take the best pictures, I would have gone professional. I would
have joined the staff of an observatory somewhere and used their equipment. Instead, I chose
a different profession — computational linguistics — and, for me, astronomy
has remained a sideline.
Tools of thought, #2: Give an example (or several)
The second tool of thought that I want to share with you is
simple: Give an example. If you're arging that there are such-and-such things,
point out at least one of them. If you're saying that something can be done in
such-and-such a way, walk us through an actual example in detail.
Giving an example helps you think clearly in several ways:
It ensures that you are talking about something real, not just arranging words.
Or, worse, rearranging someone else's words without having found an
actual point of disagreement.
It immediately raises useful questions: "Are there other examples? Are they
very different from this one? How would we know whether something is an example of this or not?"
You might even find out that there are no examples. I've heard of this
happening in a mathematics thesis defense — the student had proved a set of
theorems about a particular set of functions, without actually identifying one of the functions,
and the examiners stumbled upon a proof that there aren't any. The same thing
happens in the real world. Don't just philosophize about the snakes of Ireland.
Go find one.
Let me practice what I preach by giving examples of the need for examples.
In an undergraduate philosophy class, I once heard a fellow student opine, "I think we
should take emotions into account, not just logic." Not sure what this person meant
by "logic," and suspecting it wasn't the same thing I meant by the same word, I had the
presence of mind to ask for an example. I'm not sure we ever got one — the
discussion took off in a different direction — but the point is, an example would
have been very instructive and would have told us things that an abstract statement
of the problem could not.
Another example: Responding to Tools of Thought #1, a correspondent says that more things
need to be "viewed in shades of gray" than I indicated. My response is that this, by itself, is not
clear enough to debate, but some examples would shed a lot of light on it.
Indeed, thinking of examples, we realize immediately that some questions have definite
"yes" and "no" answers ("Were you born in the United States?"), and others pertain to
gradients ("Are you tall?"). Still others might have numerous discrete possibilities
rather than just two ("What country are you a citizen of?"). If you start
looking for shades of gray in people's nationality, you will find a lot of interesting
cases you hadn't thought of before (dual citizenship, stateless individuals, etc.), but,
I contend, you will not find shades of gray. On the other hand, if you try to classify
everyone as either "short" or "tall" with no smooth gradient from one to the other, you'll
fail to do justice to the facts.
(And the same goes for classifying people by race.)
Are there other examples that behave differently from
any of these? That's for you to explore.
Fox News is reporting triumphantly that last fall's
sequestration of federal funds
only caused "one layoff" of a federal employee.
If true, that's because the economic harm fell not on the government itself,
but on the companies that supply the government with goods and services.
Government contractors aren't people that appear and vanish on a whim —
they employ human beings who need jobs. And if the government becomes an
irregular, unreliable customer, it's going to have to pay more for the same
goods and services than a regular customer would. That's basic economics
and is unavoidable in a free market.
Several people lately have told me that they think I'm good at explaining
complicated things and debating complex issues. In the next few Notebook
entries, I want to reveal some of my tools of thought and explanation.
You can decide for yourself whether they're good ones.
Tool of thought #1 is to list the alternative possibilities.
That is, decide what you're trying to choose between.
Typically, this will be something like half a dozen alternatives,
not just two. A common mistake is to think that the first two
possibilities that you think of are the only ones.
In fact, it's important to keep asking whether there's an
important one that you haven't thought of yet. Making a list
can help you ask the question because it can suggest what form
another alternative might take.
For example, once, when reading a paper about the abortion controversy,
I focused on the question, "When does the fetus acquire human rights?"
and named the possibilities: suddenly at conception, suddenly at birth,
suddenly at some other time, or gradually. If you choose "gradually,"
you have to say what it means to have only partial human rights.
If you choose "suddenly at some other time" you have to say what time and
give a good reason for it. And so on — you see how the list
helps you reason about the issue.
Working through a complete list of possibilities was called inductio
in medieval philosophy. That's not what "induction" means today in either
science or mathematics, but it's the source of the notion.
A complete list of possibilities is not the same thing as a list of
positions that people actually hold — but when scientific or
historical evidence is involved, the latter may be what you want.
(In dealing with controversies, there's little point in
considering positions that have never been
advocated by anyone.) For instance, when I talk about evolution to
church groups, I present them with a "menu of possible beliefs" so that
they can see the possibilities and give a name to each one. I only
present positions that have been advocated seriously and with at least
a little credibility.
The point is, when you have a list of possibilities, you're defended against
two mistakes. One mistake would be to think that two positions are the only ones.
The other mistake would be to "see everything in shades of gray" by not
distinguishing clearly between alternatives. Shades of gray may be genuine,
but often they are just the result of seeing the picture out of focus.
UPSes aren't just for computers
(An electrical adventure)
Here you see a 10-year-old UPS (uninterruptible power supply)
that I just fixed up by replacing the battery.
Behind it there's a story.
On the morning of April 30, Athens, Georgia, had a disastrous wind storm.
For about two hours we had 50-mph wind gusts, which blew down trees and
took out electrical power lines all over town. For us, it led to a six-hour
power outage.
Unfortunately, when the power went out, Melody was in her
lift chair (electrically powered recliner),
which she is using while she recuperates from hip surgery.
It relies on motors to make it lean back or sit up straight.
What this means is, when the power is out, you can't get out of the chair.
The manufacturer provides "battery backup" in the form of two 9-volt batteries
in the power pack. They are supposed to enable you to straighten up the chair once,
and then they're used up. In our experience, they didn't even do that, and
furthermore, they tested "good" after we tried it. Somehow I don't think they were
even trying to do their job.
So, starting this afternoon, the chair is powered through an old computer UPS
which I've revived (see below). That will provide several minutes of normal
operation, at least — we've verified it. It also keeps our cordless telephone
system working.
I made two minor changes to the UPS. I took out the beeper (a piezosounder) so
it won't beep at us all night. (Be careful if you do this yourself;
when working on a UPS, make sure it's unplugged from the power line and
the batteries, and remember that there can still be high voltage in capacitors.)
The other change was to label the "restart" button, which has to be pressed to
make the UPS start after it has shut itself down due to low batteries, and in some
other circumstances.
Other kinds of medical equipment deserve UPSes — CPAP machines, for example.
I wouldn't use a consumer-grade UPS on equipment needed to keep someone alive
(such as, maybe, an oxygen concentrator) — for that, you need medical-grade
electronics. But if an outage would merely be inconvenient, not life-threatening,
then by all means use a UPS to protect against it.
When a computer UPS stops working, 90% of the time it just needs a new battery.
The rechargeable lead-acid "gel cells" are only good for three to five years — much
less if they are discharged deeply or are stored rather than used.
You can take a thrown-away UPS to Batteries Plus,
spend $40 to $80, and emerge with it restored to be as good as new.
You should test your UPS after a power failure,
since the batteries will suffer heavy wear and tear while running down,
and they're likely to fail if they were old to begin with.
Yes, they're rechargeable, but they're designed to stay nearly fully
charged all the time. A hundred 15-minute power outages are no problem,
but a 6-hour power outage that runs the batteries completely down is
something else entirely. The same goes for batteries in safety lights
and the like.
If your UPS doesn't have a self-test that it can run, then just unplug it from the wall
and see how long your computer runs. If you're not satisfied with the results,
get new batteries.
And write the date on the new batteries with a silver Sharpie.
[Addendum:] One APC UPS required 48 hours of charging before it resumed
acting normal. For the first whole day, it reported a state of charge that
was low (20% or so) and decreasing, as if it were out of its mind. Apparently,
it needed two days to both charge the batteries and run enough self-tests to
convince itself that the batteries were all right (which I had already
verified with a voltmeter and a separate charger).
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