If you drive up 148th early in the morning this time of year, there’s usually a lot of steam coming off of Larson Lake.
This morning I stopped to take a few pictures, and I found myself thinking about the fact that Alice Cooper was probably teeing off right about then.
Keith is right, this is just too good to pass up: a spam email whose intended victims are people who want to hack into other people’s computers.
Finally, some vigilante justice on the internet. String ‘em up, boys!
Speaking of the ever-escalating War on Spam, in the last week my blog has received dozens of porn-spam comments (which I’ve deleted), and most of them have been posted to this particular entry: Wedding Cake Planning. I have no idea why.
A year ago today, hurricane Katrina hit the Gulf Coast of Mississippi. It also caused damage in nearby New Orleans, but the most intense portion of the storm — and the most severe damage — occurred in the area around Bay St. Louis and Waveland, east of Pass Christian. Several members of Megan’s family lost their homes and everything in them: Granny, Marsha, Gloria, Lyndon, Buster, and a few others I’m not remembering right now.
Is it just me, or does Katrina seem like a lot more than a year ago?
A few days after the hurricane hit, Megan and I went to Gulfport to help relatives in the area.
In hindsight, it was fun for us in some ways. We spent our days touring the area, taking thousands of pictures of unbelievable destruction, helping dig through the debris for a few mementos, and taking trips back and forth to Mobile for gasoline and other supplies. In the evenings we returned to Melba’s house in Gulfport, where we all hung out and talked about what had happened by flashlights and candlelight, saving the generator’s power for the fans that would run all night. When National Guard helicopters landed nearby to drop off fresh water and ice, we ran to the park and watched the scene unfold.
We also met various people who had survived harrowing ordeals. Like Greg Campbell, who rescued Diane Brugger from a tree she was clinging to after her husband Tony had been swept away along with their home. To walk through the wreckage with people like that and hear them calmly tell their stories was an emotionally powerful experience that I still can’t properly describe.
The ugliness of New Orleans was most of what we heard about on the battery-powered portable radio, but in Mississippi all we saw was people pulling together and helping each other through a tough time. There were many random acts of kindness and compassion, and we never heard a single story of anyone being attacked in any way or losing anything to looters. When I got back home and saw all the coverage of the thugs of New Orleans, it pissed me off so much that I wrote angry letters to a few editors about the sleaze they sell.
Here’s the link to the photos I posted after our first post-Katrina trip to Mississippi, and here are the photos from our return three weeks later.
Our trips to the Gulf Coast after Katrina included a lot more laughter and smiling than you might imagine, not least because we were lucky enough to not lose a single life in the family. Even Lyndon’s dog survived. Check out Lyndon’s house, and imagine what that dog experienced. Lyndon suffered a heart attack last week. He had surgery and last we heard he’s doing better. Hang in there, Lyndon — after all your family has been through, a heart attack is just a bump in the road.
The day Granny left Pass Christian, she talked about Katrina as if she were a person. “Katrina, that hussy, she took everything.” Granny’s family had lost everything to hurricane Camille back in 1969, too. But after Katrina, Granny decided that two once-in-a-lifetime hurricanes are enough for one lifetime, so she and Marsha moved to Atlanta.
Happy birthday, Katrina. You bitch.
“Only two players have ever truly owned their swings: Moe Norman and Ben Hogan. I want to own mine. That’s where the satisfaction comes from.”
- Tiger Woods, speaking to Jaime Diaz of Golf Digest
Hey Mom, hope you like this picture of your four sons. We’re not getting into any kind of trouble, not fighting with teachers or the law or each other, just playing a bit of golf on a sunny day like perfect little gentlemen. Didn’t we turn out great?
I played golf today with my brothers at Willows Run (Coyote Creek course). We’ve all played together as a foursome a few times before, but not for many years. By the way, for those who don’t know us, the order in the photo is Doug-Brad-Greg-Ken. I’m the oldest (by age it goes Doug-Greg-Ken-Brad) and the shortest (that order also goes Doug-Greg-Ken-Brad).
Greg, Brad, and I are golfers, dogged victims of inexorable fate. We’ve all gone through phases of loving and hating the game, phases of playing well and often, not well and not often, and other less logical combinations.
Ken, on the other hand, doesn’t play except for a rare round with friends or his brothers. Some years he never gets the clubs out at all.
Today Ken shot 119, and the rest of us were in the 86-97 range. (That’s my faux-modest way of saying I shot the low score, of course.)
We had great weather and great conditions. We started behind a group outing, but they had a shotgun start earlier in the day and the foursome we were following had started on #9. So we had to wait a bit on the front nine, but suddenly on #9 we had nobody ahead of us on the rest of the course, because they were all done. So on the back nine we never waited for anyone or had anyone close behind. It’s pretty rare to get that on a sunny summer weekend at a busy course.
I meant to hit my hybrid more today, because I’ve been hitting it well at the range in the last week, and in my last round of golf I hit some good shots with it. But that club surprised me with its inconsistency — I only hit it three times, twice poorly.
My driver, though, was the best it’s been all year. I hit 2-iron pretty well off the first tee, so tried driver on #2 and hit it long and straight, so I stuck with the driver all day. I hit a bunch of good drives that left me wedge shots to the par 4s, and had makeable birdie putts on a couple of par 5s (both of which I missed). I started snap-hooking it on the last few holes, but hey I’m the oldest and I was probably getting a bit tired.
Greg had a new Ping driver he was hitting really well. He has all new Ping clubs this year, and he hit some great shots with them. Ken hit Greg’s new driver quite a few times, and grooved a simple little swing that consistently knocked a 200-yard low fade down the middle. One of the fun things about golfing with Ken is that he’s always like a guy the first time out, eager to figure out how to advance the ball. The last time Ken hit Greg’s driver well, Greg wasn’t hitting it very well that day and Ken got a free driver at the end of the round. But today the new Ping was still in Greg’s bag when he left.
It was a fun round, and everyone hit some great shots and terrible shots. I had an interesting stretch on holes 5 through 9: birdie, birdie triple-bogey, triple-bogey, birdie. Effortless shots to the green on three of those holes, hand-jarring mis-hits on the other two. That’s so me.
By the 15th hole, we were all warmed up and enjoying our private back nine with no other golfers around. I hit a sneaky long drive, a low draw that bounced and rolled a mile, not least because the second bounce was a big forward leap off a cart path and back into the fairway. Greg then hit his new driver with the swing of the day, a long high draw that landed just short of mine and stopped quickly. Both balls were about 300 yards off the tee.
Brothers golf offers a great combination of competition and comfort, rivalry and familiarity. The next hole, #16, is a short par 4 with a very narrow fairway that curves left around a water hazard. Water left all the way, trees and rough terrain long and right. The green is only 250 yards away, so both Greg and I went for it after our big drives on the previous hole. And we both wound up in trouble right of the fairway, which we exacerbated by hitting poor shots from there on the way to double bogeys. Brad and Ken hit sensible shots off the tee, knocked it on in two, and Brad sunk a 25-footer for birdie while Ken merely 2-putted for par.
And a good time was had by all. We should do this more often.
Hmm, today isn’t going as planned. I was going to work from home and get some things done that require a bit of peace and quiet. But last night I suddenly couldn’t get into Outlook Web Access. I haven’t had any problems with this before, so I figured it was something temporary. But this morning, same deal. So I drove Megan to work, and tried to connect from her building. Same problem. So I tried Outlook, but I haven’t run Outlook on this laptop since moving to Exchange 2007 last week, so I had to delete and re-create my profile, and now I’ve been waiting nearly an hour for all my folders to re-synch so that I can have that ultra-productive day I need to have today. Geez.
Anyway, I’ve been catching up on my RSS feeds. Lots of good stuff happening in the Open XML world, which I’ll be blogging about over on MSDN later today. But I also enjoyed reading the latest from Juan Cole. It’s great to see him giving John Bolton the respect he deserves. With all Bolton has done to help this country, from backing the Contras to sabotaging the UN to lobbying for fewer restrictions on chemical weapons and being a paid stooge of the Taiwan government, he has earned it. That’s why I’ve been a big Bolton fan for years. If you’re afraid, and wish everyone else was scared too, Bolton can help. He understands how you feel.
OK, I better get back to work …
How can you tell if a big number is prime? The number 23,571,113,171,923, say: is that prime? Where do you start?
Sure, you could write a program to check every integer up to the square root of your number, and if none of those divide evenly into it then you have a prime. But suppose you wanted to figure this kind of thing out without a computer? (Really, people used to do stuff like this.)
10 and its close cousins 2 and 5
I’ll bet if the number above ended in 0, most folks would intuitively know it isn’t prime. Ending in 0 is a sure-fire clue that the number is probably divisible by 10, don’t you think? (Assuming base-10 notation, of course.)
And if the number ends in 2, 4, 6, or 8, most folks would intuitively know that it’s even, divisible by 2, and therefore not prime.
When you’re checking whether a number is divisible by two, did you ever think about why you only need to check the last digit? One way to look at it is that you only need to check the last digit because that’s how much greater your number is than a known multiple of 10, and 10 is divisible by 2. That same sort of thinking applies to determining whether a number is divisible by greater powers of 2. It works like this:
To check if a number is divisible by 2, you only need to check whether the last 1 digits are divisible by 2, because 10 is divisible by 2.
To check if a number is divisible by 4, you only need to check whether the last 2 digits are divisible by 4, because 100 is divisible by 4.
To check if a number is divisible by 8, you only need to check whether the last 3 digits are divisible by 8, because 1000 is divisible by 8.
To check if a number is divisible by 16, you only need to check whether the last 4 digits are divisible by 16, because 10000 is divisible by 16.
And for identical reasons, since 10 is 2 times 5, this sort of thinking works for checking whether a number is divisible by powers of 5:
Check the last 1 digits for divisibility by 5 (because 10 is divisible by 5)
Check the last 2 digits for divisibility by 25 (because 100 is divisible by 25)
Check the last 3 digits for divisibility by 125 (because 1000 is divisible by 125)
Check the last 4 digits for divisibility by 625 (because 10000 is divisible by 625)
Well, that’s just dandy. But what about checking for divisibility by numbers that aren’t factors of 10, the base of our numbering system?
Divisible by 3 or 9?
Many people know this one: to determine whether a number is divisible by 3, add up the digits in the number. If the result is divisible by 3, then the original number is divisible by 3 too. You can use this as a quick way to show that the number mentioned above is not divisible by 3.
Note that you can also add up the digits of the result of the calculation, to determine whether it is divisible by 3, and continue collapsing your number until it gets down to something that’s obviously divisible by 3 or not. So in our example above, the digits of 23,571,113,171,923 add up to 46, whose digits add up to 10, whose digits add up to 1, which is not divisible by 3, so neither is the original number.
Divisibility by 9 works the same way: if the digits add up to a number that’s divisible by 9, then — and only then — the original number was also divisible by 9.
As it says in all those math books, “proof of this assertion will be left as an exercise for the reader.”
Divisible by 7?
This is a personal favorite of mine: remove the last digit, double it, and subtract that from the remaining number. This manipulation preserves the 7-divisibility of the original number. (Proving this one is even more fun than the 3s/9s rule.)
For example, is 142857 divisible by 7?
Take off the 7, double it to 14, subtract that from 14285: the result is 14271
Take off the 1, double it to 2, subtract that from 1427: result is 1425
Take off the 5, double it to 10, subtract that from 142: result is 132
Take off the 2, double it to 4, subtract that from 13: result is 5
And 5 isn’t divisible by 7, so neither is 142857.
Divisible by 11?
For Divisibility by 11, you take the first digit, subtract the 2nd digit, add the 3rd digit, and so on, all the way to the end of the number. The result of this process will be exactly as “divisible by 11″ as your original number. Specifically, the result has the same remainder when divided by 11 as your original number has when divided by 11. (Proving this one is a bit simpler than the case for 7 above.)
Is 121 divisible by 11? Yes, because 1-2+1=0, the remainder when 121 is divided by 11. Is 142857 divisible by 11? Yes, because 1-4+2-8+5-7=-11, the “remainder” when 142857 is divided by 11. (If the remainder is divisible by 11, so is the original number. Prove that, Pythagoras.)
Divisible by larger primes?
There are many more of these types of tricks for larger primes factors, but they grow increasingly complex as the factors get larger. Well, some are simple, such as the rule for 19, which is like the rule for 7 except you add the doubled digit instead of subtracting it. I used to know these up through 29, but don’t use them much any more and can’t remember 13, 17, 23 and 29. Here’s a page with the rules for testing divisibility by all the primes less than 50.
“On the factorization of large numbers”
The French mathematician Marin Mersenne made an assertion in 1644 whose validity was still being openly debated over 200 years later. I’m not going to bother to explain it (check out Mersenne.org if you’re really interested) except to say that it involves predicting whether numbers of the form 2 to the N minus 1 are prime.
As of 1903, it was still unknown whether M67 (Mersenne number 67), which is 2 raised to the 67th power less one, was a prime. If it was proved to not be prime, then Mersenne’s conjecture would be disproven. The problem is, Mersenne’s numbers grew very rapidly, and it could take a person months to do the longhand arithmetic involved in searching for divisors of large numbers. M67, for example, is over 20 digits long.
So when mathematician F. N. Cole demonstrated that M67 was not a prime in 1903, it was an impressive achievement. And there’s a great story of how Cole announced his finding, which was written up by Eric Temple Bell in his essay “The Queen of Mathematics.” I’ve quoted Bell’s description below, from my copy in James R. Newman’s 4-volume hardcover book series “The World of Mathematics,” published by Simon & Schuster in 1956. (My Dad had these books in the living room, and so do I. They’re great stuff if you like math stories, and they’ve been re-issued in a Dover paperback edition.)
Anyway, here is Bell’s description of Cole’s feat from Newman’s book:
I should like here to preserve a small bit of history before all the American mathematicians of the first half of the twentieth century are gone. When I asked Cole in 1911 how long it had taken him to crack M67 he said “three years of Sundays.” But this, though interesting, is not the history. At the October, 1903, meeting in New York of the American Mathematical Society, Cole had a paper on the program with the modest title On the factorization of large numbers. When the chairman called on him for his paper, Cole — who was always a man of very few words — walked to the board and, saying nothing, proceeded to chalk up the arithmetic for raising 2 to the sixty-seventh power. Then he carefully subtracted 1. Without a word, he moved over to a clear space on the board and multiplied out, by longhand,
193,707,721 x 761,838,257,287
The two calculations agreed.
Mersenne’s conjecture — if such it was — vanished into the limbo of mathematical mythology. For the first and only time on record, an audience of the American Mathematical Society vigorously applauded the author of a paper delivered before it. Cole took his seat without having uttered a word. Nobody asked him a question.
Man, if that story doesn’t give you goosebumps, what does?
I was looking through my photos for a shot of Mount Si Golf Course from the top of Mount Si, and came across this shot of Megan at Harrington Golf Course last August. So I decided to make it the header for this week. See, I’m the decider around here.
It’s official: Pluto is no longer a planet. After 76 years as an imposter, experts have put an end to Pluto’s attempts to “take the magic out of the solar system” and have reclassified it as a “dwarf” planet. You see, Pluto’s not big enough to be a planet, and its orbit doesn’t follow the official rules for planets.
I’m a bit worried. When one of those chunks of rock and ice decides to become a martyr and crash into Earth on a suicide mission, we’ll regret the policies that led them to feel marginalized like this. Oh well, if we get into a War on Interplanetary Terrorism it’s nice to know we have a “War President” ready, willing and able to do the needful.
There has been a dramatic increase in the volume of blog spam in recent weeks. I’ve seen colleagues from all around the world complaining about it, and many sites have added CAPTCHA logic to try to weed out the spam.
CAPTCHA stands for (roughly) “Completely Automated Public Turing test to tell Computers and Humans Apart,” and the concept is simply this: add a required step for posting on a blog that will identify whether the sender is a human or a computer program. For example, some sites (Tom’s comes to mind) display a few characters that are distorted in a way that prevents OCR software from reading them accurately, and you have to decipher the characters and then type them in. If you’re a human with a normally functioning brain, it’s not too hard to do, but the spam-bots can’t get past that step.
I started to install a CAPTCHA add-on on this blog a while back, but ran into some technical issues and never finished it up. And frankly, some days I’m glad I didn’t. The bastardized English in which many of the porn spam comments are written can sometimes provide a nice moment of amusement, and it doesn’t take more than a few seconds to scan a couple dozen new messages and mark them as spam.
But I’m thinking there’s an approach that I’d like to implement eventually, when technology like this is widely available. If I could install a filter like that, I think I’d be ready to turn the tables: instead of me being amused by randomly generated spam comments that nobody else sees, you could all be amused by randomly generated collections of photos that I never see.
Stay tuned, developers are surely working around the clock to serve this market …
