Intel's Ronler Acres Plant

Silicon Forest

Sunday, May 29, 2011

The Tourist



Rented The Tourist on DVD from Redbox this evening. We have Angelina Jolie playing a beautiful secret agent (where have we seen that before?) and Johnny Depp playing the hapless tourist from Wisconsin. When I first heard about this movie I thought it was probably based on the book which I read last year. I mean we've got many of same elements, spies, beautiful women, master criminals, and Venice. Well, it might be based on the book, but you wouldn't be able to tell that from watching it. There was nothing else the same. It was enjoyable, not a real thriller, more light-hearted, Plenty of scenes with Angelina being ravenous, er, ravishing. And then there was the screwball twist at the end that just made me shake my head. And why can't Johnny comb his hair?

Update February 2017 replaced missing picture.

Company's Comin'

My wife looks out the window today and notices our old Christmas tree lying at the edge of the dismal swamp. When I dumped it there back in January it was the greenest thing there. Now the swamp is full-tilt green and the ol' Christmas tree, well, it's kinda orange, like a sore thumb. We might be getting company this summer, and sweetie pie decides something needs to be done about this eye-sore. So I take my hand clippers and start cutting it down to size and, lo and behold! What do I find?


Bird's nest with two eggs. Apparently abandoned, no mama bird in evidence, near or far. Surprised the 'coons didn't get them, they were only a foot or two from the ground. The nest was in the middle of the tree, so maybe that made it too much work. I surprised a 'coon in front of the house today. He high tailed it around the corner, quick as his fat little butt could waddle.

Update: I just corrected a bunch of typos. I can't believe how many errors I made in the original.
Seven months later: I just found another typo. Will I ever learn to type?
Update February 2017 replaced missing picture.

The Black Bottle

This bottle was on the table at lunch the other day. No markings, no label, no indication of what was inside. It looked like ink. Shoot, it even looked poisonous. As we were at a Chinese restaurant, it was just soy sauce, but I could not bring myself to pick it up until I saw someone else use it. Weird.

Update February 2017 replaced missing picture.


Saturday, May 28, 2011

The Hangover Part II

My wife and I went to see The Hangover Part II at the local Regal-plex this afternoon. We saw the original when it came out and it was funny. This one was not as funny. Mostly it was people being stupid and rude, sometimes amazingly rude and getting polite applause anyway. However, when we got to the end, they find a camera with some pictures from their misadventures, and those were funny. Only question I have is whether they would have been as funny without having watched the whole movie before hand.


Tickets for the 5:30 show were $10.50. I guess that makes it an evening show, not afternoon. It's still daylight outside right now, so I'm a little confused. Because my wife is a frequent flyer, she qualified for a free small popcorn. Well, you need a drink to wash down the popcorn, so I popped for a small diet coke. The small coke is 32 ounces. What's a big one? A gallon?

Update February 2017 replaced missing picture.

Commercials

I just ordered a ROKU internet box for my TV. $80 from Amazon. I spent a couple of hours reading about different devices this morning and finally decided cheaper is better. Not cheapest, next to cheapest. We shall see.

We have a DVR (Digital Video Recorder) that we rent from Frontier (formerly Verizon) for the ridiculous price of $30 a month, but we use the heck out of it. We can watch whatever dramas we want when we are ready, not just when they come on, and we don't have to sit through the ads, though we still have to futz with the fast forward and reverse buttons to skip over the ads, and that can be tedious.

I find most TV commercials are extremely boring and / or annoying, but there are also some that are very clever that I don't mind seeing. Once. Once is usually enough. More than that and they quickly become annoying. So I was thinking, how about a commercial channel? All commercials all the time! If you ever wanted to see what was going on in commercial land you could switch to that channel and in an hour you could probably watch all the new commercials made in the last week. Get your fix of mass marketing all at once.

Then I got to wondering how much a TV show is worth. It takes a bunch of money to produce a TV drama, just guessing I would say maybe a million dollars an episode. I mean just look at all the people listed in the credits, all the locations, all the props. And you have to produce the episode in a week. I think a million bucks is a fair estimate. But the show gets broadcast to millions of viewers. There are about 15 minutes of commercials in each one hour of broadcast time, so if you are charging a $100,000 (one hundred thousand dollars) per minute, you could bring in 1.5 million dollars, which would make the whole endeavor worth while. If a million people watch the show, then the advertisers are paying a buck-fifty for every viewer, and since only about half of the ads are watched, and only ten percent of them are actually in the advertisers sights, the advertisers are paying $30 for each viewer, or $1 per viewer per 30 second commercial.

Of course, any one of these numbers could be off by a factor of ten or even a hundred, which would make all my carefully wrought calculations worthless, but I think I am hitting pretty close to the mark. A show needs to pay for itself up front, broadcasters aren't going to waste valuable air time on something that isn't paying for itself. After the initial prime time broadcast things can get a little easier. The show has already paid for itself, so any money that can be made now is gravy. Remember the printing press model of capitalism.

All of which is a long way of saying that one dollar per hour of commercial free video entertainment is a fair price.

Friday, May 27, 2011

Video Sites

I signed up with Netflix back in December when I bought a Logitech Review. It runs $10 a month and provides shows over the internet as well as one DVD at a time through the mail. Sometime later I heard that Amazon Prime was also offering videos over the internet. We had already signed up for the Prime service, so that was like a free bonus. Maybe we don't need Netflix anymore.

The we discovered The Closer, and we have been watching several episodes a week. It has been on the air for several years, so there are a bunch of episodes out there. For a while we were getting enough from Verizon's TV service to keep us entertained, but then basketball season for the Trailblazers ended, and we needed more! It turns out that neither Netflix nor Amazon offer old episodes of The Closer over the net. We could get old episodes on DVD from Netflix, but that would require planning ahead, so I went poking around on the net to see what I could find.

I found something called Sidereel, that apparently keeps track of shows and provides links to where you can find the shows. Old episodes of The Closer are available from iTunes and from Amazon, for a price. Individually they aren't much, a couple of bucks maybe, but if you are consuming 20 or 30 videos a month, that can add up. So let's see what other links there are. Oh, look, there's a whole bunch of free links. Most of them connect to to something called Megavideo. I've tried some of the other free links as well, and they also seem to lead to Megavideo. This is kind of weird. I have heard of iTunes and Amazon, but I have never heard of Megavideo outside of my computer screen. Whatever. In any case, we can watch old episodes of The Closer off of the Megavideo web site. Well, we can watch one episode at a time. Try to watch two in a row and you run into a time limit and the video stops.



So now I'm thinking of signing up with Megavideo. The price is only ten dollars, oh wait, that isn't a dollar sign, what is it? Is that a Euro sign? It is and ten Euros translates to around fifteen dollars. Where is this company based? Hmm, doesn't seem to be based anywhere. It only exists in cyber-space. So why would they choose the Euro over the dollar? Probably because they are infidels. In any case, with the proliferation of server farms, you would not actually need to have your own hardware, no matter how much storage you need. You would need some office space for programmers, accountants and marketeers, and that's about it. You could be located anywhere.

So now all I need is a new box to connect my TV to the internet, and I should be able to get shut of Frontier's overpriced TV package. I could probably cancel Netflix as well, but my kids seem to be using it, so maybe I'll let that one continue.

There is the problem of legality. Since Megavideo is nominally a video sharing site, the holders of The Closer's copyright could ask that the videos be taken down, so I would have signed up for nothing. There is another weird thing, and that is for every episode of The Closer, Sidereel lists a dozen or so different links to different videos on Megavideo. How does Sidereel know where all those videos are? Megavideo doesn't seem to keep track. They have a search function, but it is very rudimentary. Do we have a bunch of pirates out there uploading TV shows and movies to Megavideo, and then posting the links on Sidereel? Seems like a lot of work for not much payback. Could Sidereel have a search engine can automatically determine the name of a video posted on the net? If they had such a capability, I would think the copyright holders (or their agents) would likewise be running such a search. Or are the episodes we are watching so old that the copyright holders don't care? Something is not quite right here, and I don't know what it is.

P.S. While I was poking around I came across a web site that had been seized by Homeland Security. How weird is that?

Update April 2016 replace missing picture. Added link to Amazon.

Thursday, May 26, 2011

Microfinance, Part II

When I was looking at microfinance before I noticed that the organization that was promoting it in the USA was soliciting donations, and I thought that was just a little odd. They had gotten a loan from some unspecified source to use for making their loans, but they were also taking donations. In that case, they must not be making a profit, at least not yet. Either their overhead or their default rate is too high. I suspect it's their overhead. All the headache that goes into vetting the applicants and then you're only collecting some miserable percentage on the small amount they borrow. It's not a booming business model.

They I realized that there is a more traditional source of money for small loans, and that is loan sharks. They charge userous rates, but evidently it's enough to make it worthwhile because they still get mentioned seven days a week on cop shows on TV. I have heard all kinds of rates quoted for loans from loan sharks. The latest rate of seven points a week comes from a new episode of Law & Order: Criminal Intent I saw last week. Seven percent a week can be done if you are turning over a high volume of merchandise. It adds up to 350% a year which is considerable, but it is paid on a weekly basis, so compounding doesn't enter into it.

An example I heard about was an immigrant who was selling kids toys at a flea market. He borrowed a thousand dollars, spent it on tricycles and kids bikes, and sold them all on Saturday at the local flea market and doubled his money. In this case $70 for the vig sounds like a good deal. He makes enough money in one day to survive until the next weekend.

There is also the illegal / recreational drug business. It can be much, much riskier because you really have to keep to the straight and narrow to avoid falling into any one of the chasms that will surround you. Even with the best people, there is still substantial risk, so there needs to be a big payoff to make it worthwhile. So you probably won't be able to get seven points if you are using the money to buy drugs.

What every good capitalist wants is a machine that prints money. You make a capital investment (the printing press), you hire a guy to run it, and you set up suppliers for your paper and ink and you go to town. The machine prints money and everything is wonderful. Of course, the government frowns on people usurping their role as the providers of all that paper and ink goodness, so a law-abiding capitalist looks for something that won't get him / her crosswise with the coppers.

Cranes working on the expansion of Intel's Ronler Acres Fab
The printing press model has made lots of money for lots of people. First it was the newspapers, now it's microchips. Printing microchips is a lot more complicated, sophisticated and precise than printing newspapers, but it's still the same model. You invest the money to buy the printing press, in this case it's several billion dollars to build a chip fabricating plant, you hire a double handful of people to run the press, and then you start cranking out chips. The chips from one sheet of paper (a silicon wafer) can bring tens of thousands of dollars. It doesn't take long for the money to start pouring in.

It can get galling when people are dealing with smaller sums of money, sums they can comprehend. I mean, who understands what a billion dollars can do? I have a hard time with it, but a thousand dollars I can understand. Say you have a guy who invests three thousand dollars, hires a someone else to do the work, whatever it is, and the business starts making ten thousand dollars a week. The employee was getting $200 a week to start, and now, even though the business is making money hand over fist, he is still barely making enough to survive. That's when you run into problems. A smart capitalist would give the worker bee a raise, it wouldn't cost him a lot, at least not compared to what he is making. A greedy capitalist would not give his employee a raise and would not care whether he was generating any ill will. The trick is not to work for the greedy capitalist, and that can be a very difficult trick to pull off.

On the other hand, paying the employee any more than is absolutely necessary is contrary to good business sense. If the employee can be easily replaced, it doesn't make sense to pay them any more. And this is where we are. We have a surplus of  people who would like to have a job that pays decent money and we do not have enough capitalists setting up printing presses.

Update February 2017 replaced missing picture.

Wednesday, May 25, 2011

Men Who Lack Female Supervision


I thought this was just great. This is what my life would be like if I wasn't married. Actually, this is kind of what my life was like before I was married.

Big New Cave


After years of hearing about the "biggest cave in the world", I was surprised to hear that the last record holder has been upstaged by the Hang Son Doong cave in Vietnam. I guess I shouldn't be surprised. There aren't too many people who go in for caving. I for one have a bit of an aversion into going into dark places where I could easily become trapped and end up wasting away like the woman in the cave in "The English Patient". There is still a great deal of wilderness on our planet, and many caves are virtually undetectable from a casual inspection of the surface.

Via Mark.

Sunday, May 22, 2011

Firefox Version 4 Problems

I just reloaded the main hard disk in my computer. I got hit by a nasty virus a few weeks ago, and while I managed to contain it enough that the computer was usable, it was still making things inconvenient.

This time I set up four partitions on the main disk:
  1. is for the normal Windows installation
  2.  is a copy of partition 1
  3. is for my stuff
  4. is space left over 
  5. is a small partition that is reserved for something or other. It's not big enough to worry about.
The idea is that if I get hit by another virus and things go South again, I can simple copy partition 2 back over partition 1, and save myself a lot of grief, like having to install a bunch of applications.

Since this is my first time down this road, I had to install all my applications individually, and Firefox is one of them, and it is causing me some trouble. First off, they changed the right-click pop-up menu. Open Link in New Tab has changed places with Open Link in New Window. Opening a new tab has been my preference for years, so for most of the last couple of days I have been inadvertantly opening new windows. This is taking some getting used to.

They moved the Home button. Where is used to be on toolbar near the top left of the screen, it is now at the far right of the address bar. The forward and back buttons have also moved to the address bar, but that is not such a big deal to me. The benefit here is that the toolbar which was taking up a lot of space for only a few useful items is now gone.

The bookmark control that would bookmark all your open tabs and put them in one folder is gone. I only mention it because I tried to use it this morning. Since I hardly ever use it, this was kind of a freak occurence.

Today I wanted to open an old spreadsheet I had made using Open Office. I didn't install Open Office, it's too big, it takes too long to load, and I don't really need it. Google Docs works fine for what I do. Since I don't have a spreadsheet application on my computer  I uploaded it to Google Docs, and Google accepted the ODS format without a squawk.

Now I discover Cut & Paste doesn't work in the spreadsheet. The first time it works fine, but the second time you try it, it doesn't cut, and it pastes the previous item you cut. Well, that sucks. I tried it from the keyboard and using the spreadsheet menu commands, and neither one worked. I look it up on Google Help and they blame Firefox. Okay, lets complain to Firefox. 

The Firefox Help Menu has a Submit Feedback item that takes you to a neat page that reminds me of the three monkeys, but it works very well, at least the first time I used it to complain about the Cut & Paste problem. But I got nothing back from them, so I complained again.
I reported a problem, and all I got was some vague statement that it might be fixed someday, maybe. What I would like is an email with the current status of the problem now and another whenever you get around to fixing it. Interim reports are of no interest. And no, I don't want to root around in your bug tracking system.
This time it didn't work. After you use it once it is seems to have the same problem as Cut & Paste: it doesn't. Which is what got us here.

There is one other feature that I am not too sure about. When you open a web page, a little spinning green thingy shows up on the corresponding tab. After a bit it goes away. A while back I installed some anti-virus program that did the same thing to every link returned by a Google search. It was going out and pre-emptively scanning the page, looking for trouble. I got rid of it, it slowed things down too much, and it never found anything. That's basically why I don't run any anti-virus software: it's too much of a headache for the amount of good it does. On the other hand, I do get hit with junk once in a while, which is how we ended up here. We shall see how this goes.

P.S. I do run Windows Firewall, which seems to work fine.
P.P.S. I use Malwarebytes when I do run into a virus.
P.P.P.S. Blogger's new editor has some problems with cursor keys, which are really annoying, but so far not annoying enough to warrant a complete post all by itself.

Update February 2017 replaced missing image.

Saturday, May 21, 2011

Election Numbers

Professor Joseph Olson of Hamline University School of Law in St. Paul , Minnesota , points out some interesting facts concerning the last Presidential election:
  • Number of States won by: Obama:19 McCain: 29
  • Square miles of land won by: Obama:580,000 McCain: 2,427,000
  • Population of counties won by: Obama:127 million McCain: 143 million
  • Murder rate per 100,000 residents in counties won by: Obama: 13.2 McCain: 2.1
Extracted from a screed sent by Steve. You can put whatever spin you like on it. My take is it that Obama won in the urban areas, and McCain won in the rural areas.

The bad thing about a democracy is it only takes 51% of the people to drag the other 49% along with them, where ever they are going, be it heaven or that other place.

Thursday, May 19, 2011

DVD Magic

I was thinking about DVD's and it occured to me that tracking the playback groove could be a bit of a trick. The tracks on a CD are microscopic, on a DVD they are even more so. If you had perfect bearings and a perfect fit between the hub and the disk, I suppose you might be able to follow the track, but bearings aren't perfect, and you had your finger in the hole in the disk, you aren't going to have a perfect fit. So how do DVD players follow the track?

I was talking to Jack about this the other day, we came up with a couple of theories:
  1. Use a servo motor to move the playback head back and forth to follow the track as it wobbles around. This suffers from the same kind of mechanical problems that got us here. Unlikely.
  2. Use a MEM (Micro Electrical Machine) mirror to deflect the laser beam to follow the track. Possible.
  3. Use several sensors that would cover the expected range of wobble and use DSP (Digital Signal Processing) to extract the data you want. There is a problem with this approach, and that is that DSP can be very power hungry. I suppose a specialized chip could be made for this purpose that would not use that much power, but without knowing more, I am still concerned.
 So I looked around. And I didn't find anything. I found many copies of the same simplistic explanation of how optical disks work, but none about how they actual manage to follow the track. Email's to Samsung and LG failed to produce even a hint.

Since apparently no one knows how these things work, I am forced to conclude that the optical disk cabal is in league with the forces of darkness.

Max Payne


A thoroughly entertaining movie, even though it was basically a compilation of every cliche in the cop movie book. The black shapes flitting around the edges of the screen were particularly effective as drug induced paranoid hallucinations. I also liked Max's Cadillac. It just seemed to fit the mood. The picture is from a scene where Max uses a Taurus Judge to some effect. It was the only gun I could positively identify. This might account for the gun's rise in popularity, much to Tam's dismay.

Photo is from the Internet Movie Firearms Data Base. They sure used a lot of guns in this movie.

If you see something, just be quiet.

A guy was unloading some equipment for an after school class in martial arts at a Beaverton elementary school this afternoon. A parent saw him carrying a long bag that looked like it could contain a gun, so she dialed 911. Two minutes later an eight man SWAT team showed up with shields and M-16's. Hoo boy! Excitement! Situation resolved peacefully, nobody got shot. Parent could have just asked someone, but no, better be safe than sorry.

Sad state of affairs. Anybody could be carrying a gun and enough ammunition to wipe out an entire class of kindergartners. Women with big purses are especially suspect. There isn't enough security in the world to prevent a determined maniac from wreaking havoc. If we are going to have an open society, we are going to have to accept certain risks.

If you see something, speak to the person you suspect. It might get you shot, but at least everyone else will have some warning that something wicked is coming their way. Calling out the coppers every time you see a woman with a big purse only raises the odds that someone will get shot for no reason at all, other than you thought the sky was falling.

Wednesday, May 18, 2011

King of the Pyramids

Pyramid of the Sun
Tallest pyramid in Mexico
Teotihuacan, Mexico

This one is in Mexico. It's the first one I've seen that gives you some idea of the size of the thing. From daring daughter.

Update August 2016 added caption.

Tuesday, May 17, 2011

The Next Three Days


The old warhorse Russell Crowe and the very pretty Elisabeth Banks star in this escape from Pittsburgh thriller, at least I think it's a thriller. Maybe it's a drama, or a psychological thriller. I don't really know what the criteria are. I liked it. Russell plays a school teacher who wants to break his wife out of jail. He really isn't prepared for a life of violent crime and it shows. His wife is teetering right on the edge, so you don't know if she is going to keep it together or flake out and blow the whole deal. Also, we don't really know whether she is guilty or not. We do know her husband believes she is innocent, but he might be a schmuck. The first half of the movie is all set up, the second half is the escape. As in all well laid plans, things go awry, but time and again they outwit their pursuers. Do they eventually get away? I'll never tell, but I wonder why they picked Caracas as a destination? Is it because we don't have an extradition treaty with Venezuela? Or might Hugo's is willingness to thumb his nose at the US have anything to do with it? I mean, we put an innocent woman in jail. Or did we?

Looking around for a picture to include, I didn't find much. Most of the scenes from the movie are just like everyday life anywhere in the US. The picture here started with the war wall from the house. He starts with a map and then starts tacking up pictures and writing notes on it using a big fat felt marker. The notes are big enough for the audience to read and they help fill in some bits without having to have conversations to explain things to the audience. Kind of like texting. YouTube makes a couple of appearances through how-to-do-it videos, though I can't tell you if it was mentioned by name. The tennis ball trick was kind of clever.

Update February 2017 replaced missing image.

WoW!


This is just the coolest thing I have seen all day, for all the reasons that Leeann mentions in her post, plus look at the size of that tail fin! I want a car with tailfins like that!

Update February 2017 replaced missing picture.

Mythology

The other day I was reading a column about a corrupt politician who kept get reelected in spite of his obvious defects, like being a corrupt SOB. The writer surmised that this was because of the dream he was selling. He was telling a story to the people, and the people liked the story so much they voted for him, regardless of what he was doing. The writer was appalled that people would continue to vote for this guy. He went on in this vein for a while.

I read this and it was a like light clicked on in my head. It explains so much about politics! You could summarize George W. Bush's dream as "Truth, Justice and the American Way!", kind of like superman. Some people summarize Barrack O'Bama's dream as rainbows and unicorns for everybody! Doesn't really matter what the dream was, they sold it, and the American people bought it.

It seems like once the election is over, the dream selling gets pushed to the back burner, and the nit-picking begins. It doesn't really matter whether the nit is a $5 fruitcake or a trillion dollar national budget item, people will use anything to try and tear down their opponents.

Near as I can tell, the whole point of nit-picking is to incite moral outrage in people, who will then commence hollering for the victim's head.

All of this is just mass-market politics and has virtually nothing to do with whatever deals are actually being hammered out behind closed doors.

Most people try to be good people, they try and do the right thing. There is a small percentage who are only looking out for themselves. This ratio is pervasive, no matter what line of work you are in, be it ditch digger or Senator.

Let's skip the out-and-out bad apples. There are always a few in the mix. You might ferret them out, or they might trip you up, but that's life.

The bigger problems come when people try to agree on what is right. It can't be done. The closer you get to an agreement, the bigger the obstacles. Things that are of no importance when you are opposite sides of an argument become mountains when you get close to agreeing.  This is were mythology comes in.

When I was a kid, it didn't seem to matter what you believed. You could believe whatever you wanted and the world went on about it's business paying you no-never-mind. To a certain extent that is still true, though now you can almost always find someone to argue with about just about anything.

Figuring out what you really believe can be a bit difficult. I see pictures of children starving in Africa, and I want to do something to help, but I am pretty sure just giving money to some charity is not going to really change anything. I hear about a horrendous crime and I want the perpetrator ground between two stones, but I realize that the justice system is error prone, and capital punishment trials cost more than life in prison, so I try to dismiss it from my mind with the vague hope that whoever the actual criminal is will get their comeuppance.

When I was in high school, I had a teacher, Mr. Cree if I recall correctly, who told us we should read and study the current issues and base our votes on facts, and not just blindly vote for whoever our friends or families or the TV told us to vote for. At the time, that seemed like good advice, but over time I have come to be skeptical of this approach. Issues have gotten so complicated, and there is so much information available, that it can easily become a full time job trying to sort out just one little issue, never mind the dozens that we are faced with everyday.

So that's where belief and mythology come in. You listen to the stories, and whoever has a story that sits better with your inner belief system will get your vote. Not that it really matters, because the political machinery is so entrenched that nothing is really going to change.

Tone of Voice

I was driving in my truck the other day and I had the radio on scan. It paused on one station and just from the speakers voice, before he even said "Jesus" or "Hallelujah", I knew it was a Christian station. I didn't pause.

Then yesterday I called the University to settle an accounting question and I got a recording with a woman's voice, but it wasn't one of those bright, perky little messages you get from a business. She sounded exactly like a stuffy academic bureaucrat who was only talking to me because she was required to. Eventually I got to a real person who was, if not charming, at least pleasant. Even better she was efficient. She dealt with me and my problem in less than a minute, and I was happy about the outcome to boot.

So whats the deal? Do people learn their tone of voice from their environment? Or do people with a certain tone of voice end up in certain kinds of jobs? Maybe that's what determines whether you get hired for any particular job or not. It's not your resume, or your qualification, or the way you dress. It's all in how you say whatever it is you say. That is just weird enough that it might be true.

Monday, May 16, 2011

Differential Equations, Part Two

After I finished part one, I got to thinking about it and realized several things.
  1. It isn't a pure math problem, it is more of an applied mechanical engineering problem.
  2. Although my niece says it is a steady state situation, it isn't. The metal plate in question starts out at a temperature of zero, heat is applied to one edge, so the plate heats up to a point where it eventually reaches equilibrium, which is steady state. So it starts in a steady state and it ends in a steady state, but in between the temperature is changing.
  3. The problem specifies we have a heat source on one edge, and heat sinks on the other three edges, but it doesn't say anything about the faces (back and front) of the plate. In this case we can presume that the faces of the plate are perfectly insulated so no heat is gained or lost from radiation. In practical terms, this is reasonable. You apply a torch to one edge of a plate and the plate will heat up. Any heat lost to the air or through radiation will be insignificant compared to the amount of heat being conducted away by the metal plate itself. In reality these losses may not be insignificant, but one thing at a time, so we are just going to pretend they don't matter in this case. After we figure out this part we can build a more sophisticated model.
  4. We don't know how thick the metal plate is, but it probably doesn't matter. The thicker the plate, the more material there is available to conduct heat, but there is also more material to heat, so these two balance each other out. If our heat source (or sink) had a limited capacity, then this would make a difference, but this is a thought experiment, so we don't have to worry about little details like this.
  5. The problem doesn't specify whether the temperature of zero is absolute, Celsius or Fahrenheit. It may not make any difference, other than the range of temperatures we find.
  6. Neither the material, nor the specific heat, nor the heat conductivity of  the material are specified. They are not necessary. Any formula that is going to calculate the actual temperature of the plate will use constants for these values. Plug in the right constant, turn the crank, and you will get the correct answer.
I think what they are looking for is a what the temperature of any point on the plate after it has reached equilibrium. Let's start with a simpler example. If you have a metal rod with a heat source on one end, a heat sink on the other, and it is insulated along it's length, eventually it will reach thermal equilibrium. Heat will be flowing in one end, and flowing out the other, but the temperature of the rod will not be changing. The heated end will be hot, the other end will be cold, and I think we can safely say that the temperature will increase uniformly along it's length from the cold end to the hot end. If we graph the temperature of the rod against it's length we will get a straight line: the temperature gradient is linear.

Let's make it a little more complicated. Say we have a disk with a heat source being applied to the center and a heat sink all around the edge. In this case as you move away from the center, the temperature will start out dropping quickly, and then more slowly as it approaches the edge. Or maybe it will start out dropping slowly and then more quickly as you get farther from the center. This is because the farther you get from the center, there is more material to suck away the heat. In any case, it is not going to be linear.

With the rectangular plate described in our problem, we have two complications. One is that the heat source is not applied to a single spot, but all along one edge, and it isn't applied evenly. The other is the shape of the plate. As you go from the top (heated) edge to the bottom, you might expect the temperature gradient to be linear. While the faces are insulated, as in our example with the rod, the sides are not, they are connected to heat sinks. So the closer you are to one edge, the faster your temperature is going to drop on the way from the top edge to the bottom. The closer you are to the center, the closer your temperature gradient will be to linear. See the graph I included in Part 1.

I don't know how to calculate that, but if I stew on it for a couple of days, I may get an idea.

I graphed the top edge temperature. Clicking on the caption will take you to the spreadsheet I used to make it.

Graph of Top Edge Temperature

Since the source temperature drops below zero, I think we can assume that the zero specified in the problem is not absolute zero, but rather a more conventional one. Also, the teacher who crafted this problem is a crafty devil. If you followed my logic in analyzing the problem, and didn't bother to check out the formula for the source temperature, you might be surprised when your temperature gradients all point the wrong way.

P.S. Here's the formula I used in the spreadsheet for cell B3:

=-2*sin(PI()*A3/$C$1)+sin(3*PI()*A3/$C$1)

The 3 in the A3 reflects the row the formula is on. Formulas on different rows will have a different number.
I added this explanation because I didn't want to mess with the spreadsheet anymore. I am not sure this is the best way to explain this.

Update October 2016 replace missing graph.

Saturday, May 14, 2011

Differential Equations

Last week my sister-in-law's daughter (does that make her my niece?) sent out an emergency broadcast looking for help on solving one of the questions on her take home final. She had been through three Indian tutors (online from India) and was waiting on a reply from a fourth, and she still had no clue on how to deal with this problem.

I took calculus in college and I would have gone on to take differential equations, but I ran into some BS that I wasn't going to deal with. The last bit of calculus was supposed to be an introduction to differential equations. For this we were supposed to memorize a bunch of really complicated equations, with no explanation of what they were for or how they worked. I just don't work like that. I want concepts and understanding. This "memorize or die approach" turned me off, so that was the end my training in mathematics.

Anyway, I heard my niece's cry for help, and while I probably would not be able to help her, I might know someone who could, and in any case I wanted to see just what this intractable problem looked like. Here it is:
Consider a rectangular plate, of size d in the y direction and size l in the x direction. At y=d the temperature is held fixed at f(x). On all other sides the plates temperature is held at 0. The plate is initially 0, everywhere. Solve du/dt = k(delta*u), 0<x<l, 0<y<d. u(0,y,t)=0, u(l,y,t)=0, u(x,0,t)=0, u(x,d,t)=f(x)=-2sin(PI*x/l)+sin(3*PI*x/l), u(x,y,0)=0.
This is how I interpret the problem (O is for an Original statement, M is for My interpretation):
O: Consider a rectangular plate, of size d in the y direction and size l in the x direction.
M: We have a thin, rectangular metal plate.

O: At y=d the temperature is held fixed at f(x).
M: The temperature along the top edge is held at a temperature that is determined by some mysterious device that depends on how far along you are from the top left hand corner. We don't know what the temperature is exactly, any kind of mysterious device may be used. It may heat the edge evenly, or at constantly increasing rate, or it may heat it more in the middle and less on the ends, or it may have apply heat randomly. In any case, once you have picked your mysterious device, it continues to apply the same amount of heat to the same locations.

O: On all other sides the plates temperature is held at 0.
M: The other three edges of our plate are in contact with refrigerated heat sinks that suck all the heat out of those three edges of the plate, holding their temperature to zero.

O: The plate is initially 0, everywhere.
M: When we start, the temperature of the entire plate is zero.

O: Solve du/dt = k(delta*u),
M: This is the crux of the problem. I think what they are asking for is a formula to determine the rate of change in temperature. du/dt is shorthand for change in temperature over change in time, i.e. how fast the temperature is rising. Delta is similar in that it represents change. So it looks like they are asking if the temperature changes by a certain factor, they want to know how fast it is changing when that happens, which doesn't really make a lot of sense, but that's probably because I don't really understand what they are talking about.

O: 0<x<l, 0<y<d.
M: These are the ranges for which we need to find solutions, i.e. we are only interested in the temperature of the various parts of the plate, we are not interested in anything outside the plate.

O: u(0,y,t)=0, u(l,y,t)=0, u(x,0,t)=0,
M: This just says that the temperature of the other three edges are held to zero, which we already know. We have a function u that takes three parameters: the X and Y coordinates of a position on the plate, and the Time. It doesn't matter what time it is, as long as the coordinates place you along one of the three refrigerated edges, the temperature will be zero.

O: u(x,d,t)=f(x)=-2sin(PI*x/l)+sin(3*PI*x/l),
M: This is the formula that models our "mysterious device". This tells us what the temperature is along the top edge of the plate.

O: u(x,y,0)=0.
M: This just says that the initial temperature of the plate is zero, something else we already knew.

My brother Andy, world wide web crawler that he is, found an MIT website that also has some good math stuff. Here's a link to a 15 page PDF of Solutions to Problems for 2D & 3D Heat and Wave Equations, which look kind of similar. I asked my friends and three of them admitted to studying differential equations in college, but none were able to recall enough to be helpful. Stu recognized it as being a Sturm-Liousville problem, whatever that is.


My niece eventually figured it out with some help from her friends:
This problem is actually more advanced than just differential equations.  In fact, I don't even think I learned the way to solve it in my math class this semester, but there is a trick that one needs to know and it makes the whole problem easier.  The trick is that u(x,y,0)=0 implies that it is a steady state.  This means du/dt = 0.  So then you only need to solve one side of the problem, cause the other side goes to zero.  My teacher always put things like this on the tests, cause he likes these kinds of tricks.  Anyway, I hope you can learn more about all this stuff.  It's complicated, but it's awesome.
For those of you who waded through all this, here is graph of a temperature gradient from a similar problem in the PDF from MIT.

I've been looking over some of this, and I think the thing that bothers me about it the most is that there doesn't seem to be much correlation between the concepts being dealt with and the symbols being written. You take algebra or geometry and you have equations that can be easily converted into instructions for a calculator or a computer program, or can even be worked by hand. The handwritten expressions of integrals and differentials are not so easily translated. Even just translating them into English can be a formidable challenge.

P.S. You wouldn't believe how much trouble I had putting in less than signs, or I don't know, maybe you would. Blogger is so stupid sometimes. I may have to move to Wordpress or something if I am going to keep this up.

Update October 2016 replaced missing graph.

Iron Sky


You'll laugh, you'll cry, you'll be effing amazed that anyone would produce such a thing. Oh, wait, maybe they didn't, maybe the trailer is all there is. Via Robert Scott Ladd on Facebook.

Obi-Wan Kenobi Is Dead, Vader Says


Read the whole fantastic report here.
Original report here.
Via the Earth Bound Misfit.

Update February 2017 replaced missing picture, replaced dead link to new copy.

Pattern Matching

Pattern matching is one of things people do really well, and something that seems to be kind of difficult for computers. Recognizing anything, from a toothbrush to a song, involves pattern matching. For a while I've been kicking around the idea of writing a computer program to look for patterns in digital data. All digital data is stored in some kind of structure. The data is only useful when it is decoded and displayed or used for something. Much digital data is stored as a sequence of bytes. Text files are one example, each byte represents one character. Most audio and video data is compressed, and the individual bytes are now just part of a stream of bits. Lose your place in the stream and your data may as well go in the bit bucket.

We got an example of this last night while we were watching The Closer. Every so often there would a little skritch-skritch sound. I didn't notice it until my wife pointed it out, and then I had to replay it five or six times before I was able to pick up on it (we were watching a recording off of the Verizon/Frontier/Motorola DVR). After that I started noticing it. Well, I noticed it at least once more. I suspect what happened is something got corrupted in the audio bit stream, and the DVR lost it's place and had to wait for a synchronization pattern to appear, and in those few milliseconds between the two events, the audio circuit got fed garbage, which we heard as skritch-skritch.

Anyway, a couple of days ago I got an error message in my browser, along with a block of data to show the
"highly trained monkeys" who were supposedly looking into the problem, and I got thinking about running a pattern recognition program on this block of data.

Pattern recognition can become very complex very quickly, but I thought I would just start with some elementary analysis: how many of each bit pattern are there in a given block of data? The first problem is how many bits are you going to look at. I mean a bit a pattern can be anywhere from one bit long to a zillion bits. Well, it can be as long as your data sample. Any file you can store on your hard drive is going to have a fixed length, and it probably doesn't make sense to look for bit patterns any longer than maybe a megabyte or so. Still, that is a very long pattern, and would require a large amount of working memory. So let's start at the other end and see where it leads.

We start with one bit, go through the file and count the number of bits set to one and the number of bits set to zero. If all of the bits are set to one, or they are all set to zero, there is no pattern and there is no further analysis to be done.

Now we can move up to two bits, which have four possible values. You also have two starting positions. You can start at the beginning of the file, or you can start one bit in and count all the combinations that start on odd boundaries.

Next we have three bits, which have eight possible values, and three possible starting offsets. Small amounts of data like these can be easily stored in working memory.

This works well for a while, but when we reach 16 bits we have 65 thousand possible values and 15 starting positions, which means we will need a megabyte of memory to use for counting. When we reach 32 bits we will need over 100 billion bytes. We would need this much memory even if the file we are analyzing is only a few thousand bytes long. Perhaps there is a better way.

At some point, which we may want to choose based on the size of the file we analyzing, we could start using a content addressable array. That is, instead of just using the value of the current bit pattern as an index into an array, we would assign an index to the bit pattern. As new bit patterns are discovered, new indices would be created. So we would need a function to convert the bit pattern to an index.

One way is to just create a list. Whenever the function is called, the list is scanned to see if that pattern already exists, and if so, then the index to that pattern is returned. If we are analyzing a lot of data, and there are a great many bit patterns, scanning the list could prove to be time consuming. In that case we would probably need to maintain a sorted list. This would make checking the list very quick, but adding each new pattern would mean considerable work (time) to rearrange the list to make room for the new entry. Since our first subject is rather small, we can probably skip this sorting business for the time being.

So now all I have to do is write the program and see what pops out.

Friday, May 13, 2011

Wendover, Utah

I have been listening to Joan Jett tunes for the last week. This is kind of unusual for me. Typically an old song will pop into my head and I’ll look it up on YouTube and play it for a day. By then I’ll have had my fill, and I will go back to my normal music-less mode. I think the deal with Joan is that 1) she is a hard rocker, and 2) I have never heard most of her stuff. Some of it was too scandalous for the airwaves, and there is a certain amount of hostility in there as well. Suits me just fine. Of course, it doesn’t hurt that she was a doll and has a heck of a smile. Pictures are nice to see, but it’s the music that keeps pulling me in.

So while I have been listening to her band, I have been looking around for information. I didn’t find much. She was in the Runaways, she did some movie work, but for the most part she has been playing Rock & Roll nonstop for the last 30 years. If she has a personal life it’s not on display.

Anyway, Ms. Jett & the Blackhearts are touring this year and one of their stops was Wendover, Utah, or more properly Wendover, Nevada, both of which combined form a wide spot in the road where Interstate 80 crosses the border on it’s way from Salt Lake City to Reno.


View Larger Map

Looking at the Google satellite view, it looks pretty forlorn. I imagine an old grocery store converted to a casino by wheeling in a couple of slot machines and a craps table. Cracked asphalt in the parking lot, tumbleweeds rolling by, and a nasty desert wind carrying salt from the nearby Bonneville Salt Flats, and I think: what a sad turn of events for such a great performer.

Then I look up Wendover and I find not one old delapidated casino, but three, big, new, bright shiny casinos with their own theater. It’s a straight shot from Salt Lake City, 120 miles down the Interstate,  not a big deal when you need some good old fashioned religion. Turns out the Blackhearts are not alone in this tour business. Looking at the schedule there seems to be a big name band appearing there once or twice a week. Okay, maybe not BIG names, but names I recognize, and some of them are not all that old.

We have the same thing going on in our neck of the woods at Chinook Winds and Spirit Mountain and maybe a couple of other places. Here they are Indian casinos but they are constantly advertising biggish-name singers and bands. Not too long ago I read that some bands were forgoing the big record deals in favor of concerts, as there was more money in performing live than they were liable to get in royalties. It seems to have blossomed into something of an industry. There always were big concerts by big names in the big concert halls, and there always were the small time bands playing in bars, but it looks like the middle tier has expanded. This is good, it means more people are making a living playing music.

Of course, it’s got to be a hard way to make a living. On the road, traveling by tour bus for months on end, living in hotels and playing two or three shows a week. Talk about your road warriors. No wonder Joan is wearing her hair short these days.

P.S. Wendover is on the Western edge of the salt flats that extend from the Great Salt Lake. There is an old, WW II era airfield. The Enola Gay made some training flights there. To the Southeast of town there is a pattern of roads that looks like it might be a development, but there is nothing there, except the roads and salt. Very odd. A salt mine perhaps?

Wanted


The only connection I can find between the name and the movie is that it is based on a comic of the same name. It starts off with David O'Hara being dangerous and almost unintelligible (he's a Scot), proceeds to James McAvoy dying of boredom as an office drone:
It's my anorexic boss' birthday. This means there's a certain amount of inter-office pressure to stand around the conference table, eating crappy food and pretending to worship her. Acting for five minutes like Janice doesn't make all our lives miserable is the hardest work I'll do all day. My job title is account manager. I used to be called an account service representative, but a consultant told us we have to manage our clients, and to not service them. I have a girlfriend who I neither manage or service. That's my best friend Barry fucking her on an Ikea kitchen table I picked up for a really good price. I'm finding it hard to care about anything these days. In fact, the only thing I do care about is the fact that I can't care about anything. Seriously, it worries me. My name is Wesley Gibson. My dad walked out on my mom when I was seven days old. Sometimes I wonder if he ever looked into my baby blue eyes and asked himself "did I just father the most insignificant asshole of the twenty-first century"?
But then Angeline Jolie comes into the picture and things get a whole lot more interesting. McAvoy's character plays the fool for about five minutes, but he finally gets some sense knocked into him, pun intended. The whole movie is way over the top. The special effects and the stunts are just amazing. Unbelievable really, but that's okay, it makes for a good story. And Angelina is always easy to watch, even with her clothes on.

Thursday, May 12, 2011

Memories, Courtesy of US News

California Bob reports:
I traded a bunch of junk to a junk man for a copy of US News & World Report, dated September 6 1971 -- before it became "Hot Naked Chicks & World Report."

Redolent with memories.  Main stories:

Nixon's 90-day freeze on wages and prices heading into third week.

Interview with Wilbur Mills, head of Ways and Means committee -- before the whole Fanne Fox jumping into the tidal basin incident, and Mills giving press conferences from Fanne Fox's dressing room at the Boston strip bar.

Unfavorable balance of payments forces Nixon to repeal gold-exchange standard (whereby foreign nations could trade their US dollars for gold).  Americans still forbidden to own gold coins or bullion.

Agreement reached with Soviets to allowed western vehicles unimpeded/unharassed access to West Berlin.

South Vietnam's president Thieu accused of rigging election.  The 220,000 US troops in VN are put on alert, told to keep off streets to avoid provoking anti-US demonstrations.

Big fluff story on Nixon's palatial homes -- "$340,000 estate" in San Clemente, and "$250,000 retreat" in Key Biscayne.

Court ordered busing faces protests (I thought Carter started that).

Voting age lowered from 21 to 18 -- widespread fear that this age group will take over local governments.  LOL.  Noted that students are more subject to demagogic appeal (true), and have "advocated changes in zoning restrictions allowing communal living of boys and girls in the same residence; relaxation of drug laws relating to marijuana, and more bicycle paths." 

Predicted that small private colleges will disappear as being economically unfeasible.

George Meany head of AFL-CIO, Frank Fitzsimmons head of Teamsters, Leonard Woodcock head of UAW, big article on the three.  Are these organizations even around anymore? 

Public service ad from Hammermill Paper urging people to write their legislators about crime -- "people can't use their own streets for fear of attack or robbery."

AT&T ad describing their new armored pay phone: "why the street corner pay phone is no longer in danger of becoming extinct."  "Vandals caused repair bills of $12 million on pay phones last year.  One solution is to remove phones.  But we're determined to improve service in spite of vandalism..."  Phone has "recessed dial molded from virtually unbreakable plastic."

Volvo ad espousing tough design of wheels, springs, shocks, engines -- fewer repairs.  (Repairing a car!  How quaint!  Now if we get a flat tire, we just buy a new car, and Toyota delivers it to the roadside.)

Lots of ads for liquor and cigarettes (Cutty Sark, Old Forester, Makers Mark, Salem, Benson & Hedges, showing dads in ties smoking in the hospital, looking at newborns, which they obviously had no hand in delivering.)

Mortgage rates at 7.75%.  Dollar worth 330 Japanese yen.  Ad for VW beetle says it cost around $2000.  US News $4.87 for 34 issues, or 14 cents an issue -- "a substantial saving."

Sir Spam-A-Lot

A spammer left a comment on one my older posts, a post about cable ties for Pete's sake, so naturally I had to find out what he is selling. Surprise, surprise, he's selling, wait for it, cable ties! But there was something odd about their website, so I wrote them a note:
Your spammer Garry left a comment on my blog, which led me to your very professional looking website. But I'm looking at the prices and for every item there are two prices listed, one with GST and one without. So now I'm wondering just what the heck is GST? I'm thinking maybe it's Georgia sales tax, so I click on the contact link and I find you are in AUSTRALIA. Nowhere on your web page does it say anything about being in AUSTRALIA. Oh, wait a minute, the URL has a little tiny .au tacked on the end. You might want to make that bit a little more prominent, especially since you are offering free shipping to all states. I mean, really? Free shipping to ALL states? Even those half a world away?

This problem is not confined to wackos from Australia, it's a problem common to many websites, especially US TV stations. They seem to think they are the only fish in the sea. I mean who in their right mind isn't familiar with KPRQ?

T-Shirt of the Day


Via Planet Peschel.

Update February 2017 replaced missing image.

Tuesday, May 10, 2011

Windows Is Wonderful, Part Umpteen Zillion

My computer got hit by a nasty virus a couple of weeks ago and I haven't taken the trouble to completely clean it out yet, so all kinds of weird things, things I have never seen before have been happening, like this error message when I tried to open YouTube. I thought it was kind of amusing. Better than a Blue Screen of Death (BSD), but I imagine that's coming.

500 Internal Server Error

Sorry, something went wrong.

A team of highly trained monkeys has been dispatched to deal with this situation.
If you see them, show them this information:
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Monday, May 9, 2011

Suburban Chaos

Michigan Mike reports:
I wish I had time to take pics, but it all happened so fast...

To wit:
Forecast rain, lowering clouds
Riding mower starts right up.
Quits mid lawn.
Seems hot.
Remove engine cover.
Hot bolt falls on hand, launches across yard.
Mouse nest on cylinder.
Close back up
No start.
No spark.
Open cover.
Crank while cover off, hot oil spray.
Primary, secondary wiring chewed, grounding.
Put shrink wrap over.
Close up.
Mow.
Hit poly cord, wrap around blade.
Undo.
TIre flat.
A/C handy.
Mow.
Park.
Drenching rain commences.
LOL not really.
I suspect A/C means air compressor, not air conditioning.

Thursday, May 5, 2011

Joan Jett and the Blackhearts


Joan Jett, The Blackhearts - I Hate Myself for Loving You

Joan Jett and the Blackhearts (Warning: link starts playing music automatically) are touring this summer including shows at a casino in Tacoma, Washington and the Jackson County Fair in Medford Oregon.

Why am I telling you this? I'm not sure. One of her songs popped into my head yesterday and I've been on a Joan Jett binge. And what a name for a band: Blackhearts. How grim is that? Sounds like something out Shakespeare, and I'm not talking about one of his comedies. Anyway I started poking around and this concert tour popped up. Tacoma is easy driving distance, but all the good seats are apparently sold out, unless you are willing to pay big bucks. Tickets for the show in Medford are considerably cheaper and go on sale tomorrow. Medford is a bit farther, but there will be much less traffic. I found out about the Oregon date from the Jetthead fan site.

I am probably not going to go, but this is the first time I have thought about going to a concert in years.

Update March 2017 replaced missing video.

Tuesday, May 3, 2011

Cloud Eight


In the past I killed many hours playing minesweeper. Eventually I quit. Recently I have taken to playing it occasionally and this morning I found a cell surrounded by eight mines. I don't think that has ever happened to me before. I have run into seven's a few times, but this was the first time for an eight.

Update February 2017 replaced missing image.

Sunday, May 1, 2011

Quote of the Day

One of the penalties for refusing to participate in politics is that you end up being governed by your inferiors. - Plato
Via Steve.

After Action Report

The Great Jackson School Neighborhood Garage Sale is over. My daughter was the big winner. She collected $100 for clothes that were sold and she didn't even have to be here. Of course, you could say the people who bought the clothes were the real winners. Who knows how many thousands of dollars went into buying all those fancy duds we sold for two or three dollars a piece. My wife claims it was only hundreds, not thousands, but then she is ever the optimist.

Traffic started out light, but it slowly picked up as the morning wore on. Usually the neighborhood is thronged with people from the get go, so it was kind of surprising that the traffic was so light. Is this because the local economy is doing better and people don't need to scrounge as much? Or is it because the economy is worse, but people have gotten smarter and are making more use of Craigslist and Ebay?

I sold a pair of studded snow tires that I bought for a mini-van we sold a few years ago. Forgot about them till now. I asked and got $20 for them. I didn't ask much because the only other times I tried to sell used tires I never got much. Given the level of interest I think I could have gotten considerably more this time.

Sold an HP 48GX calculator for $50. Bought it several years ago when I took off on a tangent that quickly petered out. I might have been able to get more for it on Ebay, that would have meant shipping it, which is kind of a hassle. and for me it wasn't worth it just for the possibility of another $20.


What do you do with a Wurlitzer Organ? My son and his cohorts picked it up somewhere and drug it home because it supposedly had a Lesley revolving speaker. It does, but evidently it doesn't have the requisite power handling capacity for what they wanted to use it for. Or maybe they just got bored. Anyway, it's been sitting in the rec room for a year, and he has gone off to college, so what do we do with it? It seems to work fine, near as I can tell anyway. It has a whole bunch switches, most of which seem to do something. Some I'm not too sure about.


I put an ad on Craig's List but I did not get a single inquiry. Maybe I set the price too low, I asked for a dollar. Next plan is to put it out by the street on the next sunny day with a free sign on it. Maybe someone while carry it away. It will take some carrying, it is kind of heavy, maybe 200 pounds.

Update February 2017 replaced missing picture. The organ eventually found a home in an adult care home. Jack and I hauled it over there and the nice lady gave us $50 for our trouble.