Hamming codes are practical things, while Shannon's analyses of codes were more abstract (though still hugely useful and important)
Consider the checksum bit. It helps to catch errors but there are 2 problems. First, if there is a double error (more likely if the checksum is on a longer string), then the error isn't caught Second, even if we know there is an error, we can't recover, but have to resend.
The easiest error-correcting code is to replace every bit with a triple copy of itself. So
101 becomes 111000111
This way, we can recover from any single error, but the scheme is very inefficient.
Hamming's simplest code takes a 4 bit message and adds 3 very special parity bits (think partial checksums) arranged in a clever way so that any one bit error can be isolated and corrected.
That's the basic idea. The details are many places, such as http://en.wikipedia.org/wiki/Hamming(7,4)

> We all know that the ice is still melting (but slower than we thought).
This year we are going to see a new record low for arctic sea ice --- surpassing even the dramatic 2007 decline.
http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/seaice.recent.arctic.png
What's really startling is that this year, both the NE and the NW passages are completely open. This animation tells the story
http://arctic.atmos.uiuc.edu/CT/animate.arctic.color.0.html
Typically, shipping through the NE passage relies on Russian icebreakers. Judging by the satellite photos, at this point the icebreakers aren't needed
Source: cryosphere today http://arctic.atmos.uiuc.edu/cryosphere/

A recent posting on Watts' blog has clarified a number of issues http://www.rifters.com/crawl/?p=1193 Questions regarding the video tape, the exact timeline, the allegation of a previous police record (he has none) are addressed in the post. The following excerpt deserves to be highlighted IMO

2. The Coverage
The Times-Herald reporter sat in the courtroom throughout the case. She knows there was no assault. She knows the choking incident never occurred. She knows that the only violence was committed by the border guards. These facts are no longer in dispute. And yet, the Times-Herald continues to report that I was found guilty of “assault”, and continues to repeat Beaudry’s allegation that I “choked” him without mentioning that an independent witness utterly discredited his testimony. Unfortunately, while the story has been picked up by numerous other newspapers, most of them simply seem to have cut-and-pasted the Times-Herald reportage. I find this discouraging. As does at least one juror, who opined:

“The Times Herald continues to print that Mr. Watts was found guilty of assault. HE WAS NOT!!! He was found guilty of obstructing/resisting, and that was due to the time that transpired between him being ordered to do something and him actually complying with the order. We were forced to decide what was a reasonable amount of time for him to comply with an order. Mr. Watts, in my opinion, was treated unfairly by Customs and Border Protection. But, unfortunately, they were not on trial.”

The following points were established during the trial. http://www.rifters.com/crawl/?p=1186

• 1. The incident occured as Watts was exiting the US. He was stopped by US border patrol for a random "exit inspection"
• 2. Watts initially got out of the car and requested an explanation. At that point, one of the border patrol officers told him to get back in the car. He did so
• 3. An officer named Beaudry rushed over to the scene, got into the car with Watts, struck him in the face and told him to get out.
• 4. Watts exited the car and Beaudry ordered him to get to the ground.
• 5. Watts did not comply, but rather demanded an explanation.
• 6. Beaudry pepper-spayed watts and threatened him with a baton. At that point Watts lay down, was handcuffed, and placed under arrest.

At no point did Watts engage in a physical confrontation with the CBP officers. Upon cross-examination the "choking" accusation and the "aggressive stance" accusations were shown to have been fabricated.
The conviction stemmed solely from point #5 Here are a couple of post-trial juror statements. One was posted on Watts own site. The other was posted as a comment to the Port Huron report on the verdict; see
http://www.thetimesherald.com/article/20100319/NEWS01/3190308/Jury-remains-out-in-Watts-trial?plckFindCommentKey=CommentKey:e3d49247-c265-47a6-9721-5713e32cc7ed



As a member of the jury that convicted Mr. Watts today, I have a few comments to make. The jury’s task was not to decide who we liked better. The job of the jury was to decide whether Mr. Watts “obstructed/resisted” the custom officials. Assault was not one of the charges. What it boiled down to was Mr. Watts did not follow the instructions of the customs agents. Period. He was not violent, he was not intimidating, he was not stopping them from searching his car. He did, however, refuse to follow the commands by his non compliance. He’s not a bad man by any stretch of the imagination. The customs agents escalted the situation with sarcasm and miscommunication. Unfortunately, we were not asked to convict those agents with a crime, although, in my opinion, they did commit offenses against Mr. Watts. Two wrongs don’t make a right, so we had to follow the instructions as set forth to us by the judge.



Peter,

I believe your description of the trial and deliberations is more accurate than you could know. As a non-conformist and “libertarian” (who has had some experiences not unlike yours) I was not comfortable with my vote, but felt deep inside that it was consistent with the oath we took as jurors. I believe nearly all the jurors searched for a legitimate reason to vote differently. In the end it came down to the question “Was the law broken?”. While I would much rather have a beer and discussion with you than Officer B. I never the less felt obligated to vote my conscience. I also believe most, if not all, the jurors sincerely hope that you are handled with a great degree of leniency, we, unfortunately have no say in that matter.

classical physics = 3 space dimensions relativistic physics = 4 dimensions (space+time) braneworld physics = 5 dimension (space+time+mass) http://superstringtheory.com/experm/exper51.html The holy grail of modern theoretical physics is the unification of quantum and relativistic theory. A key idea here is the possibility that there might be extra, hard-to-perceive dimensions. The braneworld theory say that the extra dimension is mass, so the mass of elementary particles might actually be fluctuating, if ever so slightly. Mass dynamics! Who knows, these ultra fine mass experiments may give us a way to test some of these crazy theories.