XMAS Newsletter

I count myself lucky to not have "friends" who send me bragging newsletters at Christmastime. My mom used to get them from some old neighbors. Moving didn't stop them — I guess my mom was too polite to refuse the request for their new address.

If you have never seen one then you have something else to be thankful for this year. These snoozeletters (I think they're boring) are a way to show how much better your family is than the poor schmucks who receive it.

"Bobby made the honor role ... Betty is the captain of her cheerleading squad ... John got promoted to Senior Executive Vice President ..."

If they're so smart, how come you can always find some gaff like the honor "role"?

Here's what I've been tempted to send out, but have never had the guts to:

We think Tommy is going to pass third grade this year — on only his 2nd try! ... Jennie is recovering nicely from the head lice. She's might even continue shaving her head; she thinks it looks good with her new piercings. ... Barb should get her license back next month, just in time for her release from prison (can you believe the judge gave her 6 months? It was only her third DUI!) ... The federal court ruled that those billboards with the pictures of people who hired hookers are unconstitutional and they've been taken down. It's about time, too; I was getting tired of people pointing and whispering as I walk by. On an unrelated note, I've been lesion free for 9 months now! ...

Hope you have a Merry Christmas, even if you don't celebrate Christmas.

(Yes, this is your card. Feel free to print it and put it on your mantle.)

'Tis the Season

I just can't seem to help it. I'm a curmudgeon when it comes to Christmas.

It's not that I'm cheap. In fact, my tendency is to be anything but cheap. But I still find myself very short of patience and Christmas cheer and it only gets worse the closer we get to Christmas.

So what is it that makes me grumpy? I'm not sure. Part of it is probably that I'm an introvert and this is the time of year when there are a lot of demands to spend time socializing. Putting on a happy face and socializing is very tiring for me. My brother, 3 of 3 among my generation (I'm 2 of 3), seems to be the opposite from me in this regard. I think he gets energy from gatherings and he just doesn't understand me. But I digress.

Another thing that drives me nuts is the need to keep things equal. If you have kids you probably know of this requirement. It means that you have to give each child the same number of gifts. The price of those gifts also has to be equal, as does the WOW! factor.

Aside # $52.37:Did you ever notice that "WOW" upside down is "MOM"?

Also, if you do the purchasing for grandparents you have to make sure that the WOW and fun factors are balanced well between your and your SO's parents.

Of course, I understand all of these requirements very well and am not prepared to simply toss them out and let the (cow) chips fall where they may. Nevertheless, trying to get everything to balance is hard. It leaves me weary and short tempered.

Another thing that bugs me is decorating. My wife and I have — er — different ideas about how to decorate. But I guess I must consider myself lucky overall if, for no other reason than that she doesn't with to go whole hog with the outdoor decorations. I'll admit it, I'm a lazy bastard. Especially where it involves working in the yard. Those outdoor decorations are expensive to buy, expensive to run, hard to store, and a pain in the bum to put up and take down. What's not to love? If any of my neighbors says anything about my lack of outdoor decorations I may just have to buy a menorah and put it in the window.

I could go on, but what's the point? So I'll just close with Bah! Humbug!

Bye-Bye, Earthlink. It's been great.

I have used Earthlink DSL for nearly four years, but today I cancelled the service. As mentioned in a previous post, Verizon has a sexy new service called FiOS. It was finally enough to tempt me to switch.

I got the cheapest and slowest FiOS internet service. Assuming that taxes and fees will be a wash, FiOS will cost me $10 less each month than I was paying with Earthlink. And now that I've done a few largish downloads I can report that FiOS is about 7 times faster than what Earthlink was able to deliver. Those are numbers I can't ignore.

But as I leave Earthlink I have to commend them for a solid service. In the four years I was with them I had very few outages. Like maybe one per year, with nothing lasting longer than a couple of hours. And the performance was consistent. There were no daily slowdowns when the kids got home from school. There were no seasonal slowdowns. Even the Victoria's Secret online fashion show didn't slow down my other internet use.

And, it must be noted, I came to Earthlink from ISDN, where I was paying about $1500 per month for 128 kilobits per second (both ways). So $50 per month for 768 kilobits down and 256 kilobits up was a real deal! FiOS is the next step. I wonder what the future will bring.

Big Ideas

First off, yes, I'll admit that I'm a bit odd. Now, with that out of the way, let's get down to the topic of infinity, shall we?

Aside #sqrt(2)/2: I promised Gene-Bob that I would discuss the cardinality of the continuum the next day, but failed to follow up, citing a discontinuity in the continuum. Interestingly enough, it was a discontinuity in Fourier series that led Georg Cantor to the discovery that all infinities were not the same.

Aside #aleph_0 + 1: My family's fascination with infinity, or at least my and 2 of 2's fascination with infinity, probably began with Buzz Lightyear, who always departed with the phrase, "To infinity, and beyond!"

So, what is infinity? You might be tempted to say that it is the largest number. But couldn't I define a number as infinity plus 1, and wouldn't that be bigger than infinity? Well, yes and no. Mathematicians avoid these kinds of problems by dodging the issue and saying that infinity is more of a concept than a quantity. It's similar to how physicists say that light is sort of a particle and sort of a wave.

Aside #many: A very strange, but very beloved friend of mine at the Looniversity of Tex-Mex at Autism, is fond, after a few beers and a couple of slices of Milto's pizza, of saying that there are really only a few numbers that really matter. For example, 1 and 2. Anything more than a very small number can be represented as "many". I think he used to cite some ancient culture that had such a limited number system. "Many" was their infinity.

Aside #0: I can't recall if my friend had a concept of zero in his numbering system. Oh, by the way, he was the accountant for one of the departments at the University.

So back in the 70's (the 1870's), a curious fellow named Georg started looking into the concept of the continuum. An example of a continuum would be the points on a line. How many are there? Is it the same number as the number of cardinal numbers?

Curious Georg decided that there were more points in the continuum than there were counting numbers (i.e. cardinal numbers). In this off-Cantor world, there are orders, or levels, of infinity. The lowest order of infinity is called aleph null.

Aside #128: As they say at the First Brobdignagian Babatist Church of Suburbia when discussing the King James Version of the Bible, "if it was good enough for JEE-sus then it's good enough for me." I think a similar statement can be made for the ASCII character set and we should be immediately suspicious of someone who proposes the use of characters that aren't in ASCII.

Aleph is the first letter of the Hebrew alphabet. And not only is it not found in ASCII, it isn't in the ISO 8859-1 character set either. So since I doubt that ℵ happens to produce a funny looking X on your screen, I'll just have to write aleph_0 and you should think "aleph null". Similarly, aleph_1 is "aleph one".

Now that we have notation nailed down, let's get back to infinity. Aleph_0 is defined as the number of counting numbers, or the number of elements in any countably infinite set. Counting numbers are a good example since it is fairly easy to construct the next in the sequence no matter where you are. So we can accept that, given infinite time we could count (list) all of the counting numbers. Don't you just love circular definitions? Okay, let's just say that you can list all of the counting numbers from zero on up, without missing any, for as long as you have the time. For example, you could list every last counting number from 1 to 1,000,000. With any luck, you now understand the concept of a set being countably infinite. The size of that set (its cardinality) is aleph_0.

The next issue is to figure out if a given infinite set is countable or not. We do this by trying to do a one-to-one mapping between the set of interest and the set of cardinals. For example, is the set of even numbers countably infinite? Well, yes it is because we can map the cardinal 1 to the even number 2, the cardinal 2 to the even number 4, and so on, for all possible even numbers. We'll never finish the job, but since we can define a one-to-one mapping that clearly won't miss any of the even numbers, and since we've already accepted that the cardinals are countably infinite, we have proven that the set of even numbers is also countably infinite. So both sets are the same size, and the size is aleph_0.

Stop! Back up. Did I just say that there are as many (positive) even numbers as there are cardinals? Yep. I did. Maybe now you're starting to understand why Curious Georg lost his mind and wound up in the looney bin.

Let's try another set: the real numbers between zero and one. Is it countably infinite? Let's make a list. Each number will be represented by an infinite set of digits, so 0.2 is written in our list as 0.20000000... (with an infinite number of 0's off to the right, so that we can distinguish it from 0.200000000...1). Here's a bit of my list (not in order):

1)  0.1000000000...
2)  0.1844765194...
3)  0.1368698456...
4)  0.1684413685...
5)  0.1277569545...
6)  0.9423655486...
7)  0.7526952756...
8)  0.3149712951...
9)  0.8211036501...
10) 0.3741098120...

Okay, I've listed every cotton-picken real number between 0 and 1! It took a while, but I did it! Now lets check to make sure that I didn't miss any. To do this I'm gonna make a new number and see if it's in my list. Like all of my numbers, my new number has an infinite number of digits in it. The first digit (to the right of the decimal) will be different from the first digit in the first entry on my list. The second digit will be different from the second digit of the second entry in the list. You following me? Let's look at my list and highlight the digits I'm looking at:

1)  0.1000000000...
2)  0.1844765194...
3)  0.1368698456...
4)  0.1684413685...
5)  0.1277569545...
6)  0.9423655486...
7)  0.7526952756...
8)  0.3149712951...
9)  0.8211036501...
10) 0.3741098120...

The red digits in my list are going to be used to create my new number using this formula: new digit = (old digit + 1) modulo 10. That's a fancy way of saying that I'll change a 0 into a 1, a 1 into a 2, a 2 into a 3, and so on, with a 9 becoming a 0. Here's the transform:

0.1864552900... becomes 0.2975663011...

Guess what? It isn't in my list. How do I know? Well, because it is different from the first number in my list in at least the first decimal place. And it is different from the second number in my list in at least the second decimal place. And it is different from the third number in my list in at least the third decimal place. And so on into infinity. So my list wasn't complete after all. I failed in producing that one-to-one mapping from the cardinals to the reals without missing any! And it can't be done!

Therefore, the set of reals (between 0 and 1, and by extension the set of all reals) is uncountably infinite. We define the number of elements in this uncountable set as aleph_1.

Later on, in a proof I haven't seen, Cantor proposes that aleph_1 = 2^aleph_0. I'll have to take his word for it.

FTP

There are so many acronyms today that it's hard to keep up with them. But it gets even harder when new acronyms are also old ones. Case in point: FTP, which has stood for File Transfer Protocol (and File Transfer Program) for more than 20 years. I use ftp every week and in a previous life I was even part of a team that wrote an ftp program (in assembly language) for a CDC supercomputer.

A couple of years ago FTP gained another definition: Fiber To (the) Premises. It means that a fiber optic cable is connected to your house. Well, yesterday, fiber came to my premises in the form of a service called FiOS, from Verizon.

I had ordered the lowest priced FiOS internet service: $39.95 for 5 Megabits per second download and 2 Megabits per second upload. This is $10 cheaper than my current ISP and at least 3 times the marketing speed. When you order FiOS internet service they also move your (main) telephone line to the fiber. In January they will start offering TV over FiOS.

The install went pretty well, though it takes a long time. Since fiber optic cable cannot transmit electricity, and since ethernet and telephones both require electricity, there has to be a big box that converts the light signals from the fiber into electrical signals on the copper that runs through the house. And that box needs a battery backup if you want your phone to continue working during a power outage. Of course, who has a non-powered (i.e. not a cordless) phone anymore? Well, besides me.

Then, too, there was the small fact that easternet cable isn't quite the same thing as telephone wahr. I had DSL, which came over the telephone wire. I didn't have ethernet cable from the exterior telephone CPE to my router. So they had to install that as well by drilling yet another hole through the exterior of my house.

When it was all done I got to setup a new username and password for my internet stuff and we verified that it really did work. Now I just have to recable the office (the router is in a different place) and make it all look nice.

Then my wife asked, "Why doesn't the phone work?"

Sigh. I forgot to test that before the installer left. I did some tests and called Verizon. They had me do the same tests, then said they'd get the installer back out. Well, he had been gone over an hour and it was well past normal quittin' time, so I had to wait until the morning to get my telephone working. Turns out that the computer which was responsible for switching my phone from the copper lines to the fiber had gotten stuck mid-way and there was a "hold" on my line. They cleared that and now everything is working as it should.

Of course, the big question is whether it is faster or not. The answer is that it depends. There are a lot of things you do on the internet which are limited by things other than your network speed. For example, when you point your browser to some site you've never visited before (or more than an hour ago) then your computer uses DNS to look up the internet address for that web site. The DNS protocol has built in delays (of up to a minute) to give the servers time to answer before throwing up an error screen. Then the HTTP protocol does a lot of chatting back and forth with lots of little delays. Finally you get your content, and unless that is big you probably won't notice any significant speed difference. Then again, there are plenty of servers on the net which are incapable of giving you what you asked for at your internet connection's speed. They were slow with DSL and are no faster with FiOS.

When all is said and done, I do expect to see some important speed increases for the stuff I do over the internet. I just have to figure out what I'm going to do with that extra $10 each month!

I See Dead People

Yesterday, my wife and I took our children to their first funeral, for Great Grand Aunt Margaret. The kids had met Aunt Margaret about two years ago when we all went down to celebrate her 90th birthday, and we thought that her funeral was a good opportunity to introduce and discuss a wide variety of topics, both practical and religious. Because they had met Margaret and had heard about her from time to time there was a connection. But they weren't so close to her as to be overcome with grief, and therefore be unable to absorb any of the other lessons.

Aside #10: It appears that death takes 10 years off your life! Margaret, who was born in 1913, was listed as 82 years old in the obituary which was published in the local paper.

The first new experience of the day was the viewing. Neither boy had ever seen a dead person up close before. Of course, an embalmed body in a funeral home viewing is quite a bit different from some of the other options. I prepared them by saying that it would look like she was sleeping — except that she wouldn't be drooling. :-)

The second lesson, which really wasn't expected, was to see how people used to deal with funeral processions (and apparently still do in small towns). As we followed the hearse to the cemetery we were preceded by a police car and ignored stop signs and traffic lights (we passed through two of the town's three lights). Other traffic on the street (i.e. going the opposite direction) even stopped and waited until we were all past! In Dallas people get upset when the traffic lights switch to allow a fire truck to zoom by on the way to an emergency! (Heck, any red light makes the majority of big city drivers furious.)

Then, of course there were lots of little things to observe, and I won't bore you further with their details. It was a good experience and there were many good little discussions. I'm glad that my children were able to experience death in such a low stress way and to see how a family handles it.

Now if I can only get them stop running with scissors ...

Global Warming?!? Balderdash!

Harrumph! Global warming my a**! Woke up this morning to find the temperature below freezing. In Texas! And yet, my kids still had to go to school!

Aside #9/5+32: Here in Texas we put on Parkas when the temperature goes below 32 degrees Celcius!

I, for one, am not going to sit still for this! I'm gonna write to my erected representatives and demand that they do something about it!

And it's not just in Texas. Oh, no, there's an ice-age coming to Europe on account of a failure of the Gulf Stream. I read it on the internet, so it must be true. How can you have an ICE AGE if there's GLOBAL WARMING? Why would the polar ice caps melt if it's so cold that France will have permafrost?

I think this cold weather is just another plot by libberralls to turn Texas into a BLUE state! They must think that if our lips and fingers are blue then we'll vote for Hillary.

Well, it ain't gonna work! We're gonna vote for George Bush in 2008! P, that is. Next in line for the throne. Just you wait.