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!
Saturday, April 29, 2006
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.
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