Here's today's junk mail -- Number 9, just like the Beatles song! If you would like to see the other junk mails, go to http://xpda.com/junkmail. You'd likely be a bit odd if you did, though.

A week ago Saturday I entered the Chili Cookoff sponsored by the Pryor Academic Excellence Foundation. I spent literally minutes preparing my fine blend of Hormel Chili. OK, so I didn't blend it. And maybe it wasn't fine. But it did take me a couple of minutes. Even so, for the fourth straight year I was disqualified! Something about the beans and the can. Here's my entry:

chili.jpg

Oh well, I'll try again next year.

Three pictures of today, weather extremes: The first was taken at Aiguilles du Midi (or something like that) in the French Alps. It's near Mt. Blanc, the highest mountain in Europe. Mike, Serge and I were planning to climb it but the weather wasn't nice to us.

chamonix9.jpg

... and in contrast to that, here's a couple of hikers (Cathy and Leann) in Death Valley earlier this year:

dv99.jpg

(You have to look close -- it's bigger than it looks.)

The third picture was taken the day of the big tornado in Oklahoma City this year:

storm.jpg

It's not a tornado, but it does look serious.

88 years ago today (or shortly afterward), the Manchu Qing dynasty in China was overthrown. Soon after that, Asia's first democracy was founded, the Republic of China. The Republic of China's National Day is today! The Republic of China is now Taiwan. Mainland China, or the People's Republic of China, celebrated it's National Day September 26. That day in 1949, the Communists led by Mao Tse Tung took over China. The old government leaders went to the island of Formosa, or Taiwan.

The U.S. recognized the old government in Taiwan as the government of all of China for a lot of years. It was the "One China" policy. They didn't officially recognize "Red China" as a country. This was pretty dumb, because they were (and are) a country.

Now it's getting even dumber, in my opinion. The U.S. says that there's still one China but mainland China is it now. The U.S. doesn't say much about Taiwan, except that they won't treat the Taiwanese president as a president and they won't let Taiwan have an embassy in Washington. But the U.S. does support Taiwan militarily. The People's Republic of China (Mainland China) says Taiwan is a "renegade province" and have promised to take them back, by force if necessary -- after 50 years of independence. Why don't these diplomats get real and admit that Taiwan is a country and China is a country? They pretend they don't know the truth.

Last night Sea Launch Co. launched a satellite into geosynchronous orbit. This was pretty neat because it's a private company (a joint venture by Boeing, a Norwegian company, a Russian company, and a Ukrainian company), and because it was launched from a modified floating oil rig out in the middle of the Pacific Ocean. Now THAT's a model rocket! DirecTV gets 30% more satellite capacity as a result. Launching near the equator gave them an increase in the earth's rotational speed (13-14% better than Cape Canaveral) for an additional boost in getting the satellite up. The satellite arrived in orbit today, so they probably were consistent in their units of measurement.

Today I went to an air show in Muskogee. Here's what I saw:

f18exhaust.jpg

This was taken looking into the rear of the engine of an F18 fighter. I was checking it out for Y2K compliance.

I am typing this on my computer. There are two or three levels of memory on this computer. The fastest level is the cache memory. It has a 4 nanosecond cycle time. That means it takes 4 nanoseconds to read what's in the memory. How long is 4 nanoseconds? It's about 47 inches.

Sunlight takes about eight and a half minutes to get to me after it leaves the sun, at least when I'm on earth. That's more than 669,000,000 mph. At that speed, you could travel around the earth almost 450 times (448.96 times at the equator) in one minute. Of course, you'd burn up long before you hit light speed from the atmospheric friction, but if you could do it that's how far you'd get.

A second is 1/60 of a minute. We're all familiar with about how long a second is (unless someone says to wait a second in which case a second might last for quite a while.) At light speed, you can travel around the earth 7 times in less than a second.

If you take a second and divide it into a thousand pieces, you get a millisecond. That's a pretty quick time period. But at light speed you could go from Pryor, Oklahoma to Los Angeles in 7 milliseconds. If you take a millisecond and divide that up into a thousand pieces, you get a microsecond. Then, if you take a microsecond and divide that up into a thousand pieces you get a nanosecond.

A nanosecond it one billionth of a second. In four nanoseconds light travels about 47 inches. This computer (and probably yours too) has memory that can be accessed before the light travels from the overhead light in this room to the floor. That's amazing!

That brings up the obvious question, "Then why do I have to wait on my computer so much?" The answer is, you're probably not waiting on the memory. You may be waiting on internet communications, the hard drive, or an inefficient program such as Microsoft Windows. (If you'd like Windows to run faster, email mailto:feedback@microsoft.com and let them know that they're too darned slow!)

Just how fast is this computer? I'm using a notebook computer. It runs faster, has more memory, and has more hard drive space than the mainframe computer they had at Oklahoma State University when I was there in the late seventies. This computer is a 400 mhz computer, which means the CPU runs at 400,000,000 cycles per second. Each machine code instruction takes a few CPU cycles to execute. The first version of DesignCAD (then ProDesign) I wrote was on an 8 mhz PC in 1984.

Sound like a lot of progress in just a few years? It is!

Pi is a number. It's 3.141592624.... with a bunch of digits following. It's an irrational number, which means it can't be represented exactly as one number divided by another. This means that it does not end up with repeating digits, like 1/9 (.111111...) or 4/7 (1.285714285714285714...).

In the 3rd century BC, Mr. Archimedes (the guy with the principle) figured out that pi was between 3 10/71 and 3 1/7. He was a pretty smart guy. About 800 years later, Tsu Chung-Chi in China calculated pi to be between 3.1415926 and 3.1415927. Nobody in Europe got it this close for another 800 years or so. In 1666, Isaac Newton (the guy with the laws) calculated pi to 17 digits.

How good is 17 digits? That's more than my Excel spreadsheets will handle, and plenty for normal floating point arithmetic on computers. But people are curious, and people want more precision. It's a good math problem, too. So people have been working to get a more precise value of pi for a lot of years.

In 1949, the army's Eniac computer computed pi to 2037 digits in about 70 hours. In 1973 Mr. Guilloud computed 1,000,000 digits of pi in a little over 23 hours on a CDC 7600 computer. 10 years later, some people computed 16,000,000 digits of pi on a Hitachi supercomputer. It took a little less than 30 hours. In 1997, one of the same guys and some others computed 51,539,600,000 digits of pi, also on a Hitachi computer. That's a LOT! (Remember all this -- there will be a test on it later.)

So I decided to get in the game. Friday, I calculated pi to 8,000,000 digits or so on this notebook PC in 2 or 3 hours running in the background. That's more and faster than was possible 15 years ago on ANY computer! Want to try it? Here's a program:

super_pi.zip

(For tech support call 800 842-4723, extension 202 or 222.)

If you ever download a program from a web site like mine, you should scan it for viruses before you run it. If you ever get a program as an email attachment, you should also scan that for viruses. I think I checked this one already.... or did I forget???

I decided to look for a bunch of digits of pi on the web. I found LOTS of web site with thousands of digits of pi, and a few with a million or more digits. Then, being the skeptic I am, I wondered, "how do I know this is right?" It's not like you can take a 500,000 digit number and multiply it out to find the circumference of a circle. Yeah, yeah, I realize this is all pretty useless, but it's interesting. At least it's interesting to me, and you're still reading, aren't you?

Anyway, I decided to compare these different "pi-to-the-nth-digit" numbers. Because they're all in different formats, I had to write a program to compare them for me. I was really surprised. Most of the values of pi you find on the web are DIFFERENT! I think it's an alien plot to keep us from reaching Europa. At least I found a couple that were consistent, so either they have the same errors or they're correct. One came from a web site in Japan with 400 million digits of pi. When I checked them with the superpi program, it checked out the same.

So where does that leave us? Here are the first 10,000 digits of pi:

pi10000.htm

If you need more than that for your precision computations, you can download pi to the nearest 8,000,000 digits (4.5 megabytes):

pi.zip

One note on this precision: If you take pi to the nearest 39 digits and use it in calculations involving a circle the size of the universe, it will be accurate to the size of a proton!

Recently some people figured out how to calculate the nth digit of pi (in hex or binary) without calculating all the preceding digits. They divided this job up into subjobs, distributed them to interested people with PCs, and came up with this last February: The 40 trillionth bit of pi is 0.

Starting at the 39,999,999,999,997th bit of pi:

1010 0000 1111 1001 1111 1111 0011 0111 0001 1101

0001 0111 0101 1001 0011 1110 0000

and in hex:

A0F9 FF37 1D17 593E 0

This was done using 126 computer from 18 different countries. It took 84,500 CPU hours on PCs. The next project? The quadrillionth bit of pi. You can help! Check out:

http://www.cecm.sfu.ca/projects/pihex/index.html

And now... PRIME NUMBERS!

Not really. The point is to think about how far math and science has come in recent history. It took 200 years to go from the "invention" of pi to Archimedes' estimate. Then it was another 1900 or so years to get the first seventeen digits. But in the past 50 years we've gone from 2,037 digits to billions of digits of pi. Where will we be in 50 more years?

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I would like to point out that I have not taken a single shot at the news media, politicians, or lawyers today. I do not intend to make a habit of this.