... to the latest relative to enter the blog world, Ginger!
My sister-in-law Ginger, inspired by the fame and fortune I am fast amassing as one of the world's most popular bloggers, has started her own blog. Actually, I'm kidding -- about my fame and fortune, that is, but not about Ginger. I think she will be a wonderful addition to my regular blog reading habit and I'm looking forward to it!
Sunday, May 14, 2006
Monday, May 08, 2006
Cool Link
I came across this web page and I thought it was just about the coolest thing ever. It's the Baby Name Wizard NameVoyager. It's a graphical representation of the top 1000 names given to American babies each decade since 1880.
We've already picked out names for our baby whether it's a boy or a girl, but it's still interesting to look through the names and see how they've changed over time. Like did you know that Agnes was the 939th most popular name for boys in the decade 1900-1909? Strange but true. And before 1940, if a baby was named Allison, it was more than likely a boy, whereas today Allison is almost exclusively a girl's name.
Anyhow, check it out, type in your favorite name, and see how popular it is or once was!
We've already picked out names for our baby whether it's a boy or a girl, but it's still interesting to look through the names and see how they've changed over time. Like did you know that Agnes was the 939th most popular name for boys in the decade 1900-1909? Strange but true. And before 1940, if a baby was named Allison, it was more than likely a boy, whereas today Allison is almost exclusively a girl's name.
Anyhow, check it out, type in your favorite name, and see how popular it is or once was!
Sunday, May 07, 2006
Adventures in Buying Clothes
My waistline is expanding, and if it weren't for a good cause, this would frighten me. Instead, it just annoys me, because it means I have to go out shopping for clothes. I have plenty of large t-shirts, and I've already bought some maternity jeans and other casual bottoms. What I really need is clothes for work.
I knew that there was a maternity clothing store in the mall in the Big City, so on Friday evening Jeff and I decided to go there and see if we couldn't find me some work-appropriate attire. I was disappointed to discover that there was very little there that I would be willing to wear in public, much less to work!
The vast majority of tops there were of the sleeveless, or even worse, of the spaghetti strap variety. Now, I don't like to wear sleeveless tops, and I recognize that I am in the minority on that. (The problem for me is that I have a condition that makes my armpits a bit of an eyesore, so for the sake of those around me, I choose not to exhibit them in public.) But spaghetti strap tops are absolutely out of the realm of possibility for a completely different reason. I am, shall we say, rather well-endowed on the best of days, and as my body makes the preparations for a baby, my endowment becomes more and more generous. This means, not only must I wear a bra at all times, but I have to wear a very supportive one, which will by necessity have large straps, a minimum of three times wider than the spaghetti straps.
While we were at the store, a saleswoman asked me if we were finding everything that we needed. I was annoyed enough that I told her no, and asked if there was anything that covered your armpits. She said that there wasn't much, because it was the season for short-sleeved shirts -- at which point I told her that short-sleeved shirts, such as the one I was wearing, did cover your armpits. Then she said that the fashions for pregnant women are based on the fashions worn by teenagers, because it made people feel younger, like how her forty-something mom was wearing short skirts and sleeveless blouses and all kinds of crazy things modeled after teenagers.
Her suggestion was that I try wearing a "shrug," a piece of clothing that is like the shoulders and upper part of a blouse or a knit sweater, and then wear one of the sleeveless tops underneath it. But when I tried on the shrugs, they ended up visually drawing attention to my large chest. One of the shrugs fit almost like an exterior bra. So the shrugs were of no help and even made the problem worse.
The only parallel between teenagers and pregnant women is that both feel awkward about their changing bodies. Does this mean that we have to display our awkwardly changing bodies for all to see? That's not what I want to do, thank you very much! I'm certainly not ashamed of my body or my growing belly, but I'm really not that interested in drawing attention to it. My idea of the ultimate summer maternity top would be a loose, short-sleeved top made of a lightweight fabric, not a form-fitting swatch of fabric that accentuates my cleavage!
This may seem like such a trite thing that I am complaining about, but in the larger scheme of things, it is actually a pretty big deal. As I have indicated before, I am the only woman in my department, and because of this, it is essential that I maintain a professional image at work. Part of the way that I maintain this professional image is to dress nicely, but not in ways that draw attention to my obviously female figure. This is not to say that I wear a loose sack over my body. I wear nice women's clothes that fit; I keep my cleavage covered, and I avoid short skirts. I usually wear some make-up too, including eye shadow, mascara, and lipstick. I wear flat shoes because I'm tall enough already and heels are just plain uncomfortable.
I know I'm a woman, and everybody at work knows I'm a woman, and nobody cares that I am not the default (white male) computer scientist. But that doesn't mean I want to dress in ways that make an issue out of the way my body is built. I don't want my male co-workers dressing in ways that bring attention to the way their bodies are built, either! The nature of our bodies is irrelevant to our ability to work at this job.
The problem is that it's hard enough to be taken seriously as a woman in a male-dominated world. Wearing revealing clothing only hurts my chances at that. The type of clothing marketed to pregnant women makes it seem like someone's conspiring to keep women from being taken seriously. If I were a paranoid type, I might start believing that it's yet another way the patriarchy keeps women down. In any case, I don't think I'll be going back to that store anytime soon.
I knew that there was a maternity clothing store in the mall in the Big City, so on Friday evening Jeff and I decided to go there and see if we couldn't find me some work-appropriate attire. I was disappointed to discover that there was very little there that I would be willing to wear in public, much less to work!
The vast majority of tops there were of the sleeveless, or even worse, of the spaghetti strap variety. Now, I don't like to wear sleeveless tops, and I recognize that I am in the minority on that. (The problem for me is that I have a condition that makes my armpits a bit of an eyesore, so for the sake of those around me, I choose not to exhibit them in public.) But spaghetti strap tops are absolutely out of the realm of possibility for a completely different reason. I am, shall we say, rather well-endowed on the best of days, and as my body makes the preparations for a baby, my endowment becomes more and more generous. This means, not only must I wear a bra at all times, but I have to wear a very supportive one, which will by necessity have large straps, a minimum of three times wider than the spaghetti straps.
While we were at the store, a saleswoman asked me if we were finding everything that we needed. I was annoyed enough that I told her no, and asked if there was anything that covered your armpits. She said that there wasn't much, because it was the season for short-sleeved shirts -- at which point I told her that short-sleeved shirts, such as the one I was wearing, did cover your armpits. Then she said that the fashions for pregnant women are based on the fashions worn by teenagers, because it made people feel younger, like how her forty-something mom was wearing short skirts and sleeveless blouses and all kinds of crazy things modeled after teenagers.
Her suggestion was that I try wearing a "shrug," a piece of clothing that is like the shoulders and upper part of a blouse or a knit sweater, and then wear one of the sleeveless tops underneath it. But when I tried on the shrugs, they ended up visually drawing attention to my large chest. One of the shrugs fit almost like an exterior bra. So the shrugs were of no help and even made the problem worse.
The only parallel between teenagers and pregnant women is that both feel awkward about their changing bodies. Does this mean that we have to display our awkwardly changing bodies for all to see? That's not what I want to do, thank you very much! I'm certainly not ashamed of my body or my growing belly, but I'm really not that interested in drawing attention to it. My idea of the ultimate summer maternity top would be a loose, short-sleeved top made of a lightweight fabric, not a form-fitting swatch of fabric that accentuates my cleavage!
This may seem like such a trite thing that I am complaining about, but in the larger scheme of things, it is actually a pretty big deal. As I have indicated before, I am the only woman in my department, and because of this, it is essential that I maintain a professional image at work. Part of the way that I maintain this professional image is to dress nicely, but not in ways that draw attention to my obviously female figure. This is not to say that I wear a loose sack over my body. I wear nice women's clothes that fit; I keep my cleavage covered, and I avoid short skirts. I usually wear some make-up too, including eye shadow, mascara, and lipstick. I wear flat shoes because I'm tall enough already and heels are just plain uncomfortable.
I know I'm a woman, and everybody at work knows I'm a woman, and nobody cares that I am not the default (white male) computer scientist. But that doesn't mean I want to dress in ways that make an issue out of the way my body is built. I don't want my male co-workers dressing in ways that bring attention to the way their bodies are built, either! The nature of our bodies is irrelevant to our ability to work at this job.
The problem is that it's hard enough to be taken seriously as a woman in a male-dominated world. Wearing revealing clothing only hurts my chances at that. The type of clothing marketed to pregnant women makes it seem like someone's conspiring to keep women from being taken seriously. If I were a paranoid type, I might start believing that it's yet another way the patriarchy keeps women down. In any case, I don't think I'll be going back to that store anytime soon.
G is for ...
Post a comment, I'll give you a letter, then write 10 things starting with that, explaining why. The letter I was given was G.
1. Grapes -- one of two things (along with string cheese) that I've had pregnancy-related cravings for. One night, I woke up and had to eat grapes. Luckily, there were grapes in the fridge. I washed a whole bowlful and shoveled them into my mouth by the handful.
2. Government -- I work for a contractor that contracts with another contractor that is paid by the government. Ultimately, your tax dollars pay for me, but I am not a government employee.
3. Green -- I am surrounded by green here in Tennessee. All the hills and mountains are covered in leafy trees, bushes, and poison ivy.
4. Games -- I love to play many different types of games, such as role-playing games, board games like Carcassonne, card games like bridge, and certain outdoor games like croquet. Mind games? No thanks, I played plenty of those when I was growing up, so I'm all done with that.
5. Gold -- the only type of jewelry I can wear. I am allergic to nickel, and jewelry made from silver and other metals usually contain a non-trivial amount of nickel. When I got my ears pierced, I chose sterling silver studs, and as a result my ears swelled and got infected. The stainless steel back of a watch causes my wrist to break out if I wear it too frequently. This is one of many reasons that I don't wear much jewelry. The only things I wear every day are my (gold) wedding and engagement rings, and I try to keep gold earrings in my ear lobes.
6. Grammar -- I am a stickler for good grammar and spelling and I tend to get upset if I discover a typo or a mistake in something I have written.
7. Gum -- I love chewing gum, especially sugar-free wintergreen-flavored gum. Unfortunately, the artificial sweeteners in the gum are off-limits at the moment. Even most sugary gum has artificial sweeteners in it! The only brand I could find that didn't have any artificial sweeteners is Double Bubble, which is kind of nasty, so I've pretty much given up chewing gum altogether.
8. Growth -- I have always been big. I was over 9.5 lbs when I was born, and I was nearly full-grown by the age of 13. Today I am one inch shy of six feet tall. My husband was a more than ten-pound baby and is also tall, and I think we are destined to have a big baby who will grow into a big grown-up.
9. Girl -- I grew up in the South, so it used to be my first instinct to call any woman under the age of 30 a "girl." For example, it was hard for me to think of a female college student as a woman rather than a girl. (To be completely fair, I never really thought of a male college student as a man, either; he was a guy. But not a "boy.") But after living in Illinois for so long, and returning to the South, it is now somewhat jarring to hear younger women referred to as "girls."
10. Grip -- I've often been told to "get a grip," but that's not really what I'm talking about here. Because of the overuse of my left arm and the twisting of that elbow for hours on end when I was practicing the violin as a child, I don't really have much of a grip with my left hand anymore. I still have trouble with hand writing and if I overuse that arm I find myself in a lot of pain. This is something that I really wish the doctor could fix, but all he can do is treat it by giving me shots in the elbow at most twice a year. I have to keep wearing my elbow brace and minimize the use of that arm.
1. Grapes -- one of two things (along with string cheese) that I've had pregnancy-related cravings for. One night, I woke up and had to eat grapes. Luckily, there were grapes in the fridge. I washed a whole bowlful and shoveled them into my mouth by the handful.
2. Government -- I work for a contractor that contracts with another contractor that is paid by the government. Ultimately, your tax dollars pay for me, but I am not a government employee.
3. Green -- I am surrounded by green here in Tennessee. All the hills and mountains are covered in leafy trees, bushes, and poison ivy.
4. Games -- I love to play many different types of games, such as role-playing games, board games like Carcassonne, card games like bridge, and certain outdoor games like croquet. Mind games? No thanks, I played plenty of those when I was growing up, so I'm all done with that.
5. Gold -- the only type of jewelry I can wear. I am allergic to nickel, and jewelry made from silver and other metals usually contain a non-trivial amount of nickel. When I got my ears pierced, I chose sterling silver studs, and as a result my ears swelled and got infected. The stainless steel back of a watch causes my wrist to break out if I wear it too frequently. This is one of many reasons that I don't wear much jewelry. The only things I wear every day are my (gold) wedding and engagement rings, and I try to keep gold earrings in my ear lobes.
6. Grammar -- I am a stickler for good grammar and spelling and I tend to get upset if I discover a typo or a mistake in something I have written.
7. Gum -- I love chewing gum, especially sugar-free wintergreen-flavored gum. Unfortunately, the artificial sweeteners in the gum are off-limits at the moment. Even most sugary gum has artificial sweeteners in it! The only brand I could find that didn't have any artificial sweeteners is Double Bubble, which is kind of nasty, so I've pretty much given up chewing gum altogether.
8. Growth -- I have always been big. I was over 9.5 lbs when I was born, and I was nearly full-grown by the age of 13. Today I am one inch shy of six feet tall. My husband was a more than ten-pound baby and is also tall, and I think we are destined to have a big baby who will grow into a big grown-up.
9. Girl -- I grew up in the South, so it used to be my first instinct to call any woman under the age of 30 a "girl." For example, it was hard for me to think of a female college student as a woman rather than a girl. (To be completely fair, I never really thought of a male college student as a man, either; he was a guy. But not a "boy.") But after living in Illinois for so long, and returning to the South, it is now somewhat jarring to hear younger women referred to as "girls."
10. Grip -- I've often been told to "get a grip," but that's not really what I'm talking about here. Because of the overuse of my left arm and the twisting of that elbow for hours on end when I was practicing the violin as a child, I don't really have much of a grip with my left hand anymore. I still have trouble with hand writing and if I overuse that arm I find myself in a lot of pain. This is something that I really wish the doctor could fix, but all he can do is treat it by giving me shots in the elbow at most twice a year. I have to keep wearing my elbow brace and minimize the use of that arm.
The Past Week's Activities
Last Saturday, we helped our friends move into their new apartment. They drove down from Maryland with a big moving truck full of their furniture and belongings. I didn't move any of the heavy stuff but I did carry in a few boxes and bags. That evening, we took them out to eat at a restaurant that we had been to when we were house-hunting but had until recently been unable to find again.
On Monday, it was "Celebrate Women in Science" day at the lab, and in honor of that fact we had a plenary speaker and a poster session. As the only woman in my department, I made a poster for this poster session. My poster was about dynamic load balancing, which is what I'm working on these days. Then, in the evening, we went out to dinner with our newly-moved-in friends.
The rest of the week was fairly uneventful, until Saturday, when we went on a day trip to the Smokies. We visited Gatlinburg, where we had a pancake lunch, and Cherokee, NC. The mountains are just beautiful and green. We got home after 8 p.m.
On Monday, it was "Celebrate Women in Science" day at the lab, and in honor of that fact we had a plenary speaker and a poster session. As the only woman in my department, I made a poster for this poster session. My poster was about dynamic load balancing, which is what I'm working on these days. Then, in the evening, we went out to dinner with our newly-moved-in friends.
The rest of the week was fairly uneventful, until Saturday, when we went on a day trip to the Smokies. We visited Gatlinburg, where we had a pancake lunch, and Cherokee, NC. The mountains are just beautiful and green. We got home after 8 p.m.
Friday, May 05, 2006
Fame and Fortune
Okay, no fortune involved, as far as I know, anyhow, but today, I am famous! I am on the front page of the NCSA webpage, ORNL in the news page (if you don't look at it today, you can search the archives for May 5, 2006), and the article is on HPC Wire.
It has to do with the research I did for my Ph.D., concerning ill-posed problems and optimization. I feel kind of bashful but pleased to be getting so much recognition. In fact, someone from a different division e-mailed me and asked me if I could talk with him about my research, because he's trying to solve ill-posed global optimization problems!
It has to do with the research I did for my Ph.D., concerning ill-posed problems and optimization. I feel kind of bashful but pleased to be getting so much recognition. In fact, someone from a different division e-mailed me and asked me if I could talk with him about my research, because he's trying to solve ill-posed global optimization problems!
Saturday, April 29, 2006
Back for More
I've been so busy for the past two weeks that I haven't had time to post here. Did you miss me?
So much has been going on that it's hard to sort through it and put it all down "on paper" (on screen? Ya got me!).
First of all, I decided to make some changes in my life at work. I felt kind of lonely and isolated, mostly because aside from the secretary, I am the only woman in my department and on the entire first floor of my building. I don't think that anyone is actively discriminating against me or anything like that, but I do think that "male culture" is slightly different than "female culture." In particular, my colleagues were always going over to the cafeteria without inviting me along. That was okay with me most of the time anyhow, because I usually bring my lunch from home. But I realized that I was missing out on a lot of the informal interactions that lead to formal collaborations. So I decided I'd just invite myself along. So I've started going to lunch with "the guys" on a regular basis, and I think it's working out really well. They don't mind me there; in fact, I think they like me. I talk some, but mostly I just listen and ask them questions when I don't understand something.
Second, I was asked to review a prospective journal paper on optimization. It was very nice of the editor to think of me as a person to review it. The editor is the man from whom I once received the nicest rejection letter ever. He's a lovely person with a very good sense of humor. Whenever I talk to him I get the sense that he really likes me and is very supportive.
Third, for the past couple of weeks we have had an endless stream of visitors. We had interviewees for our special postdoctoral fellowship as well as for a joint lab/university position. It was hard to remember who came for what and who talked about what. We had to attend their seminars every day. By the end, I had found the optimal chair to sit in: it's this chair that's right on the air conditioning vent, which kept me cold and therefore awake during these (boring) seminars in this completely dark room. Out of all the candidates, there were no women interviewees for the postdoc, but two women interviewing for the lab/university position. My boss was the committee chairman for both search committees, so he was extra busy with hosting these visitors.
Fourth, we bought a new car! It's a brand new, blue 2006 Chevy Impala. We named it Priscilla. We still have Gundar, too, and I will continue to drive him to work every day. Except maybe this summer, when it's really hot and I'm feeling particularly miserable because...
I AM PREGNANT!
Yes, amazingly, the better half and I are reproducing. I personally did not believe this was possible. I figured that one or the other of us was infertile, but evidently not. It's due at the end of September/beginning of October. I didn't want to say anything on this blog until I let my boss know. I told him last week and now he knows that I'm going to have to take some time off in the fall. He was totally cool with it and very understanding because he has three children of his own. I was paranoid about telling him (it's hard being the only woman in the department!) but it all worked out fine.
Anyhow, that's about it from the news department. Stay tuned next time for some more math!
So much has been going on that it's hard to sort through it and put it all down "on paper" (on screen? Ya got me!).
First of all, I decided to make some changes in my life at work. I felt kind of lonely and isolated, mostly because aside from the secretary, I am the only woman in my department and on the entire first floor of my building. I don't think that anyone is actively discriminating against me or anything like that, but I do think that "male culture" is slightly different than "female culture." In particular, my colleagues were always going over to the cafeteria without inviting me along. That was okay with me most of the time anyhow, because I usually bring my lunch from home. But I realized that I was missing out on a lot of the informal interactions that lead to formal collaborations. So I decided I'd just invite myself along. So I've started going to lunch with "the guys" on a regular basis, and I think it's working out really well. They don't mind me there; in fact, I think they like me. I talk some, but mostly I just listen and ask them questions when I don't understand something.
Second, I was asked to review a prospective journal paper on optimization. It was very nice of the editor to think of me as a person to review it. The editor is the man from whom I once received the nicest rejection letter ever. He's a lovely person with a very good sense of humor. Whenever I talk to him I get the sense that he really likes me and is very supportive.
Third, for the past couple of weeks we have had an endless stream of visitors. We had interviewees for our special postdoctoral fellowship as well as for a joint lab/university position. It was hard to remember who came for what and who talked about what. We had to attend their seminars every day. By the end, I had found the optimal chair to sit in: it's this chair that's right on the air conditioning vent, which kept me cold and therefore awake during these (boring) seminars in this completely dark room. Out of all the candidates, there were no women interviewees for the postdoc, but two women interviewing for the lab/university position. My boss was the committee chairman for both search committees, so he was extra busy with hosting these visitors.
Fourth, we bought a new car! It's a brand new, blue 2006 Chevy Impala. We named it Priscilla. We still have Gundar, too, and I will continue to drive him to work every day. Except maybe this summer, when it's really hot and I'm feeling particularly miserable because...
I AM PREGNANT!
Yes, amazingly, the better half and I are reproducing. I personally did not believe this was possible. I figured that one or the other of us was infertile, but evidently not. It's due at the end of September/beginning of October. I didn't want to say anything on this blog until I let my boss know. I told him last week and now he knows that I'm going to have to take some time off in the fall. He was totally cool with it and very understanding because he has three children of his own. I was paranoid about telling him (it's hard being the only woman in the department!) but it all worked out fine.
Anyhow, that's about it from the news department. Stay tuned next time for some more math!
Friday, April 14, 2006
Adventures with Logarithms
You've probably heard this joke (or a variant) before:
The ark lands after The Flood. Noah lets all the animals out. Says, "Go forth and multiply." Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there," say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly," say the snakes. "We're adders, and we need logs to multiply."
(Source: Math Jokes page)
The question is, do you understand what the snakes are talking about (i.e. what makes this joke funny)? If not, read on, and learn the secrets of logarithms and the workings of the slide rule!
What's 10 × 10? It's 100, but recall that we can also write it as 102. Basically, when we're multiplying, we just collect all the like bases (10 in this example), and add their exponents together (1+1 = 2).
So what's 2 × 4 × 12? It's 96, but we could write it as 25x 31, because 2 × 4 × 12 = 2 × 4 × 4 × 3 = 21 × 22 × 22 × 31 = 21+2+2 × 3.
We can even use the nifty exponent-adding trick for fractional powers. For example, the square root of 2, sqrt(2), is 21/2 in exponential notation. Likewise, the cube root of 2, cubrt(2), is 21/3. So if we had 25 × sqrt(2), we could express it as 25+1/2 = 211/2.
Suppose we wanted to express the number 2 in terms of a power of ten. The question is, for what value of x does 10x = 2? We know that 100 = 1 < 2 < 101 = 10, so 0 < x < 1. And the square root of 10 is approximately 3.16, so 0 < x < 1/2. The fourth root of 10, 101/4, is approximately 1.78, so now we know that 1/4 < x < 1/2. We could keep going at this all day, computing 103/8 and comparing it with 2, squeezing x between tighter and tighter bounds, until we came up with an answer that we decided was "close enough." Or, we could take the easy way out, and use a calculator to compute the logarithm (base ten) of 2, because that's exactly what a logarithm is. The solution to log10(y) tells you the exponent x that makes 10x equal y. Incidentally, log10(2) = 0.30103 (to 5 decimal places).
The logarithm's base is denoted by the subscripted number. We could use any base we wanted, as long as it's a positive number; the most common base is ten because that's the base of our number system. Other common bases are 2 (especially for things dealing with [binary] computers), and e, which approximately equals 2.71828 and is an awesome math constant with lots of nifty features, despite the fact that it is an irrational number.
What's the difference between the number whose logarithm is 0.30103 and whose logarithm is 1.30103? Recall that from the definition, the first number must be 100.30103 = 2, and the second number must be 101.30103 = 100.30103+1 = 100.30103 × 101 = 2 × 10 = 20. So, we can see that this is a little bit like scientific notation: the number after the decimal point gives us a number between 1 and 10, and the number before the decimal point tells us what power of ten to multiply by. The decimal part is called the mantissa, and the whole number part is called the characteristic.
The characteristic gives you an idea of what order of magnitude the number is. For example, if log(x) = 3.77815, you may have no idea what 100.77815 is, but you would know that x is somewhere between 1000 (=103) and 10000 (=104). (x actually equals 6000.)
Now we have discussed more than enough to understand the joke about the snakes. The snakes were adders, and the only way to multiply by using the addition operation is with logs. But logarithms are much more than fodder for a joke!
In the 1630's, William Oughtred connected two seemingly unrelated ideas -- the additive properties of logarithms and the additive properties of measurement -- to invent the slide rule. If log(x) + log(y) = log(xy), then if you could represent these quantities by distances, the sum of their distances should equal a distance representing their product. This is the concept behind the slide rule, "a mechanical analog computer, consisting of calibrated strips, usually a fixed outer pair and a movable inner one, with a sliding window called the cursor" (Wikipedia). Slide rules were commonly used for science and engineering calculations until they were made obsolete by the electronic calculator and the computer. But slide rules are still great and as a professional mathematician I am proud to say that I own one.
The Wikipedia article on slide rules lists several advantages to slide rules. One big one is that slide rules require you to think about the reasonableness of your results. The result of multiplying 2.5 × 3.5 on a slide rule appears identical to the result of multiplying 25 × 350, because on the slide rule you work only with the mantissa, not the characteristic. For this reason you always have to keep the order of magnitude of your calculation straight in your head. This helps you to remain aware of the calculation so that you're less likely to accept an erroneous result. Too often I see people plugging numbers into a calculator or computer, and naively assuming that the output is absolutely correct. For this reason I think that it could be pedagogically beneficial to use slide rules in math classes.
You now know more than you ever wanted to know about logarithms and slide rules, and I hope that if you ever hear that joke again, your laugh will be full of humor rather than nervousness and math anxiety. I hope that by adding this bit of knowledge about logs to your knowledge base, your life will multiply in richness! (Ha ha, what a crazy mathematician I am!)
References:
http://mathworld.wolfram.com/Logarithm.html
http://en.wikipedia.org/wiki/Common_logarithm
http://en.wikipedia.org/wiki/Slide_rule
The ark lands after The Flood. Noah lets all the animals out. Says, "Go forth and multiply." Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there," say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly," say the snakes. "We're adders, and we need logs to multiply."
(Source: Math Jokes page)
The question is, do you understand what the snakes are talking about (i.e. what makes this joke funny)? If not, read on, and learn the secrets of logarithms and the workings of the slide rule!
What's 10 × 10? It's 100, but recall that we can also write it as 102. Basically, when we're multiplying, we just collect all the like bases (10 in this example), and add their exponents together (1+1 = 2).
So what's 2 × 4 × 12? It's 96, but we could write it as 25x 31, because 2 × 4 × 12 = 2 × 4 × 4 × 3 = 21 × 22 × 22 × 31 = 21+2+2 × 3.
We can even use the nifty exponent-adding trick for fractional powers. For example, the square root of 2, sqrt(2), is 21/2 in exponential notation. Likewise, the cube root of 2, cubrt(2), is 21/3. So if we had 25 × sqrt(2), we could express it as 25+1/2 = 211/2.
Suppose we wanted to express the number 2 in terms of a power of ten. The question is, for what value of x does 10x = 2? We know that 100 = 1 < 2 < 101 = 10, so 0 < x < 1. And the square root of 10 is approximately 3.16, so 0 < x < 1/2. The fourth root of 10, 101/4, is approximately 1.78, so now we know that 1/4 < x < 1/2. We could keep going at this all day, computing 103/8 and comparing it with 2, squeezing x between tighter and tighter bounds, until we came up with an answer that we decided was "close enough." Or, we could take the easy way out, and use a calculator to compute the logarithm (base ten) of 2, because that's exactly what a logarithm is. The solution to log10(y) tells you the exponent x that makes 10x equal y. Incidentally, log10(2) = 0.30103 (to 5 decimal places).
The logarithm's base is denoted by the subscripted number. We could use any base we wanted, as long as it's a positive number; the most common base is ten because that's the base of our number system. Other common bases are 2 (especially for things dealing with [binary] computers), and e, which approximately equals 2.71828 and is an awesome math constant with lots of nifty features, despite the fact that it is an irrational number.
What's the difference between the number whose logarithm is 0.30103 and whose logarithm is 1.30103? Recall that from the definition, the first number must be 100.30103 = 2, and the second number must be 101.30103 = 100.30103+1 = 100.30103 × 101 = 2 × 10 = 20. So, we can see that this is a little bit like scientific notation: the number after the decimal point gives us a number between 1 and 10, and the number before the decimal point tells us what power of ten to multiply by. The decimal part is called the mantissa, and the whole number part is called the characteristic.
The characteristic gives you an idea of what order of magnitude the number is. For example, if log(x) = 3.77815, you may have no idea what 100.77815 is, but you would know that x is somewhere between 1000 (=103) and 10000 (=104). (x actually equals 6000.)
Now we have discussed more than enough to understand the joke about the snakes. The snakes were adders, and the only way to multiply by using the addition operation is with logs. But logarithms are much more than fodder for a joke!
In the 1630's, William Oughtred connected two seemingly unrelated ideas -- the additive properties of logarithms and the additive properties of measurement -- to invent the slide rule. If log(x) + log(y) = log(xy), then if you could represent these quantities by distances, the sum of their distances should equal a distance representing their product. This is the concept behind the slide rule, "a mechanical analog computer, consisting of calibrated strips, usually a fixed outer pair and a movable inner one, with a sliding window called the cursor" (Wikipedia). Slide rules were commonly used for science and engineering calculations until they were made obsolete by the electronic calculator and the computer. But slide rules are still great and as a professional mathematician I am proud to say that I own one.
The Wikipedia article on slide rules lists several advantages to slide rules. One big one is that slide rules require you to think about the reasonableness of your results. The result of multiplying 2.5 × 3.5 on a slide rule appears identical to the result of multiplying 25 × 350, because on the slide rule you work only with the mantissa, not the characteristic. For this reason you always have to keep the order of magnitude of your calculation straight in your head. This helps you to remain aware of the calculation so that you're less likely to accept an erroneous result. Too often I see people plugging numbers into a calculator or computer, and naively assuming that the output is absolutely correct. For this reason I think that it could be pedagogically beneficial to use slide rules in math classes.
You now know more than you ever wanted to know about logarithms and slide rules, and I hope that if you ever hear that joke again, your laugh will be full of humor rather than nervousness and math anxiety. I hope that by adding this bit of knowledge about logs to your knowledge base, your life will multiply in richness! (Ha ha, what a crazy mathematician I am!)
References:
http://mathworld.wolfram.com/Logarithm.html
http://en.wikipedia.org/wiki/Common_logarithm
http://en.wikipedia.org/wiki/Slide_rule
Tuesday, April 11, 2006
Adventures with Dad and Marvis
This weekend's visit from Dad and Marvis was also fun. They arrived Saturday night, and we got a chance to talk. I was reminiscing about what it was like when I went to school in England, which prompted me to show them the school scenes from Monty Python's The Meaning of Life. You'd think those guys went to school in England or something!
The next morning, we went out to breakfast and then to the Secret City Commemorative Walk, which memorializes the people who came to work at Oak Ridge during the Manhattan Project. Marvis' dad and mom both worked here, and their names were there on the wall.
Our car's rear tires have had a slow leak for a while, so on Saturday we took it in to get the leak repaired. We also knew that our brakes were hurting, but we didn't quite know how bad off they were. So we took the car in on Sunday to get it repaired. Dad and Marvis dropped us off at the nearby movie theater and we watched the movie The Shaggy Dog while we waited for our car to be repaired. I thought it was a funny move, but I think I enjoyed it more than Jeff did.
Maybe the internet knows the answer to this question -- is it normal for your brand new brakes to squeal? Jeff said maybe they had some dust on them, but could that last for three days?
The next morning, we went out to breakfast and then to the Secret City Commemorative Walk, which memorializes the people who came to work at Oak Ridge during the Manhattan Project. Marvis' dad and mom both worked here, and their names were there on the wall.
Our car's rear tires have had a slow leak for a while, so on Saturday we took it in to get the leak repaired. We also knew that our brakes were hurting, but we didn't quite know how bad off they were. So we took the car in on Sunday to get it repaired. Dad and Marvis dropped us off at the nearby movie theater and we watched the movie The Shaggy Dog while we waited for our car to be repaired. I thought it was a funny move, but I think I enjoyed it more than Jeff did.
Maybe the internet knows the answer to this question -- is it normal for your brand new brakes to squeal? Jeff said maybe they had some dust on them, but could that last for three days?
Thursday, April 06, 2006
Fun with Dad and Marvis
Dad and Marvis came for a visit this past weekend. We had a lot of fun together.
They arrived on Saturday at about 1 p.m. Of course the first thing we did was the obligatory new house tour. Then I took them to the Mediterranean takeout place to get us some lunch. The guy at the Mediterranean place, after learning that they were my parents, gave them each a free dessert to go along with their meal.
After we ate our lunch, we went to an enormous used bookstore in Knoxville, where Dad found a book on European gardens (as it turns out, he hasn't seen all of them yet!), Marvis found some reading, and Jeff found some books of riddles and brain teasers. I guess I'm the only one who came out of there empty-handed!
That evening, Jeff cooked his delicious Jambalaya (always a big hit wherever he makes it and with whomever he makes it for) and we watched the basketball games on TV. We also had ice cream for dessert.
I had mentioned that I wanted to plant some lavender, and Dad and Marvis were thoughtful enough to bring some lavender plants, along with some rosemary and thyme plants. Then, they planted them for me. So I got my lavender scent garden without having to actually do any work! (I think maybe next time I'll mention to them that I want a million dollars, just in case.)
They had to leave on Sunday morning, because they were in transit to Florida to visit Marvis' sister and mother. I made some blueberry pancakes for them. It turned out that I had gotten out more blueberries than were needed, so on the last pancake, Dad used up all the blueberries. It was more blueberry than pancake. He chose to eat it, and I asked him how he liked his blueberry with a little pancake.
We were sad to see them go, and said "We'll have to do this again." "How about next weekend, when we're on our way back?" they suggested. And so we agreed. We're expecting them back on Saturday night.
They arrived on Saturday at about 1 p.m. Of course the first thing we did was the obligatory new house tour. Then I took them to the Mediterranean takeout place to get us some lunch. The guy at the Mediterranean place, after learning that they were my parents, gave them each a free dessert to go along with their meal.
After we ate our lunch, we went to an enormous used bookstore in Knoxville, where Dad found a book on European gardens (as it turns out, he hasn't seen all of them yet!), Marvis found some reading, and Jeff found some books of riddles and brain teasers. I guess I'm the only one who came out of there empty-handed!
That evening, Jeff cooked his delicious Jambalaya (always a big hit wherever he makes it and with whomever he makes it for) and we watched the basketball games on TV. We also had ice cream for dessert.
I had mentioned that I wanted to plant some lavender, and Dad and Marvis were thoughtful enough to bring some lavender plants, along with some rosemary and thyme plants. Then, they planted them for me. So I got my lavender scent garden without having to actually do any work! (I think maybe next time I'll mention to them that I want a million dollars, just in case.)
They had to leave on Sunday morning, because they were in transit to Florida to visit Marvis' sister and mother. I made some blueberry pancakes for them. It turned out that I had gotten out more blueberries than were needed, so on the last pancake, Dad used up all the blueberries. It was more blueberry than pancake. He chose to eat it, and I asked him how he liked his blueberry with a little pancake.
We were sad to see them go, and said "We'll have to do this again." "How about next weekend, when we're on our way back?" they suggested. And so we agreed. We're expecting them back on Saturday night.
Thursday, March 30, 2006
Adventures in Gubmint
This week, I went to the DC-area to participate in a panel evaluating proposals solicited by the Department of Energy. It was the first time I'd ever done anything like that, so I didn't really know what to expect. I learned a lot, most of it related to the proposal writing and evaluation process.
The first thing I learned was to never, ever connect through Newark. If you have to change terminals (as I did), you have to leave the secure area and go back through security again. I had an hour layover and thanks to the metal rivets on my clothes, I got personally searched and nearly missed my flight.
But I didn't miss the flight, and made it to the hotel where I was staying and where the panel was, by 8 p.m. Just in time to see my colleague, who was on the Tuesday panel (I was on the Wednesday panel), leaving for dinner. So I caught up with him and another colleague who turned out to also be on the Wednesday panel, and we all went out to dinner together.
The next morning was the panel. The first proposal on the table was one of the three that I reviewed. The DOE program manager knew that I'd never done this before, so instead of having me go first, he asked one of the other reviewers to talk about the proposal. After that I was able to chime in with my comments about the proposal. Basically there was fifteen minutes allotted to each proposal, and the three people who had reviewed that proposal gave overviews of the proposal. Everyone else was welcome to ask questions and make comments too. I didn't talk much at all, except during the time allotted to each of the proposals I reviewed. Mostly I just listened and tried to absorb what people were saying. Obviously the review is supposed to be confidential so I can't say much more than that about it. I can say, however, that they kept us well-fed throughout the day, which was nice. My friend on the Tuesday panel said that the lunch they served on Tuesday had shrimp, but ours didn't have anything nearly so fancy. Good thing we were the last panel of reviewers; otherwise, today's panel might have been served peanut butter and jelly!
After the panel was over, I went out to eat with a friend from our undergraduate days and his wife. This is the same friend who was here in February, interviewing. It turns out that he was offered a job, and they decided to accept it and move to Oak Ridge! And he starts at the beginning of May! I was really excited to hear the news, and didn't feel too bad when the evening was over, knowing that we'd soon be seeing them here!
I am insane, so I booked a flight leaving at 6:45 a.m. this morning. That meant I had to get up at 4 a.m. Luckily for me, the colleague who was also on the Wednesday panel decided to accompany me in my rental car back to the airport. This helped keep me awake, plus he was able to help with directions, so I didn't have to rely on my foggy, directionally-challenged brain. I made it back home without incident, this time going through Cleveland rather than Newark. Upon arriving home, I took a nap before eating some lunch and making my way to work.
At work we have a frantic schedule at the moment; we've suddenly learned that we are supposed to benchmark our code on one of the leadership-level supercomputers by Tuesday. This code is a work in progress and has not yet been ported to any large-scale machine, so this poses quite a challenge. At the moment we're having trouble getting it to compile on that machine, because the compiler doesn't like the way we use templates. Luckily that is not my part of the job at the moment; right now I'm supposed to be writing a benchmarking code that records the timings of each of the operators in the code (e.g. multiplication, addition, etc.). I still have to finish that. Unfortunately, by being on that panel, I've missed a day and a half of time that could have been spent working on this. But I think the knowledge I have gotten from serving on that panel made the trip worthwhile.
The first thing I learned was to never, ever connect through Newark. If you have to change terminals (as I did), you have to leave the secure area and go back through security again. I had an hour layover and thanks to the metal rivets on my clothes, I got personally searched and nearly missed my flight.
But I didn't miss the flight, and made it to the hotel where I was staying and where the panel was, by 8 p.m. Just in time to see my colleague, who was on the Tuesday panel (I was on the Wednesday panel), leaving for dinner. So I caught up with him and another colleague who turned out to also be on the Wednesday panel, and we all went out to dinner together.
The next morning was the panel. The first proposal on the table was one of the three that I reviewed. The DOE program manager knew that I'd never done this before, so instead of having me go first, he asked one of the other reviewers to talk about the proposal. After that I was able to chime in with my comments about the proposal. Basically there was fifteen minutes allotted to each proposal, and the three people who had reviewed that proposal gave overviews of the proposal. Everyone else was welcome to ask questions and make comments too. I didn't talk much at all, except during the time allotted to each of the proposals I reviewed. Mostly I just listened and tried to absorb what people were saying. Obviously the review is supposed to be confidential so I can't say much more than that about it. I can say, however, that they kept us well-fed throughout the day, which was nice. My friend on the Tuesday panel said that the lunch they served on Tuesday had shrimp, but ours didn't have anything nearly so fancy. Good thing we were the last panel of reviewers; otherwise, today's panel might have been served peanut butter and jelly!
After the panel was over, I went out to eat with a friend from our undergraduate days and his wife. This is the same friend who was here in February, interviewing. It turns out that he was offered a job, and they decided to accept it and move to Oak Ridge! And he starts at the beginning of May! I was really excited to hear the news, and didn't feel too bad when the evening was over, knowing that we'd soon be seeing them here!
I am insane, so I booked a flight leaving at 6:45 a.m. this morning. That meant I had to get up at 4 a.m. Luckily for me, the colleague who was also on the Wednesday panel decided to accompany me in my rental car back to the airport. This helped keep me awake, plus he was able to help with directions, so I didn't have to rely on my foggy, directionally-challenged brain. I made it back home without incident, this time going through Cleveland rather than Newark. Upon arriving home, I took a nap before eating some lunch and making my way to work.
At work we have a frantic schedule at the moment; we've suddenly learned that we are supposed to benchmark our code on one of the leadership-level supercomputers by Tuesday. This code is a work in progress and has not yet been ported to any large-scale machine, so this poses quite a challenge. At the moment we're having trouble getting it to compile on that machine, because the compiler doesn't like the way we use templates. Luckily that is not my part of the job at the moment; right now I'm supposed to be writing a benchmarking code that records the timings of each of the operators in the code (e.g. multiplication, addition, etc.). I still have to finish that. Unfortunately, by being on that panel, I've missed a day and a half of time that could have been spent working on this. But I think the knowledge I have gotten from serving on that panel made the trip worthwhile.
Thursday, March 23, 2006
Adventures in Houseselling
We are no longer homeowners twice over. Yesterday was the closing on our house in Illinois. It was successful for us and we are now quite a bit richer (at least until the money goes to the folks we owe it to!).
The buyer ran into a bit of bad luck, though. From what I understand, the inspector ran the dishwasher when he was inspecting the house, and forgot to go back and look at it, so he didn't notice that it hadn't drained. The water left standing in the bottom of the dishwasher ate away all the seals, and the water leaked out. When the buyer went for the final walkthrough yesterday morning, they discovered that the kitchen floor was wet and damaged. We had put down a new laminate floor before selling the house and apparently some of the tiles were warped. The buyer was (understandably) upset and tried to back out of the sale or at least renegotiate, but our lawyer and our realtor convinced her that she couldn't. Instead of going after us for the damage to the floor, she needs to go after the home inspector. Our realtor said he thought that once it dried, the floor would be just fine. Still, it's got to be upsetting to buy a house and have this be your first experience with the house. I think she's going to have to buy a new dishwasher. Maybe that will be covered by the home warranty that we bought for her at closing.
Anyhow, it's not our problem and we are no longer the owners of two houses! I am looking forward to having the money that we were paying for that mortgage. It will be nice to have that extra income.
The buyer ran into a bit of bad luck, though. From what I understand, the inspector ran the dishwasher when he was inspecting the house, and forgot to go back and look at it, so he didn't notice that it hadn't drained. The water left standing in the bottom of the dishwasher ate away all the seals, and the water leaked out. When the buyer went for the final walkthrough yesterday morning, they discovered that the kitchen floor was wet and damaged. We had put down a new laminate floor before selling the house and apparently some of the tiles were warped. The buyer was (understandably) upset and tried to back out of the sale or at least renegotiate, but our lawyer and our realtor convinced her that she couldn't. Instead of going after us for the damage to the floor, she needs to go after the home inspector. Our realtor said he thought that once it dried, the floor would be just fine. Still, it's got to be upsetting to buy a house and have this be your first experience with the house. I think she's going to have to buy a new dishwasher. Maybe that will be covered by the home warranty that we bought for her at closing.
Anyhow, it's not our problem and we are no longer the owners of two houses! I am looking forward to having the money that we were paying for that mortgage. It will be nice to have that extra income.
Monday, March 20, 2006
Pareto-Optimal Healthcare
There are some things in life that don't mix: oil and water, Hatfields and McCoys, Pepsi and milk, my mother and my father, and profit and healthcare.
While the first pairs on my list are universally known to be incompatible, the last one may come as a shock to you. After all, don't we, citizens of the United States, land o' capitalism, have access to the best healthcare in the world?
Yes, yes we do! We have the best healthcare that money can buy. And therein lies the problem. Healthcare is expensive, and those who need it the most can generally least afford it.
Remember last week when I was talking about Pareto optimization, or trying to find the best solution to a problem with multiple conflicting objectives? The problem of healthcare in a capitalistic scenario is a Pareto optimization problem, with many complicated and conflicting objectives that can be boiled down to two main objectives: 1, minimize cost, and 2, maximize public health.
There are many different solutions to this problem, each with varying degrees of practicality. Of course we could choose a solution in which no money is spent but everyone is ill, or we could go to the opposite extreme and eradicate every single germ. The best solution lies somewhere in between.
If we say that minimizing ill-health is equivalent to maximizing health, then we could use the same graph as before, substituting "Ill-Health" for "Effort" on the y-axis. Once again we have a continuum of optimal solutions, and the final solution is based on the values of those who make the decision.
The problem is that the values of those who make the decision are skewed toward minimizing costs instead of minimizing ill-health. Today's healthcare landscape is run by corporations, with the objective of maximizing profit taking higher priority than maximizing public health.
In a for-profit insurance model, the underwriter agrees to insure a number of people for a certain rate per person. (Rates for different people might be different, depending on age, status, health history, and what they want covered.) The money collected from each individual goes into a pool that is used to pay the claims of the policyholders and the expenses of the underwriter. Any money left over is profit.
This is why if you try to apply for an individual health insurance policy, you are screened so carefully and (assuming you are approved) the cost is so high. The insurance company wants to make sure that you are a good investment; that statistically speaking, you are within a certain limit of acceptable risk. They hope that you pay your premium regularly and that you never make a claim.
Group policies, such as policies provided by employers, often accept anyone without any conditions on their prior health history. Insurers make money on these policies because they have a guaranteed pool size over which any risks can be amortized, and they charge more per head than they would charge a person whose health risks had been screened.
There is a law that requires that health insurance companies offer policies to anyone who has been previously covered for a period of two years or more. The loophole in that piece of legislation is that the cost of the premium is not regulated. The sickly sister of a friend of mine was approaching the birthday at which she would no longer be covered by her parents' health insurance policy. Sure, she could have health insurance, but only if she could afford a monthly premium of $2700!
Tragically, the requirements for obtaining health insurance, namely good health and the means to pay for it, preclude from obtaining health insurance those who by definition need it the most: the ill who cannot afford treatment. But even people who have access to health insurance are often denied the coverage they need.
True story #1: A mentally ill man with full health coverage is told that he must travel one hundred miles round trip to visit an in-network psychiatrist, despite the dozens of available psychiatrists in a ten-mile radius. If he chooses to see a local psychiatrist, he must pay for the appointment himself, at a cost of $200 or more.
True story #2: A five-year-old girl is in the hospital this past November through February because her transplanted liver is failing and she needs a new liver. The family of the five-year-old girl has comprehensive health care coverage with a yearly limit of $2 million. The plan year is the calendar year. The re-insurer (the people who insure the insurance company) decides that because the bills for the November and December hospitalization were not received until January, they counted for 2006 instead of 2005, and by mid-February, the family has exhausted the $2 million annual limit.
The behavioral profile illustrated by these true stories makes sense under the charters by which corporations operate, that the short-term bottom line takes first priority. It doesn't make sense under the charters of common sense or decency, however.
In the first case, the insurance company was trying to save themselves a buck now, but neglected to consider their later losses when the mentally ill man (who was incapable of driving 100 miles round trip on a weekly basis, and could not afford the cost of seeing a local doctor) stopped receiving psychiatric care and brought harm to himself or another of their clients. (Actually, the man's family appealed the decision to their state's regulatory agency, and it was reversed.)
In the second case, the insurance company was trying to get out of its obligations by bending its rules and looking for any possible violation of the rules by the little girl's family. This is a tactic used by the mentally ill man's insurance company too, and I anticipate that should they be forced to reverse their decision, the girl's family will have a hard time getting them to honor their obligations.
The problem is that with all the focus on profit, the insurance companies have forgotten about what they're really insuring: people. If I lose my house in a mudslide, it's traumatic, it's scary, it's unfortunate, but it's just things. If I get really sick, on the other hand, it's my life that could be lost if the money to pay for the care that I need doesn't come through.
I'm a numbers junkie (I was counting sheep by 17's last night!) but I know where the realm of numbers leaves off and the realm of real people takes priority. The well-being of my fellow human beings is a whole lot more important than the dividends I get to record on Schedule D of my 1040 form. But of course the dividends can be a big temptation for some folks, which makes it all the more important to remove the for-profit aspect from the equation.
What is the solution to this problem? Well, there is no single solution to this problem, as I have already indicated. I just think we need to move along the curve of Pareto solutions away from maximizing profits and towards maximizing public health. I think that doctors and nurses perform a valuable service to our society, and should be remunerated handsomely. I think that hospitals should be run efficiently and the managers of the hospitals should be sufficiently rewarded for their work. But they should operate clinics and hospitals under the concept that the care of patients is the foremost priority, and I strongly believe that all hospitals and clinics should be run as not-for-profit organizations.
I think that similarly, health insurance companies should be not-for-profit organizations, to eliminate any temptation to stiff real life human beings in exchange for a fatter bottom line. I would support a national health insurance program; for example, expanding Medicare/Medicaid to include premium-paying workers.
I know I've lost some people to the rhetoric against government programs by now, but quite honestly, if working people paid premiums to the government instead of to a private insurance company, there would be no change except that the premium would go down.
We already pay our money into a pool. (In fact, we pay twice: once for the indigent and elderly [Medicare tax] and once for ourselves.) My employer and I pay more than $900/month to a large health insurance company. Jeff and I don't use anywhere near that much in coverage every month. The money goes into a pool that pays for my colleague's asthma medication, or the neighbor kid's strep throat, or prenatal checkups for a woman I've never met. It also goes to pay the salaries of the insurance company's employees, but a big chunk of it goes for corporate overhead, such as shareholders' dividends, advertising, and nine-figure bonuses for the CEO, for example, overhead that would be eliminated from a government plan.
Some reports say that a single-payer Medicare system could be supported on a 9% payroll tax: 2% coming from the employee's pay, and 7% coming from the employer. If that were the case, my employer and I would be paying about half of what we're paying now for health insurance. Sounds like a deal to me!
People rail against the inefficiency of government (myself included), but Medicare is actually the most efficient health insurance company in the United States. Less than a nickel of every dollar is spent on overhead. In contrast, the best private insurance companies spend roughly twelve cents per dollar on overhead. According to some reports, my insurance company spends more than a quarter of every dollar on overhead! Wouldn't it be nice if that money went to saving lives instead of fighting against legitimate claims by mentally ill men or critically ill children?
I hate taxes too. I can count my money with the best of 'em. But I don't think that paying for the well-being of my fellow citizens is such a bad thing. (As we've seen, I'm already doing it when I pay my private health insurance premium.) The thing I don't understand is how we in this country can place such a high priority on the unborn (e.g. South Dakota's recent anti-abortion laws and my own state's proposed constitutional amendment) and such a low priority on the already born!
A man who is near and dear to the hearts of most Americans once said, "Therefore, whatever you want men to do to you, do also to them, for this is the Law and the Prophets." (Matthew 7:12, ESV) (This is not to say that the Golden Rule is unique to Christianity.) It bewilders me that so few people actually heed his words. If I were ill, I would like for others to help me get over my illness and get back on my feet. It's only fair that if I want others to do this for me, I should contribute my part in doing this for them. Let's take care of each other like we're supposed to!
There is a lot more to say about Pareto-optimal healthcare, but I had to Pareto-optimize this post for length, substance, and time spent researching and writing, so this is all I have to say for now. There are many interesting articles out there on the topic. Two comprehensive articles that I found were
http://www.bostonreview.net/BR30.6/geyman.html
and
http://www.pnhp.org/facts/why_the_us_needs_a_single_payer_health_system.php
and I encourage you to read them both.
While the first pairs on my list are universally known to be incompatible, the last one may come as a shock to you. After all, don't we, citizens of the United States, land o' capitalism, have access to the best healthcare in the world?
Yes, yes we do! We have the best healthcare that money can buy. And therein lies the problem. Healthcare is expensive, and those who need it the most can generally least afford it.
Remember last week when I was talking about Pareto optimization, or trying to find the best solution to a problem with multiple conflicting objectives? The problem of healthcare in a capitalistic scenario is a Pareto optimization problem, with many complicated and conflicting objectives that can be boiled down to two main objectives: 1, minimize cost, and 2, maximize public health.
There are many different solutions to this problem, each with varying degrees of practicality. Of course we could choose a solution in which no money is spent but everyone is ill, or we could go to the opposite extreme and eradicate every single germ. The best solution lies somewhere in between.
If we say that minimizing ill-health is equivalent to maximizing health, then we could use the same graph as before, substituting "Ill-Health" for "Effort" on the y-axis. Once again we have a continuum of optimal solutions, and the final solution is based on the values of those who make the decision.
The problem is that the values of those who make the decision are skewed toward minimizing costs instead of minimizing ill-health. Today's healthcare landscape is run by corporations, with the objective of maximizing profit taking higher priority than maximizing public health.
In a for-profit insurance model, the underwriter agrees to insure a number of people for a certain rate per person. (Rates for different people might be different, depending on age, status, health history, and what they want covered.) The money collected from each individual goes into a pool that is used to pay the claims of the policyholders and the expenses of the underwriter. Any money left over is profit.
This is why if you try to apply for an individual health insurance policy, you are screened so carefully and (assuming you are approved) the cost is so high. The insurance company wants to make sure that you are a good investment; that statistically speaking, you are within a certain limit of acceptable risk. They hope that you pay your premium regularly and that you never make a claim.
Group policies, such as policies provided by employers, often accept anyone without any conditions on their prior health history. Insurers make money on these policies because they have a guaranteed pool size over which any risks can be amortized, and they charge more per head than they would charge a person whose health risks had been screened.
There is a law that requires that health insurance companies offer policies to anyone who has been previously covered for a period of two years or more. The loophole in that piece of legislation is that the cost of the premium is not regulated. The sickly sister of a friend of mine was approaching the birthday at which she would no longer be covered by her parents' health insurance policy. Sure, she could have health insurance, but only if she could afford a monthly premium of $2700!
Tragically, the requirements for obtaining health insurance, namely good health and the means to pay for it, preclude from obtaining health insurance those who by definition need it the most: the ill who cannot afford treatment. But even people who have access to health insurance are often denied the coverage they need.
True story #1: A mentally ill man with full health coverage is told that he must travel one hundred miles round trip to visit an in-network psychiatrist, despite the dozens of available psychiatrists in a ten-mile radius. If he chooses to see a local psychiatrist, he must pay for the appointment himself, at a cost of $200 or more.
True story #2: A five-year-old girl is in the hospital this past November through February because her transplanted liver is failing and she needs a new liver. The family of the five-year-old girl has comprehensive health care coverage with a yearly limit of $2 million. The plan year is the calendar year. The re-insurer (the people who insure the insurance company) decides that because the bills for the November and December hospitalization were not received until January, they counted for 2006 instead of 2005, and by mid-February, the family has exhausted the $2 million annual limit.
The behavioral profile illustrated by these true stories makes sense under the charters by which corporations operate, that the short-term bottom line takes first priority. It doesn't make sense under the charters of common sense or decency, however.
In the first case, the insurance company was trying to save themselves a buck now, but neglected to consider their later losses when the mentally ill man (who was incapable of driving 100 miles round trip on a weekly basis, and could not afford the cost of seeing a local doctor) stopped receiving psychiatric care and brought harm to himself or another of their clients. (Actually, the man's family appealed the decision to their state's regulatory agency, and it was reversed.)
In the second case, the insurance company was trying to get out of its obligations by bending its rules and looking for any possible violation of the rules by the little girl's family. This is a tactic used by the mentally ill man's insurance company too, and I anticipate that should they be forced to reverse their decision, the girl's family will have a hard time getting them to honor their obligations.
The problem is that with all the focus on profit, the insurance companies have forgotten about what they're really insuring: people. If I lose my house in a mudslide, it's traumatic, it's scary, it's unfortunate, but it's just things. If I get really sick, on the other hand, it's my life that could be lost if the money to pay for the care that I need doesn't come through.
I'm a numbers junkie (I was counting sheep by 17's last night!) but I know where the realm of numbers leaves off and the realm of real people takes priority. The well-being of my fellow human beings is a whole lot more important than the dividends I get to record on Schedule D of my 1040 form. But of course the dividends can be a big temptation for some folks, which makes it all the more important to remove the for-profit aspect from the equation.
What is the solution to this problem? Well, there is no single solution to this problem, as I have already indicated. I just think we need to move along the curve of Pareto solutions away from maximizing profits and towards maximizing public health. I think that doctors and nurses perform a valuable service to our society, and should be remunerated handsomely. I think that hospitals should be run efficiently and the managers of the hospitals should be sufficiently rewarded for their work. But they should operate clinics and hospitals under the concept that the care of patients is the foremost priority, and I strongly believe that all hospitals and clinics should be run as not-for-profit organizations.
I think that similarly, health insurance companies should be not-for-profit organizations, to eliminate any temptation to stiff real life human beings in exchange for a fatter bottom line. I would support a national health insurance program; for example, expanding Medicare/Medicaid to include premium-paying workers.
I know I've lost some people to the rhetoric against government programs by now, but quite honestly, if working people paid premiums to the government instead of to a private insurance company, there would be no change except that the premium would go down.
We already pay our money into a pool. (In fact, we pay twice: once for the indigent and elderly [Medicare tax] and once for ourselves.) My employer and I pay more than $900/month to a large health insurance company. Jeff and I don't use anywhere near that much in coverage every month. The money goes into a pool that pays for my colleague's asthma medication, or the neighbor kid's strep throat, or prenatal checkups for a woman I've never met. It also goes to pay the salaries of the insurance company's employees, but a big chunk of it goes for corporate overhead, such as shareholders' dividends, advertising, and nine-figure bonuses for the CEO, for example, overhead that would be eliminated from a government plan.
Some reports say that a single-payer Medicare system could be supported on a 9% payroll tax: 2% coming from the employee's pay, and 7% coming from the employer. If that were the case, my employer and I would be paying about half of what we're paying now for health insurance. Sounds like a deal to me!
People rail against the inefficiency of government (myself included), but Medicare is actually the most efficient health insurance company in the United States. Less than a nickel of every dollar is spent on overhead. In contrast, the best private insurance companies spend roughly twelve cents per dollar on overhead. According to some reports, my insurance company spends more than a quarter of every dollar on overhead! Wouldn't it be nice if that money went to saving lives instead of fighting against legitimate claims by mentally ill men or critically ill children?
I hate taxes too. I can count my money with the best of 'em. But I don't think that paying for the well-being of my fellow citizens is such a bad thing. (As we've seen, I'm already doing it when I pay my private health insurance premium.) The thing I don't understand is how we in this country can place such a high priority on the unborn (e.g. South Dakota's recent anti-abortion laws and my own state's proposed constitutional amendment) and such a low priority on the already born!
A man who is near and dear to the hearts of most Americans once said, "Therefore, whatever you want men to do to you, do also to them, for this is the Law and the Prophets." (Matthew 7:12, ESV) (This is not to say that the Golden Rule is unique to Christianity.) It bewilders me that so few people actually heed his words. If I were ill, I would like for others to help me get over my illness and get back on my feet. It's only fair that if I want others to do this for me, I should contribute my part in doing this for them. Let's take care of each other like we're supposed to!
There is a lot more to say about Pareto-optimal healthcare, but I had to Pareto-optimize this post for length, substance, and time spent researching and writing, so this is all I have to say for now. There are many interesting articles out there on the topic. Two comprehensive articles that I found were
http://www.bostonreview.net/BR30.6/geyman.html
and
http://www.pnhp.org/facts/why_the_us_needs_a_single_payer_health_system.php
and I encourage you to read them both.
Monday, March 13, 2006
Finally Feeling Healthy
Finally I feel a lot better. Looking back on it, I probably shouldn't have gone to work on Thursday. I came in for a half day on Friday but I couldn't last any longer than that so I left and went to the doctor. My husband also went to the doctor, so we had double walk-in appointments at the same time at this ambulatory care center that I went to for my arm one of the first weeks I was in town. The doctors gave us antibiotics for our secondary infections and sent us on our way. We had our prescriptions filled at Kroger while we stocked up on chicken soup, sparkling water, and juice. Then we went home and sat around trying to recover from our excursion.
On Saturday I felt much better, like I was finally on the mend, but we didn't do much of anything that day because I didn't want to push myself. That meant skipping out on our weekly role-playing game, which was unfortunate but had to be done. On Sunday I felt even better and I was able to do a few chores around the house without getting too exhausted.
The big problem has been that the weather has been absolutely gorgeous for the past week, and I've been too sick to go outside and enjoy it! Now, just as I'm getting well, it's supposed to storm and cool off again. That kind of sucks.
Springtime is definitely here, however. We've had daffodils in bloom for a couple of weeks here. I've noticed that they are pervasive: we have a big patch of them in our front lawn, I see them by the side of the road all the time, and they seem to grow like weeds. The flowering pears are out too, and I may have seen a redbud or two but I'm not sure. One thing I've noticed is the striking absence of tulips. I have yet to see a single tulip, in my yard, my neighbors' yards, or anywhere. So I don't know what to make of that.
On Saturday I felt much better, like I was finally on the mend, but we didn't do much of anything that day because I didn't want to push myself. That meant skipping out on our weekly role-playing game, which was unfortunate but had to be done. On Sunday I felt even better and I was able to do a few chores around the house without getting too exhausted.
The big problem has been that the weather has been absolutely gorgeous for the past week, and I've been too sick to go outside and enjoy it! Now, just as I'm getting well, it's supposed to storm and cool off again. That kind of sucks.
Springtime is definitely here, however. We've had daffodils in bloom for a couple of weeks here. I've noticed that they are pervasive: we have a big patch of them in our front lawn, I see them by the side of the road all the time, and they seem to grow like weeds. The flowering pears are out too, and I may have seen a redbud or two but I'm not sure. One thing I've noticed is the striking absence of tulips. I have yet to see a single tulip, in my yard, my neighbors' yards, or anywhere. So I don't know what to make of that.
Thursday, March 09, 2006
Wiped Out!
Whatever I was coming down with on Monday got progressively worse, until I ended up having to go home at about 2:00, because I just couldn't think or concentrate. Actually, I had to psych myself up to get myself feeling good enough to drive home. Driving requires a lot of concentration!
I stayed home all day Tuesday, too. Yesterday, I tried to get up and go to work, but to no avail. I slept very little on Tuesday night, and I felt worse on Wednesday morning than I'd felt all day Tuesday. So I spent yesterday recuperating too.
This morning, I wasn't at 100%, but I was feeling good enough to do a light day of work. Also, a classmate of mine is here today, giving a talk, and I wanted to see his talk. The nice thing is, going to a talk is an acceptable and low-effort way to spend my time.
I spent a lot of time watching daytime TV. I was too sick to do much more than be a spectator. My better half was also sick, which made it hard because neither of us could really wait upon the other. Mostly we just complained a lot to each other, and took turns getting food.
Also, I had read on the internet that a good way to get rid of a smoky smell is to dip a towel in a half vinegar-half water solution, wring it out, and then sling the towel over your head like a helicopter blade. On my way home from work on Monday, I stopped at the grocery store to buy some vinegar, because I figured that for $1.29 I wouldn't mind trying to see if this home remedy would help dispel this smoky smell. So on Monday evening, I gave it a try. It was a great effort to swing that towel around while at only about 40% power, but it was worth it, because it worked! It didn't get rid of all the smoke, but it definitely cut down on it. So this is a shout-out to my new friend vinegar, the odor neutralizer.
I'm at about 75% power right now, and this is a definite improvement. I think I'll last the whole day today.
I stayed home all day Tuesday, too. Yesterday, I tried to get up and go to work, but to no avail. I slept very little on Tuesday night, and I felt worse on Wednesday morning than I'd felt all day Tuesday. So I spent yesterday recuperating too.
This morning, I wasn't at 100%, but I was feeling good enough to do a light day of work. Also, a classmate of mine is here today, giving a talk, and I wanted to see his talk. The nice thing is, going to a talk is an acceptable and low-effort way to spend my time.
I spent a lot of time watching daytime TV. I was too sick to do much more than be a spectator. My better half was also sick, which made it hard because neither of us could really wait upon the other. Mostly we just complained a lot to each other, and took turns getting food.
Also, I had read on the internet that a good way to get rid of a smoky smell is to dip a towel in a half vinegar-half water solution, wring it out, and then sling the towel over your head like a helicopter blade. On my way home from work on Monday, I stopped at the grocery store to buy some vinegar, because I figured that for $1.29 I wouldn't mind trying to see if this home remedy would help dispel this smoky smell. So on Monday evening, I gave it a try. It was a great effort to swing that towel around while at only about 40% power, but it was worth it, because it worked! It didn't get rid of all the smoke, but it definitely cut down on it. So this is a shout-out to my new friend vinegar, the odor neutralizer.
I'm at about 75% power right now, and this is a definite improvement. I think I'll last the whole day today.
Monday, March 06, 2006
Sunday, March 05, 2006
Adventures in Optimization
I think it's safe to say that optimization is my area of expertise. My dissertation was on the application of an optimization method to a problem arising in geophysics. My boss is putting me on all these proposals as the optimization expert. And the other day, I was asked to serve on a DOE review panel for a couple of proposals involving optimization.
This explains why optimization is always on my mind, then. And it explains why this blog entry is all about optimization! (Well, that and the fact that some people just come here for the math. Gotta know your audience!)
Once again, never fear, non-mathematicians! I'm not going to get all technical on you. Why would I want to relive all the technical details in my off time, after all?
Optimization is the process of finding the best possible configuration or solution to a problem. The best solution is called the optimal solution, or optimum, and the configuration at which we obtain the optimal solution is the optimizer. So, for example, if we want to buy at least three oranges from Kroger at the cheapest possible price, then the optimum might be $1.00, with the optimizer of the oranges that are 3 for a dollar.
Usually when we have an optimization problem, we also have a constraint. That is, we might want to buy no fewer than three oranges, but no more than a dozen, and minimize the price per orange. So maybe there is a bag of a dozen oranges that sells for $3, and a crate of a gross (144) selling for $5, in addition to the 3 for a dollar deal. Well, the crate price is definitely the cheapest per orange (about 3.5 cents per orange!) but it doesn't meet our constraints. So instead we must choose the bag of a dozen oranges for $3, which comes out to a quarter per orange.
Sometimes in an optimization problem, we have two conflicting objectives we wish to satisfy. For example, the other day I had a shopping list that was pretty much evenly divided between food items and drugstore items. If I wanted to minimize the dollar cost of buying everything on my list, I could buy all the drugstore items at Kmart for a pretty good price, and then head over to Kroger and buy all the food items. But I was also kind of tired (it was 6 p.m. on a Friday, after a long day of work!) so another, conflicting objective was to minimize my effort. The drugstore items were also available at Kroger, but they would cost slightly more. Which solution was better: going to two stores, or going to one store but paying more?
It would be nice if I could incorporate these conflicting objectives into a single problem. But how can I quantify "effort?" I could say that time is money, and express the problem like this:
minimize [(cost of shopping) + (my hourly pay rate) × (time spent shopping)].
The trouble with this approach is that the effort of shopping isn't always the same. For example, it takes much more effort to shop when you're hungry or sick with the flu than when you're well-rested and not in a hurry. So "effort" doesn't seem to readily translate into terms of money.
Optimization problems like these, with conflicting objectives that can't readily be combined, are called Pareto optimization problems. They are pervasive in the fields of economics, engineering, and mathematics.
Depending on how important each objective is, there can be a huge continuum of solutions. For example, if my only objective was to minimize the cost of the items on my list, I might hit several stores, compare all the prices, compile a list of the cheapest prices, and buy from a large number of stores. Of course, this process would take hours and I would have expended a great deal of effort. At the other extreme, I could pay someone to go to the store and buy all those items for me. This would require little effort but probably cost more than I would want it to.
Qualitatively, if we were to draw a graph of cost versus effort, it might look something like the following.
The x-axis (left to right) represents cost, and the y-axis (up and down) represents effort. The dotted lines represent the minimum possible cost and effort. The red dot where they intersect represents the (impossible) minimum combination of cost and effort. The blue curve represents all the possible minimum combinations of cost and effort; in other words, at any of the green dots on the curve, any decrease in cost will come at the expense of more effort, and vice versa.
You may be wondering how I could draw such a curve in real life. Well, I do have a means of converting effort to money (pay rate × time). I could quantify effort by weighting that quantity depending on how tired I am. I could set up the problem like this:
minimize (1- w) × (Cost) + w × (Effort),
where 0 < w < 1 is the weight I assign to effort. So on days when I am feeling chipper and adventurous, maybe I will assign w = 0.1, and on days when I am in bed with the flu, maybe w = 0.9. In other words, there are many Pareto optimal solutions to this problem, and I simply select the one that best suits my needs.
I mentioned before that Pareto optimization problems are central to economics and engineering. You can see from my example that the same sort of analysis could be applied to many economic issues.
As for engineering, hydrogeologists might want to determine the configuration of an underground aquifer using data from several different exploration methods, such as seismic data, borehole data, and electromagnetic data. All of these methods give different pictures of the aquifer. How do we combine the data to give us the most accurate picture?
Once we've figured out the configuration of the aquifer, we can now understand how the geology will affect the transport of a contaminant. What is the best way to clean up the contaminant, while minimizing environmental impact, cost, and time?
Suppose we want to route messages through a dynamically changing network where the cost of a path is determined by several non-additive cost functions. How do we find the best path?
Suppose we create a robot that needs to make sequential decisions in a changing environment. How can the robot make those choices?
These are all very difficult problems, and unfortunately, there are no unique solutions. The solutions generally depend on the priorities of the people posing the problems.
This explains why optimization is always on my mind, then. And it explains why this blog entry is all about optimization! (Well, that and the fact that some people just come here for the math. Gotta know your audience!)
Once again, never fear, non-mathematicians! I'm not going to get all technical on you. Why would I want to relive all the technical details in my off time, after all?
Optimization is the process of finding the best possible configuration or solution to a problem. The best solution is called the optimal solution, or optimum, and the configuration at which we obtain the optimal solution is the optimizer. So, for example, if we want to buy at least three oranges from Kroger at the cheapest possible price, then the optimum might be $1.00, with the optimizer of the oranges that are 3 for a dollar.
Usually when we have an optimization problem, we also have a constraint. That is, we might want to buy no fewer than three oranges, but no more than a dozen, and minimize the price per orange. So maybe there is a bag of a dozen oranges that sells for $3, and a crate of a gross (144) selling for $5, in addition to the 3 for a dollar deal. Well, the crate price is definitely the cheapest per orange (about 3.5 cents per orange!) but it doesn't meet our constraints. So instead we must choose the bag of a dozen oranges for $3, which comes out to a quarter per orange.
Sometimes in an optimization problem, we have two conflicting objectives we wish to satisfy. For example, the other day I had a shopping list that was pretty much evenly divided between food items and drugstore items. If I wanted to minimize the dollar cost of buying everything on my list, I could buy all the drugstore items at Kmart for a pretty good price, and then head over to Kroger and buy all the food items. But I was also kind of tired (it was 6 p.m. on a Friday, after a long day of work!) so another, conflicting objective was to minimize my effort. The drugstore items were also available at Kroger, but they would cost slightly more. Which solution was better: going to two stores, or going to one store but paying more?
It would be nice if I could incorporate these conflicting objectives into a single problem. But how can I quantify "effort?" I could say that time is money, and express the problem like this:
minimize [(cost of shopping) + (my hourly pay rate) × (time spent shopping)].
The trouble with this approach is that the effort of shopping isn't always the same. For example, it takes much more effort to shop when you're hungry or sick with the flu than when you're well-rested and not in a hurry. So "effort" doesn't seem to readily translate into terms of money.
Optimization problems like these, with conflicting objectives that can't readily be combined, are called Pareto optimization problems. They are pervasive in the fields of economics, engineering, and mathematics.
Depending on how important each objective is, there can be a huge continuum of solutions. For example, if my only objective was to minimize the cost of the items on my list, I might hit several stores, compare all the prices, compile a list of the cheapest prices, and buy from a large number of stores. Of course, this process would take hours and I would have expended a great deal of effort. At the other extreme, I could pay someone to go to the store and buy all those items for me. This would require little effort but probably cost more than I would want it to.
Qualitatively, if we were to draw a graph of cost versus effort, it might look something like the following.
The x-axis (left to right) represents cost, and the y-axis (up and down) represents effort. The dotted lines represent the minimum possible cost and effort. The red dot where they intersect represents the (impossible) minimum combination of cost and effort. The blue curve represents all the possible minimum combinations of cost and effort; in other words, at any of the green dots on the curve, any decrease in cost will come at the expense of more effort, and vice versa.
You may be wondering how I could draw such a curve in real life. Well, I do have a means of converting effort to money (pay rate × time). I could quantify effort by weighting that quantity depending on how tired I am. I could set up the problem like this:
minimize (1- w) × (Cost) + w × (Effort),
where 0 < w < 1 is the weight I assign to effort. So on days when I am feeling chipper and adventurous, maybe I will assign w = 0.1, and on days when I am in bed with the flu, maybe w = 0.9. In other words, there are many Pareto optimal solutions to this problem, and I simply select the one that best suits my needs.
I mentioned before that Pareto optimization problems are central to economics and engineering. You can see from my example that the same sort of analysis could be applied to many economic issues.
As for engineering, hydrogeologists might want to determine the configuration of an underground aquifer using data from several different exploration methods, such as seismic data, borehole data, and electromagnetic data. All of these methods give different pictures of the aquifer. How do we combine the data to give us the most accurate picture?
Once we've figured out the configuration of the aquifer, we can now understand how the geology will affect the transport of a contaminant. What is the best way to clean up the contaminant, while minimizing environmental impact, cost, and time?
Suppose we want to route messages through a dynamically changing network where the cost of a path is determined by several non-additive cost functions. How do we find the best path?
Suppose we create a robot that needs to make sequential decisions in a changing environment. How can the robot make those choices?
These are all very difficult problems, and unfortunately, there are no unique solutions. The solutions generally depend on the priorities of the people posing the problems.
Friday, March 03, 2006
Adventures in Math
I know some folks come here just for the math, so here's another little piece of math to keep you coming back.
The other day I got an interesting e-mail from my fearless sister-in-law Ginger. (Ginger is a closet mathematician, but she just doesn't know it yet. I got her addicted to Sudoku, and now she's sending me math e-mails. It's only a matter of time before she starts doing calculus for fun.) Anyhow, here's what the message says:
1. GRAB A CALCULATOR. (YOU WON'T BE ABLE TO DO THIS ONE IN YOUR HEAD)
2. KEY IN THE FIRST THREE DIGITS OF YOUR PHONE NUMBER (NOT THE AREA CODE)
3. MULTIPLY BY 80
4. ADD 1
5. MULTIPLY BY 250
6. ADD THE LAST 4 DIGITS OF YOUR PHONE NUMBER
7. ADD THE LAST 4 DIGITS OF YOUR PHONE NUMBER AGAIN.
8. SUBTRACT 250
9. DIVIDE NUMBER BY 2
DO YOU RECOGNIZE THE ANSWER?
I tried it on my old phone number in Illinois, 367-5384. (As an aside, that was the coolest phone number ever. It spelled DORKETH. One can be so fortunate only once in life, I suppose.)
3. 367 x 80 = 29,360
4. 29,360 + 1 = 29,361
5. 29,361 x 250 = 7,340,250
6. 7,340,250 + 5,384 = 7,345,634
7. 7,345,634 + 5,384 = 7,351,018
8. 7,351,018 – 250 = 7,350,768
9. 7,350,768/2 = 3,675,384
That is indeed a familiar number! It's the original phone number I started out with.
This trick will work with any phone number. I know you're all asking why. At least, the folks who are in this for the math are, and they're the ones who count (ha ha! a little math humor there!) so I'll now explain how this trick works.
First of all, remember from elementary school how starting from the decimal point and going to the leftt, we have the ones place, then the tens place, then the hundreds, etc.? In each of those slots, we can put any integer from 0 to 9, and this represents a number. The number is just the sum of each of those integers times the proper power of ten; for example,
436 = 6 x 1 + 3 x 10 + 4 x 100
= 6 + 30 + 400
= 436.
So, if we were to write out our phone number as an integer, we could write it as
abcdefg = g x 1 + f x 10 + e x 100 + d x 1000 + c x 10,000 + b x 100,000 + a x 1,000,000 = g + 10 f + 100 e + 1000 d + 10,000 c +100,000 b + 1,000,000 a
= g + f0 + e00 + d000 + c0,000 + b00,000 + a,000,000
= abcdefg.
So, following the above algorithm:
3. abc x 80 = (c + 10 b + 100 a) x 80 = 80 c + 800 b + 8000 a.
4. (80 c + 800 b + 8000 a) + 1 = 80 c + 800 b + 8000 a + 1.
5. (80 c + 800 b + 8000 a + 1) x 250 = 20,000 c + 200,000 b + 2,000,000 a + 250.
6. (20,000 c + 200,000 b + 2,000,000 a + 250) + defg = 20,000 c + 200,000 b + 2,000,000 a + 250 + g + 10 f + 100 e + 1000 d.
7. (20,000 c + 200,000 b + 2,000,000 a + 250 + g + 10 f + 100 e + 1000 d) + defg = 20, 000 c + 200,000 b + 2,000,000 a + 250 + 2 g + 20 f + 200 e + 2000 d
= 250 + 2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a.
8. (250 + 2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a) – 250 = 2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a.
9. (2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a)/2 = g + 10 f +100 e + 1000 d + 10,000 c + 100,000 b + 1,000,000 a
= g + f0 + e00 + d000 + c0,000 + b00,000 + a,000,000
= abcdefg (!)
I thought this was a cute trick. I wrote all the steps out there, but you can see, if you gather like terms, that after step 5, we have 2 x a,bc0,000 + 250. (The 250 is just there to throw you off the track.) After step 7, we have 2 x a,bcd,efg + 250, and after we take away the extraneous 250, we obtain 2 x a,bcd,efg. Finally, in the last step, we divide by two and get back the original number.
I have to admit that I did follow step one and pull out the old calculator when I first tried this trick. Although perhaps it would have been more fun to do it with my trusty slide rule or my new abacus that I bought in San Francisco. Until next time, math fans!
The other day I got an interesting e-mail from my fearless sister-in-law Ginger. (Ginger is a closet mathematician, but she just doesn't know it yet. I got her addicted to Sudoku, and now she's sending me math e-mails. It's only a matter of time before she starts doing calculus for fun.) Anyhow, here's what the message says:
1. GRAB A CALCULATOR. (YOU WON'T BE ABLE TO DO THIS ONE IN YOUR HEAD)
2. KEY IN THE FIRST THREE DIGITS OF YOUR PHONE NUMBER (NOT THE AREA CODE)
3. MULTIPLY BY 80
4. ADD 1
5. MULTIPLY BY 250
6. ADD THE LAST 4 DIGITS OF YOUR PHONE NUMBER
7. ADD THE LAST 4 DIGITS OF YOUR PHONE NUMBER AGAIN.
8. SUBTRACT 250
9. DIVIDE NUMBER BY 2
DO YOU RECOGNIZE THE ANSWER?
I tried it on my old phone number in Illinois, 367-5384. (As an aside, that was the coolest phone number ever. It spelled DORKETH. One can be so fortunate only once in life, I suppose.)
3. 367 x 80 = 29,360
4. 29,360 + 1 = 29,361
5. 29,361 x 250 = 7,340,250
6. 7,340,250 + 5,384 = 7,345,634
7. 7,345,634 + 5,384 = 7,351,018
8. 7,351,018 – 250 = 7,350,768
9. 7,350,768/2 = 3,675,384
That is indeed a familiar number! It's the original phone number I started out with.
This trick will work with any phone number. I know you're all asking why. At least, the folks who are in this for the math are, and they're the ones who count (ha ha! a little math humor there!) so I'll now explain how this trick works.
First of all, remember from elementary school how starting from the decimal point and going to the leftt, we have the ones place, then the tens place, then the hundreds, etc.? In each of those slots, we can put any integer from 0 to 9, and this represents a number. The number is just the sum of each of those integers times the proper power of ten; for example,
436 = 6 x 1 + 3 x 10 + 4 x 100
= 6 + 30 + 400
= 436.
So, if we were to write out our phone number as an integer, we could write it as
abcdefg = g x 1 + f x 10 + e x 100 + d x 1000 + c x 10,000 + b x 100,000 + a x 1,000,000 = g + 10 f + 100 e + 1000 d + 10,000 c +100,000 b + 1,000,000 a
= g + f0 + e00 + d000 + c0,000 + b00,000 + a,000,000
= abcdefg.
So, following the above algorithm:
3. abc x 80 = (c + 10 b + 100 a) x 80 = 80 c + 800 b + 8000 a.
4. (80 c + 800 b + 8000 a) + 1 = 80 c + 800 b + 8000 a + 1.
5. (80 c + 800 b + 8000 a + 1) x 250 = 20,000 c + 200,000 b + 2,000,000 a + 250.
6. (20,000 c + 200,000 b + 2,000,000 a + 250) + defg = 20,000 c + 200,000 b + 2,000,000 a + 250 + g + 10 f + 100 e + 1000 d.
7. (20,000 c + 200,000 b + 2,000,000 a + 250 + g + 10 f + 100 e + 1000 d) + defg = 20, 000 c + 200,000 b + 2,000,000 a + 250 + 2 g + 20 f + 200 e + 2000 d
= 250 + 2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a.
8. (250 + 2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a) – 250 = 2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a.
9. (2 g + 20 f + 200 e + 2000 d + 20,000 c + 200,000 b + 2,000,000 a)/2 = g + 10 f +100 e + 1000 d + 10,000 c + 100,000 b + 1,000,000 a
= g + f0 + e00 + d000 + c0,000 + b00,000 + a,000,000
= abcdefg (!)
I thought this was a cute trick. I wrote all the steps out there, but you can see, if you gather like terms, that after step 5, we have 2 x a,bc0,000 + 250. (The 250 is just there to throw you off the track.) After step 7, we have 2 x a,bcd,efg + 250, and after we take away the extraneous 250, we obtain 2 x a,bcd,efg. Finally, in the last step, we divide by two and get back the original number.
I have to admit that I did follow step one and pull out the old calculator when I first tried this trick. Although perhaps it would have been more fun to do it with my trusty slide rule or my new abacus that I bought in San Francisco. Until next time, math fans!
Wednesday, March 01, 2006
Adventures in San Francisco
San Francisco is one of my favorite cities in the world. I have fond memories of it as a young child, as a college student, and now as an adult.
When I was five, my family spent a year in Davis, California, close enough to San Francisco to visit the city fairly frequently. I have fond memories of the Exploratorium and Golden Gate Park from those days. As a college student, I spent a summer doing research at SRI International in Menlo Park, California, close enough to San Francisco to visit the city on several occasions. I have fond memories of Golden Gate Park, the Golden Gate Bridge, Chinatown, Cable Cars, and more, from those days.
On Friday night, Jeff and I rode the cable cars and it was a lot of fun. Just riding the cable cars is fun, but sharing the experience with him is what made it a wonderful experience. On Saturday morning, we took a ferry to Alcatraz. I had never been to Alcatraz before, so this was a new experience for both of us. The audio tour is narrated by a former correctional officer of the prison, and also features the points of view of another officer and two former inmates. It was just fascinating. Alcatraz was a very safe and efficiently run prison. The hardest thing the prisoners faced was the feeling of deprivation. The view from the island is just spectacular: San Francisco on one side, Marin County and the Northern side of the bay on the other. The punishment of seeing and sometimes even hearing all that you're being deprived of must have been severe.
On Saturday we also visited Ghirardelli Square and Fisherman's Wharf. At the wharf was a museum called musee mechanique, with a lot of old amusement machines, such as one that showed 3-D slides of the 1906 earthquake, and another that was a dummy that would just laugh and laugh.
On Sunday it rained all day, but we didn't let this stop us from having fun. We used our bus passes to go to the Golden Gate Bridge, where we took a lot of pictures and walked part of the way across the bridge. Because of the cold rain, we did stop touring a little earlier than we might have otherwise.
We woke up early on Monday morning, took the shuttle to the airport, and got home by 9 p.m. It was a fun trip, but we were glad to be home.
When I was five, my family spent a year in Davis, California, close enough to San Francisco to visit the city fairly frequently. I have fond memories of the Exploratorium and Golden Gate Park from those days. As a college student, I spent a summer doing research at SRI International in Menlo Park, California, close enough to San Francisco to visit the city on several occasions. I have fond memories of Golden Gate Park, the Golden Gate Bridge, Chinatown, Cable Cars, and more, from those days.
On Friday night, Jeff and I rode the cable cars and it was a lot of fun. Just riding the cable cars is fun, but sharing the experience with him is what made it a wonderful experience. On Saturday morning, we took a ferry to Alcatraz. I had never been to Alcatraz before, so this was a new experience for both of us. The audio tour is narrated by a former correctional officer of the prison, and also features the points of view of another officer and two former inmates. It was just fascinating. Alcatraz was a very safe and efficiently run prison. The hardest thing the prisoners faced was the feeling of deprivation. The view from the island is just spectacular: San Francisco on one side, Marin County and the Northern side of the bay on the other. The punishment of seeing and sometimes even hearing all that you're being deprived of must have been severe.
On Saturday we also visited Ghirardelli Square and Fisherman's Wharf. At the wharf was a museum called musee mechanique, with a lot of old amusement machines, such as one that showed 3-D slides of the 1906 earthquake, and another that was a dummy that would just laugh and laugh.
On Sunday it rained all day, but we didn't let this stop us from having fun. We used our bus passes to go to the Golden Gate Bridge, where we took a lot of pictures and walked part of the way across the bridge. Because of the cold rain, we did stop touring a little earlier than we might have otherwise.
We woke up early on Monday morning, took the shuttle to the airport, and got home by 9 p.m. It was a fun trip, but we were glad to be home.
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