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2016 July 31
Rotation about an axis that doesn't exist in space
Uploaded early because I'm busy. See you in August!
Mathematical thought of the day...
In 2-dimensional space, things can rotate about an axis that is not in the 2-dimensional space. (Consider for example the hands of a clock; their axle isn't in the plane in which they rotate.)
In 3-dimensional space this is not possible. In 3-dimensional space, if something rotates, its axis is in a direction that the 3-dimensional space can describe.
Surprisingly, this holds true for all odd- and even-number of dimension spaces. If I understand it right, odd-dimensional spaces contain all their possible axes of rotation; even-dimensional ones don't.
This is connected, in a roundabout way, with the fact that odd-degree polynomials are obligated to cross the X-axis (because they go up and one end and down at the other) while even-degree polynomials (parabolas or lumpy parabola-like curves) can stay on one side of the X-axis for their full extent. That is, odd-degree polynomials always have real roots, but even-degree polynomials sometimes don't.
The connection between the two is the theory of eigenvectors and eigenvalues, which I wish I understood better. I've been filling gaps in my knowledge of mathematics, and there's always more math out there!
Here's a Windows programming problem that was driving me batty.
I was trying to make an icon for a client's software package, and I wanted
to make a round icon (like the icon for Chrome or RStudio), which of course
is actually a square icon that is transparent outside of a circular image.
I mastered the arcane art of
using transparency
in Visual Studio's icon editor.
Also, along the way, I came across IcoFX, which I highly
recommend. It is a much better icon editor.
But what drove me batty was that when I dragged the icon file onto my desktop to look
at it, it had a faint square border, like the third example here:
I figured something was wrong with the icon and kept looking for a thin row of
pixels that had failed to be marked transparent, or something.
No... The icon of an icon file is not the icon in it, but rather that icon
with a bit of a border added! That's how Windows tells you you're looking at the
icon file rather than an executable that actually contains the icon.
D'oh!
The first two examples in my picture are an executable using that icon, and a shortcut
to it.
This, by the way, is not my client's icon. It is something I put together very hastily
as an example; it's just a truncated digit "1" on a transparent field.
Here is the full field of the AT65EDQ. Same equipment as yesterday's picture (scroll down to see it),
same observing session, stack of
17 1-minute exposures, in town, under a sky where the Milky Way was barely visible
(but that's better than it has been here for years!).
At the top is the Trifid ("3-part") nebula M20, accompanied by a bluish reflection
nebula to the north. At the bottom is the Lagoon Nebula (M8), so named by Agnes Clerke,
apparently because of the dark lane of foreground dust that seems to isolate part of it
from the rest the way a lagoon is isolated from the ocean.
There is less light pollution in Athens, Georgia, than there used to be.
On two consecutive nights (July 26 and 27) I was able to see the brightest parts
of the Milky Way from my driveway. Nothing like the view I had around 1981, when
this side of Athens wasn't built up, and I once saw the North America Nebula with
the naked eye, and the Horsehead with a telescope; but better than recent years.
I credit it to Athens' change to shielded LED streetlights.
This picture was taken for equipment familiarization, not top-quality results,
but it's not bad. You're looking at M16, the Eagle Nebula, with the "Pillars of Creation"
(pillars of dark dust) in the middle of it. I'm testing a friend's
AT65EDQ flat-field refractor (65 mm aperture, f/6.5). This is a stack
of twenty 1-minute exposures with a Nikon D5300, with the telescope on my AVX
mount, with PEC but no guiding corrections. This is the central part of the image.
One of the things that make me saddest about this presidential election — other
than the poor quality of the leading candidates — is the amount of angry, illogical
trash-talk that I'm hearing in place of political debate.
Facts, please. Give me facts.
If you're going to say that such-and-such a politician "ruined our country and took
away our rights," I'm going to press you. What did he ruin?
Name some rights you lost — what are some things you are no longer
allowed to do?
You might have a legitimate case. But you'll have to give me the details.
Vague exaggerations won't do. Vague exaggerations aren't facts.
Please note that I am not defending Obama.
If anything, I'm lamenting that he has gotten too little intelligent criticism!
And the same goes for the candidates now.
We want facts, not trash-talk.
I am glad to report that the transplanted thermostat works well.
I've had a chance to test it in the most extreme conditions
(120 F in the attic on the other side of the wall) and have confirmed
that its thermometer reading
stays within about 1 F of the nearby air temperature.
That's good enough for me.
The wall is very well insulated, with gypsum wallboard, then 3/4-inch of foil-foam
insulation and 3 inches of fiberglass. To that I added, behind the thermostat
only, an additional inch and a half of styrofoam.
I also took great care to fill the hole that the wire comes through.
I made it no larger than necessary in the first place, and then, after
installing the thermostat, plucked a tuft of fiberglass and stuffed it
into the hole alongside the wire.
To my surprise, my measurements showed
one of the biggest ways heat crosses the wall near the
thermostat is conduction by the cable! Makes sense... copper is a very
good heat conductor, so I made sure the last foot or two of cable runs
under some insulation rather than out in the hottest area.
For now, the thermostat stands 1/4 inch off the wall on stacks of washers.
They, however, may not be necessary.
I call this success. This 40-degree difference between one side of the wall
and the other is the greatest it will ever be. In the winter, the attic is
warmed by sunlight (just as in the summer), and it often runs above 60 F
on the coldest days. That means the temperature difference across the wall in
the winter is negligible.
Alert readers already know that we've replaced our downstairs air conditioning system
with a Carrier Infinity 19-SEER system that includes humidity control.
But what's going on upstairs?
The upstairs home office has a separate HVAC system, and today (July 23) I corrected an
engineering error that had been made when it was built 25 years ago.
The thermostat was as badly placed as a thermostat could be. Here's all that was wrong:
The thermostat was on an outside wall...
with a 1-inch hole in the sheetrock where the wires came through...
near a skylight, so that the sun would shine on it every afternoon...
near the top of the stairs, so it picked up a good bit of air from outside the zone it controlled...
and it was over a laser printer that generated heat.
Admittedly the last item was my fault, not theirs. And the second item was corrected with spackle
when I upgraded the thermostat a few years ago. But the third item — the afternoon sunlight —
was a serious problem.
Today I fixed it. I pulled new cables and put the thermostat near my desk, away from the
sun and from heat-generating equipment. It's still on an outside wall (this is an attic
and outside walls are almost all we have!), but I've added extra insulation behind it and will
put the thermostat on standoffs away from the wall if I have to.
All this was preceded by a couple of weeks of exploration and planning. The challenge was
finding the Southwest Passage — that is, finding that our remaining front attic is connected
to the side attic by a small hole. (When we built rooms in a rectangular area in the middle of
the attic, we of course tried to use all the space, so the remaining attic space was left in
disconnected segments.) Then I had to "fish" a rope through the Southwest Passage to a place
where I could actually stand. Using the rope, I pulled the cable; then I went back and attached
it to the wall in several strategic places. Finally I spackled the hole from the old thermostat
and labeled both ends of the old thermostat cable, which we left in place with both ends accessible
because we may one day
have some other need for low-voltage communication between the two ends of the upstairs suite.
It's all over but waiting for the spackle to dry and then sanding and painting it.
And there may actually be a new HVAC system upstairs soon, so I left the cable longer than
it had to be.
The other day I was advised that The University of Georgia is going to correct
a serious architectural mistake that it made in 1968.
The building that contains the Science Library and Boyd Graduate Studies Research Center,
two wings joined by a shared lobby, can only be entered from the east and the north.
I can forgive them for leaving out the west, since it's the back of the library,
but the lack of a south entrance is a serious inconvenience.
Many of the science departments are more or less directly south of this building.
Above you see the view looking south from the lobby.
There's a roof (of a basement) on which you cannot
walk, and then a cavernous opening that leads to the loading dock.
I am told that the lobby is going to be extended southward over the roof,
and there will be a plaza (that you can walk on) over the loading-dock cavern,
leading southeastward to the green lawn
that runs between two rows of science buildings.
This entry is addressed to my fellow Christians, although others may
find it of interest in helping to understand America's complicated and unsatisfying
pre-election political situation. It came from a discussion on Facebook.
For some years, many Christians, especially evangelicals, have taken it for granted that
one of our two presidential candidates represents Christian values much better than the other one
— some say, "is God's choice" — and that all godly people should vote for that one.
This year, that assumption clearly doesn't hold. Many of us see serious problems,
not just with the politics but even with the fitness for office, of both leading candidates.
Many have been jolted out of the assumption that God always picks a candidate.
(God never promised to endorse a candidate!)
We are back in the situation that Christian voters considered normal before the Reagan era
— neither candidate represents us very well, and we have to
choose between mixed bags.
I'm not going to say which one to vote for, or whether to vote for a third party as a protest.
The details that might influence our choice are still unfolding.
But I will make some recommendations:
(1) Do not ignore relevant facts.
Do not get so focused on one fact or a few facts about one candidate that you ignore the rest.
(2) Try to figure out what will actually happen
if a candidate is elected, not just what the candidate says will happen.
(3) Beware of gossip;
get information from reliable sources; admit that the truth is complicated.
(4) Beware of anger.
Some people follow politics for the thrill of getting angry, especially if they can claim it is righteous anger.
Cultivating anger will make you gullible about gossip and blind to relevant facts.
(5) Do not take sides more strongly than you need to.
This is not a ball game with the thrill of
rooting for one side and booing the other.
And it is certainly not a choice between God and the devil.
It is the making of a difficult decision — hiring an executive for our government.
(6) Understand that politicians view evangelicals as a voting bloc,
an easily-manipulated one. Of course, it is good if they can only get our vote by representing us well,
but try to see behind shallow campaign tactics. They want to get our vote at minimum cost.
That can mean taking a few litmus-test positions while ignoring us on all other issues.
(7) Pray for guidance, and pray for our country.
(8) Vote.
(9) Don't forget to vote for offices other than president.
A lot of things are keeping us busy right now, and one is the replacement
of our increasingly finicky central air conditioning system, which was,
if memory serves us right, 27 years old.
The good news is that the new one will use only 40% as much electricity as
the old one. The solution to energy conservation is efficiency, and
air conditioners (as well as cars and many other machines) have gotten a lot more
efficient in the past two or three decades.
So if you have an old air conditioner, or an old car, it may pay to replace it
with a newer one simply to save energy.
As we lament the recent tragedies in Louisiana and Minnesota,
we should be thankful for the miniature video cameras that made it
possible for us to know about them.
Miniature video cameras have become a powerful force for
justice in the world.
And that means we need to be thankful for CMOS image sensor technology,
especially the Sony Exmor
product line, which is widely used
in smartphones because it
performs very well in dim light.
My Christian perspective is that we should thank God for the engineers
who developed the sensors. They were doing God's work at least as much
as the people who used the results to campaign for justice — even
though they were unaware of how their work would be used, and even
though they were most likely not Christians.
We think of religion and morality as belonging to the "humanities" or to the
world of person-to-person interaction only, not engineering.
But the diligent work of integrated circuit engineers did at least as much
for justice in this situation as any protest march.
Please note that I am not pre-judging any particular incident.
I have not even viewed the videos myself and am aware that they are
not the only possible evidence. But I am thankful that
miniature video cameras preserve evidence.
Without them, we might not even be able to ask the questions.
I am aghast at the mass shooting of police officers in Dallas
that occurred under the cover of a protest march.
Multiple wrongs do not make a right.
The pursuit of justice is not a football game of police versus protesters,
where you have to root for one side and boo the other.
Most police officers are honest and professional, and
most protesters are peacefully promoting a worthy cause.
Let's
support our
local police and hold them to a high standard.
We used to look at telephone numbers to judge whether they were
long distance. In the same way, everyone today needs to know how to read
e-mail and web addresses to see if they are what they claim to be.
Key ideas: (1) The last part of the address tells you who it really
belongs to; blah.blah.microsoft.com is Microsoft but
microsoft.blah.blah.com is not! (2) You must
mouse over a link (in e-mail or on the Web) to see where
it really goes
(that is, put your mouse cursor on it without clicking);
the address written in the link can be
completely fake, as can the "from" address on e-mail.
The ending of the address may tell you what country the site is registered in.
Usually, .com and .net are businesses, mostly in the United States;
two-letter codes designate other countries, such as .ru for Russia
and .in for India.
Obviously, the U.S. Internal Revenue Service is not going to have a .ru suffix.
Nor is a business going to have an .edu suffix (educational institution),
although computers at .edu sites are often broken into by hackers.
Also watch out for addresses that are very long and contain more than one
full address. Sometimes they are tricking a legitimate site into forwarding
you to an illicit one.
It is this: Which "good old days" do we want to go back to? If all we really need
to do is "restore" our country to its historic goodness and greatness, exactly what past era
should we be trying to re-create?
My answer: None of them. Do we want to bring back racism, bullying, 65-year life expectancies,
or even secondhand smoke? Of course not. (Especially not the 65-year life expectancies.
That's getting too close!)
False memory of a past golden age is a problem here, and it seems particularly to have infected
some of my fellow Christians, who imagine that at some time in the past, we were a nation of
virtuous Christians and just need to go back to that era.
The illusion has several causes. We remember what was good about the past, not what was bad.
We listen to wise old people and imagine that they never made mistakes,
that they were as mature at 15 as they are at 70.
We look back to our childhood and imagine that the world in those days
was really as simple and innocuous
as we children thought.
Mixed in with this are the memories of adults who led a sheltered life
and who are often just remembering life in a smaller town, not a
more virtuous nation. And there's a lot that people just didn't know. For example, fifty
years ago, only police officers and medics knew how common
child abuse really was, and they often felt powerless to stop it. Was that really a better world?
On a more mundane level, back when "the crime rate was so low you didn't have lock your doors"
it wasn't that low; you just weren't hearing about the burglaries.
Of course there were things to like about the past, especially if you led a privileged life.
But the past golden age that you remember wasn't real.
Note: Not for a moment am I saying there are no new evils.
There is a steady supply of new bad things that must be opposed.
But that is not the same as saying we need to go back to the past.
Not at all!
If you ever have occasion to install a small, low-end window air conditioner,
here are a couple of hints.
The accordion-fold plastic that extends from the sides of the air conditioner
isn't very good at keeping heat (or bugs or lizards) out of the house.
To fix that, my usual practice is to cut pieces of foam-core poster board
(from an art supply store) and stick them in place with double-sided tape,
attaching them to the frame in front of the accordion-pleated stuff.
Many low-end air conditioners only blow forward and sideways, not up or down.
To keep this one from blowing directly on me, I added a deflector, made of thin
acrylic plastic (left over from an unused light fixture — but you can
buy it at glass shops). The bending was done with a heat gun (the kind used
for stripping paint), and it's held in place with double-stick tape.
It's a good idea to make a heavy paper prototype first, to get the size right.
If you're on a graduate-student budget, the prototype can be the finished product.
I have finally gotten to have an extended astrophotography session with the
Nikon D5300, and results were quite encouraging.
I pushed it to its limit because site conditions were so bad — I was in
my driveway in Athens, under hazy skies through which only 4th-magnitude stars
were visible. But I got results, and the camera served me well.
For all of these pictures, I was using a borrowed
Nikon 180-mm f/2.8 ED AI (not AF) telephoto lens,
secured on the AVX mount with a pair of rings as
Jerry Lodriguss suggests.
All of the pictures are stacks of 1-minute exposures with the
D5300 at ISO 400, corrected with dark frames, flat fields, and flat darks.
Please bear in mind that all of these pictures are far less than what the equipment
can achieve at a darker site in clearer air. I wanted to push the camera to its
limits, and it performed well.
This familiar field in Sagittarius is a stack of just four 1-minute exposures
because I was dodging trees. (Dodging trees? Yes, the earth is rotating relative
to the sky, so the trees are moving against the sky.) Not much to add by way
of commentary... I was delighted at how well this picture turned out.
Another familiar field, and it turned out surprisingly well considering the
murky sky conditions. This is a stack of ten 1-minute exposures.
Compare this picture taken at a dark site
with a 300-mm lens.
Here's the Scutum Star Cloud, and unlike the pictures above, this one is not cropped;
it shows that the stars are sharp to the corners of the image.
The star cluster M11 is at the upper left, M26 below center, and NGC 6649 at lower right.
The high dynamic range of the D5300 helps keep the bright centers of the star
clusters from being overexposed.
The constellation Ophiuchus is mottled with dark dust clouds in front of clouds
of stars. All this is extremely hard to photograph through a hazy
sky, but I did it.
In the picture above, to the right of the center, you can see a meandering dark
cloud shaped remarkably like a snake. It is the Snake Nebula (Barnard 72).
Below is an enlarged part of the same picture.
The arrow points to the very obscure
planetary nebula NGC 6369, whose brightness is given as magnitude 16.66
in Simbad; that is for blue light (B), and the V magnitude, not given,
is probably more like 13 or 14.
This little-known nebula puzzled me when I was taking the pictures.
It was right in the center of the images when I played them back, in the field,
to check focus and tracking. And, magnified, it doesn't look like a star!
I wondered what was going on that might distort one star and not
all the others.
This picture is the victim of considerably more contrast-stretching than the others.
The stretching may have brought out a trace of fixed-pattern
noise similar to the "Canon tartan." But only a trace. In general, the D5300
is free of stripes and streaks, and its overall noise level is low.
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