Look at the graph: conventional oil and natgas are in decline. Note the super optimistic growth assumptions for unconventional gas and oil. What is the methodology behind this extrapolation? That's the question people should be asking themselves.
Natgas price is at historic lows. Low prices mean small profits mean decreasing investment. These days the unconventional gas industry is facing something of a bust:
Define the function f(x) = (x+2)/(x+1) a function of this type is called a fractional linear transformation
Set x0=1 and iterate using f(x) x1=f(x0) = 3/2=1.5 x2=f(x1)= 7/5=1.4 x3=f(x2) = 17/12 ~ 1.4167 x4=f(x3)=41/29 ~ 1.4138 x5=f(x4)=99/70 ~ 1.4143 x6=f(x5) =239/169 ~ 1.4142
These fractions approximate, indeed converge to the square root of 2
It turns out that in this particular case these fractions are the best possible approximations for sqrt(2)
We know that 1.4142 are the 1st 6 digits of sqrt(2)
sqrt(2) ~ 1+f1 where f1=0.4142.... 1/f1 = 2+f2 where f2=0.41421... 1/f2 = 2+f3 where f3=0.41421...
actually f1=f2=f3=.... ad infinitum
This means that sqrt(2) = 1+ 1/(2+1/(2+1/(2+...)))) The last expression is called a continued fraction
the numbers in it are obtained by subtracting away the whole part taking the reciprocal, subtracting away the whole part, etc
The amazing thing is that for square roots this process isn't random but repeats cyclically. For sqrt(2) the cycle is particularly simple we start with 1 and after that all the #s we get are 2
The numbers 1 1+1/2=3/2 1+1/(2+1/2) = 7/5 1+1/(2+1/(2+1/2)) = 17/12 are the fractions that result from truncating the continued fractions These fractions are the best possible approximations for sqrt(2) ("best possible" has a precise meaning that we don't need to get into here)
Now here is the punchline.
Notice how we get the same fractions by iterating f(x) and by doing the continued fraction expansion
This doesn't happen for all square roots. More interestingly, there can be an infinite overlap in the two sequences of approximations O'Dorney figured out when this happens
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)
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.”
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.
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.
Cut the knot: the best Mathematics site
on
Math Awareness Month
·
· Score: 3, Informative
The best hands-on mathematics experience, hands down, is at
The topics are accessible, and often accompanied with applets.
I've used this material to give math talks to high school kids - they love it.
Here is a real favourite:
Make a polygon by picking a bunch of points on graph paper (just the grid intersection points) and connecting these points by straight lines. The spiky looking thing is technically called a lattice polygon. A really cool way to calculate the area is to (A) count the grid points strictly inside the polygon (B) count the grid points lying exactly on the edges and vertices, then do (A)+(B)/2-1 Voila!
(However, the so-inclined may prefer to fool around with this by themselves, first!)
There are many^(many) phenomena out there like pick's theorem. Call them math paradoxes, or theorems, or whatever, but there's lots of mathematics that is easy to perceive and is mysterious as anything. Mathematics awareness can begin by first learning about and experiencing these brain bending phenomena, and then SEEKING an explanation.
Re:universal ratio: YOU are too a part of the plan
on
The Golden Ratio
·
· Score: 1
This is well know for the Fibonacci sequence
F(n+1)/F(n) tends in the limit to the golden ratio
Slashdot Mirror
alt dot org slash nethack
watch the ttyrecs
choose the name that's right for you
dare to compare
The headline is based on the latest IEA (International Energy Agency) forecast called the "2012 World Energy Outlook"
Follow the link to a graph of what is being forecast and to the report in question:
http://earlywarn.blogspot.fr/2012/11/iea-us-to-be-worlds-largest-oil-producer.html
Look at the graph: conventional oil and natgas are in decline.
Note the super optimistic growth assumptions for unconventional gas and oil.
What is the methodology behind this extrapolation? That's the question people should be asking themselves.
Natgas price is at historic lows. Low prices mean small profits mean decreasing investment.
These days the unconventional gas industry is facing something of a bust:
http://www.nytimes.com/2012/10/21/business/energy-environment/in-a-natural-gas-glut-big-winners-and-losers.html?pagewanted=all&_r=0
How well does that fit with the optimistic growth scenario?
Also, the IEA does not exactly have a sterling reputation for balanced impartial forecasts:
http://www.guardian.co.uk/environment/2009/nov/09/peak-oil-international-energy-agency
Just because something is a headline, doesn't mean it's true. Time will tell, of course.
Here is a calculation to illustrate the main idea
Define the function f(x) = (x+2)/(x+1)
a function of this type is called a fractional linear transformation
Set
x0=1
and iterate using f(x)
x1=f(x0) = 3/2=1.5
x2=f(x1)= 7/5=1.4
x3=f(x2) = 17/12 ~ 1.4167
x4=f(x3)=41/29 ~ 1.4138
x5=f(x4)=99/70 ~ 1.4143
x6=f(x5) =239/169 ~ 1.4142
These fractions approximate, indeed converge to the square root of 2
It turns out that in this particular case these fractions are the best possible approximations for sqrt(2)
We know that 1.4142 are the 1st 6 digits of sqrt(2)
sqrt(2) ~ 1+f1 where
f1=0.4142....
1/f1 = 2+f2 where
f2=0.41421...
1/f2 = 2+f3 where
f3=0.41421...
actually f1=f2=f3=.... ad infinitum
This means that
sqrt(2) = 1+ 1/(2+1/(2+1/(2+...))))
The last expression is called a continued fraction
the numbers in it are obtained by subtracting away the whole part taking the reciprocal, subtracting away the whole part, etc
The amazing thing is that for square roots this process isn't random but repeats cyclically. For sqrt(2) the cycle is particularly simple
we start with 1 and after that all the #s we get are 2
The numbers
1
1+1/2=3/2
1+1/(2+1/2) = 7/5
1+1/(2+1/(2+1/2)) = 17/12
are the fractions that result from truncating the continued fractions
These fractions are the best possible approximations for sqrt(2) ("best possible" has a precise meaning that we don't need to get into here)
Now here is the punchline.
Notice how we get the same fractions by iterating f(x) and by doing the continued fraction expansion
This doesn't happen for all square roots.
More interestingly, there can be an infinite overlap in the two sequences of approximations
O'Dorney figured out when this happens
http://www.maa.org/abstracts/mf2010-abstracts.pdf
See page 13
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/
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:
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.
The best hands-on mathematics experience, hands down, is at
http://www.cut-the-knot.org/
The topics are accessible, and often accompanied with applets.
I've used this material to give math talks to high school kids - they love it.
Here is a real favourite:
Make a polygon by picking a bunch of points on graph paper (just the grid intersection points) and connecting these points by straight lines. The spiky looking thing is technically called a lattice polygon. A really cool way to calculate the area is to (A) count the grid points strictly inside the polygon (B) count the grid points lying exactly on the edges and vertices, then do (A)+(B)/2-1 Voila!
The applet and explanation is here:
http://www.cut-the-knot.org/ctk/Pick.shtml
(However, the so-inclined may prefer to fool around with this by themselves, first!)
There are many^(many) phenomena out there like pick's theorem. Call them math paradoxes, or theorems, or whatever, but there's lots of mathematics that is easy to perceive and is mysterious as anything. Mathematics awareness can begin by first learning about and experiencing these brain bending phenomena, and then SEEKING an explanation.
This is well know for the Fibonacci sequence F(n+1)/F(n) tends in the limit to the golden ratio