Contra Dancing and Mathematics
Last week I met Larry Copes at the American Mathematical Society and Mathematical Association of America joint meetings in Baltimore, MD, USA. He gave an presentation on the mathematics of contra dancing. He tried to find what I call an omnicontra dance, a dance that omninates through all of the possible dance positions. After some searching and discarding of dance steps that would be rather unnatural, he found 4 good dances.
I too have done some work with the mathematics of contra dancing. I relate it to group theory and compare it to changing a mattress. My article states that the contra dancing foursomes group is the group of symmetries of a square, also called D4. In addition, the overall procedure of passing down the line in contra dancing is also a group, Dn, where n is the number of foursomes in the dance. Today I tried to find the overall group of all of these actions, for eight contra dancers. I used some software to find a group with 384 elements in it; this contains some steps that would never occur in a contra dance, such as the next set of foursomes circling around before the previous set has finished its moves and switched the two partners. I think it may have 64 elements, but am not certain.
Then I actually went out contra dancing and danced in 6 of the dances. It is quite different actually dancing it then analyzing it. I met quite a few people tonight, mostly women. What struck me the most is that people from ordinary walks of life, with little or no knowledge of mathematics, are able to execute all these moves in the required order and move about in a group with maybe hundreds of elements in it. The band was good - a group named Orion. It is also a good way to introduce people to group theory. If I ever teach a course in college abstract algebra, when I get to the group theory part, I will invite my class to the local contra dance. The best way to learn mathematics may be to become a part of mathematics, and contra dancing certainly does that.
A Journey through Blogrealm
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2003/01/25
Internet Threat
I have seen my Internet service get worse and worse the past few months. On the web it seems that every site that you go to, other than personal sites like mine, throw uninvited popup windows in your face, as well as ads on the page. These slow down downloading of the web page, and can even lead to a weird looking page. If you use Norton Internet Security's ad blocking, and go to an editorial on the Washington Post, you will get a misshapen window. I suppose the ads are so tied to the structure of the page that eliminating them results in a weird page.
Viruses are becoming more threatening, too. Actually it is just one virus, w32.Klez.H @ mm, which sees fit to pull names off address books for both From: and To: blocks, and I get lots of virus messages accusing me of sending something I didn't send. And spam is getting worse. The latest spam atrocity was something that pulled names from address books and paired them with random email addresses. I then get squawks from places that can't receive the email saying that I, Linda Rodriguez (not a real name), with my correct email address, sent something to them and that it failed for some reason. In my opinion, spam such as this is a virus.
Today I could not get money out of a Bank of America ATM. That was probably due to an attack on servers by a Code Red like virus. Even non-Internet activities such as banking are affected. I think it would help if people put antivirus and site protection software on their computers and servers and use it. That would greatly limit the effectiveness of these Internet monsters. I checked my computer this morning and found no viruses.
I have seen my Internet service get worse and worse the past few months. On the web it seems that every site that you go to, other than personal sites like mine, throw uninvited popup windows in your face, as well as ads on the page. These slow down downloading of the web page, and can even lead to a weird looking page. If you use Norton Internet Security's ad blocking, and go to an editorial on the Washington Post, you will get a misshapen window. I suppose the ads are so tied to the structure of the page that eliminating them results in a weird page.
Viruses are becoming more threatening, too. Actually it is just one virus, w32.Klez.H @ mm, which sees fit to pull names off address books for both From: and To: blocks, and I get lots of virus messages accusing me of sending something I didn't send. And spam is getting worse. The latest spam atrocity was something that pulled names from address books and paired them with random email addresses. I then get squawks from places that can't receive the email saying that I, Linda Rodriguez (not a real name), with my correct email address, sent something to them and that it failed for some reason. In my opinion, spam such as this is a virus.
Today I could not get money out of a Bank of America ATM. That was probably due to an attack on servers by a Code Red like virus. Even non-Internet activities such as banking are affected. I think it would help if people put antivirus and site protection software on their computers and servers and use it. That would greatly limit the effectiveness of these Internet monsters. I checked my computer this morning and found no viruses.
2003/01/23
Influence, Honesty, and being to the point
Yesterday I attended a talk about the strategies of influence. He mentioned how you could influence people to buy toys in January, for instance. You bring the toy out into the market in November. Tout it as a good Christmas gift for your kids. Then suddenly terminate it on December 10 and send every parent to Scare City (because of scarcity of the toy). Then bring it out in the middle of January. All that pent-up demand explodes, and the toy sells in January. He also says that gasoline stations used to charge extra if a credit card was used to buy the gasoline. But then they offered cash discounts instead. That is like six of one and half a dozen of the other. A premium for credit card use is the same as a cash discount: you pay more by charging than by paying cash.
To me this is playing tricks on the public. Confronted with the gasoline station, I would tell them that cash discounts still mean that they are charging a premium for credit card use. When they say that is the usual price of gasoline, I would reply that there is no such thing as a usual price for gasoline!. All prices are relative to each other, and cash discounts are the same as credit card premiums. Tell them like it is. Expose their deception. I'm not sure why they are teaching people to behave like this.
Today we discussed table topics in Toastmasters, where a Topicsmaster gives you a subject to talk about in 1-2 minutes. You learn that if you don't know anything about the subject, that you make something up or change the subject. I.e., you be evasive. I am not sure this is proper training either. But I had to do it today. I was called to tell people what "pterion" meant. I told them honestly that I did not know, and that I could make a good guess by noticing that pter- means wing; for example, a rotating-wing flying machine is a helicopter. I was way off the mark this time (it is a medical term), but at least I was honest about it.
It even debases the language. It means that not has no meaning. It is just a filler word. When Nixon says "I am not a crook", he means that he is a crook. When Gary Hart denies an improper relationship with Donna Rice, that means he had such a relationship. When stock brokers tell customers that Enron is "Buy", they mean it's "Sell". When Iraq says it does not have weapons of mass destruction, and especially when it says it in 12,200 pages, that means that it does have weapons of mass destruction. So if you have a sexually free relationship with your wife, and you hold a public office, such as governor or senator, and you are asked if you had an "improper" relationship with a certain woman last night, change the subject or tell them that you prefer not to discuss it. For if you say you had an affair, then that means you had one. If you say you did not have an affair, that means you had one. The only way you can say you did not have one is not to comment on the subject. If Bill Clinton had done this when he was President, he would have been more effective, and our President today would be Al Gore.
Yesterday I attended a talk about the strategies of influence. He mentioned how you could influence people to buy toys in January, for instance. You bring the toy out into the market in November. Tout it as a good Christmas gift for your kids. Then suddenly terminate it on December 10 and send every parent to Scare City (because of scarcity of the toy). Then bring it out in the middle of January. All that pent-up demand explodes, and the toy sells in January. He also says that gasoline stations used to charge extra if a credit card was used to buy the gasoline. But then they offered cash discounts instead. That is like six of one and half a dozen of the other. A premium for credit card use is the same as a cash discount: you pay more by charging than by paying cash.
To me this is playing tricks on the public. Confronted with the gasoline station, I would tell them that cash discounts still mean that they are charging a premium for credit card use. When they say that is the usual price of gasoline, I would reply that there is no such thing as a usual price for gasoline!. All prices are relative to each other, and cash discounts are the same as credit card premiums. Tell them like it is. Expose their deception. I'm not sure why they are teaching people to behave like this.
Today we discussed table topics in Toastmasters, where a Topicsmaster gives you a subject to talk about in 1-2 minutes. You learn that if you don't know anything about the subject, that you make something up or change the subject. I.e., you be evasive. I am not sure this is proper training either. But I had to do it today. I was called to tell people what "pterion" meant. I told them honestly that I did not know, and that I could make a good guess by noticing that pter- means wing; for example, a rotating-wing flying machine is a helicopter. I was way off the mark this time (it is a medical term), but at least I was honest about it.
It even debases the language. It means that not has no meaning. It is just a filler word. When Nixon says "I am not a crook", he means that he is a crook. When Gary Hart denies an improper relationship with Donna Rice, that means he had such a relationship. When stock brokers tell customers that Enron is "Buy", they mean it's "Sell". When Iraq says it does not have weapons of mass destruction, and especially when it says it in 12,200 pages, that means that it does have weapons of mass destruction. So if you have a sexually free relationship with your wife, and you hold a public office, such as governor or senator, and you are asked if you had an "improper" relationship with a certain woman last night, change the subject or tell them that you prefer not to discuss it. For if you say you had an affair, then that means you had one. If you say you did not have an affair, that means you had one. The only way you can say you did not have one is not to comment on the subject. If Bill Clinton had done this when he was President, he would have been more effective, and our President today would be Al Gore.
2003/01/22
Copycat
The revelation that Cc, a genetic clone of a calico cat named Rainbow, not only does not look like Rainbow, but has a personality radically different from her, is of extraordinary importance. It says that cloning is not what we figured it was. One can't make a copy of a person simply by putting his genes into a zygote and bringing it to term. But identical twins are so much like each other that they can't be told apart. I know from experience, when I met a pair of such twins. They are certainly closer than Cc and Rainbow. This means the womb must have something to do with it. It seems that if two cats are genetically identical but grew in different wombs, they become two different looking cats. I would suspect the same if the two had grown in the same womb but not at the same time, but am not certain of this. Two identical twins grew in the same womb at the same time, so this accounts for their near identicalness. So it seems that people who want to make a copy of themselves for posterity can forget about it. It is a major finding in our understanding of life and of ourselves, and of course, of cats. Meow.
The revelation that Cc, a genetic clone of a calico cat named Rainbow, not only does not look like Rainbow, but has a personality radically different from her, is of extraordinary importance. It says that cloning is not what we figured it was. One can't make a copy of a person simply by putting his genes into a zygote and bringing it to term. But identical twins are so much like each other that they can't be told apart. I know from experience, when I met a pair of such twins. They are certainly closer than Cc and Rainbow. This means the womb must have something to do with it. It seems that if two cats are genetically identical but grew in different wombs, they become two different looking cats. I would suspect the same if the two had grown in the same womb but not at the same time, but am not certain of this. Two identical twins grew in the same womb at the same time, so this accounts for their near identicalness. So it seems that people who want to make a copy of themselves for posterity can forget about it. It is a major finding in our understanding of life and of ourselves, and of course, of cats. Meow.
Annual Leave Wars
Yesterday I got my paycheck and found that I had been charged for 9 more hours of leave than I had asked for. I had emailed my supervisor and her secretary several times that I was going to have Dec 30 be my regular day off, part of a 5-4 plan where I work 9 days of 9 hours each instead of 10 days of 8 hours in two weeks. I had intended to change the regular day off in the middle of the month, but for some reason they changed it at the end of the last month and charged me with 9 hours leave when I wanted a regular day off there. It seems that they want the official leave form instead of emails. A case of inflexible bureaucracy. But it gets worse. I had received an award of 16 hours off, and wanted to take 27 hours off to go to a conference. So I told them I wanted to take 11 hours of annual leave and 16 hours of award. But it seems they can't divide 16 by 9. It's true, 9 won't go into 16 evenly. So therefore I was going to take 9 hours of annual leave the first day, 2 hours of annual leave and 7 hours of award the next day, and 9 hours of award the last day. They could not get that second day straight.
My wife's workplace is no better. She works part time, so in 2 weeks she works 5 full-time days. This workplace can't do a 2 and 5 rhythm very well. For a while she worked 2 days one week and 3 the next, which is the same as 16 hours one week and 24 the next. That's reasonable. But the payroll people insist else Kingdom Come that each week must contain 20 hours of work. So now she is working one 4-hour day each week. She now goes to work 6 days instead of 5 in 2 weeks, with the same number of work hours, but spending more personal hours commuting, and consuming more oil.
It seems that mathematics is one discipline not well understood in today's society and we suffer because of it. By the way, did I say that 9 days of 9 hours was the same as 10 days of 8 hours above? That's 81=80. That doesn't match very well, but unless we can think of 81=80 at times, most of our music would never exist; see, for example, http://sonic-arts.org/dict/syncom.htm. At work they do let me have one hour off every two weeks.
Yesterday I got my paycheck and found that I had been charged for 9 more hours of leave than I had asked for. I had emailed my supervisor and her secretary several times that I was going to have Dec 30 be my regular day off, part of a 5-4 plan where I work 9 days of 9 hours each instead of 10 days of 8 hours in two weeks. I had intended to change the regular day off in the middle of the month, but for some reason they changed it at the end of the last month and charged me with 9 hours leave when I wanted a regular day off there. It seems that they want the official leave form instead of emails. A case of inflexible bureaucracy. But it gets worse. I had received an award of 16 hours off, and wanted to take 27 hours off to go to a conference. So I told them I wanted to take 11 hours of annual leave and 16 hours of award. But it seems they can't divide 16 by 9. It's true, 9 won't go into 16 evenly. So therefore I was going to take 9 hours of annual leave the first day, 2 hours of annual leave and 7 hours of award the next day, and 9 hours of award the last day. They could not get that second day straight.
My wife's workplace is no better. She works part time, so in 2 weeks she works 5 full-time days. This workplace can't do a 2 and 5 rhythm very well. For a while she worked 2 days one week and 3 the next, which is the same as 16 hours one week and 24 the next. That's reasonable. But the payroll people insist else Kingdom Come that each week must contain 20 hours of work. So now she is working one 4-hour day each week. She now goes to work 6 days instead of 5 in 2 weeks, with the same number of work hours, but spending more personal hours commuting, and consuming more oil.
It seems that mathematics is one discipline not well understood in today's society and we suffer because of it. By the way, did I say that 9 days of 9 hours was the same as 10 days of 8 hours above? That's 81=80. That doesn't match very well, but unless we can think of 81=80 at times, most of our music would never exist; see, for example, http://sonic-arts.org/dict/syncom.htm. At work they do let me have one hour off every two weeks.
Invade Iraq or no? What would Jesus do?
Pressure is developing to invade Iraq. Should the US do that? On the one hand, it seems that the US wants a favorable regime there so that it can get access to the 112 billion barrels of oil there. But on the other hand, Saddam Hussein has been one of the most threatening dictators in the region: he has invaded two neighboring countries and has used poison gas to kill about 5,000 Kurds. Further, he is suspected of harboring weapons of mass destruction. The world would be a better place without him.
Maybe Jesus would be of help here. He said, "Let he who has not sinned throw the first stone." That means that a force would be organized to overthrow the Iraqi government, but it would include only nations that don't themselves have weapons of mass destruction. This may be unrealistic since so many large nations have these weapons. So maybe if it is decided to go in and overthrow him, it would be a UN force that would do it, including French, German, and Russian troops. Iraq would then become a UN protectorate after the government is overthrown. This most likely would be a war, but it may be good not to call it one. Call it a police action. Saddam is a criminal, like the DC snipers were, and needs to be brought before justice. I foresee eventually a day in which war is just as unacceptable as ordinary crime to settle disputes, and I hope that the case of Iraq is a first step in that direction.
Pressure is developing to invade Iraq. Should the US do that? On the one hand, it seems that the US wants a favorable regime there so that it can get access to the 112 billion barrels of oil there. But on the other hand, Saddam Hussein has been one of the most threatening dictators in the region: he has invaded two neighboring countries and has used poison gas to kill about 5,000 Kurds. Further, he is suspected of harboring weapons of mass destruction. The world would be a better place without him.
Maybe Jesus would be of help here. He said, "Let he who has not sinned throw the first stone." That means that a force would be organized to overthrow the Iraqi government, but it would include only nations that don't themselves have weapons of mass destruction. This may be unrealistic since so many large nations have these weapons. So maybe if it is decided to go in and overthrow him, it would be a UN force that would do it, including French, German, and Russian troops. Iraq would then become a UN protectorate after the government is overthrown. This most likely would be a war, but it may be good not to call it one. Call it a police action. Saddam is a criminal, like the DC snipers were, and needs to be brought before justice. I foresee eventually a day in which war is just as unacceptable as ordinary crime to settle disputes, and I hope that the case of Iraq is a first step in that direction.
2003/01/20
Mathematics Conference
I took time out from my normal routine to go to a national mathematics conference in Baltimore last week. Baltimore's Inner Harbor is an attractive place. It is especially attractive at night where I saw the full moon hanging alongside the World Trade Center as a backdrop to the tall shafts of the frigate Constitution. The World Trade Center is an interesting building. It is five-sided, with a pentagon-shaped base, so that it looks attractive from any angle, since you always see at least two sides. It is unfortunate that its name and shape both remind us of a horror that occurred nearly a year and a half ago.
The conference brought me back to my graduate school days. I attended 44 talks, including three major addresses, and interviewed for several jobs. The most interesting talk was by Joe Silverman, who showed that elliptic curves occur all over the place in mathematics. The last presentation showed how laptop computers could be used to demonstrate mathematical concepts such as the graphs of quadratic and cubic equations. I wish I had access to some of those tools when I was growing up.
I took time out from my normal routine to go to a national mathematics conference in Baltimore last week. Baltimore's Inner Harbor is an attractive place. It is especially attractive at night where I saw the full moon hanging alongside the World Trade Center as a backdrop to the tall shafts of the frigate Constitution. The World Trade Center is an interesting building. It is five-sided, with a pentagon-shaped base, so that it looks attractive from any angle, since you always see at least two sides. It is unfortunate that its name and shape both remind us of a horror that occurred nearly a year and a half ago.
The conference brought me back to my graduate school days. I attended 44 talks, including three major addresses, and interviewed for several jobs. The most interesting talk was by Joe Silverman, who showed that elliptic curves occur all over the place in mathematics. The last presentation showed how laptop computers could be used to demonstrate mathematical concepts such as the graphs of quadratic and cubic equations. I wish I had access to some of those tools when I was growing up.
Martin Luther King Day
Today is a holiday in which we are to celebrate the life of Rev. Dr. Martin Luther King, Jr. Workers get a day off. Children get a holiday from school, and many people attend celebrations in Rev. King's honor. Some think that this day is mainly for African Americans; after all, it was the treatment of African Americans in the 1950s and 1960s that led to Rev. King's movement and to his untimely death. This is not so. This day is for everyone. Rev. King's message is that the pursuit of happiness is something that belongs to everyone, regardless of religion, sexual orientation, race and so forth. It is a day to recognize that despite all our differences, we are all essentially alike. Children in Chesterfield County, Virginia, had to go to school today because it snowed in December. Why couldn't they have chosen some other day, such as a teacher workday? But teachers made the most of it anyway. They departed from their usual lessons to devote time in their classes to Dr. King and his message.
Today is a holiday in which we are to celebrate the life of Rev. Dr. Martin Luther King, Jr. Workers get a day off. Children get a holiday from school, and many people attend celebrations in Rev. King's honor. Some think that this day is mainly for African Americans; after all, it was the treatment of African Americans in the 1950s and 1960s that led to Rev. King's movement and to his untimely death. This is not so. This day is for everyone. Rev. King's message is that the pursuit of happiness is something that belongs to everyone, regardless of religion, sexual orientation, race and so forth. It is a day to recognize that despite all our differences, we are all essentially alike. Children in Chesterfield County, Virginia, had to go to school today because it snowed in December. Why couldn't they have chosen some other day, such as a teacher workday? But teachers made the most of it anyway. They departed from their usual lessons to devote time in their classes to Dr. King and his message.
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