The mirror paradox, and the lightness of air

The “mirror paradox” (why does a mirror reverse left and right but not up and down?) has been around for quite a while. I think I first encountered it reading a Straight Dope book back in the 1970’s. My advisor asked several of us the question when I was in graduate school in the ‘80’s. If you Google “mirror paradox” you will get a fair number of hits (like thisthis and this) that explain the paradox. Most of the explanations are long and involved, far longer and more involved than they need to be.

I should note that I enclose mirror paradox in quotes because it’s not really a paradox. It’s another case in which the problem is stated in misleading terms.

First, here’s the answer: A mirror does not reverse left and right, or up and down; it reverses in and out. To prove that to yourself, take and arrow or anything else with a pointed end, and stand in front of a mirror. Point the arrow to your left. The mirror image of the arrow also points to your left. Point it up, and the reflection also points up. Point the arrow in towards the mirror and the reflected arrow points out, towards you.

I sent this explanation in to the Straight Dope people, and they responded that I was right (or course) but that the explanation wasn’t satisfying. I think they wanted more philosophy.

Looking at left and right hands is confusing, because you tend to assign leftness or rightness based on the assumed perspective of an individual. In the case of the mirror paradox, you assign leftness or rightness to your reflection based on what an actual person would perceive if the mirror image were an actual person. But just ignore the imagined person in the mirror that seems to be raising the wrong hand. It’s not really a person, it’s just a reflection. Use an arrow to avoid confusion.

And now the last of my trick questions. This is not really a trick question, but it is kind of a nerdy question. Everyone knows that air is light and water is heavy. In fact, water is more than 800 times heavier than air. Most people have heard a weather forecaster talk about relative humidity, and understand that “humid” air contains water vapor, or water molecules, mixed in with the air. The question is this: is humid air heavier, the same weight, or lighter than the same volume of dry air?

The answer, and another question

Here’s the answer to the question I asked in the last post: There is no place on Earth where the sun will not shine on the north side of a house.

It’s possible to answer the question with a little fairly common knowledge and some observation. The knowledge you need is that close to the poles in the summer, the sun does not set but instead goes all the way around the horizon, South, East, North and

West. The observation you need is to notice that in the northern hemisphere summer, the sun rises north of East and sets north of West. That means, of course, that the sun shines on the north side of a house in the morning and in the evening. Given that, it seems reasonable to me that you might assume that since the sun shines for part of the day on the north face of a house in the midlatitudes, where most of us live, and for part of the day at the North Pole, there probably isn’t anywhere in between those where the sun doesn’t shine on the north face of a house at some time in the day. And if you assumed that, you would be right.

You can demonstrate it mathematically, but there really isn’t any reason to do it.

Remember, I said it was a trick question.

Most of the information I gave was true but misleading. I mentioned that the sun stays below the horizon all day long for some winter days north of the Arctic Circle. And I mentioned that the noon-day sun is north of the zenith when you’re in the northern tropics. I didn’t mention that the sun never sets on some summer days north of the Arctic Circle, and t didn’t say that the sun has to shine on the north face at noon, only that it must never shine on the north face of a house.

Here’s another trick question.

If you look at your image in a mirror and extend your right hand towards the mirror, the image in the mirror seems to extend its left hand towards you. But if you extend your hand up, the image does the same. So, why does a mirror reverse left and right, but not up and down?

House construction, part 1

I’m going to start posting our progress on the new house we intend to build. This will help us keep track of when and what we’re doing.

So far, I have walked the back property line, which is about 700 feet. All of the corners are marked, but the back line is thickly wooded, so it’s not possible to get a good sight line from one marker to the other. From the approximate center of the rear line, I measured to the approximate center of the property, where we want to locate the house. I also cut branches and a few small trees to make a walkable path up to the center of the lot.

This is the property map from the Floyd County GIS site. Our new property is in blue. It totals about five acres. The map is oriented so north is up.

new lot map This is the area with satellite imagery instead of line maps. The arrow is pointing to our current house.

new lot sat image

The two southerly lots slope generally along the property lines from the back line towards Lavender Trail, the curving road in this image. The upper lot slopes down towards Lavender Trail and towards Fouche Gap Road, the road at the upper right of the image. On a sloping lot, the short axis of a house should generally be aligned with the slope. On our lot, the slope is about 40 degrees east of south. That means if we align the house with the slope, we won’t have a south-facing wall.

I have mentioned before my efforts to have south-facing glass in our current house to get the maximum solar gain in the winter. With sliding glass doors in the living room and two bedrooms, we get nice and toasty on a sunny winter day, even if the temperature is below freezing outside. We both want that in our new house, and that presents a problem.

We might get something close to what we want by making sure we have windows on the southeast-facing side and the southwest-facing side. Or we might orient the house somewhere between due south and 40 degrees east of south. But orienting the house more towards south means pushing the southeast corner further downslope. That’s what I did with our current house, and I don’t want to end up with the southeast corner of the house as far above grade as the southeast corner of our current house; that would defeat at least one of our purposes in building a new house.

Back when I was planning our current house, more than 15 years ago, you could buy books of house plans at the grocery store. I had 15 to 20 of them. These days, house plans are mostly online. Leah and I spent a while Saturday looking at some. None were exactly what we wanted, and only a few (so far) were even close. We are almost certainly going to have to modify a plan, or have a local drafter draw up plans to our specifications, as I did with our current house.

The next step for us is to map the slope. That will tell us how critical it is to keep the house oriented along the slope of the land. We won’t do anything more, including clearing for the drive and the house site, until the buyers of my mother’s house can actually get to closing.

Here is one more restriction on house location.

twisted tree

Leah and I both had the same reaction when we saw this: we have to keep this tree. Leah thinks the picture doesn’t quite capture the spirit of this tree, with two twisted main trunks and one wild trunk heading off towards who-knows-where. I haven’t decided whether it’s spooky, but I haven’t been there at night yet.

Here’s a special, bonus, trick question.

As everyone probably knows, the Earth’s axis is tilted by 23.4 degrees from “up”. That’s why we have seasons. The tropics are south of 23.4 degrees (for us in the northern hemisphere). If you go south of that, the sun will go north of straight up (the zenith) at noon in the summer. If you live north of that, the sun never gets north of the zenith at noon. If you live north of 66.6 degrees (the arctic circle), you will have some days in the winter where the sun never gets above the horizon.

So here’s the trick question: how far north do you have to go so that the sun never shines on the north side of a house oriented exactly north and south, and east and west? (Assuming the house is on flat land with nothing to provide shade anywhere near it)

Catching up

A few things have happened in the last week, so this is a catch-up post.

First, we had to call an ambulance last Friday, October 17, because Leah was having severe abdominal pain and vomiting. This is the second time we’ve had to do that. The first time was in 2011. That resulted in surgery to fix an intestinal blockage. The blockage was the caused by adhesions and scarring from the colon cancer surgery she had back in 1999.

Leah has had relatively minor episodes several times this year. An x-ray in July had shown what was characterized as a chronic, partial blockage. A colonoscopy in early September (Leah’s second this year) did not show anything in the colon, so we (and presumably the doctors) were left not really knowing what was going on.

This time there was no question that something bad was happening. Fortunately, Leah began feeling better fairly quickly and the blockage, if that is, indeed what it was, resolved with no surgery. She had one CT scan and an x-ray while she was in the ER, and at least two x-rays after she was admitted. The first scans they took during this stay seemed consistent with the July x-ray, but a later scan where they followed an x-ray opaque liquid through her small intestine showed quick passage, indicating no blockage in the small intestine. At one time her surgeon thought it might be gastroenteritis, but that did not seem to be the case.

In any event, Leah came home on Tuesday and has been on a liquid/soft diet since. They told her at the hospital that it might take two weeks to get back to normal.

That means two weeks without huevos rancheros.

Once Leah made it home, I started tramping over our new property to find the middle of the lot, which is where we plan to build. The most work I did was clearing a wide enough path to drive our side-by-side 4-wheeler (a Kawasaki Mule) up to the site with a chainsaw and other tools. There are lots and lots of trees, ranging from small enough to cut with large lopping shears to large enough to require a lot of planning before cutting with a chainsaw. Clearing for construction will take a bulldozer, and the operator said he wants the trees uncut so he can uproot them with his dozer. That’s fine with me.

And, finally, on Thursday I performed an experiment with a free-range dog. Leah has been telling me to take Zeke with me and let him roam freely while I work. She thinks it will let him get all his wandering urges out of his system. So I put him up in the front of the Mule and we rode up to the lot.

Zeke wandered around while I worked, and gradually left orbit. I didn’t see him again for about two hours, when he plodded up my newly-made path to greet me. One a scale of one to 10 (with one being perfectly clean and 10 being completely covered with mud and cow manure) he was about a three. Not too bad, but he needed a bath.

He was tired. Here he is resting after Leah and I went back up so I could show her what I had been doing. The tree with the yellow ribbon around it is the approximate center of the lot.


Later in the evening we began hearing some noises from Zeke’s direction. He was lying on his bed at the end of the sofa. And then a revolting odor wafted up in my direction. I wasn’t sure which end of the dog it came from, but eventually we figured out that he was burping. That continued through the evening. I had to keep a box of matches nearby. He woke Leah up at about 5:30, and Leah woke me from a dream (I didn’t mind; I was dreaming about writing reports at work.) I had to take Zeke outside to relieve himself. He has been having intestinal disturbances of his own all day today (Friday), and his burps can still cause paint to peel. I’m hoping he can work this out of his system.

The good news is that he came back to me. That’s encouraging. But I don’t think the wanderlust is over, and when he wanders, it seems he’s living up to the omnivore name. I’ll try this experiment again. Maybe Leah’s prediction will be right.