Objective truth

If you think there is no objective reality, that nobody can be objectively right, then you also think that you yourself can't possibly be objectively wrong. What sounds like a humble position is actually an arrogant one.

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Short notes

Melody is back home and she and I are both recovering. (I managed to get very tired, and possibly pick up a stomach virus or something, while hanging around the hospital.) To our delight, Melody can already walk about as well as before the operation — which is not very well, but it will get better!

As for the absence of people in waiting rooms, I can identify a few factors. Visiting hours are now unrestricted. Patient rooms are all private and have room for visitors. And hospital stays are much shorter than forty years ago. Instead of letting a disease or recovery process run its course in the hospital, doctors have realized it's safer to get the patient away from the dangerous environment (noise, interruptions, and risk of infection) as soon as they no longer need services that only the hospital can provide.

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Mars

Late last night I got another picture of Mars with the same equipment and technique as several recent pictures. It's not as sharp as I'd like, but it shows a prominent dark feature, Syrtis Major.

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Short notes

Melody is well on the road to recovery from her hip operation. I've been spending a lot of time with her, and I've noticed something about the hospital: It's not crowded with visitors the way hospitals were in the 1970s... at least, the lobby isn't. There's hardly anyone to be seen. Yet I know the hospital is quite full. What is the explanation, I wonder? More generous policies allowing visitors to be in the patients' rooms?

I did meet one interesting person in the waiting room before the surgery on Friday: a Georgia Power linesman who works in my neighborhood and was able to tell me the route by which electricity gets to my house. I won't put that information here, of course, because information about the power grid is the sort of thing terrorists would like to get hold of, but I've had an interesting time looking at the power lines as I drive around and, for the first time, understanding them.

My UGA colleage David Stooksbury, climatologist, suggests that people should put on a helmet (football, soccer, bicycle, etc.) when there's a tornado warning. It's not enough just to hide in a small room. I don't have a helmet of any kind. It's enough to tempt me to buy a hard hat, or maybe a surplus army helmet, or something. (Not a Prussian army helmet — it would act as a lightning rod!)

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Hip success

Although there were some unusual risks in this case, Melody's hip replacement went smoothly, and so far there is no sign of complications.

We thank over 100 people who have sent their best wishes (mainly via Facebook) and hope everyone understand that we are not in a position to reply personally to everything. Melody is not taking phone calls or using the Internet yet, but she is on track to a good recovery.

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Hip day

Today (April 25), Melody will be having her left hip replaced at Athens Regional Medical Center. We have waited more than a year for this because other medical complications had to be resolved first. Your prayers are requested. I will post updates here and on Facebook. The update may not appear here for a couple of days.

Assuming all goes well, she'll have the other hip replaced a few months later.

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Mars, April 23

Here's my best Mars picture yet, taken on the evening of April 23 (April 24 Universal Time) with the same 8-inch telescope and other equipment as other recent planetary pictures. Mare Sirenum is the long hook-shaped feature to the lower right of center.

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Affirmative action right and wrong

In the wake of the Supreme Court's ruling about affirmative action, I want to point out a few things about this difficult issue. In my experience, most people understand only one side of the controversy and are quite unaware of the other — except, of course, those who misunderstand both sides. So hang on to your hat...

The justification behind affirmative action is that even with no intent to discriminate, if people follow traditional practices and remain connected together in traditional ways, they will perpetuate past discrimination. Look at the University of Georgia, which was "whites only" until the 1960s. If we keep serving the same segment of society, especially the families of alumni, we will continue to serve whites more than blacks, even without any ongoing intent to discriminate. Crucially, switching to a color-blind policy is not enough if people remain connected together in the same ways. The purpose of affirmative action is to counteract these unintentional forces that perpetuate discrimination.

That said, it's obvious that two wrongs do not make a right. If person A mistreats person B and favors person C, then fifty years later, you do not fix this by having person D mistreat person E in favor of person F. That is just another injustice, even if person F belongs to a historically disadvantaged minority.

That is why I think affirmative action is justified only at the level of recruiting, advertising, and social connections, not at the level of actual qualifications, school admissions, or hiring. Groups don't have rights; people do. I would even say that until you grant the same rights to every individual, you have not overcome racism; if you think of everything as needing to be allotted to racial groups, you're still judging people by their race, not as individuals.

There has been a lot of misunderstanding here. Some people grasp the need for affirmative action, but not too clearly, and push for quota systems, as if justice were only for groups, not for individuals. Quotas, in my opinion, are always unjust to individuals. (I get this from the same deontological ethics that tells me racism is wrong in the first place.)

Others grasp clearly the fact that two wrongs don't make a right, and running a little too far with this idea, they reject any attempt to overcome unintentional discrimination by reaching out to disadvantaged groups.

Maybe the term "affirmative action" has become dangerously ambiguous and we should talk about it in some other way — several different ways depending on exactly what we mean. Quotas, no; overcoming social barriers, yes.

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Mars, evening of April 20

Here's Mars around 11 p.m. on the evening of the 20th (Easter Sunday). Again, this is a stack of thousands of video frames through the 8-inch telescope. Compared to the pictures from a few days earlier, Mars has rotated; the north pole is still at the upper left, but Mare Acidalium is now to the lower left of center. This picture was sharp enough that I enlarged it to 1.5 times the usual size.

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Jupiter and Mars from April 12

I also got some good planetary images on the evening of April 12. Here's Jupiter with its satellite Europa, one of the last good views of Jupiter I'll get this season because there happens to be a big tree just west of my telescope, and Jupiter will soon be hidden behind it:

Here's Mars, later in the evening. Because the rotational period of Mars is close to 24 hours, the view is much the same as in the previous entry, taken a day earlier, but the image may be a bit sharper. The bright spot just below center is Olympus Mons (Nix Olympica).

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Three planets and the Moon from April 11

On the evening of April 11, I had a very productive astrophoto session with the 8-inch telescope. Each of these pictures was taken with a Meade 8-inch Schmidt-Cassegrain telescope, a 3× Barlow lens, and a DFK camera. The moon images here are "close-ups" at three times the magnification used for the moonscapes I posted earlier. Each picture is a composite of thousands of video frames, aligned with Autostakkert 2 or RegiStax 6 and sharpened with RegiStax 6.

Jupiter:

Mars (with the polar cap at the upper left and Mare Acidalium at top):

Saturn (very low in the sky, viewed through turbulent air):

The gleaming lunar crater Aristarchus, with unusual valleys adjacent to it:

And finally, the large crater J. Herschel, with its pock-marked floor:

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EXIFLOG for logging your photographs

I've just rolled out a new version of EXIFLOG, a program I wrote to help me log my astrophotos a few years ago. It reads all the picture and video files that you select, and it produces a single text file with the exposure data for all of them. With Canon DSLRs, it can also read the sensor temperature (at the time the picture was taken) and tell you whether long-exposure noise reduction was on. With other brands of digital cameras (including video), you get some basic information, but not quite as much.

EXIFLOG is free. Click on the picture for more information.

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Cranesbill (Carolina geranium)

This is a close-up of the tiny flowers of a cranesbill plant. Cranesbill grows like a weed in Georgia and is everywhere in April but scarce later in the year. The picture was taken with my Canon 60Da and Sigma 105/2.8 macro lens.

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Feast Day of the Resurrection of Our Lord

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My new telescope cart

Here is my new telescope cart, in finished form. I use it to avoid having to carry the 8-inch telescope all the way from the cabinet in the house to the pier in the back yard.

Here it is, with the dust cover on. It's a 16×30-inch service cart from Harbor Freight with some homemade additions.

Here you see it with the dust cover removed. In the top tray, I've glued some heavy foam blocks to keep the telescope from getting scuffed or rolling around. The foam looks rugged because it's salvaged from another project. This is heavy-duty form, of the kind used in equipment cases, and I seem to recall it was bought from McMaster-Carr. Multiple layers of foam cut from a camping pad would also work. You could also cut up one of the semicircular foam "noodles" that people lie on to exercise their backs.

Finally, here it is, in use. Note that the eyepiece box gets to ride along, too. One of the great conveniences of having the cart is that I can carry everything in one trip; also, the pier doesn't have to be uncovered when I get to it, because the telescope can wait on the cart.

These aren't the best pictures I could have taken; I took them in rather dim light because I wanted to go ahead and get this entry posted. I think they're good enough to serve the purpose.

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Moonscapes and Mars

The air was even more turbulent on the evening of the 10th than the 9th, but by taking pictures in infrared light (with a DMK camera and filter), I managed to get something. The moonscapes were taken with the 8-inch telescope without additional optics; for Mars I added a 3× converter. Each of these is a stack of the best 50% of about 3500 video frames.

Here's the great crater Copernicus, with more light on it than the previous day:

Here's Sinus Iridum, also known as the Bay of Rainbows:

And here is a stretch from the dark-floored crater Plato (at lower right) to the craterlet-filled large shallow crater J. Herschel (left).

Finally, here's Mars. The video looked like complete mush, but after processing, the picture shows appreciable detail, including Mare Acidalium (Acidalia Planitia) at the top.

All of these pictures have north at the top, without reflections or inversions.

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News update

I said earlier that these are busy times. Not only do I have plenty of work to do, but we are literally counting the hours until Melody's hip replacement surgery, scheduled (finally!) for April 25 (about 14 days and 14 hours from the time I write this). She has been having a rough time with osteoarthritis. The surgery was delayed for many months while minor medical complications were tracked down and dealt with. Now she has the go-ahead, and we would appreciate your prayers. I'm working at home a lot and giving her as much help as I can.

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What the Heartbleed HTTPS bug means to you
(Time to change passwords!)

You've probably heard about the Internet's latest near-disaster, which (for reasons unknown to me) is named Heartbleed.

Briefly: As you know, HTTPS connections (secure web connections, as distinct from ordinary HTTP) are encrypted. You use them to communicate securely with your bank, shopping sites, and so forth.

The problem is that one widely used implementation of SSL (i.e., HTTPS) is vulnerable to hackers who can retrieve passwords and, occasionally, other information by manipulating a defect in the program.

This is a defect on the part of the web sites themselves, not on your computer. You do not need to patch your computer. This is not a virus and will not infect it.

In general, banks and big commercial sites are not affected. Google and Facebook were affected, as were any number of smaller sites that use open-source software to save money. Click here for details.

What should you do? Change your passwords on important sites. But don't do it until the affected site has been fixed. If you change your password on a site that is still vulnerable, change it again when the vulnerability is repaired.

But keep things in perspective. If somebody impersonates me on a shopping site that stores my credit card, I might have a problem. If somebody gets hold of my password for the Ford Escape owners' discussion forum, well, I don't think I have a lot to worry about — such a person couldn't spend my money or do anything else really destructive, other than maybe post some embarrassing messages that would instantly be recognized as fake — so I don't think I'll worry too much about that one.

How do you make up a good password? Most importantly, remember that people will try to guess it, and some people will use computers to try all the words in the dictionary. Your password must not be a single word in any language (spelled forward or backward) and should not contain a year between 1950 and the present. (A hacker's computer can be programmed to try xxx1950, xxx1951, etc., where xxx is every word in the dictionary.)

The best way to make a password secure is to make it long — have it contain two or more words and a number. Many sites require that you also add a punctuation mark. (Hint: If you do, don't put it between words; put it in a word, as in thisex.ample.)

One thing I like to do is include a common word, misspelled so that if anyone glances over my shoulder and sees it, they almost certainly won't notice the error and will remember the correct spelling instead.

Don't be paranoid — don't panic — but do be careful.

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Jupiter, the Moon, and Mars

As you know, Mars is presently closer to the earth than it has been in several years. Also, I've just gotten my 8-inch telescope back into action. Here are the fruits of my astrophotography session on the evening of the 9th.

First, here's Jupiter, through rather unsteady air:

This is a stack of the best 50% of a few thousand video images, recorded with FireCapture (as raw un-de-Bayered images), de-Bayered with FireCapture's utility, stacked with AutoStakkert 2, and enhanced with RegiStax 6. The advantages of recording un-de-Bayered images is that the files are much smaller and the recording goes faster and more smoothly since less computation is done on the fly. I used the 8-inch telescope with a 3× Barlow lens and a DFK color camera.

Then, three moonscapes, around the craters (respectively) Copernicus, Plato, and Clavius. The good thing about the Moon is that when the air is unsteady, I can work at lower magnification and still get a sharp picture.

These are black-and-white infrared images taken with a DMK camera; same telescope, but without the 3× magnifier.

Finally, here is a poor picture of Mars, which was low in the sky at the time. The air was even less steady than earlier, and Mars was not high enough to give a good view. But you can see that it is Mars.

Equipment and technique the same as with Jupiter.

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Busy time

I haven't gone away — I'm just doing a lot of work, including deep immersion in the R programming language. Which leads to the following pun, presented to me by Sharon:

"What is pirates' favorite programming language?"

"Arrr!" ("R!")

"No, they are sailors, and their first love is the C."

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Jupiter again

Putting the 8-inch telescope back into service for a second night, I took this picture of Jupiter on April 1. The air was not especially steady. Best 50% of 3600 video frames, Meade LX200 8-inch, Meade 3x Barlow lens, and DFK camera.

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The anti-mathematical mindset

[Revised.]

Today, as I often do on April 1, I'm going to write about something in the broad category of foolishness. My jumping-off point is a rant that you may have seen being passed around social media, in which a parent objects to his elementary-school child's arithmetic homework involving a number line. This is being held up as an example of baffling nonsense, although my own opinion is that if the father can't understand it, he shouldn't be trusted with a tape measure.

The assignment was to find the distance between two numbers on a number line and explain why someone else's answer came out 10 too high. He was supposed to subtract 316 by moving left 100 steps three times, then 10 steps one time, and then 1 step six times. His mistake was that his jump of 10 actually spanned 20.

The father wanted to throw out the number line and do pencil-and-paper subtraction, thereby missing the point.

Let's back up and look at the broader context.

There are several levels on which a person might understand numbers and arithmetic. On Level 0, the lowest level, numbers are just meaningless tokens — all numbers are like telephone numbers — you can write them down and reproduce them, but they don't mean much, if anything.

People on Level 0 can learn a game called "arithmetic" played with these meaningless tokens. I give you 51 and 23 and tell you to do the addition game; you give me back 74. If I had asked for the subtraction game, you would have given me back 28. And so on.

Some people on Level 0 are surprisingly good at this game, and they think they're good at mathematics. In fact, however, if you stay on Level 0, arithmetic is almost useless to you. You don't know when to do arithmetic or what to do with the results. Or, at most, your knowledge of when to do it consists of a large collection of unrelated recipes to be followed step by step, with no overarching insight, and no easy way to recognize when you're following the wrong recipe.

By the end of first grade, most of us have reached Level 1, where numbers are the result of counting. At this level, you have a definite feel for the way some numbers are bigger than others: 100 is a lot more than 20, and 20 is a lot more than 2, but 21 is only slightly more than 20. On Level 1 you can start to understand fractions, at least dimly, by thinking of a large pile of apples being divided into smaller piles. Still, large numbers are hard to distinguish, and it's hard to see any relationships between numbers other than simple addition.

Level 2 is the next step up. On Level 2, numbers are like distances. This is what number lines help you visualize. Addition means moving to the right; subtraction means moving to the left; multiplication means making the same move repeatedly; and so on. You can move left past 0 to get to negative numbers. You can move part of the way between numbered points, and that's where fractions are useful.

Level 2 is also where geometry becomes possible. You can put two number lines at right angles and draw a graph. You can even go into three-dimensional space (or more) with several number lines pointing in different directions.

Crucially, the number line doesn't enable you to calculate anything you couldn't have calculated without it. Its purpose is to help you understand what the numbers and calculations mean.

For example, a number line is where you can easily see that 195 is much closer to 200 than to 100, and that (30, 40, 50) are equally spaced but (30, 42, 48) are not. This kind of understanding doesn't come from pencil-and-paper arithmetic, even though you can use pencil-and-paper arithmetic to verify it.

In fact, I've just realized that many times, when people think I'm doing pencil-and-paper arithmetic in my head, I'm actually visualizing a number line. It's a handy tool.

Level 3 is what I call the level of algebra, where you can think about the operations performed on numbers separately from the numbers themselves. A very simple example of algebra is the insight that if you start with a number, add another number, and then subtract the number you added, you end up with what you started with. This is true regardless of what the numbers are.

I'm not sure whether it makes sense to count levels higher than 3. There's certainly a lot more to mathematics. But let me tie up a few loose ends.

First: knowing mathematics is not the same as knowing notations. A mathematical problem is not impossibly hard just because it contains symbols that you've never seen. People who are stuck on Level 0 have trouble distinguishing ideas from notations. The father who was baffled by the number line may simply never have seen one. That doesn't mean the children couldn't understand it.

Second: calculators haven't eliminated the need for mathematical knowledge — not at all! If anything, calculators distinguish more sharply between people who know what numbers mean and people who don't. Anyone can push buttons, but who knows which buttons to push?

Third: "Word problems" are the only kind that real life gives you. If you don't like "word problems," you don't like mathematics. Real-life situations will not tell you to play the addition game on 72 + 39. In real life, the answer to a mathematical problem is often not even a number — it is a decision, such as "It costs less in the long run to do this than to do that."

The skills needed for "word problems" are, in my opinion, more like reading, writing, and logic than like arithmetic. It is like moving from a spelling test to a mystery story. You have to know what information is in the numbers, and how it's arranged logically, and what you're trying to find out. The classic way to bungle a word problem is to throw all the numbers together and start doing arithmetic without asking a clear question and reasoning about how to find the answer.

One last note: It pains me that people brag about being bad at mathematics. It's one thing to say humbly that you haven't studied much of it, but why boast that you can't do it? Nobody boasts about having trouble reading or driving a car.

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