From the Manifesto Club comes this news of a poem removed by the AQA (the awarding body for A-level exams and GCSE's) from the GCSE (General certificate of secondary education) syllabus in Great Britain.
The poem is entitled "Education for Leisure" and was written by the award-winning poet, Carol Ann Duffy. It can be found here.
Syllabi change all the time, but this case is special, since the decision to remove it was spurred by an exam invigilator, Pat Schofield, who apparently felt the poem glorified knife crime. She is quoted as saying, "I think it is absolutely horrendous - what sort of message is that to give to kids who are reading it as part of their GCSE syllabus?"
What's next, banning The Charge of the Light Brigade because it glorifies suicidal military exploits?
The AQA itself responded with these weasel words: "The decision to withdraw the poem was not taken lightly and only after due consideration of the issues involved. We believe the decision underlines the often difficult balance that exists between encouraging and facilitating young people to think critically about difficult but important topics and the need to do this in a way which is sensitive to social issues and public concern."
It looks like Carol Ann Duffy got the last laugh, however. She's written a response entitled Mrs. Schofield's GCSE. How fitting that Schofield, like Bowdler, will pass into the language as a synonym for small-minded censorship.
Mrs Schofield's GCSE
Carol Ann Duffy
You must prepare your bosom for his knife,
said Portia to Antonio in which
of Shakespeare's Comedies? Who killed his wife,
insane with jealousy? And which Scots witch
knew Something wicked this way comes? Who said
Is this a dagger which I see? Which Tragedy?
Whose blade was drawn which led to Tybalt's death?
To whom did dying Caesar say Et tu? And why?
Something is rotten in the state of Denmark - do you
know what this means? Explain how poetry
pursues the human like the smitten moon
above the weeping, laughing earth; how we
make prayers of it. Nothing will come of nothing:
speak again. Said by which King? You may begin.
Friday, October 31, 2008
Monday, October 20, 2008
McCain Mangles English Again
I wrote about this before. John McCain mangles English almost as much as George Bush. On two occasions he's used the nonexistent word "epitat" instead of "epithet", and now a report from the Boston Globe has him saying "predicate" instead of "precedent".
Sunday, October 19, 2008
Guitarist Tony McManus in Elora
One of the nicest things about having a blog is meeting interesting people online, and then in real life. (Of course, you also meet some unpleasant loonies, but that's fodder for another post.)
Last May Recursivity got some fan mail from Tony McManus, a guitarist who lives in nearby Elora, Ontario. Actually, calling him a "guitarist" is somewhat of an understatement; he has been called "the best Celtic guitarist in the world". Tony studied ring theory under Peter Vámos at the University of Exeter before giving up mathematics for music.
Tony was kind enough to leave tickets for me and my family to attend his concert in Elora, and last night we all went. Tony's music was phenomenal, combining an intense virtuosity with a percussive style that left the audience breathless. He predominantly played Celtic tunes, but there was quite a lot of variety (including a Bulgarian piece and two pieces played on a special guitar, designed by a Toronto guitar maker, that sounds like a sitar). The variety of sounds he can get from a guitar made me really envious. In between tunes, Tony told us a lot of great stories about drunk Celtic musicians. We all had a terrific time.
Tony was accompanied by Rolly Brown, a fingerpicker now living in Bucks County, Pennsylvania, near where I grew up. In addition to guitar, Rolly is an acupuncturist, a Tai Chi instructor, and he raises Australian dogs. Rolly played some Reverend Gary Davis, Steve Mann, and he closed with a take-off on Julie Gold's "From a Distance" (made famous by Nanci Griffith) written by Jay Mankita in 1992: "From a Dog's Stance". The audience was in stitches.
If you ever get a chance to see Tony McManus or Rolly Brown, take it! Tony gives concerts and workshops all across the world. I guarantee you'll have a great time.
Sunday, October 05, 2008
Thursday, September 25, 2008
My Favorite Living Mathematician
Ionica Smeets, of the Dutch website Wiskundemeisjes (Math girls), recently asked me to name my favorite living mathematician. Her version of my answer, and some additional text, can be found (in Dutch) here.
Smeets also kindly allowed me to post my response here.
1. Who is your favorite still living mathematician?
I have many favorites, and it's hard to choose: Alf van der Poorten, Carl Pomerance, Michel Mendès France, Donald Knuth, Adi Shamir, Manuel Blum, just to name a few. But if you force me to choose, I think I would have to say that my favorite is the Dutch mathematician Hendrik W. Lenstra, Jr.
2. Why do you admire him/her?
I admire the beauty of his results and his talent for exposition. To list just two of his famous results:
- the Lenstra-Lenstra-Lovász algorithm for lattice basis reduction, which led to a fast algorithm for factoring polynomials with integer coefficients, and has also given us new ways to attack cryptosystems
- the Lenstra elliptic curve factoring algorithm, which allows us to efficiently find small factors of very large numbers
3. What is special about his/her work?
First, Hendrik Lenstra has a really deep understanding of algebra, so intimate that he can see almost instantly how to solve problems that would take others hours or days.
Second, his exposition is always precise. Unlike some other top-flight mathematicians, who are often a little too casual in their proofs, Hendrik doesn't feel it is beneath his dignity to provide details. When you read one of his papers, you get the feeling that every sentence has been chosen with economy and clarity in mind.
Third, Lenstra has a wide variety of interests, and doesn't hesitate to think seriously about things that others might dismiss as 'recreational'. I point in particular to his work on the mathematics of the Dutch artist M. C. Escher and his delightful paper on profinite Fibonacci numbers.
4. Have you ever worked together?
Yes, we wrote one paper together, "Continued fractions and linear recurrences", which appeared in the journal Mathematics of Computation in 1993. To explain what we did, I have to remind your readers about the two subjects of the title.
Every real number has an essentially unique expansion as a continued fraction, that is, an expression of the form x = a+1/(b+1/(c+ ....)), where all the terms, except possibly the first, are positive integers. For example, π = 3+1/(7+1/(15+ 1/(1 + ...))). When you truncate a continued fraction after n terms, you get better and better rational approximations to the original number. For example, one term of the continued fraction for π gives 3, two terms gives 22/7, three terms gives 333/106, four terms gives 355/113, etc. These fractions are called the convergents and are usually written as pn / qn .
Another thing your readers probably know about is linear recurrences. A simple example of a linear recurrence is the recurrence that gives the Fibonacci numbers: each term of the Fibonacci sequence is the sum of the two previous. When we generalize this to "each term is a linear combination of a fixed number of previous terms", we get the sequences defined by linear recurrences with constant coefficients.
In our paper we combined these two ideas, and asked, "When are the sequences pn and qn linear recurrences?" The answer is not unexpected: this situation can occur if and only if the original number is the root of a quadratic equation, such as the square root of 2, or the golden ratio. However, the proof was unexpectedly hard, and we had to rely on a very deep theorem, the Hadamard quotient theorem of Alf van der Poorten. Later, Andrew Granville found a simpler argument that avoided the need for this difficult theorem.
5. What kind of person is he/she?
Hendrik Lenstra is very much a picture of the traditional European intellectual: always impeccably dressed in a suit and tie, knowledgeable in many fields, and not afraid to show it, sometimes at the expense of those who know less. (I remember once him laughing at me because I did not know whether the root of a word was Latin or Greek.) But he is also extremely kind. Once, when I was hospitalized in the Netherlands following a talk in Leiden, he came to visit me each day in the hospital, bringing me excellent things to read, including The Assault by Dutch author Harry Mulisch.
Hendrik exhibits a playful sense of humor and appreciates a good pun. It was he who once told me about the longest "square" in English: hotshots, which can be written as (hots)2 . (The longest squares I know in Dutch are tenten and kerker .) I also remember him quipping that "Shakespeare's plays weren't written by Shakespeare, but by another man with the same name." (It gets more profound the more you think about it!)
Hendrik is a collector of unusual and antiquarian books. He has a fondness for the Greek poet Homer. Knowing my interest in the crank mathematical literature, he once gave me a copy of the crackpot work The Life-Romance of an Algebraist by George Winslow Pierce, a book I still treasure in my personal collection.
6. Is there a nice story you know about him/her?
One of my nicest memories of time spent with Hendrik was our trip to watch the annular solar eclipse visible from southern Ontario on May 10, 1994. An annular eclipse occurs when the Moon comes between the Sun and the Earth, but is farther away than normal, so that all but a tiny outer ring of the Sun is covered. The sky took on a very unusual appearance, and you could see images of the sun in the diffraction patterns made by the leaves on the trees.
Hendrik wrote a paper called "Mathematics and misunderstanding" which I have not been able to read, since it has appeared only in Dutch. But a reviewer of the paper summed up the argument as follows: "It is the author's contention that the true motivation for doing mathematical research is insight into one's own lack of understanding. The hallmark of the true researcher is his or her ability to recognize, in a seemingly wholly satisfactory theory, points which on closer inspection appear to be not fully understood and hence need further clarification."
Hendrik does not like saying in a paper that something "must be true". He once wrote to me as follows:
"I am not as dogmatic about this as X, who used to ask me when I was a student: if something MUST be true, then IS it true? I think the answer is yes, but X apparently had a supernatural fear that if you FORCE something it may become recalcitrant and misbehave."
For some other quotes of Hendrik Lenstra, see here.
Smeets also kindly allowed me to post my response here.
1. Who is your favorite still living mathematician?
I have many favorites, and it's hard to choose: Alf van der Poorten, Carl Pomerance, Michel Mendès France, Donald Knuth, Adi Shamir, Manuel Blum, just to name a few. But if you force me to choose, I think I would have to say that my favorite is the Dutch mathematician Hendrik W. Lenstra, Jr.
2. Why do you admire him/her?
I admire the beauty of his results and his talent for exposition. To list just two of his famous results:
- the Lenstra-Lenstra-Lovász algorithm for lattice basis reduction, which led to a fast algorithm for factoring polynomials with integer coefficients, and has also given us new ways to attack cryptosystems
- the Lenstra elliptic curve factoring algorithm, which allows us to efficiently find small factors of very large numbers
3. What is special about his/her work?
First, Hendrik Lenstra has a really deep understanding of algebra, so intimate that he can see almost instantly how to solve problems that would take others hours or days.
Second, his exposition is always precise. Unlike some other top-flight mathematicians, who are often a little too casual in their proofs, Hendrik doesn't feel it is beneath his dignity to provide details. When you read one of his papers, you get the feeling that every sentence has been chosen with economy and clarity in mind.
Third, Lenstra has a wide variety of interests, and doesn't hesitate to think seriously about things that others might dismiss as 'recreational'. I point in particular to his work on the mathematics of the Dutch artist M. C. Escher and his delightful paper on profinite Fibonacci numbers.
4. Have you ever worked together?
Yes, we wrote one paper together, "Continued fractions and linear recurrences", which appeared in the journal Mathematics of Computation in 1993. To explain what we did, I have to remind your readers about the two subjects of the title.
Every real number has an essentially unique expansion as a continued fraction, that is, an expression of the form x = a+1/(b+1/(c+ ....)), where all the terms, except possibly the first, are positive integers. For example, π = 3+1/(7+1/(15+ 1/(1 + ...))). When you truncate a continued fraction after n terms, you get better and better rational approximations to the original number. For example, one term of the continued fraction for π gives 3, two terms gives 22/7, three terms gives 333/106, four terms gives 355/113, etc. These fractions are called the convergents and are usually written as pn / qn .
Another thing your readers probably know about is linear recurrences. A simple example of a linear recurrence is the recurrence that gives the Fibonacci numbers: each term of the Fibonacci sequence is the sum of the two previous. When we generalize this to "each term is a linear combination of a fixed number of previous terms", we get the sequences defined by linear recurrences with constant coefficients.
In our paper we combined these two ideas, and asked, "When are the sequences pn and qn linear recurrences?" The answer is not unexpected: this situation can occur if and only if the original number is the root of a quadratic equation, such as the square root of 2, or the golden ratio. However, the proof was unexpectedly hard, and we had to rely on a very deep theorem, the Hadamard quotient theorem of Alf van der Poorten. Later, Andrew Granville found a simpler argument that avoided the need for this difficult theorem.
5. What kind of person is he/she?
Hendrik Lenstra is very much a picture of the traditional European intellectual: always impeccably dressed in a suit and tie, knowledgeable in many fields, and not afraid to show it, sometimes at the expense of those who know less. (I remember once him laughing at me because I did not know whether the root of a word was Latin or Greek.) But he is also extremely kind. Once, when I was hospitalized in the Netherlands following a talk in Leiden, he came to visit me each day in the hospital, bringing me excellent things to read, including The Assault by Dutch author Harry Mulisch.
Hendrik exhibits a playful sense of humor and appreciates a good pun. It was he who once told me about the longest "square" in English: hotshots, which can be written as (hots)2 . (The longest squares I know in Dutch are tenten and kerker .) I also remember him quipping that "Shakespeare's plays weren't written by Shakespeare, but by another man with the same name." (It gets more profound the more you think about it!)
Hendrik is a collector of unusual and antiquarian books. He has a fondness for the Greek poet Homer. Knowing my interest in the crank mathematical literature, he once gave me a copy of the crackpot work The Life-Romance of an Algebraist by George Winslow Pierce, a book I still treasure in my personal collection.
6. Is there a nice story you know about him/her?
One of my nicest memories of time spent with Hendrik was our trip to watch the annular solar eclipse visible from southern Ontario on May 10, 1994. An annular eclipse occurs when the Moon comes between the Sun and the Earth, but is farther away than normal, so that all but a tiny outer ring of the Sun is covered. The sky took on a very unusual appearance, and you could see images of the sun in the diffraction patterns made by the leaves on the trees.
Hendrik wrote a paper called "Mathematics and misunderstanding" which I have not been able to read, since it has appeared only in Dutch. But a reviewer of the paper summed up the argument as follows: "It is the author's contention that the true motivation for doing mathematical research is insight into one's own lack of understanding. The hallmark of the true researcher is his or her ability to recognize, in a seemingly wholly satisfactory theory, points which on closer inspection appear to be not fully understood and hence need further clarification."
Hendrik does not like saying in a paper that something "must be true". He once wrote to me as follows:
"I am not as dogmatic about this as X, who used to ask me when I was a student: if something MUST be true, then IS it true? I think the answer is yes, but X apparently had a supernatural fear that if you FORCE something it may become recalcitrant and misbehave."
For some other quotes of Hendrik Lenstra, see here.
Wednesday, September 17, 2008
I Won't Be Attending Graduation at the University of Alberta Any Time Soon
...and here's why.
A publicly-funded university shouldn't be instructing its students to do something "for the glory of God".
You can write the President of the University of Alberta, Indira V. Samarasekera, to express your displeasure with her university's actions.
A publicly-funded university shouldn't be instructing its students to do something "for the glory of God".
You can write the President of the University of Alberta, Indira V. Samarasekera, to express your displeasure with her university's actions.
City Puzzle
What country's current capital city has a name that can be cyclically shifted some number of letters to get the name of its former capital?
Wednesday, September 03, 2008
My New Book is Out!
My new book, A Second Course in Formal Languages and Automata Theory, is out!
Here's a web page that tells you a little more about the book. And, if you absolutely have to have your own copy, you can buy it at Amazon or Barnes and Noble.
Here's a web page that tells you a little more about the book. And, if you absolutely have to have your own copy, you can buy it at Amazon or Barnes and Noble.
Sunday, August 24, 2008
Failed Olympic Medal Predictions
Leading up to the Olympics, there was a lot of hype about the work of Colorado College economist Daniel K. N. Johnson and his predictions about the Olympic medal count. For example, he was interviewed on NPR and featured in the Wall Street Journal. Prof. Johnson's method was based on five factors only: GDP per capita, total population, political structure, climate, and home-nation bias, and was touted as "remarkably accurate".
Now the results are in. Here are Johnson's predictions of the top ten medal winners, compared to the actual total these countries won:
Rating a prediction p as good if .75r ≤ p ≤ 1.25r, where r is the actual result, I'd say Johnson made 3 good predictions out of his top 10: China, USA, and Italy. And he made some really bad ones, including Hungary, Great Britain, and Australia. Altogether, Johnson's predictions don't deserve a place at the podium.
Now the results are in. Here are Johnson's predictions of the top ten medal winners, compared to the actual total these countries won:
| Country | Johnson's prediction | Actual result |
| USA | 103 | 110 |
| Russia | 95 | 72 |
| China | 89 | 100 |
| Germany | 66 | 41 |
| Japan | 37 | 25 |
| Hungary | 31 | 10 |
| Italy | 29 | 28 |
| Great Britain | 28 | 47 |
| France | 27 | 40 |
| Australia | 26 | 46 |
Rating a prediction p as good if .75r ≤ p ≤ 1.25r, where r is the actual result, I'd say Johnson made 3 good predictions out of his top 10: China, USA, and Italy. And he made some really bad ones, including Hungary, Great Britain, and Australia. Altogether, Johnson's predictions don't deserve a place at the podium.
Monday, August 18, 2008
Extraordinary Sports Events
Watching the Olympics this week reminds me of some of my favorite extraordinary events in sports:
1. Dorando Pietri's Marathon: Pietri, an unknown entrant in the 1908 London marathon, led the field as the race entered the final segment in the stadium, but was so exhausted and confused that he started going the wrong way around the track. Within sight of the finish line, he collapsed multiple times and had to be helped over the line by race officials. Although apparently the winner, he was later disqualified because of the help he received.
2. Emil Zátopek's Marathon: Having already won the 5K and 10K races at the 1952 Olympics in Helsinki, Zátopek decided at the last minute to enter the marathon, despite having never run the race before. He won.
3. Tom Dempsey's 63-yard field goal: Dempsey, born without a right foot and right hand, kicked a 63-yard field goal, the longest in NFL history, to give the New Orleans Saints a 19-17 win over the Detroit Lions. I think this is one of the most exciting moments in professional football.
4. Berkeley-Stanford football game, 1982: I was listening to this game on the radio, and couldn't believe my ears. With 4 seconds left, and Berkeley trailing 20-19 on a last-minute Stanford field goal, Berkeley returned the kick-off 55 yards to win 25-20. What made the return special was the use of 5 laterals and the fact that the Stanford band, believing the game won, went onto the field and created additional chaos, with the trombone player getting flattened at the conclusion. This event is so special that among Cal alumni it is simply known as "The Play". The next week, Berkeley street vendors were selling a t-shirt with a diagram of the play, ending in a music note representing the trombone.
5. Jordan Snipes' 2005 shot: With 0.6 seconds left in overtime and Guilford College trailing Randolph-Macon 89-88, Jordan Snipes rebounded the ball and launched a full-court shot that swished the hoop at the other hand, giving his team a 91-89 victory. Then a news team asked him to re-enact the shot, and he made it again.
6. Bonnie Richardson, a Texas high school student, won the state's team championship -- all by herself. Richardson, the only student from her school, Rochelle High, to compete, won the high jump and 200 meters, placed second in the long jump and and 100 meters, and finished 3rd in the discus, for a total of 42 team points.
7. Cliff Young's Ultramarathon: Young, a 61-year-old sheep farmer, entered the Sydney-to-Melbourne footrace (a distance of 875 kilometers) in 1983. Despite wearing work boots, Young outran the world-class athletes by not sleeping, finishing 9 hours in front of his closest competitor. He then split the $10,000 first prize among 5 other runners and didn't keep a cent for himself.
8. Jennifer Jones' curling shot: I don't know anything at all about curling, despite having lived in Canada since 1990. But this shot by Jennifer Jones in the 2005 Scott Tournament of Hearts is so spectacular, one can enjoy it just for the geometry.
9. Dave Wottle's 800 m Finish: Wottle, known for wearing a golf cap while running, had an unbelievable kick in the 1972 Olympics to come from behind to win the 800 meters.
1. Dorando Pietri's Marathon: Pietri, an unknown entrant in the 1908 London marathon, led the field as the race entered the final segment in the stadium, but was so exhausted and confused that he started going the wrong way around the track. Within sight of the finish line, he collapsed multiple times and had to be helped over the line by race officials. Although apparently the winner, he was later disqualified because of the help he received.
2. Emil Zátopek's Marathon: Having already won the 5K and 10K races at the 1952 Olympics in Helsinki, Zátopek decided at the last minute to enter the marathon, despite having never run the race before. He won.
3. Tom Dempsey's 63-yard field goal: Dempsey, born without a right foot and right hand, kicked a 63-yard field goal, the longest in NFL history, to give the New Orleans Saints a 19-17 win over the Detroit Lions. I think this is one of the most exciting moments in professional football.
4. Berkeley-Stanford football game, 1982: I was listening to this game on the radio, and couldn't believe my ears. With 4 seconds left, and Berkeley trailing 20-19 on a last-minute Stanford field goal, Berkeley returned the kick-off 55 yards to win 25-20. What made the return special was the use of 5 laterals and the fact that the Stanford band, believing the game won, went onto the field and created additional chaos, with the trombone player getting flattened at the conclusion. This event is so special that among Cal alumni it is simply known as "The Play". The next week, Berkeley street vendors were selling a t-shirt with a diagram of the play, ending in a music note representing the trombone.
5. Jordan Snipes' 2005 shot: With 0.6 seconds left in overtime and Guilford College trailing Randolph-Macon 89-88, Jordan Snipes rebounded the ball and launched a full-court shot that swished the hoop at the other hand, giving his team a 91-89 victory. Then a news team asked him to re-enact the shot, and he made it again.
6. Bonnie Richardson, a Texas high school student, won the state's team championship -- all by herself. Richardson, the only student from her school, Rochelle High, to compete, won the high jump and 200 meters, placed second in the long jump and and 100 meters, and finished 3rd in the discus, for a total of 42 team points.
7. Cliff Young's Ultramarathon: Young, a 61-year-old sheep farmer, entered the Sydney-to-Melbourne footrace (a distance of 875 kilometers) in 1983. Despite wearing work boots, Young outran the world-class athletes by not sleeping, finishing 9 hours in front of his closest competitor. He then split the $10,000 first prize among 5 other runners and didn't keep a cent for himself.
8. Jennifer Jones' curling shot: I don't know anything at all about curling, despite having lived in Canada since 1990. But this shot by Jennifer Jones in the 2005 Scott Tournament of Hearts is so spectacular, one can enjoy it just for the geometry.
9. Dave Wottle's 800 m Finish: Wottle, known for wearing a golf cap while running, had an unbelievable kick in the 1972 Olympics to come from behind to win the 800 meters.
Wednesday, August 06, 2008
Little League's Not For Atheists
When I was a kid, I desperately wanted to play in Little League baseball. I never did, although exactly why is lost in time. Was it because there was no Little League where I lived, or because I wasn't good enough, or some other reason? I can't remember. But maybe it was all for the best, because the Little League thinks that atheists can't be good baseball players.
Want proof? Look at the Little League Pledge, which is
I trust in God
I love my country
And will respect its laws
I will play fair
And strive to win
But win or lose
I will always do my best
Despite protests, Little League refuses to change or modify its pledge. When criticized, LL hides behind the claim that "it is not, and has never been, required to be recited by any person involved with Little League Baseball or Softball". But you can be damn sure if the Pledge said, "I trust in Allah", they'd be really quick to change it.
I don't understand why belief in magical beings has anything to do with playing baseball, and it's too bad that Little League does.
Update: Jerry K. reminds me about this column by my colleague Josh Benaloh.
Want proof? Look at the Little League Pledge, which is
I trust in God
I love my country
And will respect its laws
I will play fair
And strive to win
But win or lose
I will always do my best
Despite protests, Little League refuses to change or modify its pledge. When criticized, LL hides behind the claim that "it is not, and has never been, required to be recited by any person involved with Little League Baseball or Softball". But you can be damn sure if the Pledge said, "I trust in Allah", they'd be really quick to change it.
I don't understand why belief in magical beings has anything to do with playing baseball, and it's too bad that Little League does.
Update: Jerry K. reminds me about this column by my colleague Josh Benaloh.
Our Moral Intuition Says Abortion is not the Same as Murder
This is an very interesting video that demonstrates how our moral intuition about abortion denies its equivalence to murder. Even the video's committed anti-abortion activists could not bring themselves to say that, were abortion made illegal again, women who abort their fetuses should receive a prison term commensurate with murder. Perhaps more surprisingly, most of these anti-abortion activists seemed to think there should be no penalty at all. The interviewer tries to get them to think more deeply about this contradiction, but without much success.
The lesson is that most people do not regard abortion as equivalent to murder, despite the rhetoric of the anti-abortion movement.
The lesson is that most people do not regard abortion as equivalent to murder, despite the rhetoric of the anti-abortion movement.
Danish Hospital Hosts Wacko Medical Meeting
From the Copenhagen Post comes this article about how the Copenhagen University Hospital agreed to host the woo-fest called the European Quantum Energy Medicine Conference, to the disgust of Danish medical professionals. One is quoted as saying, "It's an extremely unfortunate signal to send when we're talking about a conference that primarily consists of completely undocumented claims, and products that don't have a shred of evidence supporting their effectiveness".
I wonder why they didn't get Radovan Karadzic to speak.
Hat-tip: Terry Polevoy.
I wonder why they didn't get Radovan Karadzic to speak.
Hat-tip: Terry Polevoy.
Tuesday, August 05, 2008
I Was Doing It Right All Along
When I was a kid, I used to sneeze and use my shirtsleeve to wipe it off. My teachers and classmates were usually horrified by this practice, but now I learn, to my surprise, that I was right all along. Well, sort of.
My pharmacy was displaying this extremely weird large poster, which is available from www.coughsafe.com:
At the same website, you can even watch a movie that teaches you how to cough and sneeze properly. Four stars!
My pharmacy was displaying this extremely weird large poster, which is available from www.coughsafe.com:
At the same website, you can even watch a movie that teaches you how to cough and sneeze properly. Four stars!
Wednesday, July 30, 2008
"Institute of Advanced Scientific Researches" Changes Name, Threatens Me
I previously commented on the odd solicitation I received from the "Institute of Advanced Scientific Researches". I observed in passing that the name was odd, as most North Americans would be more likely to use "research" instead of "researches".
Over the past couple of days, the Institute has apparently changed its name to the "Institute of Advanced Scientific Research". But instead of thanking me for correcting their English, they are now threatening me.
I have now received several incoherent e-mail messages from "Zahra K. Khalafi" who claims to be the "Director of Institute of Advanced Scientific Research" and accuses me of writing "fake" and "counterfeit" messages. He states he will "take action by the law and we will see you in court in USA or CANAD" [sic] and asks if I am a "Canadian government agent". Really, I have no idea what he is complaining about. I found his institute's solicitation odd, and I said so. I found his Institute's name odd, and he apparently changed it. It seems to me he should be grateful.
If Mr. Khalafi wants to encourage other researchers to join his efforts, inviting people to join editorial boards and then threatening to sue them is probably not the optimal way to go about it.
Over the past couple of days, the Institute has apparently changed its name to the "Institute of Advanced Scientific Research". But instead of thanking me for correcting their English, they are now threatening me.
I have now received several incoherent e-mail messages from "Zahra K. Khalafi" who claims to be the "Director of Institute of Advanced Scientific Research" and accuses me of writing "fake" and "counterfeit" messages. He states he will "take action by the law and we will see you in court in USA or CANAD" [sic] and asks if I am a "Canadian government agent". Really, I have no idea what he is complaining about. I found his institute's solicitation odd, and I said so. I found his Institute's name odd, and he apparently changed it. It seems to me he should be grateful.
If Mr. Khalafi wants to encourage other researchers to join his efforts, inviting people to join editorial boards and then threatening to sue them is probably not the optimal way to go about it.
Saturday, July 26, 2008
Another Healie-Feelie Book
The recent flood in my basement ruined a perfectly good book. Actually, the book was perfectly awful: it is Healing Crystals and Gemstones: From Amethyst to Zircon by Flora Peschek-Böhmer and Gisela Schreiber. (I won't say how it came to be in my basement, but I will say that I don't own it.)
This book is typical of the "healing crystal" literature: a lack of understanding of basic geology and chemistry, combined with healing claims that are not substantiated in any way, resulting in dangerous advice for people with serious health conditions.
The book is littered with errors. Even the very first sentence is incorrect, when it claims that all gemstones originate from hot magma. (Opal, for example, can be sedimentary.) The authors claim "jasper ... always has a trigonal structure", when in fact jasper essentially doesn't form crystals at all. On page 150, the authors claim that fluorite is "also known as feldspar", when in fact feldspar is an entirely different mineral. On page 75, the authors confuse native antimony with the mineral stibnite, which is actually antimony sulfide. On page 85 the authors claim that that aragonite is silicon dioxide, not calcium carbonate. The mineral Charoite is consistently misspelled as "Chaorite". They claim that the crystal structure of Herkimer diamonds is similar to that of real diamond, when in fact they crystallize in completely different systems. They claim that kunzite is "aluminum acetate-lithium", when in fact it is a lithium aluminum silicate; no acetate at all is contained in it. They claim that Magnesite "consists almost entirely of pure magnesium", when in fact it is just magnesium carbonate. They claim that Magnesite "was first discovered in Africa", when in fact its co-type localities are in Greece and Italy.
The authors recommend the use of various minerals without noting health problems associated with them. For example, the authors recommend actinolite to stimulate "the inner organs such as the liver and the kidneys", but fail to note that the tiny fibers of actinolite have been associated with severe and potentially life-threatening respiratory disorders. They recommend using orpiment "externally as a powder to treat sexual disorders", but this is not a good idea, as orpiment is arsenic sulfide.
But the most serious problem with the book is the repeated and unsubstantiated health claims, all made without a single reference to any study in support of them. Someone with serious health problems might be persuaded to use the entirely ineffective remedies suggested in this book instead of seeking effective medical treatment. Cancer is unlikely to be helped by toumaline, sugilite, or lapis lazuli. High blood pressure cannot be improved with sodalite, lapis, or chrysoprase. Diabetes sufferers will find no relief with citrine or pyrite. Kidney ailments will not be improved with jade. For ulcers you should see your family doctor, not wear jasper or topaz.
Ahh, well, I doubt any of this will convince the healie-feelie crowd. When they're done with this, they can move on to the other immortal works of Flora Peschek-Böhmer, such as Urine Therapy: Nature's Elixir for Good Health. Urine therapy, in case you didn't know, consists of drinking your own urine. Great idea! You can use it to wash down some crystals of orpiment.
This book is typical of the "healing crystal" literature: a lack of understanding of basic geology and chemistry, combined with healing claims that are not substantiated in any way, resulting in dangerous advice for people with serious health conditions.
The book is littered with errors. Even the very first sentence is incorrect, when it claims that all gemstones originate from hot magma. (Opal, for example, can be sedimentary.) The authors claim "jasper ... always has a trigonal structure", when in fact jasper essentially doesn't form crystals at all. On page 150, the authors claim that fluorite is "also known as feldspar", when in fact feldspar is an entirely different mineral. On page 75, the authors confuse native antimony with the mineral stibnite, which is actually antimony sulfide. On page 85 the authors claim that that aragonite is silicon dioxide, not calcium carbonate. The mineral Charoite is consistently misspelled as "Chaorite". They claim that the crystal structure of Herkimer diamonds is similar to that of real diamond, when in fact they crystallize in completely different systems. They claim that kunzite is "aluminum acetate-lithium", when in fact it is a lithium aluminum silicate; no acetate at all is contained in it. They claim that Magnesite "consists almost entirely of pure magnesium", when in fact it is just magnesium carbonate. They claim that Magnesite "was first discovered in Africa", when in fact its co-type localities are in Greece and Italy.
The authors recommend the use of various minerals without noting health problems associated with them. For example, the authors recommend actinolite to stimulate "the inner organs such as the liver and the kidneys", but fail to note that the tiny fibers of actinolite have been associated with severe and potentially life-threatening respiratory disorders. They recommend using orpiment "externally as a powder to treat sexual disorders", but this is not a good idea, as orpiment is arsenic sulfide.
But the most serious problem with the book is the repeated and unsubstantiated health claims, all made without a single reference to any study in support of them. Someone with serious health problems might be persuaded to use the entirely ineffective remedies suggested in this book instead of seeking effective medical treatment. Cancer is unlikely to be helped by toumaline, sugilite, or lapis lazuli. High blood pressure cannot be improved with sodalite, lapis, or chrysoprase. Diabetes sufferers will find no relief with citrine or pyrite. Kidney ailments will not be improved with jade. For ulcers you should see your family doctor, not wear jasper or topaz.
Ahh, well, I doubt any of this will convince the healie-feelie crowd. When they're done with this, they can move on to the other immortal works of Flora Peschek-Böhmer, such as Urine Therapy: Nature's Elixir for Good Health. Urine therapy, in case you didn't know, consists of drinking your own urine. Great idea! You can use it to wash down some crystals of orpiment.
Strange Solicitation
Today I received an odd solicitation to join the editorial board of a journal I've never heard of, the Journal of Advanced Researches on Computer Science. It is published by an institute I've never heard of, the "Institute of Advanced Scientific Researches".
The solicitation was strange for a number of reasons. First, this "Institute" seems to publish (or want to publish) 16 different journals; yet as I write this, many of them seem to have no editorial board listed. Second, the name of the Institute itself is odd; no native English speaker would be likely refer to "researches", as "research" is typically a mass noun, like "information". Also, the solicitation letter was filled with grammatical errors. Third, I can find no information about this "Institute" online, nor any of the people associated with it, except for the person who wrote the solicitation letter, "Kavin Kalfi".
So, does anyone else know about this "Institute"?
The solicitation was strange for a number of reasons. First, this "Institute" seems to publish (or want to publish) 16 different journals; yet as I write this, many of them seem to have no editorial board listed. Second, the name of the Institute itself is odd; no native English speaker would be likely refer to "researches", as "research" is typically a mass noun, like "information". Also, the solicitation letter was filled with grammatical errors. Third, I can find no information about this "Institute" online, nor any of the people associated with it, except for the person who wrote the solicitation letter, "Kavin Kalfi".
So, does anyone else know about this "Institute"?
Friday, July 25, 2008
Friday Moose Blogging
Here are some photos by my colleague Doug Payne, taken during his recent trip to Algonquin Park. No surprise, there's a moose or two. Moose twins, too.
Thursday, July 24, 2008
SIGAPL dissolved
A sad day for the APL community: SIGAPL, the ACM special interest group on APL, has been dissolved by the ACM SIG governing board.
I first learned APL in 1973 at the IBM Scientific Center in Philadelphia (long gone). At the insistence of my father, I had written to several large computing companies, asking for a summer job. Only IBM replied favorably, and I had a rather intimidating interview with Ken Iverson and Adin Falkoff in their offices on Market Street. To my delight, they hired me for a vague project about whether it was better to learn APL by reading other people's programs first, or writing one's own.
I remember going home with a copy of the APL\360 user's manual, which was initially very mysterious to me, and had an exotic smell like bacon. I had learned programming from Kemeny's book on BASIC, and APL was a revelation. I immediately took to the language and ended up spending the next few years of my life involved in APL in various ways: coding in APL for financial institutions, writing my own extended precision arithmetic package and selling it to IBM, etc. I was programming on IBM machines, using a printing terminal with an APL typeball.
I soon discovered the newsletter of SIGAPL, called "Quote-Quad". (The unusual name comes from the special APL symbol for character input, which was formed by typing a "quad" (shift-L) and overstriking it with a quote (shift-K).) At that time I eagerly awaited every issue, filled with incredible one-liners that accomplished results you would need hundreds of lines in BASIC to duplicate, puzzles like the self-replicating APL expression puzzle (type it in and you get exactly the same result back), and proposals to extend APL in bizarre and mind-expanding ways. It was really the golden age of APL.
It's clear that the passion and excitement about APL has decreased since then, although I still use APL on at least a weekly basis to do experimental mathematics: Dyalog APL on my Sun workstation, and APLX on my Macintosh. In many ways it is far superior to Maple and Mathematica, although the lack of easy availability of extended precision and symbolic arithmetic is a pain. I can code a quick-and-dirty solution to a problem faster in APL than I can in any other language. People who see it always stare open-mouthed: what is that? they say, and they want to borrow a manual.
The dissolution of SIGAPL is the passing of an age.
I first learned APL in 1973 at the IBM Scientific Center in Philadelphia (long gone). At the insistence of my father, I had written to several large computing companies, asking for a summer job. Only IBM replied favorably, and I had a rather intimidating interview with Ken Iverson and Adin Falkoff in their offices on Market Street. To my delight, they hired me for a vague project about whether it was better to learn APL by reading other people's programs first, or writing one's own.
I remember going home with a copy of the APL\360 user's manual, which was initially very mysterious to me, and had an exotic smell like bacon. I had learned programming from Kemeny's book on BASIC, and APL was a revelation. I immediately took to the language and ended up spending the next few years of my life involved in APL in various ways: coding in APL for financial institutions, writing my own extended precision arithmetic package and selling it to IBM, etc. I was programming on IBM machines, using a printing terminal with an APL typeball.
I soon discovered the newsletter of SIGAPL, called "Quote-Quad". (The unusual name comes from the special APL symbol for character input, which was formed by typing a "quad" (shift-L) and overstriking it with a quote (shift-K).) At that time I eagerly awaited every issue, filled with incredible one-liners that accomplished results you would need hundreds of lines in BASIC to duplicate, puzzles like the self-replicating APL expression puzzle (type it in and you get exactly the same result back), and proposals to extend APL in bizarre and mind-expanding ways. It was really the golden age of APL.
It's clear that the passion and excitement about APL has decreased since then, although I still use APL on at least a weekly basis to do experimental mathematics: Dyalog APL on my Sun workstation, and APLX on my Macintosh. In many ways it is far superior to Maple and Mathematica, although the lack of easy availability of extended precision and symbolic arithmetic is a pain. I can code a quick-and-dirty solution to a problem faster in APL than I can in any other language. People who see it always stare open-mouthed: what is that? they say, and they want to borrow a manual.
The dissolution of SIGAPL is the passing of an age.
Wednesday, July 23, 2008
Christian Compassion
From the Toronto Sun comes this heartwarming story of Christian compassion.
Sex offender Patrick White is really, really sorry that he committed fraud and sex-related offenses in the US and Canada. He's really, really sorry that he sexually abused mentally retarded men. In fact, he's so sorry that he will pay for counselling for his victims, but only if it's "Christian counselling".
How generous!
Never fear, White is assured of a place in his Christian heaven, because, as he says, "God has forgiven me".
Sex offender Patrick White is really, really sorry that he committed fraud and sex-related offenses in the US and Canada. He's really, really sorry that he sexually abused mentally retarded men. In fact, he's so sorry that he will pay for counselling for his victims, but only if it's "Christian counselling".
How generous!
Never fear, White is assured of a place in his Christian heaven, because, as he says, "God has forgiven me".
Mark Shea Thinks Scientists Are Stupid, Makes Gaffe
Over at Catholic Exchange, Mark Shea relates an anecdote that demonstrates, for him, that scientists are sadly lacking in emotional intelligence:
Long ago, I remember watching some film about human evolution narrated by Richard Leakey, Jr. It was interesting as such films go, but you got the sense as it went along that it explained everything at the cost of leaving everything out—like scientists in a Far Side cartoon analyzing humor.
The crowning moment of the film, for me, was when Leakey stood in front of the gorgeous twenty-thousand-year-old cave paintings in Lascaux, France and, with genuine puzzlement in his voice, wondered aloud “Why did they do this? What was the purpose?”
I had the distinct impression he would have expressed equal bafflement were he standing in the Louvre. There seemed to be a gene missing somewhere. He was a man who knew a great deal about human origins and yet, however smart he was, there was something about him that was radically out of touch with, well, what it meant to be human. You felt he needed tape on his glasses, a pocket protector, high water trousers and D&D dice in his pocket to complete the image he seemed to project with such earnest unconsciousness.
I'm a little skeptical that the film went exactly as Shea claims it did. People's memories are notoriously unreliable, and events are rewritten in brains to conform to a person's individual narrative: in this case, Shea's commitment to the Catholic faith as the essential guide to understanding the world.
But assuming Shea's memory was correct, he seems to have entirely missed the point of Leakey's question. Shea doesn't seem to have any awareness that there is a debate among archaeologists about Lascaux's purpose. Was it continuously occupied, or only visited periodically? Was it part of a shaman's ritual to improve chances during the hunt, a record of previous successful hunts, or simply a decoration? Why are there no images of reindeer, which formed a major part of the diet of the artists? Do the painted dots really represent an accurate map of the night sky, as suggested by Michael Rappenglueck?
If you have scientific training, then questions like these seem natural and interesting. If you don't, and are immersed in dogma that preaches simple answers to difficult questions, then even asking this kind of question demonstrates some moral failing. I'd wager that Leakey knows a lot more about people, and their goals, desires, and questions, than Mark Shea does.
Long ago, I remember watching some film about human evolution narrated by Richard Leakey, Jr. It was interesting as such films go, but you got the sense as it went along that it explained everything at the cost of leaving everything out—like scientists in a Far Side cartoon analyzing humor.
The crowning moment of the film, for me, was when Leakey stood in front of the gorgeous twenty-thousand-year-old cave paintings in Lascaux, France and, with genuine puzzlement in his voice, wondered aloud “Why did they do this? What was the purpose?”
I had the distinct impression he would have expressed equal bafflement were he standing in the Louvre. There seemed to be a gene missing somewhere. He was a man who knew a great deal about human origins and yet, however smart he was, there was something about him that was radically out of touch with, well, what it meant to be human. You felt he needed tape on his glasses, a pocket protector, high water trousers and D&D dice in his pocket to complete the image he seemed to project with such earnest unconsciousness.
I'm a little skeptical that the film went exactly as Shea claims it did. People's memories are notoriously unreliable, and events are rewritten in brains to conform to a person's individual narrative: in this case, Shea's commitment to the Catholic faith as the essential guide to understanding the world.
But assuming Shea's memory was correct, he seems to have entirely missed the point of Leakey's question. Shea doesn't seem to have any awareness that there is a debate among archaeologists about Lascaux's purpose. Was it continuously occupied, or only visited periodically? Was it part of a shaman's ritual to improve chances during the hunt, a record of previous successful hunts, or simply a decoration? Why are there no images of reindeer, which formed a major part of the diet of the artists? Do the painted dots really represent an accurate map of the night sky, as suggested by Michael Rappenglueck?
If you have scientific training, then questions like these seem natural and interesting. If you don't, and are immersed in dogma that preaches simple answers to difficult questions, then even asking this kind of question demonstrates some moral failing. I'd wager that Leakey knows a lot more about people, and their goals, desires, and questions, than Mark Shea does.
Sunday, July 20, 2008
Rutgers Graduate Student Finds New Prime-Generating Formula
Studying prime numbers is like playing the guitar. No, really, let me explain.
The guitar is a simple instrument: six strings, some frets, a sound hole. You strum with the right hand, and form chords with the left. What could be simpler? Any reasonably coordinated person can learn to play a simple song, such as "Heart of Gold", passably in a few hours.
In the same way, the prime numbers have a simple definition: the integers greater than 1 that are divisible only by themselves and 1. Any reasonably intelligent person can learn to test a small number for primality, or understand Euclid's proof that there are infinitely many prime numbers, in a short amount of time.
Yet the guitar is also fiendishly difficult. Those studying classical guitar know well how some pieces take hundreds of hours to master. Techniques such as tremolo might take years, especially if you start learning as an adult.
In the same way, the prime numbers contain within them enough subtlety that many problems remain unsolved after hundreds of years. Goldbach conjectured in 1742 that every even number greater than 2 is the sum of two primes, and today this conjecture is still unsolved. (It is known to hold for every even number less than 1018.) And a proof of the Riemann hypothesis, which would have extremely important consequences for the distribution of primes, will net you a million dollars from the Clay Mathematics Institute -- probably more than you'll get from appearing on American Idol.
For a long time mathematicians have sought a simple formula that would generate all the prime numbers, or even infinitely many distinct prime numbers. Some have even gone so far as to claim that no such formula exists -- a statement of very questionable veracity that depends entirely on one's definition of "formula". If you define formula to mean "polynomial with integer coefficients", then it's not hard (and I leave it as a challenge to the reader) to prove that no such polynomial can generate only primes, other than the trivial example of a constant polynomial. Euler's polynomial x2 + x + 41 comes close: it generates primes for x = 0, 1, 2, ..., 39, but fails at x = 40.
A slight variation, though, leads to a genuine prime-generating polynomial. It is a consequence of the Davis-Matiyasevich-Putnam-Robinson work on Hilbert's 10th problem that there exists a multivariate polynomial with integer coefficients that takes on only negative and prime values when integers are substituted for the variables, and every prime is generated by some choice of the variables. In 1976, Jones, Sato, Wada, and Wiens actually wrote down such a polynomial. It has 26 variables.
Another prime-generating formula comes from a 1947 paper of W. H. Mills. Mills proved that there exists a real number A such that [ A3n ] is a prime number for all integers n ≥ 1. Here [ x ] is the greatest integer function, the greatest integer ≤ x. Unfortunately, nobody knows a good way to calculate A other than testing the numbers the formula is supposed to generate for primality, and then constructing A by working backwards.
So many people have worked on the prime numbers that it seems unlikely that there could be a simple prime-generating function that has been overlooked until now.
Rutgers graduate student Eric Rowland has defied the odds, however, and has found a new one. In a paper just published in a journal I edit, the Journal of Integer Sequences, Rowland defines his formula and proves it generates only 1's and primes. (1 is generally not accepted as a prime number, for a variety of reasons. For one thing, if 1 were a prime, then positive integers would not have a unique factorization into primes.) To be precise, I should say that the unusual property of the formula was originally conjectured by a team led by Matt Frank at a mathematics summer school in 2003 where Rowland was attending, but it was not proved until now.
Here is Rowland's formula. We define a(1) = 7, and for n ≥ 2 we set
a(n) = a(n-1) + gcd(n,a(n-1)).
Here "gcd" means the greatest common divisor. So, for example, we find a(2) = a(1) + gcd(2,7) = 8. The prime generator is then a(n) - a(n-1), the so-called first differences of the original sequence.
For example, here are the first 23 values of the a sequence:
7, 8, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69
and here are the first differences of these values:
1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23
If we ignore the 1's, then, the Rowland formula starts by generating the primes 5, 3, 11, 3 (again), and 23. The reader can easily program up the formula and find lots more primes. Removing duplicates, the first few are
5, 3, 11, 23, 47, 101, 7, 13, 233, 467, 941, 1889, 3779, 7559, 15131, 53, 30323, ...
Why does it work? The proof is too involved to give here, but it is not that difficult. The interested reader can go to Rowland's paper for the details.
Rowland has been involved with mathematics for some time. He attended UC Santa Cruz and graduated with highest honors in math in 2003. Since then he has been a graduate student at Rutgers University, studying with Doron Zeilberger. Rowland describes himself as an "experimental mathematician", and uses the computer algebra system Mathematica for his experiments. Rowland tells me that he tried to prove the formula from time to time over a four-year period, but once the crucial insight was found, "I had an outline of the proof within a few days and all the details within a few weeks."
Are there any other formulas like Rowland's? Apparently yes. Benoit Cloitre, a French mathematician, recently proved that if you set b(1) = 1 and
b(n) = b(n-1) + lcm(n,b(n-1)) for n ≥ 2,
then b(n)/b(n-1)-1 is either 1 or prime for all n ≥ 2.
Will Rowland's formula lead to more efficient ways to generate large primes? If so, cryptographers would love it. But it seems unlikely. As Rowland explains in his paper, his formula only produces the prime p after first generating (p-3)/2 1's, so it takes a really long time to generate a large prime. He has a method for skipping over those useless 1's, but doing so essentially requires an independent test for primality.
Are there still unsolved properties of Rowland's prime generator? Yes. For example, is there anything special about the choice a(1) = 7? Other choices, such as a(1) = 8, always generate primes and 1's, but others, such as a(1) = 532, do not. (This choice generates 9 after less than 20 steps.) However, Rowland conjectures that for each starting value of a(1), there exists a point after which the first differences are always either 1 or prime. Rowland also doesn't know if his formula eventually generates all odd primes, although he believes it probably does.
Rowland has a number of other projects in the works. He told me, "I'm working on several things, mostly trying to finish up a backlog of papers. But one newer project is putting bounds on the frequency of 1's in the Kolakoski word. Another is something I'm not ready to fully divulge, but it has to do with values of the p-adic logarithm. A longer term project of mine is extending what is known about the arithmetic of Pascal's triangle modulo m and, generally, additive cellular automata."
What problem would Rowland most like to solve? "I'd really like to solve the 3n+1 problem, because I think it would tell us something very interesting about representations of integers. Dividing by 2 in base 2 just means dropping the last 0, and mapping n -> 3n+1 in base 3 just means appending 1. The problem is that we don't know how to get these two bases to talk to each other -- and of course perhaps there isn't a way -- but a solution to the 3n+1 problem might show us how to do this."
Solving the 3n+1 problem would indeed be a great achievement. In the meantime, however, he can take pleasure in his prime formula. Blending simplicity and mystery, Eric Rowland's formula is a delightful composition in the music of the primes, one everyone can enjoy.
Update, July 31 2008: Rowland has his own post describing his discovery.
The guitar is a simple instrument: six strings, some frets, a sound hole. You strum with the right hand, and form chords with the left. What could be simpler? Any reasonably coordinated person can learn to play a simple song, such as "Heart of Gold", passably in a few hours.
In the same way, the prime numbers have a simple definition: the integers greater than 1 that are divisible only by themselves and 1. Any reasonably intelligent person can learn to test a small number for primality, or understand Euclid's proof that there are infinitely many prime numbers, in a short amount of time.
Yet the guitar is also fiendishly difficult. Those studying classical guitar know well how some pieces take hundreds of hours to master. Techniques such as tremolo might take years, especially if you start learning as an adult.
In the same way, the prime numbers contain within them enough subtlety that many problems remain unsolved after hundreds of years. Goldbach conjectured in 1742 that every even number greater than 2 is the sum of two primes, and today this conjecture is still unsolved. (It is known to hold for every even number less than 1018.) And a proof of the Riemann hypothesis, which would have extremely important consequences for the distribution of primes, will net you a million dollars from the Clay Mathematics Institute -- probably more than you'll get from appearing on American Idol.
For a long time mathematicians have sought a simple formula that would generate all the prime numbers, or even infinitely many distinct prime numbers. Some have even gone so far as to claim that no such formula exists -- a statement of very questionable veracity that depends entirely on one's definition of "formula". If you define formula to mean "polynomial with integer coefficients", then it's not hard (and I leave it as a challenge to the reader) to prove that no such polynomial can generate only primes, other than the trivial example of a constant polynomial. Euler's polynomial x2 + x + 41 comes close: it generates primes for x = 0, 1, 2, ..., 39, but fails at x = 40.
A slight variation, though, leads to a genuine prime-generating polynomial. It is a consequence of the Davis-Matiyasevich-Putnam-Robinson work on Hilbert's 10th problem that there exists a multivariate polynomial with integer coefficients that takes on only negative and prime values when integers are substituted for the variables, and every prime is generated by some choice of the variables. In 1976, Jones, Sato, Wada, and Wiens actually wrote down such a polynomial. It has 26 variables.
Another prime-generating formula comes from a 1947 paper of W. H. Mills. Mills proved that there exists a real number A such that [ A3n ] is a prime number for all integers n ≥ 1. Here [ x ] is the greatest integer function, the greatest integer ≤ x. Unfortunately, nobody knows a good way to calculate A other than testing the numbers the formula is supposed to generate for primality, and then constructing A by working backwards.
So many people have worked on the prime numbers that it seems unlikely that there could be a simple prime-generating function that has been overlooked until now.
Rutgers graduate student Eric Rowland has defied the odds, however, and has found a new one. In a paper just published in a journal I edit, the Journal of Integer Sequences, Rowland defines his formula and proves it generates only 1's and primes. (1 is generally not accepted as a prime number, for a variety of reasons. For one thing, if 1 were a prime, then positive integers would not have a unique factorization into primes.) To be precise, I should say that the unusual property of the formula was originally conjectured by a team led by Matt Frank at a mathematics summer school in 2003 where Rowland was attending, but it was not proved until now.
Here is Rowland's formula. We define a(1) = 7, and for n ≥ 2 we set
a(n) = a(n-1) + gcd(n,a(n-1)).
Here "gcd" means the greatest common divisor. So, for example, we find a(2) = a(1) + gcd(2,7) = 8. The prime generator is then a(n) - a(n-1), the so-called first differences of the original sequence.
For example, here are the first 23 values of the a sequence:
7, 8, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69
and here are the first differences of these values:
1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23
If we ignore the 1's, then, the Rowland formula starts by generating the primes 5, 3, 11, 3 (again), and 23. The reader can easily program up the formula and find lots more primes. Removing duplicates, the first few are
5, 3, 11, 23, 47, 101, 7, 13, 233, 467, 941, 1889, 3779, 7559, 15131, 53, 30323, ...
Why does it work? The proof is too involved to give here, but it is not that difficult. The interested reader can go to Rowland's paper for the details.
Rowland has been involved with mathematics for some time. He attended UC Santa Cruz and graduated with highest honors in math in 2003. Since then he has been a graduate student at Rutgers University, studying with Doron Zeilberger. Rowland describes himself as an "experimental mathematician", and uses the computer algebra system Mathematica for his experiments. Rowland tells me that he tried to prove the formula from time to time over a four-year period, but once the crucial insight was found, "I had an outline of the proof within a few days and all the details within a few weeks."
Are there any other formulas like Rowland's? Apparently yes. Benoit Cloitre, a French mathematician, recently proved that if you set b(1) = 1 and
b(n) = b(n-1) + lcm(n,b(n-1)) for n ≥ 2,
then b(n)/b(n-1)-1 is either 1 or prime for all n ≥ 2.
Will Rowland's formula lead to more efficient ways to generate large primes? If so, cryptographers would love it. But it seems unlikely. As Rowland explains in his paper, his formula only produces the prime p after first generating (p-3)/2 1's, so it takes a really long time to generate a large prime. He has a method for skipping over those useless 1's, but doing so essentially requires an independent test for primality.
Are there still unsolved properties of Rowland's prime generator? Yes. For example, is there anything special about the choice a(1) = 7? Other choices, such as a(1) = 8, always generate primes and 1's, but others, such as a(1) = 532, do not. (This choice generates 9 after less than 20 steps.) However, Rowland conjectures that for each starting value of a(1), there exists a point after which the first differences are always either 1 or prime. Rowland also doesn't know if his formula eventually generates all odd primes, although he believes it probably does.
Rowland has a number of other projects in the works. He told me, "I'm working on several things, mostly trying to finish up a backlog of papers. But one newer project is putting bounds on the frequency of 1's in the Kolakoski word. Another is something I'm not ready to fully divulge, but it has to do with values of the p-adic logarithm. A longer term project of mine is extending what is known about the arithmetic of Pascal's triangle modulo m and, generally, additive cellular automata."
What problem would Rowland most like to solve? "I'd really like to solve the 3n+1 problem, because I think it would tell us something very interesting about representations of integers. Dividing by 2 in base 2 just means dropping the last 0, and mapping n -> 3n+1 in base 3 just means appending 1. The problem is that we don't know how to get these two bases to talk to each other -- and of course perhaps there isn't a way -- but a solution to the 3n+1 problem might show us how to do this."
Solving the 3n+1 problem would indeed be a great achievement. In the meantime, however, he can take pleasure in his prime formula. Blending simplicity and mystery, Eric Rowland's formula is a delightful composition in the music of the primes, one everyone can enjoy.
Update, July 31 2008: Rowland has his own post describing his discovery.
Friday, July 18, 2008
Friday Moose Blogging
Here's a great youtube video of 2 baby moose and their mother playing in a sprinkler in an Alaskan backyard.
When a Creationist Says the Sky is Blue...
When a creationist says the sky is blue...
go outside and check.
That's the wise advice of my friend and co-author, Wesley Elsberry.
It seems particularly apt this week, with yet another outbreak of creationist misrepresentation:
I don't think creationists are always dishonest, but (1) they uncritically accept anything that supports their view instead of examining it critically and (2) they are not particularly concerned with making sure that their sources are correct.
go outside and check.
That's the wise advice of my friend and co-author, Wesley Elsberry.
It seems particularly apt this week, with yet another outbreak of creationist misrepresentation:
- Over at Uncommon Descent, William Dembski claims, citing Michael Asher, that "The American Physical Society, an organization representing nearly 50,000 physicists, has reversed its stance on climate change and is now proclaiming that many of its members disbelieve in human-induced global warming." Only problem is, the American Physical Society has done nothing of the sort. Instead, the APS's Forum on Physics & Society has published an issue with two opposing articles, one in favor of the human-caused global warming theory and one attempting to cast doubt on it. The latter article was written by Christopher Monckton, a man with apparently no scientific training who has a history of statements of debatable veracity.
Even Asher himself has been forced to concede that his description of the Forum on Physics & Society's issue was incorrect, admitting in an update at the bottom in a much smaller typeface that "After publication of this story, the APS responded with a statement that its Physics and Society Forum is merely one unit within the APS, and its views do not reflect those of the Society at large." - Next, at The Panda's Thumb, Nick Matzke points out that Casey Luskin gets nearly everything wrong when describing the Alternberg meeting. Luskin claims the NCSE opposed the meeting for political reasons (false; it didn't oppose it at all) and that Rutgers philosopher Jerry Fodor was one of the Alternberg 16 (false, as one can easily check here). Even more importantly, Luskin imagines the meeting as some sort of significant challenge to the theory of evolution, when in fact the participants claim just the opposite.
- Finally, I've been contacted by some cretin named Bill Crofut, who proclaims himself a "an unlettered Traditional Roman Catholic, militant young-Earth Biblical creationist and geocentrist". Crofut proffered a quote by Birch and Ehrlich from a 1967 Nature article as evidence against evolution. Only problem is, the quote was stripped of context and is a well-known quote mine. When confronted with the evidence of his misrepresentation, Crofut told me he was "a son of Satan".
I don't think creationists are always dishonest, but (1) they uncritically accept anything that supports their view instead of examining it critically and (2) they are not particularly concerned with making sure that their sources are correct.
Thursday, July 17, 2008
World Religious Leaders Praise Saudi King's Anti-Atheist Bigotry
Saudi King Abdullah spoke at a Madrid conference sponsored by the Muslim World League, and spoke against religious extremism. Good, as far as it goes.
Unfortunately, he whitewashed the role of religion in the world's problems. According to King Abdullah, religion (especially his) is blameless, claiming that "Islam is a religion of moderation and tolerance". Ironically, the conference apparently took place in Spain instead of Saudi Arabia, because Saudi Arabia is "the only Arab Muslim country to ban all non-Islamic religious practices on its soil, even though it has a large community of expatriates professing other faiths."
Instead, he chose to blame the world's problems on "secularism" and atheists: "If we wish this historic meeting to succeed, we must focus on the common denominators that unite us, namely, deep faith in God, noble principles, and lofty moral values, which constitute the essence of religion" and that the world's problems are "a consequence of the spiritual void from which people suffer when they forget God, and God causes them to forget themselves." Despite blaming the world's problems on atheists, he also denied their existence, claiming that "we all believe in one God, who sent messengers for the good of humanity in this world and the hereafter".
Did any of the 200 religious and political leaders present speak against this anti-atheist bigotry? Nope. Instead, they fell over themselves to praise King Abdulalh. Ronald Lauder, president of the World Jewish Congress, "said the conference was a 'significant and timely development.'" Catholic Cardinal Tauran called it "an act of great courage". Jesse Jackson apparently called the speech "a distinguished one in its contents and noble message" (may not be an exact quote). Abdullah Tariq said, "It is a great beginning of a valuable call from a generous King."
I'm really sick of hypocritical religious leaders telling me that not accepting their wild and unsupported claims about their deities is some sort of moral failing. It's religion that is to blame for Saudi Arabia's medieval treatment of women. It's religion that is to largely blame for the Saudi hijackers who crashed planes into the World Trade towers on September 11. It's religion that is largely to blame for overpopulation and our worsening ecological crisis. Let's have some religious leaders forthrightly admit this, and then we can have some dialogue.
Unfortunately, he whitewashed the role of religion in the world's problems. According to King Abdullah, religion (especially his) is blameless, claiming that "Islam is a religion of moderation and tolerance". Ironically, the conference apparently took place in Spain instead of Saudi Arabia, because Saudi Arabia is "the only Arab Muslim country to ban all non-Islamic religious practices on its soil, even though it has a large community of expatriates professing other faiths."
Instead, he chose to blame the world's problems on "secularism" and atheists: "If we wish this historic meeting to succeed, we must focus on the common denominators that unite us, namely, deep faith in God, noble principles, and lofty moral values, which constitute the essence of religion" and that the world's problems are "a consequence of the spiritual void from which people suffer when they forget God, and God causes them to forget themselves." Despite blaming the world's problems on atheists, he also denied their existence, claiming that "we all believe in one God, who sent messengers for the good of humanity in this world and the hereafter".
Did any of the 200 religious and political leaders present speak against this anti-atheist bigotry? Nope. Instead, they fell over themselves to praise King Abdulalh. Ronald Lauder, president of the World Jewish Congress, "said the conference was a 'significant and timely development.'" Catholic Cardinal Tauran called it "an act of great courage". Jesse Jackson apparently called the speech "a distinguished one in its contents and noble message" (may not be an exact quote). Abdullah Tariq said, "It is a great beginning of a valuable call from a generous King."
I'm really sick of hypocritical religious leaders telling me that not accepting their wild and unsupported claims about their deities is some sort of moral failing. It's religion that is to blame for Saudi Arabia's medieval treatment of women. It's religion that is to largely blame for the Saudi hijackers who crashed planes into the World Trade towers on September 11. It's religion that is largely to blame for overpopulation and our worsening ecological crisis. Let's have some religious leaders forthrightly admit this, and then we can have some dialogue.
Sunday, July 06, 2008
All People of Good Will Agree With Me
Dr. Henry Morgentaler, the single person most responsible for making abortion safe and legal in Canada, was recently given a national award, the Order of Canada. Not surprisingly, the Catholic hierarchy is outraged. But their outrage took a pernicious dimension when Archbishop Thomas Collins of the Toronto archdiocese said in interview that he called on "all people of good will, to protest this act of dishonour".
Archbishop Collins evidently believes that one cannot be a person of good will and still support the right to abortion. I've met a lot of anti-abortion activists. Most are sincere people who, though misguided, honestly believe that they are acting ethically. But so do people who argue for the right to abortion. It is really offensive for the Archbishop to suggest that the only way you can be a "person of good will" is to agree with the Catholic Church's position.
Archbishop Collins evidently believes that one cannot be a person of good will and still support the right to abortion. I've met a lot of anti-abortion activists. Most are sincere people who, though misguided, honestly believe that they are acting ethically. But so do people who argue for the right to abortion. It is really offensive for the Archbishop to suggest that the only way you can be a "person of good will" is to agree with the Catholic Church's position.
Thursday, July 03, 2008
William Carlos Williams with a Handtruck
From my niece Rachel comes this inspired bit of silliness: an English professor couldn't find the departmental handtruck, so he put out a request on the local listserv. In response, he got 12 odes to the missing handtruck, done in the style of William Carlos Williams, John Donne, and other famous poets. I particularly like this one, by Carl Rapp.
This Is Just to Say
I have pinched
the hand truck
that I happened to run across in
a convenient location
and which
you were probably
saving
for your own future toils
Forgive me
it was so “dependable”
so red
and so obviously up for grabs
Can't you just hear Garrison Keillor reciting it?
This Is Just to Say
I have pinched
the hand truck
that I happened to run across in
a convenient location
and which
you were probably
saving
for your own future toils
Forgive me
it was so “dependable”
so red
and so obviously up for grabs
Can't you just hear Garrison Keillor reciting it?
Monday, June 30, 2008
Journalistic Credulity
Continuing with the theme of crappy journalism, this weekend on Wait Wait ... Don't Tell Me!, I learned about a hoax perpetrated on the New York Times back in 1992.
Rick Marin wrote an article about "grunge music" and the Seattle alternative music scene that appeared in the "Styles" section on November 15. Apparently he wanted a lexicon of slang, and so he turned to Seattle-based Sub Pop Records for advice. Sales rep Megan Jasper reportedly just made up a bunch of phrases on the spot, such as
Swingin' on the flippity-flop: hanging out
Harsh realm: bummer
Cob nobbler: loser
Lamestain: uncool person
This made-up lexicon was swallowed whole by Marin, and the Times apparently printed it without any fact-checking.
Maybe Marin isn't representative of journalism as a whole, but the lesson still is that a good journalist ought to be skeptical of all claims, and make a serious effort to fact-check. Rick Marin: what a lamestain!
Rick Marin wrote an article about "grunge music" and the Seattle alternative music scene that appeared in the "Styles" section on November 15. Apparently he wanted a lexicon of slang, and so he turned to Seattle-based Sub Pop Records for advice. Sales rep Megan Jasper reportedly just made up a bunch of phrases on the spot, such as
Swingin' on the flippity-flop: hanging out
Harsh realm: bummer
Cob nobbler: loser
Lamestain: uncool person
This made-up lexicon was swallowed whole by Marin, and the Times apparently printed it without any fact-checking.
Maybe Marin isn't representative of journalism as a whole, but the lesson still is that a good journalist ought to be skeptical of all claims, and make a serious effort to fact-check. Rick Marin: what a lamestain!
Friday, June 27, 2008
Science Unites - Religion Divides
Here's an article about my friend Mark Gluck, a Rutgers neuroscientist who organized a joint Israeli-Palestinian conference on Alzheimer's disease. It's a good example of the best science can offer: people of different backgrounds, politics, and religion joining together to solve real problems in a spirit of scientific inquiry.
Religion and ancient animosities would have kept these scientists apart. Rational and skeptical inquiry can unite them.
Religion and ancient animosities would have kept these scientists apart. Rational and skeptical inquiry can unite them.
Thursday, June 26, 2008
Peter McKnight Not Confused by Expelled
Peter McKnight, writing in the Vancouver Sun, gives a clear-headed appraisal of the crackpot documentary Expelled, which has just opened in Canada. Among the best tidbits, Ben Stein is reported to have replied, "It's none of their f---ing business" when McKnight asked him about the ADL statement on Expelled.
I predict that Expelled will flop even more egregiously in Canada than it did in the US. Reasons: there are not as many far-right religious crackpots in Canada; Canadians don't really care so much about US church-state battles; it's only playing in a relatively small number of theatres; and the producers are so desperate they're giving tickets away to a freethought group.
I predict that Expelled will flop even more egregiously in Canada than it did in the US. Reasons: there are not as many far-right religious crackpots in Canada; Canadians don't really care so much about US church-state battles; it's only playing in a relatively small number of theatres; and the producers are so desperate they're giving tickets away to a freethought group.
Sunday, June 22, 2008
Oh, the Inanity! Slack in The Scientist
I've never read anything by Gordy Slack before, but based on this opinion piece in The Scientist, I'm not likely to in the future. Slack tries to defend the ID crowd, but all he comes up with is a confused mess.
Slack claims that ID advocates "make a few worthy points". But his examples demonstrate nothing of the sort.
1. Slack says, "While there is important work going on in the area of biogenesis, for instance, I think it's fair to say that science is still in the dark about this fundamental question." (Judging from the context, it seems that Slack really means abiogenesis.) He continues, "I think it is disingenuous to argue that the origin of life is irrelevant to evolution. It is no less relevant than the Big Bang is to physics or cosmology." This is just idiotic. Evolution is, by definition, what happens after there is a replicator to replicate. What came before is certainly relevant to biology, but it is not, strictly speaking, part of evolution itself. Even if some magical sky fairy created the first replicator, it wouldn't change all we know about the mechanisms of evolution today. Slack compares the Big Bang to physics, but then he doesn't compare the origin of life to biology, but rather to evolution. Isn't it clear that the analogy is faulty?
I disagree with Slack that we've made little progress in understanding abiogenesis. (What is this paper, chopped liver?) But even if mainstream science has made little progress, what progress has ID made? Nothing. No scientific papers, no testable models, no predictions. Nada. Zilch.
2. Slack says, "Second, IDers also argue that the cell is far more complex than Darwin could have imagined 149 years ago when he published On the Origin of Species." And so what? ID advocates weren't the ones to discover the cell's complexity, and they weren't the first to observe it was more complex than originally thought. (Darwin, by the way, knew well that the cell was not an undifferentiated blob of protoplasm; the nucleus was discovered in 1833.) And Darwin got lots of things wrong, so why is it even relevant to modern evolutionary biology what Darwin thought 149 years ago? The ID advocates would only have a worthwhile point if mainstream biologists were denying the complexity of cellular processes. But they don't. Mainstream biologists discovered the complexity. So what's the point?
3. Slack says, "Millions of people believe they directly experience the reality of a Creator every day, and to them it seems like nonsense to insist that He does not exist. Unless they are lying, God's existence is to them an observable fact. Denying it would be like insisting that my love for my children was an illusion created by neurotransmitters." I don't understand why something should be considered true simply because millions of peeople believe it. After all, there are probably millions of people who believe in witches, or that Elvis is still alive, or that 9/11 was a vast government conspiracy. But without evidence to support these claims, there's no reason why I need to take them seriously. Slack's comparison to "love for my children" being an "illusion" is remarkably inapposite. As a materialist, my guess is that love is, indeed, a product of neurotransmitters. But that doesn't mean that the experience of love is an "illusion". The neurotransmitters create the experience, but that doesn't mean the experience doesn't exist. Belief in a deity, however, is different. You can have the experience of a supernatural presence, but that doesn't mean the experience corresponds to anything outside your head. I don't see why Slack doesn't understand the difference.
4. Finally, Slack says that those who accept evolution can be dogmatic followers, too. "I met dozens of people there who were dead sure that evolutionary theory was correct though they didn't know a thing about adaptive radiation, genetic drift, or even plain old natural selection." Any field has dogmatic followers. But this has nothing to do whether ID is correct, is science, or has anything useful to say.
The really big point, the one that Slack misses completely, is the transparent dishonesty of nearly everything about intelligent design. ID advocates have to lie, because the evidence for evolution is so strong that they have no choice. That's something that even John Derbyshire understands, but Slack doesn't display any awareness of it.
All in all, this is one of the lamest defenses of ID I've ever seen.
Slack claims that ID advocates "make a few worthy points". But his examples demonstrate nothing of the sort.
1. Slack says, "While there is important work going on in the area of biogenesis, for instance, I think it's fair to say that science is still in the dark about this fundamental question." (Judging from the context, it seems that Slack really means abiogenesis.) He continues, "I think it is disingenuous to argue that the origin of life is irrelevant to evolution. It is no less relevant than the Big Bang is to physics or cosmology." This is just idiotic. Evolution is, by definition, what happens after there is a replicator to replicate. What came before is certainly relevant to biology, but it is not, strictly speaking, part of evolution itself. Even if some magical sky fairy created the first replicator, it wouldn't change all we know about the mechanisms of evolution today. Slack compares the Big Bang to physics, but then he doesn't compare the origin of life to biology, but rather to evolution. Isn't it clear that the analogy is faulty?
I disagree with Slack that we've made little progress in understanding abiogenesis. (What is this paper, chopped liver?) But even if mainstream science has made little progress, what progress has ID made? Nothing. No scientific papers, no testable models, no predictions. Nada. Zilch.
2. Slack says, "Second, IDers also argue that the cell is far more complex than Darwin could have imagined 149 years ago when he published On the Origin of Species." And so what? ID advocates weren't the ones to discover the cell's complexity, and they weren't the first to observe it was more complex than originally thought. (Darwin, by the way, knew well that the cell was not an undifferentiated blob of protoplasm; the nucleus was discovered in 1833.) And Darwin got lots of things wrong, so why is it even relevant to modern evolutionary biology what Darwin thought 149 years ago? The ID advocates would only have a worthwhile point if mainstream biologists were denying the complexity of cellular processes. But they don't. Mainstream biologists discovered the complexity. So what's the point?
3. Slack says, "Millions of people believe they directly experience the reality of a Creator every day, and to them it seems like nonsense to insist that He does not exist. Unless they are lying, God's existence is to them an observable fact. Denying it would be like insisting that my love for my children was an illusion created by neurotransmitters." I don't understand why something should be considered true simply because millions of peeople believe it. After all, there are probably millions of people who believe in witches, or that Elvis is still alive, or that 9/11 was a vast government conspiracy. But without evidence to support these claims, there's no reason why I need to take them seriously. Slack's comparison to "love for my children" being an "illusion" is remarkably inapposite. As a materialist, my guess is that love is, indeed, a product of neurotransmitters. But that doesn't mean that the experience of love is an "illusion". The neurotransmitters create the experience, but that doesn't mean the experience doesn't exist. Belief in a deity, however, is different. You can have the experience of a supernatural presence, but that doesn't mean the experience corresponds to anything outside your head. I don't see why Slack doesn't understand the difference.
4. Finally, Slack says that those who accept evolution can be dogmatic followers, too. "I met dozens of people there who were dead sure that evolutionary theory was correct though they didn't know a thing about adaptive radiation, genetic drift, or even plain old natural selection." Any field has dogmatic followers. But this has nothing to do whether ID is correct, is science, or has anything useful to say.
The really big point, the one that Slack misses completely, is the transparent dishonesty of nearly everything about intelligent design. ID advocates have to lie, because the evidence for evolution is so strong that they have no choice. That's something that even John Derbyshire understands, but Slack doesn't display any awareness of it.
All in all, this is one of the lamest defenses of ID I've ever seen.
Thursday, June 19, 2008
Psychic's Report Basis for Child Abuse Investigation
An appalling story out of Barrie: the Simcoe County District School Board reportedly started an investigation into sexual abuse of a child after receiving a report from a psychic consulted by the child's educational assistant at the school.
As reported by Canadian Press, the psychic claimed "a youngster whose name started with "V" was being sexually abused by a man between 23 and 26 years old" and so the Children's Aid Society was called to investigate.
If the facts are as reported, this is a horrifying and ridiculous intrusion into family life based on utter nonsense. The Simcoe County District School Board owes the parent and child an apology.
As reported by Canadian Press, the psychic claimed "a youngster whose name started with "V" was being sexually abused by a man between 23 and 26 years old" and so the Children's Aid Society was called to investigate.
If the facts are as reported, this is a horrifying and ridiculous intrusion into family life based on utter nonsense. The Simcoe County District School Board owes the parent and child an apology.
Tuesday, June 17, 2008
The Davis-Weller Study on HIV Transmission Misrepresented Again
In 1999, Davis and Weller published a paper in Family Planning Perspectives entitled "The Effectiveness of Condoms in Reducing Heterosexual Transmission of HIV". Their meta-study combined results from other studies about couples where one partner was HIV-positive and the other not, with respect to how often a condom was used. Unfortunately, their conclusions (and the conclusions of an earlier study by Weller alone) have been systematically misrepresented by conservative Christian activists.
I've written about this misrepresentation before. In 1993, Harold Albrecht, a local MP, misrepresented the earlier study by claiming that "An analysis by researchers at the University of Texas estimates that when condoms are used, the risk of acquiring HIV from an infected partner is 31 per cent over a year's time."
Now the work of Davis and Weller has been misrepresented again. Our local paper, the Kitchener-Waterloo Record, has a "Community Editorial Board", where local residents are tapped to write a series of opinion pieces. (I was on the Board in 2000, and you can see my columns here.) Yesterday the Record carried this column by Harriette Mostert, who is described as a "part-time teacher and a longtime community volunteer".
Mostert claimed that this NIH report says that "HIV/AIDS carries a 15 per cent risk of transmission even with a condom". However, the NIH report was referring to the Davis-Weller study, and it is being misrepresented again.
The Davis-Weller study found that using a condom reduces the risk of HIV transmission by 85%. Now, you might think that Mostert's 15% figure is just 100%-85%, and so she's correct. But you would be wrong.
Davis and Weller were studying the reduction in risk obtained when using a condom; Mostert incorrectly labels this the "risk of transmission". They're not the same at all. I think most people would interpret "risk of transmission" as meaning "the chances that you will get the disease in a single encounter", and indeed, that's the interpretation I got when I asked several people what they thought it means. Or maybe it means "the chances that you will get the disease in a year"? The lack of units should raise warning bells in the mind of any educated person.
The answer is that Davis and Weller found that in one year, 6.7 infections per 100 person-years occurred when a condom is not used, and 0.9 infections per 100 person-years occurred when a condom is always used. The reduction in risk is therefore (6.7-0.9)/6.7, or approximately 85%. Contrary to Mostert, the "risk of transmission" when using a condom is less than 1 infection in 100 person years. There's no way this can be characterized as "15%".
Mostert uses this bogus figure to argue for "chastity or monogamy", and smugly concludes "Interestingly, this is also consistent with the ideals set out in many faith communities." She fails to note that the very study she cites concludes "These data provide strong evidence for the effectiveness of condoms for reducing sexually transmitted HIV."
I've written about this misrepresentation before. In 1993, Harold Albrecht, a local MP, misrepresented the earlier study by claiming that "An analysis by researchers at the University of Texas estimates that when condoms are used, the risk of acquiring HIV from an infected partner is 31 per cent over a year's time."
Now the work of Davis and Weller has been misrepresented again. Our local paper, the Kitchener-Waterloo Record, has a "Community Editorial Board", where local residents are tapped to write a series of opinion pieces. (I was on the Board in 2000, and you can see my columns here.) Yesterday the Record carried this column by Harriette Mostert, who is described as a "part-time teacher and a longtime community volunteer".
Mostert claimed that this NIH report says that "HIV/AIDS carries a 15 per cent risk of transmission even with a condom". However, the NIH report was referring to the Davis-Weller study, and it is being misrepresented again.
The Davis-Weller study found that using a condom reduces the risk of HIV transmission by 85%. Now, you might think that Mostert's 15% figure is just 100%-85%, and so she's correct. But you would be wrong.
Davis and Weller were studying the reduction in risk obtained when using a condom; Mostert incorrectly labels this the "risk of transmission". They're not the same at all. I think most people would interpret "risk of transmission" as meaning "the chances that you will get the disease in a single encounter", and indeed, that's the interpretation I got when I asked several people what they thought it means. Or maybe it means "the chances that you will get the disease in a year"? The lack of units should raise warning bells in the mind of any educated person.
The answer is that Davis and Weller found that in one year, 6.7 infections per 100 person-years occurred when a condom is not used, and 0.9 infections per 100 person-years occurred when a condom is always used. The reduction in risk is therefore (6.7-0.9)/6.7, or approximately 85%. Contrary to Mostert, the "risk of transmission" when using a condom is less than 1 infection in 100 person years. There's no way this can be characterized as "15%".
Mostert uses this bogus figure to argue for "chastity or monogamy", and smugly concludes "Interestingly, this is also consistent with the ideals set out in many faith communities." She fails to note that the very study she cites concludes "These data provide strong evidence for the effectiveness of condoms for reducing sexually transmitted HIV."
Thursday, June 12, 2008
Google Maps Easter Egg
Eric Veach of Google just spoke here at Waterloo about Google Maps in the J. W. Graham medal seminar. He told us about various strategies involved in making Google Maps work, including prerendering the maps, and dividing the work up so it can be done in parallel, with more processors allocated to denser parts of the world.
He also revealed the following easter egg: try getting driving directions from San Francisco, CA, to Sydney, Australia. The resulting itinerary takes about 41 days, but that's because much of the trip isn't by car.
He also revealed the following easter egg: try getting driving directions from San Francisco, CA, to Sydney, Australia. The resulting itinerary takes about 41 days, but that's because much of the trip isn't by car.
Wednesday, June 11, 2008
The Open Problem Garden
The Open Problem Garden is a fledgling site that deserves more contributions.
There's not very much information about the purpose of the site, but from what I can gather, it's intended to be a repository for open problems in mathematics and theoretical computer science. I think that's a great idea, but the number of contributions is still pretty small (only about 150 problems so far). If you know some good open problems, please consider adding them to the site.
I added a a problem about discrete iterations, which I'll repeat here because it is so easy to state, yet frustratingly difficult to solve.
Start with two integers, a and b, with a > b > 0. Now repeatedly replace b with a mod b, counting the number of steps it takes to get to 0, and call this P(a,b). For example, if we start with a = 35 and b = 22, we get
35 mod 22 = 13
35 mod 13 = 9
35 mod 9 = 8
35 mod 8 = 3
35 mod 3 = 2
35 mod 2 = 1
35 mod 1 = 0
It took 7 steps to get down to 0, so P(35,22) = 7.
The question is, at what rate does P(a,b) grow? It's not hard to see that for some a, P(a,b) can be as big as Ω(log a). (Take a = lcm(1,2,..., n)-1 and b = n.) But what's a good upper bound? I conjecture it's O((log a)2), but the best that's been proven so far is O( a1/3).
Oh, and by the way -- I offer $50 for the solution to this problem.
There's not very much information about the purpose of the site, but from what I can gather, it's intended to be a repository for open problems in mathematics and theoretical computer science. I think that's a great idea, but the number of contributions is still pretty small (only about 150 problems so far). If you know some good open problems, please consider adding them to the site.
I added a a problem about discrete iterations, which I'll repeat here because it is so easy to state, yet frustratingly difficult to solve.
Start with two integers, a and b, with a > b > 0. Now repeatedly replace b with a mod b, counting the number of steps it takes to get to 0, and call this P(a,b). For example, if we start with a = 35 and b = 22, we get
35 mod 22 = 13
35 mod 13 = 9
35 mod 9 = 8
35 mod 8 = 3
35 mod 3 = 2
35 mod 2 = 1
35 mod 1 = 0
It took 7 steps to get down to 0, so P(35,22) = 7.
The question is, at what rate does P(a,b) grow? It's not hard to see that for some a, P(a,b) can be as big as Ω(log a). (Take a = lcm(1,2,..., n)-1 and b = n.) But what's a good upper bound? I conjecture it's O((log a)2), but the best that's been proven so far is O( a1/3).
Oh, and by the way -- I offer $50 for the solution to this problem.
Friday, June 06, 2008
Which Plumber Would You Choose?
This is an advertisement at the corner of Victoria and Margaret Streets in Kitchener, Ontario:
On the left: Mike the Plumber, with a Christian cross replacing the "t" in "the".
On the right: TIger Plumbing, with (apparently) no religious references in their advertisement.
I'd definitely choose Tiger Plumbing. It doesn't matter to me one whit what religion my plumber is; what I care about is how good he or she will do their job, how quickly they can come, and how reasonable their prices are. But I definitely wouldn't choose anyone who explicitly announces their religion in their ad, either, because that suggests an unhealthy preoccupation with their creed, not to mention the insinuation that they are somehow more reliable/honest/reputable simply because they adhere to some particular religion.
On the left: Mike the Plumber, with a Christian cross replacing the "t" in "the".
On the right: TIger Plumbing, with (apparently) no religious references in their advertisement.
I'd definitely choose Tiger Plumbing. It doesn't matter to me one whit what religion my plumber is; what I care about is how good he or she will do their job, how quickly they can come, and how reasonable their prices are. But I definitely wouldn't choose anyone who explicitly announces their religion in their ad, either, because that suggests an unhealthy preoccupation with their creed, not to mention the insinuation that they are somehow more reliable/honest/reputable simply because they adhere to some particular religion.
Tuesday, June 03, 2008
The Best That Theists Can Provide?
Here's a attack on skepticism and atheism by Edward Tingley, a professor at Augustine College in Ottawa. It's not very good.
Tingley seems to concede that there's no evidence for the Christian god. But that doesn't mean his god doesn't exist. Oh no! We must seek his god with our "heart". But what is the "heart"? Tingley says it isn't "feelings". But he doesn't say clearly what it is.
Tingley says the atheist can't distinguish between a god that doesn't exist and a god that does exist, but hides. But the theist can't distinguish between these alternatives, either. And a god that hides might just as well be no god at all, for how could we possibly know what that god did or what he/she wants? Maybe god really wants us all to be atheists, and salvation is reserved for those who don't believe.
The easiest way to see how Tingley's argument fails is to take his essay, and every time "God" appears, substitute "Odin":
"If we do not know that Odin even exists, we hardly know how he behaves. So we cannot begin this ascent with any dogmatic presumption about his behavior. Maybe, if he exists, Odin would show himself directly to our senses. But maybe he wouldn’t. Maybe he would hide from us..."
"What reason do I have to subordinate the possibility of Odin's existence to the powers of my senses?"
"All of the people who say that they are “atheists through skepticism, because they see no evidence that Odin exists,” are patently unthinking people, since by virtue of turning skeptic, no one has ever done anything—employed any logic, gathered any evidence, found any way forward—to reach a conclusion about whether Odin exists. So these atheists have not reached a conclusion; they have made a commitment."
If TIngley tried to use these kind of arguments to convince people that belief in Odin was justifiable, most would just laugh. And yet they are supposed to be good arguments against atheism and for his theism. Go figure.
Addendum: Does anyone else see the irony in someone insulting skepticism while teaching at an institution that demands the following statement of faith:
We subscribe without cavil to each of the clauses in the earliest general confession of the Church known as the Apostles' Creed:
I believe in God, the Father almighty, creator of heaven and earth.
I believe in Jesus Christ, His only Son, our Lord. He was conceived by the power of the Holy Spirit and born of the Virgin Mary. He suffered under Pontius Pilate, was crucified, died, and was buried. He descended to the dead. On the third day He rose again. He ascended into heaven and sits at the right hand of God, the Father Almighty. From thence He shall come to judge the living and the dead.
I believe in the Holy Spirit, the holy catholic* Church, the communion of saints, the forgiveness of sins, the resurrection of the body, and the life everlasting. Amen.
* "universal"
Yup, that sure sounds like someone who is committed to an impartial search for truth!
Tingley seems to concede that there's no evidence for the Christian god. But that doesn't mean his god doesn't exist. Oh no! We must seek his god with our "heart". But what is the "heart"? Tingley says it isn't "feelings". But he doesn't say clearly what it is.
Tingley says the atheist can't distinguish between a god that doesn't exist and a god that does exist, but hides. But the theist can't distinguish between these alternatives, either. And a god that hides might just as well be no god at all, for how could we possibly know what that god did or what he/she wants? Maybe god really wants us all to be atheists, and salvation is reserved for those who don't believe.
The easiest way to see how Tingley's argument fails is to take his essay, and every time "God" appears, substitute "Odin":
"If we do not know that Odin even exists, we hardly know how he behaves. So we cannot begin this ascent with any dogmatic presumption about his behavior. Maybe, if he exists, Odin would show himself directly to our senses. But maybe he wouldn’t. Maybe he would hide from us..."
"What reason do I have to subordinate the possibility of Odin's existence to the powers of my senses?"
"All of the people who say that they are “atheists through skepticism, because they see no evidence that Odin exists,” are patently unthinking people, since by virtue of turning skeptic, no one has ever done anything—employed any logic, gathered any evidence, found any way forward—to reach a conclusion about whether Odin exists. So these atheists have not reached a conclusion; they have made a commitment."
If TIngley tried to use these kind of arguments to convince people that belief in Odin was justifiable, most would just laugh. And yet they are supposed to be good arguments against atheism and for his theism. Go figure.
Addendum: Does anyone else see the irony in someone insulting skepticism while teaching at an institution that demands the following statement of faith:
We subscribe without cavil to each of the clauses in the earliest general confession of the Church known as the Apostles' Creed:
I believe in God, the Father almighty, creator of heaven and earth.
I believe in Jesus Christ, His only Son, our Lord. He was conceived by the power of the Holy Spirit and born of the Virgin Mary. He suffered under Pontius Pilate, was crucified, died, and was buried. He descended to the dead. On the third day He rose again. He ascended into heaven and sits at the right hand of God, the Father Almighty. From thence He shall come to judge the living and the dead.
I believe in the Holy Spirit, the holy catholic* Church, the communion of saints, the forgiveness of sins, the resurrection of the body, and the life everlasting. Amen.
* "universal"
Yup, that sure sounds like someone who is committed to an impartial search for truth!
Saturday, May 31, 2008
"Religion is a Lie" is a Lie
This name of this domain, religionisalie.com, promises something completely different from what it delivers. While it pretends to be critical of religion, in fact it is nothing more than the usual gibberish-for-Jesus.
When your product is intellectually bankrupt, is it any wonder that you have to lie to sell it?
When your product is intellectually bankrupt, is it any wonder that you have to lie to sell it?
Tuesday, May 27, 2008
Pretentious Sign Contest
OK, let's have a pretentious sign contest!
The winner will receive a prize.
Rules: the sign should be as pretentious as possible, saying something simple in a flowery or ridiculously verbose way.
Here's my nomination:
Translation: "Be nice to the janitor! Put trash in trash cans."
Now, it's up to you.
The winner will receive a prize.
Rules: the sign should be as pretentious as possible, saying something simple in a flowery or ridiculously verbose way.
Here's my nomination:
Translation: "Be nice to the janitor! Put trash in trash cans."
Now, it's up to you.
Monday, May 26, 2008
Expelled a Failure!
Well, no surprise to anyone who's followed the story, but the ID documentary Expelled is essentially dead in theatres.
According to Box Office Mojo, not even creationists are dumb enough to pay good money to watch this turkey. After its opening weekend, Expelled attendance fell off exponentially in weekend gross, with each weekend earning less than 1/2 the previous. Theatre count also decreased each week; only 83 theatres nationwide are showing this loser now. Similarly, the amount taken in per theatre decreased each week, down to this week's $423/theatre. You could probably get more by showing Battlefield Earth.
According to Box Office Mojo, not even creationists are dumb enough to pay good money to watch this turkey. After its opening weekend, Expelled attendance fell off exponentially in weekend gross, with each weekend earning less than 1/2 the previous. Theatre count also decreased each week; only 83 theatres nationwide are showing this loser now. Similarly, the amount taken in per theatre decreased each week, down to this week's $423/theatre. You could probably get more by showing Battlefield Earth.
Saturday, May 24, 2008
Oreo Innumeracy
"30% Less Fat per 2 Cookies"? How much less fat per 1 cookie?
OK, I can think of a plausible reason* why it's phrased that way, but mathematically, it just sounds stupid.
* Because 2 cookies is the serving size, and maybe there's a legal requirement that any claims about "less fat" must be expressed in terms of the serving size.
OK, I can think of a plausible reason* why it's phrased that way, but mathematically, it just sounds stupid.
* Because 2 cookies is the serving size, and maybe there's a legal requirement that any claims about "less fat" must be expressed in terms of the serving size.
Friday, May 23, 2008
Strange Duck Behavior
It feels like something out of a Gary Larson cartoon.
The local ducks have suddenly learned to hang out on rooftops. I've lived in the same house for 18 years, and I've never seen this before, but suddenly, this year, more and more ducks and geese are perching and even sometimes nesting on rooftops.
Here are two pictures I took yesterday of a duck on the house next door, a good 20 feet above the ground. It looks like he is surveying the territory prior to swooping down and nabbing some unsuspecting child.
Be afraid. Be very afraid.
The local ducks have suddenly learned to hang out on rooftops. I've lived in the same house for 18 years, and I've never seen this before, but suddenly, this year, more and more ducks and geese are perching and even sometimes nesting on rooftops.
Here are two pictures I took yesterday of a duck on the house next door, a good 20 feet above the ground. It looks like he is surveying the territory prior to swooping down and nabbing some unsuspecting child.
Be afraid. Be very afraid.
Thursday, May 22, 2008
Royalists in France
One of the things I find embarrassing about Canada is its devotion to the monarchy; it seems remarkably childish to me. As columnist Allan Fotheringham once remarked, "Grown-up nations do not need, as head of state, a woman -- however nice --who lives across a large ocean in a castle in a foreign country."
But on a recent trip to France, I saw something even more strange: a poster for the Alliance Royale. This is, believe it or not, a political movement to restore the monarchy in France. It seems largely spearheaded by someone named Yves-Marie Adeline, who actually has a blog for his royalist views. There is also an FAQ which is remarkable for its obliqueness, although it does forthrightly admit that "A law that applies uniformly to everyone leads to injustice".
Luckily, this party hasn't won any seats, as far as I can tell. Indeed, they seem to be garnering something like .03% of the vote.
But on a recent trip to France, I saw something even more strange: a poster for the Alliance Royale. This is, believe it or not, a political movement to restore the monarchy in France. It seems largely spearheaded by someone named Yves-Marie Adeline, who actually has a blog for his royalist views. There is also an FAQ which is remarkable for its obliqueness, although it does forthrightly admit that "A law that applies uniformly to everyone leads to injustice".
Luckily, this party hasn't won any seats, as far as I can tell. Indeed, they seem to be garnering something like .03% of the vote.
Wednesday, May 21, 2008
Is IDiocy Genetic?
Far-right crackpot Phyllis Schlafly weighs in on Expelled, repeating the usual lie that "Dr. Richard Sternberg, a biologist ... lost his position at the prestigious Smithsonian Institution after he published a peer-reviewed article that mentioned intelligent design."
Now I see that her son, Roger Schlafly, has the same affliction: about the transparent effort to relabel creationism as intelligent design in the book Of Pandas and People he writes: "Judge Jones found that the Pandas book was subsequently edited to remove references to creationism, and made inferences about the motives of the Pandas authors. I think that it is bizarre to denigrate folks for complying with a court decision."
This transparent effort to exonerate the writers of Of Pandas and People for their editing just won't fly. It is completely obvious to anyone with connected brain cells that the replacement of "creationism" with "intelligent design" was not a good-faith effort to "comply with a court decision", but a dishonest and deceptive way to make an end-run around the intent of the decision.
Roger Schlafly thinks "Evolutionists [are] preoccupied with motives". But in the law, as in everyday life, motive is often taken into account when judging the actions of people: Actus non facit reum nisi mens sit rea.
It seems that, in this case, IDiocy has a genetic component.
Now I see that her son, Roger Schlafly, has the same affliction: about the transparent effort to relabel creationism as intelligent design in the book Of Pandas and People he writes: "Judge Jones found that the Pandas book was subsequently edited to remove references to creationism, and made inferences about the motives of the Pandas authors. I think that it is bizarre to denigrate folks for complying with a court decision."
This transparent effort to exonerate the writers of Of Pandas and People for their editing just won't fly. It is completely obvious to anyone with connected brain cells that the replacement of "creationism" with "intelligent design" was not a good-faith effort to "comply with a court decision", but a dishonest and deceptive way to make an end-run around the intent of the decision.
Roger Schlafly thinks "Evolutionists [are] preoccupied with motives". But in the law, as in everyday life, motive is often taken into account when judging the actions of people: Actus non facit reum nisi mens sit rea.
It seems that, in this case, IDiocy has a genetic component.
Tuesday, May 20, 2008
Science Quiz
This is the laboratory of a Nobel-prize winning scientist, located on a street in Europe bearing the name of that scientist. Whose laboratory is it?
Monday, May 19, 2008
Paris
One of the nicest things about France is that streets are named after writers, painters, mathematicians, scientists, and other people of accomplishment. Here's a picture of a street sign in the 14th arrondissement, showing a street named after Étienne Bezout (1730-1783).
I became interested in Bezout a few years ago when I wrote an article entitled "Origins of the Analysis of the Euclidean Algorithm" for Historia Mathematica. One of Bezout's accomplishments was his textbook, Cours de Mathématiques à l'Usage des Gardes du Pavillon et de la Marine, which went through dozens of editions, first under Bezout, and later, at the hands of others. Supposedly even Napoleon I learned mathematics from Bezout's book.
Do Books on Atheism Belong in the Science Section?
Here's a picture of the science section at a bookstore in Trudeau airport in Montreal:
Among the books prominently displayed are
I don't understand why these books aren't in the religion or philosophy section.
Among the books prominently displayed are
- Richard Dawkins, The God Delusion
- Christopher Hitchens, The Portable Atheist
- Michael Onfray, In Defense of Atheism
I don't understand why these books aren't in the religion or philosophy section.
Saturday, May 17, 2008
Denyse O'Leary Will Teach You The Craft of Writing
Oh, boy, I really can't wait for this workshop, where I can pay $359 to hear Denyse O'Leary, dean of Canadian journalism, instruct me on how to construct sentences --- like this one:
Phyllis Schlafly, the nemesis of radical feminists who is just SO not invited to Hill Clinton's inagural (which may never happen anyway, the way things are going) puts in her two cents worth on the Expelled movie about the trials of being an intelligence design theorist in an ivy league of Darwin cultists:
It really takes an exceptional talent to combine this much fatuousness, name-calling, misspelling, and an inability to provide the correct name of her own movement, all in a single sentence.
Phyllis Schlafly, the nemesis of radical feminists who is just SO not invited to Hill Clinton's inagural (which may never happen anyway, the way things are going) puts in her two cents worth on the Expelled movie about the trials of being an intelligence design theorist in an ivy league of Darwin cultists:
It really takes an exceptional talent to combine this much fatuousness, name-calling, misspelling, and an inability to provide the correct name of her own movement, all in a single sentence.
Tuesday, May 06, 2008
Your Daily Dose of Woo
One of the commenters led me to this website of Richard Bartlett, a Seattle chiropractor who thinks he can heal people using quantum mechanics.
The website consists of the most absurd woo, such as "Matrix Energetics is a complete system of healing, self-care and transformation. It is a transferable and teachable phenomenon, powered by intent, which has a physical and observable effect every time. Complete beginners as well as seasoned health care practitioners are able to perform and utilize this work to affect change-with no waiting and no running of energy. Anyone can learn this skill and practice Matrix Energetics."
Well, if it has a physical and observable effect "every time", let's see some peer-reviewed studies that prove it. Are there any? The website doesn't provide any. It does have a section called "Research", where you can read about "polycontrast interference photography", which seems to be yet another form of woo.
Bartlett seems to have a cartoon understanding of quantum mechanics, such as when he writes
"There’s something called the Heisenberg Uncertainty Principle. What that says, essentially, is you cannot observe a system without entering into that observation and therefore changing it. Scientifically, this means that if you look at something and attempt to measure its velocity, you lose track of its actual location. If you try and track its location, you lose the ability to measure its velocity. You can never actually measure both at the same time; you can observe one and change the other."
You can bet that with seminar costing as much as $545 a shot, with multiple levels, Bartlett is raking in the cash from gullible sick people.
The website consists of the most absurd woo, such as "Matrix Energetics is a complete system of healing, self-care and transformation. It is a transferable and teachable phenomenon, powered by intent, which has a physical and observable effect every time. Complete beginners as well as seasoned health care practitioners are able to perform and utilize this work to affect change-with no waiting and no running of energy. Anyone can learn this skill and practice Matrix Energetics."
Well, if it has a physical and observable effect "every time", let's see some peer-reviewed studies that prove it. Are there any? The website doesn't provide any. It does have a section called "Research", where you can read about "polycontrast interference photography", which seems to be yet another form of woo.
Bartlett seems to have a cartoon understanding of quantum mechanics, such as when he writes
"There’s something called the Heisenberg Uncertainty Principle. What that says, essentially, is you cannot observe a system without entering into that observation and therefore changing it. Scientifically, this means that if you look at something and attempt to measure its velocity, you lose track of its actual location. If you try and track its location, you lose the ability to measure its velocity. You can never actually measure both at the same time; you can observe one and change the other."
You can bet that with seminar costing as much as $545 a shot, with multiple levels, Bartlett is raking in the cash from gullible sick people.
Reply to William Lane Craig
Two readers of this blog have pointed out this post at William Lane Craig's blog. In the post, he responds to a question about my debate with Kirk Durston. Craig says I exhibit "ignorance on parade".
Well, there's a lot of ignorance to go around. My debate was with Durston, not with Craig. I was responding to Durston's claim (made at 05:37) that "Mathematics dictates that time itself would have had to have a beginning at some point in the past." In the debate that Durston took part in just a few days earlier at McMaster University, he claimed that Hilbert, in his 1925 paper, "On the Infinite" had proved mathematically that there could not be an infinite regress of causes." But this is not true. All Hilbert did in that paper was claim that then-current consensus about the physical universe was that no infinite quantities existed in it. That's a far cry from any kind of mathematical proof. William Lane Craig, like anyone else, can go read Hilbert's paper and verify that this is the case.
I pointed out that in fact, there is nothing mathematical that rules out an infinite regress of causes. For example, you could have an event at time -(n+1) causing an event at time -(n) for all positive integers n. Thus, an event at time -2 causes an event at time -1, an event at time -3 causes an event at time -2, etc. There is nothing logical or mathematical to rule this out. You can even have an infinite regress of causes if time has a beginning. If time begins at time 0, then you can have an event at time 1/(n+1) causing an event at time 1/n for all positive integers n. Thus, for example, an event at time 1/3 causes an event at time 1/2, an event at time 1/4 causes an event at time 1/3, etc. Again, nothing logical or mathematical rules this out.
Now you might say that once we bring our current state of physical knowledge into the picture, the first scenario is ruled out. But even modern physicists consider the possibility of infinite time-like curves that occur in the past of some other point; for example, in their study of Malament-Hogarth spacetime. Thus, I would contend that apologists like Durston and Craig have a really naive view of spacetime, one that is essentially based on the understanding of 100 years ago, not modern physics.
When I called Durston on this at the debate, his response was really comical. Here it is as I have transcribed it, beginning at 1:06:48:
"First, regarding Hilbert. He [Shallit] pulled a mathematical trick
there. Those of you who are used to summing infinite series
will know that if the x decreases exponentially, it comes to a
finite value. So let me explain how this really works.
Let's assume... now I don't know whether he's saying that.
Has he dodged the issue here, as to whether or not the past is
infinite or not? So let's assume the past is infinite. So
let's call this debate time 0, this hour here of the debate is
time 0. The next hour after this will be time 0+1, time 2, and
so forth. And in the past, we'll go to, the last hour before
this debate will be negative 1 hour, hour negative 2, and so forth.
Now if you want to assume, and this is to illustrate why there's
a problem of traversing an actual infinite series in
reality. Let's say that each step in the series is one hour
long. Now what he seems to be arguing, or what he's insisting
here, I'm not sure, is that Hilbert, that the past can be
infinite, that is, there's an actual hour infinitely separated
from this one here. So let's call that -infinity. We'll never
get there by getting in a time machine and going back, so let's
just take a quantum leap back into the past, we're now at minus
infinity. Now some of those of you who are familiar with
infinite set theory might be a little uncomfortable at this
point because if the past is, if you're saying it actually is
infinite, what you mean is that there actually is an hour back
there that is infinitely separated from this one. So let's
count our way down now. Infinity minus 1, infinity minus 2.
It's one hour each, not an exponentially decreasing amount of
time like that little equation he put up there, but just a
steady hour each time.
Or you could go with a multi-universe, this universe is a
product of another universe, and we're working our way down
from -infinity to the present. At what point in time will you
arrive at 0? You will never traverse an infinite series in
reality if you must stop at a discrete amount of time for a
constant amount of time in between. And that pretty much lays
to rest this notion that time itself can be infinite as far as
the past goes. It can be potentially infinite. you can do
lots of mathematical things, I can hold my hands together and
say there's an infinite number of mathematical points, no
problem, those are imaginary. But the moment you have a
discrete amount, that occupies a discrete amount of time, like
a minute, or a second, or an hour, and it is not decreasing
then suddenly you have a problem, if you want to actually
traverse that infinite series in reality."
After Durston's casual slur on my character at the beginning, this is completely incoherent. My equation was not "exponential", so that criticism is nonsensical. Secondly, it is perfectly possible to have an infinite past without having any point at infinite distance from the current time; for example, we could define times -1, -2, -3, etc., without having to define an actual point called "-infinity". (In exactly the same way, the negative integers are an infinite set that does not contain an integer called "-infinity".) This is not exactly a controversial point, but it is a misconception common to undergraduates. Mr. Durston, a graduate student, should know better.
Craig doesn't seem to understand what the debate was about. He says, "What's really peculiar is Shallit's "that was then, but this is now" move—as though views of mathematical existence are tied to the times!", thereby entirely missing the point. Hilbert's claim was about the 1925 understanding of physical existence, not mathematical existence. And anyway, views of mathematical existence do change through time. Consider, for example, the views of people like Brouwer.
Craig says, "On Shallit's view the universe still came into being a finite time ago and therefore requires an external cause." No, I didn't say that at all, and I don't hold that. In my second example, I said that "you can have an event at time 1/(n+1) causing an event at time 1/(n) for all positive integers n". This doesn't say anything about time 0, and it is logically possible to have an infinite chain of causes stretching back in this way, with nothing happening at time 0 at all - an uncaused beginning.
In general, Craig seems to have an extremely naive, almost childish view of infinity. Read Craig's reply to Sobel. On page 9 he says, "Imagine an actually infinite regress of past causes terminating in the present effect. In this case, the regress of causes terminating, say, yesterday, or, for that matter, at any day in the infinite past, has exactly the same number of causes as the regress terminating in the present. This seems absurd, since the entire regress contains all the same causes as any selected partial regress plus an arbitrarily large number of additional causes as well. Or again, if we number the causes, there will be as many odd-numbered causes as there are causes, which seems absurd, since there are an equally infinite number of even-numbered causes in the series in addition to the self-same odd-numbered causes."
It seems that what bothers Craig is perfectly understandable to any mathematician: namely, that the set of positive integers has the same cardinality as the set of integers greater than n (for any positive n), and the same cardinality as the set of even positive integers. All this was well understood 125 years ago, but it seems the Christian apologists haven't caught up.
Altogether, I would say these arguments by Durston and Craig are embarrassingly naive.
Well, there's a lot of ignorance to go around. My debate was with Durston, not with Craig. I was responding to Durston's claim (made at 05:37) that "Mathematics dictates that time itself would have had to have a beginning at some point in the past." In the debate that Durston took part in just a few days earlier at McMaster University, he claimed that Hilbert, in his 1925 paper, "On the Infinite" had proved mathematically that there could not be an infinite regress of causes." But this is not true. All Hilbert did in that paper was claim that then-current consensus about the physical universe was that no infinite quantities existed in it. That's a far cry from any kind of mathematical proof. William Lane Craig, like anyone else, can go read Hilbert's paper and verify that this is the case.
I pointed out that in fact, there is nothing mathematical that rules out an infinite regress of causes. For example, you could have an event at time -(n+1) causing an event at time -(n) for all positive integers n. Thus, an event at time -2 causes an event at time -1, an event at time -3 causes an event at time -2, etc. There is nothing logical or mathematical to rule this out. You can even have an infinite regress of causes if time has a beginning. If time begins at time 0, then you can have an event at time 1/(n+1) causing an event at time 1/n for all positive integers n. Thus, for example, an event at time 1/3 causes an event at time 1/2, an event at time 1/4 causes an event at time 1/3, etc. Again, nothing logical or mathematical rules this out.
Now you might say that once we bring our current state of physical knowledge into the picture, the first scenario is ruled out. But even modern physicists consider the possibility of infinite time-like curves that occur in the past of some other point; for example, in their study of Malament-Hogarth spacetime. Thus, I would contend that apologists like Durston and Craig have a really naive view of spacetime, one that is essentially based on the understanding of 100 years ago, not modern physics.
When I called Durston on this at the debate, his response was really comical. Here it is as I have transcribed it, beginning at 1:06:48:
"First, regarding Hilbert. He [Shallit] pulled a mathematical trick
there. Those of you who are used to summing infinite series
will know that if the x decreases exponentially, it comes to a
finite value. So let me explain how this really works.
Let's assume... now I don't know whether he's saying that.
Has he dodged the issue here, as to whether or not the past is
infinite or not? So let's assume the past is infinite. So
let's call this debate time 0, this hour here of the debate is
time 0. The next hour after this will be time 0+1, time 2, and
so forth. And in the past, we'll go to, the last hour before
this debate will be negative 1 hour, hour negative 2, and so forth.
Now if you want to assume, and this is to illustrate why there's
a problem of traversing an actual infinite series in
reality. Let's say that each step in the series is one hour
long. Now what he seems to be arguing, or what he's insisting
here, I'm not sure, is that Hilbert, that the past can be
infinite, that is, there's an actual hour infinitely separated
from this one here. So let's call that -infinity. We'll never
get there by getting in a time machine and going back, so let's
just take a quantum leap back into the past, we're now at minus
infinity. Now some of those of you who are familiar with
infinite set theory might be a little uncomfortable at this
point because if the past is, if you're saying it actually is
infinite, what you mean is that there actually is an hour back
there that is infinitely separated from this one. So let's
count our way down now. Infinity minus 1, infinity minus 2.
It's one hour each, not an exponentially decreasing amount of
time like that little equation he put up there, but just a
steady hour each time.
Or you could go with a multi-universe, this universe is a
product of another universe, and we're working our way down
from -infinity to the present. At what point in time will you
arrive at 0? You will never traverse an infinite series in
reality if you must stop at a discrete amount of time for a
constant amount of time in between. And that pretty much lays
to rest this notion that time itself can be infinite as far as
the past goes. It can be potentially infinite. you can do
lots of mathematical things, I can hold my hands together and
say there's an infinite number of mathematical points, no
problem, those are imaginary. But the moment you have a
discrete amount, that occupies a discrete amount of time, like
a minute, or a second, or an hour, and it is not decreasing
then suddenly you have a problem, if you want to actually
traverse that infinite series in reality."
After Durston's casual slur on my character at the beginning, this is completely incoherent. My equation was not "exponential", so that criticism is nonsensical. Secondly, it is perfectly possible to have an infinite past without having any point at infinite distance from the current time; for example, we could define times -1, -2, -3, etc., without having to define an actual point called "-infinity". (In exactly the same way, the negative integers are an infinite set that does not contain an integer called "-infinity".) This is not exactly a controversial point, but it is a misconception common to undergraduates. Mr. Durston, a graduate student, should know better.
Craig doesn't seem to understand what the debate was about. He says, "What's really peculiar is Shallit's "that was then, but this is now" move—as though views of mathematical existence are tied to the times!", thereby entirely missing the point. Hilbert's claim was about the 1925 understanding of physical existence, not mathematical existence. And anyway, views of mathematical existence do change through time. Consider, for example, the views of people like Brouwer.
Craig says, "On Shallit's view the universe still came into being a finite time ago and therefore requires an external cause." No, I didn't say that at all, and I don't hold that. In my second example, I said that "you can have an event at time 1/(n+1) causing an event at time 1/(n) for all positive integers n". This doesn't say anything about time 0, and it is logically possible to have an infinite chain of causes stretching back in this way, with nothing happening at time 0 at all - an uncaused beginning.
In general, Craig seems to have an extremely naive, almost childish view of infinity. Read Craig's reply to Sobel. On page 9 he says, "Imagine an actually infinite regress of past causes terminating in the present effect. In this case, the regress of causes terminating, say, yesterday, or, for that matter, at any day in the infinite past, has exactly the same number of causes as the regress terminating in the present. This seems absurd, since the entire regress contains all the same causes as any selected partial regress plus an arbitrarily large number of additional causes as well. Or again, if we number the causes, there will be as many odd-numbered causes as there are causes, which seems absurd, since there are an equally infinite number of even-numbered causes in the series in addition to the self-same odd-numbered causes."
It seems that what bothers Craig is perfectly understandable to any mathematician: namely, that the set of positive integers has the same cardinality as the set of integers greater than n (for any positive n), and the same cardinality as the set of even positive integers. All this was well understood 125 years ago, but it seems the Christian apologists haven't caught up.
Altogether, I would say these arguments by Durston and Craig are embarrassingly naive.
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