So, I have a question for my loyal readers (all four and that robot run by Google).
If you are going on a trip and decide to drive but you know that the airplane is going to fly with or without you, and that "your" seat is going to be empty, are you now producing the equivalent CO2 of flying+driving?
That is, the car you drive is producing X kg of CO2 for the trip, and there is an empty seat in an airplane and if you were in that seat, it would count as Y kg of CO2, are you responsible for X+Y kg of CO2, or just X kg of CO2?
I don't want to say what I think; I want your thoughts.
Before you answer, consider this scenario and question: You and your neighbor are part of the neighborhood watch and you are both going to the police station for a neighborhood watch meeting. Are you responsible for the emissions of both vehicles if your neighbor offers to carpool and you refuse?
Saturday, March 28, 2009
Friday, March 27, 2009
What is the name of the largest star?
Question from dear son:
What is the name of the largest star?
Well, for the moment, let us assume that we can only discuss stars that were named by humans. That is, there may be many stars larger than the one I am going to discuss, but we have not discovered them yet. If some other intelligent life form out in the universe has, we do not know about it...
The largest known star in terms of size, radius, diameter, whatever, is named VY Canis Majoris. VY Canis Majoris is between about 1800 and 2100 times larger than our sun.
DS wants to know why VY Canis Majoris is named as it is. The star is in the constellation Canis Major, thus its surname. From what I can tell, VY comes from the person who first cataloged the star, A.N. Vyssotsky. Yeah, that's helpful.
Vy Canis Majoris is a relatively cold star with a photosphere temperature of only about 3500 Kelvins (5840 degrees Fahrenheit). Our sun has a photosphere temperature of about 6000 kelvins, or about 11,000 degrees Fahrenheit. In general, the larger the star, the cooler its surface.
Someone with a six-year-old has already answered this question, and I'm going to steal one of their graphics. Go back to my post about Pluto and the graphic of the solar system. It's approximately to scale, with the sun off the screen. Here's our sun compared with Vy Canis Majoris. Vy CMa would reach past the orbit of Saturn.
Here's another graphic that shows relative sizes of celestial bodies. As you go from one frame to the next (say, 2 to 3), the last object in the first frame is the first object in the next frame. Going from 2 to 3, you see the size differences between Jupiter and the other planets and Jupiter and the sun and Sirius. This does not have VY Canis Majoris on it, but it'll be in the last frame, just a bit bigger than VV Cephei A.
Everything I've talked about so far has been in terms of radius, volume, whatever. Another measure of "size" is mass. VY Canis Majoris is only about 30 to 40 times as massive as our sun. The most massive stars that we know about include HD_269810, Eta Carinae, the Pistol Star, and WR102ka, each of which is about 150 times as massive as our sun. These massive, luminuous stars are expected to end in super novae in the next million years or so. Depending on the details of the super nova, these stars will either end as neutron stars or possibly black holes. A neutron star will form if what's left after the super nova is less than about three times the mass of the sun. Otherwise, a black hole will form.
Will our sun become a black hole?
No.
Our sun's evolution from now until about six billion years from now will be as follows:
In about four billion years, the hydrogen at the sun's core will be used up and it'll start fusing helium into carbon and oxygen. As this happens, it'll expand a great deal and become a red dwarf. Its surface will reach the orbit of Mercury. The sun will expand and contract several times during its red dwarf phase. At some point, about 30 million years after it becomes a red dwarf, the sun will expand out to Earth's orbit. When this happens, a large amount of material (up to about 50% of the sun's mass) will continue moving outward and will be lost to space.
After that happens, the core of the sun will collapse to about the size of the Earth. Because of its mass, it cannot collapse any further and it'll become a white dwarf, with a core temperature of more than 100,000 kelvins. Its density will be about a million times larger than the density of the earth, and its core will be carbon and oxygen. The white dwarf will cool, and after a very long time (hundreds to thousands of billions of years), it should become a cold lump of degenerate matter, called a black dwarf. None of these black dwarves should exist right now because the universe is only about 15 billion years old.
What is the name of the largest star?
Well, for the moment, let us assume that we can only discuss stars that were named by humans. That is, there may be many stars larger than the one I am going to discuss, but we have not discovered them yet. If some other intelligent life form out in the universe has, we do not know about it...
The largest known star in terms of size, radius, diameter, whatever, is named VY Canis Majoris. VY Canis Majoris is between about 1800 and 2100 times larger than our sun.
DS wants to know why VY Canis Majoris is named as it is. The star is in the constellation Canis Major, thus its surname. From what I can tell, VY comes from the person who first cataloged the star, A.N. Vyssotsky. Yeah, that's helpful.
Vy Canis Majoris is a relatively cold star with a photosphere temperature of only about 3500 Kelvins (5840 degrees Fahrenheit). Our sun has a photosphere temperature of about 6000 kelvins, or about 11,000 degrees Fahrenheit. In general, the larger the star, the cooler its surface.
Someone with a six-year-old has already answered this question, and I'm going to steal one of their graphics. Go back to my post about Pluto and the graphic of the solar system. It's approximately to scale, with the sun off the screen. Here's our sun compared with Vy Canis Majoris. Vy CMa would reach past the orbit of Saturn.
Here's another graphic that shows relative sizes of celestial bodies. As you go from one frame to the next (say, 2 to 3), the last object in the first frame is the first object in the next frame. Going from 2 to 3, you see the size differences between Jupiter and the other planets and Jupiter and the sun and Sirius. This does not have VY Canis Majoris on it, but it'll be in the last frame, just a bit bigger than VV Cephei A.Everything I've talked about so far has been in terms of radius, volume, whatever. Another measure of "size" is mass. VY Canis Majoris is only about 30 to 40 times as massive as our sun. The most massive stars that we know about include HD_269810, Eta Carinae, the Pistol Star, and WR102ka, each of which is about 150 times as massive as our sun. These massive, luminuous stars are expected to end in super novae in the next million years or so. Depending on the details of the super nova, these stars will either end as neutron stars or possibly black holes. A neutron star will form if what's left after the super nova is less than about three times the mass of the sun. Otherwise, a black hole will form.
Will our sun become a black hole?
No.
Our sun's evolution from now until about six billion years from now will be as follows:
In about four billion years, the hydrogen at the sun's core will be used up and it'll start fusing helium into carbon and oxygen. As this happens, it'll expand a great deal and become a red dwarf. Its surface will reach the orbit of Mercury. The sun will expand and contract several times during its red dwarf phase. At some point, about 30 million years after it becomes a red dwarf, the sun will expand out to Earth's orbit. When this happens, a large amount of material (up to about 50% of the sun's mass) will continue moving outward and will be lost to space.
After that happens, the core of the sun will collapse to about the size of the Earth. Because of its mass, it cannot collapse any further and it'll become a white dwarf, with a core temperature of more than 100,000 kelvins. Its density will be about a million times larger than the density of the earth, and its core will be carbon and oxygen. The white dwarf will cool, and after a very long time (hundreds to thousands of billions of years), it should become a cold lump of degenerate matter, called a black dwarf. None of these black dwarves should exist right now because the universe is only about 15 billion years old.
Wednesday, March 25, 2009
Women and science in history...today
Today as I was looking across the (one of four) conference room during a talk, something struck me.
I was not being blinded by a bunch of bald heads. In fact, there were a lot fewer balding, white men in the audience than young, fully covered heads. Many of these heads also sported a couple of feet of hair, and a reasonable amount of the skin under the heads was dark. While the sciences may be more liberal in its acceptance of long-haired hippy freaks, it is by no means dominated by them. Those with long hair here are, with few exceptions, female, and scientists never have time to go get a tan.
This is the first conference I've been to where it is clear that the old guard of white males has mostly died out. Now, it may be a little sad that these people are dieing, but I think it's great that they're not being replaced by the same people from a good-old-boy network.
To be sure, I'm not claiming that this group of old, white, balding men were awful (many of the one just starting to be gray and bald came of age during the feminist revolution of the 60s after all), but it is nice to see a much greater diversity than in the past.
Also, this trend is an actual trend. When I first started attending these meetings, pretty much everybody was male, old, white, bald, or had some combination of those "features."
I was not being blinded by a bunch of bald heads. In fact, there were a lot fewer balding, white men in the audience than young, fully covered heads. Many of these heads also sported a couple of feet of hair, and a reasonable amount of the skin under the heads was dark. While the sciences may be more liberal in its acceptance of long-haired hippy freaks, it is by no means dominated by them. Those with long hair here are, with few exceptions, female, and scientists never have time to go get a tan.
This is the first conference I've been to where it is clear that the old guard of white males has mostly died out. Now, it may be a little sad that these people are dieing, but I think it's great that they're not being replaced by the same people from a good-old-boy network.
To be sure, I'm not claiming that this group of old, white, balding men were awful (many of the one just starting to be gray and bald came of age during the feminist revolution of the 60s after all), but it is nice to see a much greater diversity than in the past.
Also, this trend is an actual trend. When I first started attending these meetings, pretty much everybody was male, old, white, bald, or had some combination of those "features."
Sunday, March 22, 2009
Is it more energy efficient to fly or to drive to your destination?
DW asked a question of me that was asked at Crunchy Chicken. Is it selfish to fly for tourism/pleasure?
Here's my take on this question. But first, it has to be framed in the "right" way.
Here's my way of asking the question, giving it two parts, each of which I will simplify into just talking about CO2 emissions at the vehicle.
1) Is it better for the environment for my family to drive or to fly to our vacation destination? Or not to go at all?
2) Is it better for the environment for me to drive or fly to a work meeting?
Let's start with 2) because it's a single person on travel and I often do not have the choice about going if I want to keep my job.
I was going to use this graphic, but it sucks. It's not clear how to account for three passengers or a ULEV vehicle.
Let's calculate based on estimates from various sources rather than a graphic. According to atmosfair.de, my business travel this week is likely to cost about 1080 kg CO2. I've read their documentation, and it seems light, but relatively well-done. It's certainly not a research article, but I don't think it's meant to be. I'm going to trust that it is approximately right.
The personal-vehicle travel, round-trip distance is about 3900 km (2400 miles). If I took my Prius, according to fueleconomy.gov, it would cost about 0.6 tonnes (metric tons) of CO2. It would also take me about 36 hours round-trip. If I took the business vehicle, an older Ford SUV, it would cost about 1.6 tonnes of CO2.
So, clearly, it would be best for the environment if I didn't go. It would probably also be best for the marriage if I didn't go (at least until I lost my job). Next best would be to drive the Prius. However, the above estimate only accounts for the CO2 cost of driving. I would need to spend at least one night each-way in a hotel. I don't want to go into the details of how much CO2 that would cost, but it would add a bit to the total trip cost. Driving the Prius may even come out to more than the air travel due to dining out for at least six meals, additional energy costs at the hotel, etc., etc., etc. I could mitigate some or a lot of that additional CO2 cost by camping and buying food from a grocer or farmer, but does anyone really think that would happen during a business trip? Perhaps if I knew the route well enough.
Now, let's answer 1). The three of us are planning a trip to Los Angeles this late Spring. Do we fly or do we drive? The round-trip driving distance is about 1600 km (1000 miles). The CO2 cost is about 0.2 tonnes of CO2, assuming 10% city and 90% freeway driving. The fueleconomy.gov estimate is almost certainly for a single driver, so let's assume that with the passengers, we double the weight of the driver, which only accounts for about 5% of the total weight (10% with the passengers). So, we would not change the total emissions by an appreciable amount.
The cost to fly? atmosfair.de claims that for three passengers, the cost would be about 1.3 metric tons of CO2 (a little over 0.4 per passenger).
So, again, it's cheaper in CO2 for us to drive our Prius. Now, the Prius is not a very common vehicle, so each person would need to do the calculation for their vehicle, but unless you drive an SUV, you are likely to put less greenhouse gas mass into the atmosphere if you drive. Also, an airplane puts the greenhouse gases into just about the worst place possible in terms of environmental damage.
Now, back to the original question. Is flying to a vacation destination selfish? Yes, of course it is. Now, that doesn't mean I think everyone needs to instantly stop traveling, but I do think people should be aware of their actions (admission is the first step or something like that). If you have to go on a long trip, you might also consider taking the train, which is much more efficient than flying.
Considering the amount of driving people in the USA do, I think we should focus on decreasing emissions from our personal vehicles (by using them less, by technology, by whatever means necessary) before we worry too much about that 10% or less effect our air travel has. Where do I get the 10%? Well, most people don't travel 1,000 miles by air for every 10,000 miles they drive. I suspect the number is much smaller. But, the total greenhouse gas emissions from air travel accounts for about 10% of transportation costs. So, not really pulling a number from my...thin air, the total amount of air travel-caused emissions is 10% or less for most people.
Driving three blocks to get groceries or coffee twice a week is much more of a selfish thing to do. I'm as guilty as everyone else.
Hi, My name is Moses and I'm a CO2 emitter.
Here's my take on this question. But first, it has to be framed in the "right" way.
Here's my way of asking the question, giving it two parts, each of which I will simplify into just talking about CO2 emissions at the vehicle.
1) Is it better for the environment for my family to drive or to fly to our vacation destination? Or not to go at all?
2) Is it better for the environment for me to drive or fly to a work meeting?
Let's start with 2) because it's a single person on travel and I often do not have the choice about going if I want to keep my job.
I was going to use this graphic, but it sucks. It's not clear how to account for three passengers or a ULEV vehicle.
Let's calculate based on estimates from various sources rather than a graphic. According to atmosfair.de, my business travel this week is likely to cost about 1080 kg CO2. I've read their documentation, and it seems light, but relatively well-done. It's certainly not a research article, but I don't think it's meant to be. I'm going to trust that it is approximately right.
The personal-vehicle travel, round-trip distance is about 3900 km (2400 miles). If I took my Prius, according to fueleconomy.gov, it would cost about 0.6 tonnes (metric tons) of CO2. It would also take me about 36 hours round-trip. If I took the business vehicle, an older Ford SUV, it would cost about 1.6 tonnes of CO2.
So, clearly, it would be best for the environment if I didn't go. It would probably also be best for the marriage if I didn't go (at least until I lost my job). Next best would be to drive the Prius. However, the above estimate only accounts for the CO2 cost of driving. I would need to spend at least one night each-way in a hotel. I don't want to go into the details of how much CO2 that would cost, but it would add a bit to the total trip cost. Driving the Prius may even come out to more than the air travel due to dining out for at least six meals, additional energy costs at the hotel, etc., etc., etc. I could mitigate some or a lot of that additional CO2 cost by camping and buying food from a grocer or farmer, but does anyone really think that would happen during a business trip? Perhaps if I knew the route well enough.
Now, let's answer 1). The three of us are planning a trip to Los Angeles this late Spring. Do we fly or do we drive? The round-trip driving distance is about 1600 km (1000 miles). The CO2 cost is about 0.2 tonnes of CO2, assuming 10% city and 90% freeway driving. The fueleconomy.gov estimate is almost certainly for a single driver, so let's assume that with the passengers, we double the weight of the driver, which only accounts for about 5% of the total weight (10% with the passengers). So, we would not change the total emissions by an appreciable amount.
The cost to fly? atmosfair.de claims that for three passengers, the cost would be about 1.3 metric tons of CO2 (a little over 0.4 per passenger).
So, again, it's cheaper in CO2 for us to drive our Prius. Now, the Prius is not a very common vehicle, so each person would need to do the calculation for their vehicle, but unless you drive an SUV, you are likely to put less greenhouse gas mass into the atmosphere if you drive. Also, an airplane puts the greenhouse gases into just about the worst place possible in terms of environmental damage.
Now, back to the original question. Is flying to a vacation destination selfish? Yes, of course it is. Now, that doesn't mean I think everyone needs to instantly stop traveling, but I do think people should be aware of their actions (admission is the first step or something like that). If you have to go on a long trip, you might also consider taking the train, which is much more efficient than flying.
Considering the amount of driving people in the USA do, I think we should focus on decreasing emissions from our personal vehicles (by using them less, by technology, by whatever means necessary) before we worry too much about that 10% or less effect our air travel has. Where do I get the 10%? Well, most people don't travel 1,000 miles by air for every 10,000 miles they drive. I suspect the number is much smaller. But, the total greenhouse gas emissions from air travel accounts for about 10% of transportation costs. So, not really pulling a number from my...thin air, the total amount of air travel-caused emissions is 10% or less for most people.
Driving three blocks to get groceries or coffee twice a week is much more of a selfish thing to do. I'm as guilty as everyone else.
Hi, My name is Moses and I'm a CO2 emitter.
Wednesday, March 18, 2009
Happy Women in History Month
March is Women in History Month, here in the US, so clearly I need to discuss the history of women in math and science. There is zero chance that I could name even 0.0000001% of the women who have been influential in science and mathematics, so I'm going to name a few who have made a difference in my view, mostly because they were absolutely phenomenal scientists. I will not name any living, women scientists who directly affected me, but there were many, and I think that most of them know how influential they were.
The women I mention below overcame great, artificial barriers to do their work. In my opinion, anyone who says women cannot do science or math as well as men should be removed from public life permanently. Mr. Summers, I'm looking at you and Barbie, in particular. There is absolutely no evidence that, given the same support and resources, women do not thrive as well as or better than men in any field. If you disagree, you are irrelevant and can go elsewhere; I'm not interested in your opinion.
Back to celebrating, with my favorite first.
Dr. Marie Curie (1867-1934)
Marie Curie is the scientist that inspired my love of science. When I was about six or seven, I read a book about her and decided that science and math would be my future. She studied radioactivity (coined the term and has a unit of measure--the Curie---named after her), discovered the elements radium and polonium, and pioneered the use of radioactive isotopes in the treatment of cancer. She became the first female professor at the University of Paris, and was the first person to be awarded two Nobel prizes.
In 1903, she was awarded, along with her husband Pierre Curie and Henri Becquerel, the Nobel Prize in Physics for their work on radiation. This was the first time a woman was awarded a Nobel Prize. In 1911, she was awarded a second Nobel Prize (and did not share it), this time in chemistry,
Her graduate student, Marguerite Perey, was the first woman to be elected to the French Academy of Sciences (Dr. Curie was refused the honor in 1911 because of sexism).
She was, is, and should continue to be an inspiration to all scientists.
Dr. Jane Goodall (1934 - present)
Jane Goodall began studying the chimpanzees in Gombe Stream National Park in Tanzania, in 1960 and continued for 45 years (I'm not sure that she's done even now). She was the first scientist to observe the creation of tools in non-humans; previously, it was known that non-humans could use tools, but that only humans were sophisticated enough to make them. She has contributed much to the field of primatology over her 45 years, and I can only hope that I will be able to put up with the scientific community for half that long.
In 1974, she founded the Jane Goodall Institute, which is active in protecting the environment.
Dr. Goodall has written too many books to list, including many children's books.
Florence Nightingale (1820 - 1910)
Florence Nightingale pioneered the use of hygiene and sterilization in military field hospitals during the Crimean War. It was her work to clean up a medical barracks in Istanbul that caused the death rate there to drop from ~43 per cent to 2 per cent. She developed a very strong desire to move health care away from cold, impersonal, crowded hospitals to the patients' homes.
In 1859, Nightingale was elected the first female member of the Royal Statistical Society.
Rear Admiral Grace Hopper, Ph.D. (1906 - 1992)
Grace Hopper was at the forefront of computer development in the 40s. She earned her Ph.D. in mathematics at Yale in 1934 and taught at Vassar from 1931 to 1943, when she joined the US Navy Reserves, where she served on the Mark I programming staff. She essentially invented the compiler, which is a bit of software that translates a human-readable programming language into machine language. COBOL, the business programming language still in use today, was based on her compiler FLOW-MATIC. She pioneered the use of reusable computer code (reducing errors and making software extensible), and was one of the developers of UNIVAC I.
More:
Dr. Lisa Randall
Dr. Rosalind Franklin
Hypatia
Mary Somerville
Caroline Herschel
Carolyn Shoemaker
Dr. Sally Ride
Dr. Olivia Judson
There are, of course, many, many more, but here's my problem: I don't have the space to talk about each and every famous influential woman in science and mathematics. Or even about my favorites. :( This page is already getting long and I'm feeling guilty about having to choose one over the others.
I may try to post some about some other people during this month. We'll see how time works out. If you have a favorite (or several), post in a comment and I will look her up and post a paragraph or so when time allows.
The women I mention below overcame great, artificial barriers to do their work. In my opinion, anyone who says women cannot do science or math as well as men should be removed from public life permanently. Mr. Summers, I'm looking at you and Barbie, in particular. There is absolutely no evidence that, given the same support and resources, women do not thrive as well as or better than men in any field. If you disagree, you are irrelevant and can go elsewhere; I'm not interested in your opinion.
Back to celebrating, with my favorite first.
Dr. Marie Curie (1867-1934)
Marie Curie is the scientist that inspired my love of science. When I was about six or seven, I read a book about her and decided that science and math would be my future. She studied radioactivity (coined the term and has a unit of measure--the Curie---named after her), discovered the elements radium and polonium, and pioneered the use of radioactive isotopes in the treatment of cancer. She became the first female professor at the University of Paris, and was the first person to be awarded two Nobel prizes.
In 1903, she was awarded, along with her husband Pierre Curie and Henri Becquerel, the Nobel Prize in Physics for their work on radiation. This was the first time a woman was awarded a Nobel Prize. In 1911, she was awarded a second Nobel Prize (and did not share it), this time in chemistry,
"in recognition of her services to the advancement of chemistry by the discovery of the elements radium and polonium, by the isolation of radium and the study of the nature and compounds of this remarkable element"She is only one of two people to receive a Nobel Prize in two different fields. The other is male and is therefore irrelevant to this discussion.
Her graduate student, Marguerite Perey, was the first woman to be elected to the French Academy of Sciences (Dr. Curie was refused the honor in 1911 because of sexism).
She was, is, and should continue to be an inspiration to all scientists.
Dr. Jane Goodall (1934 - present)
Jane Goodall began studying the chimpanzees in Gombe Stream National Park in Tanzania, in 1960 and continued for 45 years (I'm not sure that she's done even now). She was the first scientist to observe the creation of tools in non-humans; previously, it was known that non-humans could use tools, but that only humans were sophisticated enough to make them. She has contributed much to the field of primatology over her 45 years, and I can only hope that I will be able to put up with the scientific community for half that long.
In 1974, she founded the Jane Goodall Institute, which is active in protecting the environment.
Dr. Goodall has written too many books to list, including many children's books.
Florence Nightingale (1820 - 1910)
Florence Nightingale pioneered the use of hygiene and sterilization in military field hospitals during the Crimean War. It was her work to clean up a medical barracks in Istanbul that caused the death rate there to drop from ~43 per cent to 2 per cent. She developed a very strong desire to move health care away from cold, impersonal, crowded hospitals to the patients' homes.
"my view you know is that the ultimate destination is the nursing of the sick in their own homes. … I look to the abolition of all hospitals and workhouse infirmaries. But it is no use to talk about the year 2000."Nightingale believed in and heavily used a data-based approach to determining how well hospitals and health care officials were caring for their patients. She was one of the first health care professionals who gathered and analyzed copious amounts of statistical data throughout her career. To present the results of her work in tracking deaths due to needlessly poor conditions, Nightingale developed the Polar-area Diagram, also known as the Rose Diagram. This diagram was derived from the pie chart, but is actually useful in comparing multiple data sets (the pie chart is just about the most useless way of presenting data imaginable).
In 1859, Nightingale was elected the first female member of the Royal Statistical Society.
Rear Admiral Grace Hopper, Ph.D. (1906 - 1992)
Grace Hopper was at the forefront of computer development in the 40s. She earned her Ph.D. in mathematics at Yale in 1934 and taught at Vassar from 1931 to 1943, when she joined the US Navy Reserves, where she served on the Mark I programming staff. She essentially invented the compiler, which is a bit of software that translates a human-readable programming language into machine language. COBOL, the business programming language still in use today, was based on her compiler FLOW-MATIC. She pioneered the use of reusable computer code (reducing errors and making software extensible), and was one of the developers of UNIVAC I.
More:
Dr. Lisa Randall
Dr. Rosalind Franklin
Hypatia
Mary Somerville
Caroline Herschel
Carolyn Shoemaker
Dr. Sally Ride
Dr. Olivia Judson
There are, of course, many, many more, but here's my problem: I don't have the space to talk about each and every famous influential woman in science and mathematics. Or even about my favorites. :( This page is already getting long and I'm feeling guilty about having to choose one over the others.
I may try to post some about some other people during this month. We'll see how time works out. If you have a favorite (or several), post in a comment and I will look her up and post a paragraph or so when time allows.
Monday, March 16, 2009
Sunday, March 15, 2009
Planets...
DM-i-L asked what's the real difference between a dwarf planet and a planet.
The IAU specification's only real difference is that the dwarf planet has not cleared its orbit. Clearing an orbit refers to removal of all small debris and most large debris from the region through which the object passes on its orbit around the star. This removal involves incorporating all of that debris into the main body or gravitationally accelerating it out of the region.
Earth has cleared its orbit of all but a few large objects. First, of course is Luna. Second, there is at least one and probably several small objects in a horseshoe orbit around Earth. Other than that, the path that Earth takes around the sun is clear. The same is true for the other seven planets:
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
The named dwarf planets, Ceres, Pluto, Eris (2003 UB313), Haumea, and Makemake (not pronounced as "make, make" but as "mocky mocky") all have other debris in their orbits.
But, what about Saturn and its dust and rings? Well, Saturn is gravitationally in control of all that junk; there's basically nothing in its orbit that isn't strongly affected by Saturn.
There are currently only eight planets in our solar system. There are hundreds of known extrasolar (out of our system) planets.
The IAU specification's only real difference is that the dwarf planet has not cleared its orbit. Clearing an orbit refers to removal of all small debris and most large debris from the region through which the object passes on its orbit around the star. This removal involves incorporating all of that debris into the main body or gravitationally accelerating it out of the region.
Earth has cleared its orbit of all but a few large objects. First, of course is Luna. Second, there is at least one and probably several small objects in a horseshoe orbit around Earth. Other than that, the path that Earth takes around the sun is clear. The same is true for the other seven planets:
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
The named dwarf planets, Ceres, Pluto, Eris (2003 UB313), Haumea, and Makemake (not pronounced as "make, make" but as "mocky mocky") all have other debris in their orbits.
But, what about Saturn and its dust and rings? Well, Saturn is gravitationally in control of all that junk; there's basically nothing in its orbit that isn't strongly affected by Saturn.
There are currently only eight planets in our solar system. There are hundreds of known extrasolar (out of our system) planets.
Saturday, March 14, 2009
Happy Pi day.
Today is March 14. In the ridiculous vernacular of the United States dates (MM/DD/YY), today is 3/14. Pi is approximated as 3.14159265. The US House of Representatives just passed a resolution designating March 14 as National Pi day.
Pi is an awesome number. Everybody knows that Pi is the ratio of the circumference of a circle to its diameter. That's for any circle in Euclidean geometry (what most of you are used to). But, this is just the beginning.
Pi is an irrational number. An irrational number is one that cannot be expressed as a ratio of two integers (as a fraction). This also means that the numbers after the decimal never stop and never repeat. You may find a pattern or two in Pi's numbers, but they won't survive long.
Pi is also a transcendental number, which means that there is no polynomial with rational coefficients of which Pi is the root. That is, there is no combination of addition, subtraction, multiplication, division, powers, roots, etc. and integers that will give you Pi. (You can do so with an imaginary number, though...more on that in a later post, perhaps.)
Pi's value to 50 decimal digits is:
Back to Pi.
Pi can be approximated by:
Pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 + ...
The more terms you include, the closer to Pi you get.
There are literally dozens of other ways to approximate Pi.
Pi is used a lot in physics and other physical sciences (geophysics, electromagnetism, hydrology, etcetera, etcetera, etcetera) because of its relation to circles, cycles, etc.
Pi is used in pretty much all mathematics.
Finally, here is my favorite mathematical relation:
e^(i*Pi) +1 = 0.
This combines the basic operators (addition, multiplication, and power) with some of the most fundamental numbers in mathematics:
square root of negative 1 = i
Pi
e, the base of the natural log, another transcendental, irrational number
1 is unity in multiplication
0 is unity in addition
Happy Pi Day (even though I despise the way of referring to dates as MM/DD/YYYY)!
Pi is an awesome number. Everybody knows that Pi is the ratio of the circumference of a circle to its diameter. That's for any circle in Euclidean geometry (what most of you are used to). But, this is just the beginning.
Pi is an irrational number. An irrational number is one that cannot be expressed as a ratio of two integers (as a fraction). This also means that the numbers after the decimal never stop and never repeat. You may find a pattern or two in Pi's numbers, but they won't survive long.
Pi is also a transcendental number, which means that there is no polynomial with rational coefficients of which Pi is the root. That is, there is no combination of addition, subtraction, multiplication, division, powers, roots, etc. and integers that will give you Pi. (You can do so with an imaginary number, though...more on that in a later post, perhaps.)
Pi's value to 50 decimal digits is:
- 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
Back to Pi.
Pi can be approximated by:
Pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 + ...
The more terms you include, the closer to Pi you get.
There are literally dozens of other ways to approximate Pi.
Pi is used a lot in physics and other physical sciences (geophysics, electromagnetism, hydrology, etcetera, etcetera, etcetera) because of its relation to circles, cycles, etc.
Pi is used in pretty much all mathematics.
Finally, here is my favorite mathematical relation:
e^(i*Pi) +1 = 0.
This combines the basic operators (addition, multiplication, and power) with some of the most fundamental numbers in mathematics:
square root of negative 1 = i
Pi
e, the base of the natural log, another transcendental, irrational number
1 is unity in multiplication
0 is unity in addition
Happy Pi Day (even though I despise the way of referring to dates as MM/DD/YYYY)!
Thursday, March 12, 2009
What does uncertainty really mean?
In science, we try to report the results of our research in careful terms so as not to over- or under-state the implications. In particular, we must acknowledge that all measurements have some associated "error." What the layperson usually thinks of as error is that a mistake was made. This is not the meaning of error when scientists speak with statistics.
I think a relatively simple example is best. If you wanted to record the temperatures in the shade under your porch compared with the temperatures in the sun every Saturday over the course of a year, you might end up with 104 observations. 52 of them might be of the temperature under the porch and the other 52 would be of the temperature in the sun. Let's say you took those observations at about 5:00 every evening. For this thought experiment, you're using two simple dial-read thermometers for the measurements (like in this image).
Let's examine some of the sources of uncertainty (error).
Now, the measurements of a single yard do not necessarily say a whole lot about the temperatures in your neighborhood. Let's assume everyone in the neighborhood took the same measurements for their backyard and we wanted to report the neighborhood's average temperatures for each week of the year. Every reading is going to be different and when compiled together, there will be an uncertainty associated with each average. For example, we might report the neighborhood temperature as:
week 9; 45 +- 7 degrees F
week 10; 46 +- 9 degrees F
week 11; 42 +- 12 degrees F
week 12; 49 +- 3 degrees F
That +-7 degrees F for week 9 has some very important implications, and it's terribly imprecise at the moment. Is that 1-, 2-, or 3-sigma standard deviation? Did you include the systematic corrections? Did you account for all of the errors? How did you calculate this 7 degrees?
I just threw out a bunch of terms that may not be familiar. Let me define one of them. What is standard deviation? It's a measure of the variability of the observations. You have a ~68.3% confidence that any of your measurements are one standard deviation away from the mean value. Let's say that everyone was so careful in their measurements and calibration that the +-7 degrees F for week 9 is the 3-sigma standard deviation. That means that 99.7% of the neighborhood measurements were within 7 degrees of the mean value, 45 degrees F. If you only reported 1-sigma, only 68.3% of your measurements were within 7 degrees of the mean.
If you were to continue these measurements over a decade, you'd be able to say something about the long-term change and the short-term variability of the temperatures in your neighborhood. If you do this right, you might notice a pattern. Here's a good discussion of long-term change vs. short-term variability; I think it's written by someone who knows how to educate people.
What's the point of this terribly long and boring discussion? Well, scientists report the errors/uncertainty in their data as a method of limiting the strength of their conclusions. When they report that 99.7% of their measurements fall within a range and that range indicates such-and-such, that means there's only a 3/1000 chance of something outside that range being important to their conclusions.
[rant]
Lots of people willingly or ignorantly seem to see scientific "uncertainty" or "error" or any other scientific language as a way to wiggle out of doing anything they don't want to do.
[/rant]
Obviously, scientists are only human; some may be sloppy and some may be dishonest. That's what peer-review and reproduction of results is about. Sometimes fraud slips through (and it's always reported as if this happens regularly), sometimes mistakes are made, but those are usually corrected rather quickly and are an embarrassment to the journal publishing the incorrect results. Often models are only approximations to reality. That's fine; they give us a way of understanding complex situations, not as a way of saying exactly what will happen.
Let's go back to measuring temperatures. Let's say that you were told that over the past 100 years, the mean temperature of the earth's lower atmosphere has increased by 0.75 degrees C, and that the data plotted here are plotted with a 95% confidence interval. (Note that these are just measurements, not models or approximations. The error bars are from the kinds of errors I discussed above.)
You are also told that this increase is very likely (>90% to >99%) to have been caused by human activity.
What does this mean?
First, what does that 95% confidence interval mean? It means that those little grey bars on the plot here are 2-sigma error bars. It essentially means that 19 of 20 observations were within the range of the bar-ends. Notice that while the errors were relatively large early in the measurements, the old measurements rarely overlap with the new measurements. That is, even if you were to take the warmest measurements from 1850 and the coldest measurements from 2000, we're still significantly warmer.
What is the meaning that there's a 90% probability that human activity has caused this warming? It means that after all the known errors in the measurements and in the models have been accounted for, we're virtually certain that this warming is due to human activity. It means that all of the other possible sources of error account for less than a 10% chance that global climate change is not mostly human-induced. It means that those who advocate doing nothing to slow down CO2 emissions are counting on a--at best--1 in 10 chance of being right.
When scientists speak in terms of uncertainty, they're being careful to note that there is noise associated with all measurements. When laypeople glom on to this language as a way to avoid doing anything because "there's uncertainty" or "there are errors in the data", they're being the opposite of careful. They're claiming that a 1 in 10 chance of not causing 1000 or more years of difficulties for our posterity is the right bet to make.
By the way, there is not a single climate model out there that can reproduce the observed mean temperature increases without including anthropogenic sources. None. There is no controversy among scientists. There may be controversy among politicians, media, and special interests, but no honest climate scientist thinks that humans are not a major cause of global climate change.
Who would take their children or grandchildren on a flight with an airline if they knew that it had a record of crashing nine times for every ten flights it operated? Who would take a flight with an airline if it even had a 1 in 10 chance of crashing?
So, why are we doing this with the future?
I think a relatively simple example is best. If you wanted to record the temperatures in the shade under your porch compared with the temperatures in the sun every Saturday over the course of a year, you might end up with 104 observations. 52 of them might be of the temperature under the porch and the other 52 would be of the temperature in the sun. Let's say you took those observations at about 5:00 every evening. For this thought experiment, you're using two simple dial-read thermometers for the measurements (like in this image).
Let's examine some of the sources of uncertainty (error).
- The dial is graduated to 2 degrees F of precision. That is, each small mark indicates 2 degrees F. You can guess that about half-way between two of the small marks is one degree. You cannot be much more precise than that.
- Each mark has some width. Should the temperature be read as 52 degrees F on the right edge, the left edge, or the center of the mark? Were you being consistent in the reading every Saturday, and for both thermometers?
- The needle of the thermometer does not stay a constant size; in warmer weather, it expands slightly and it contracts slightly in cold weather. Does this matter? It depends on how precise you want to be.
- Are you reading the thermometers at the exact same time every day?
- This particular thermometer is on a swivel mount; is it always in the same spot?
- How well calibrated are your thermometers?
- Do both thermometers record the same temperature when placed in the same location for the same amount of time?
Now, the measurements of a single yard do not necessarily say a whole lot about the temperatures in your neighborhood. Let's assume everyone in the neighborhood took the same measurements for their backyard and we wanted to report the neighborhood's average temperatures for each week of the year. Every reading is going to be different and when compiled together, there will be an uncertainty associated with each average. For example, we might report the neighborhood temperature as:
week 9; 45 +- 7 degrees F
week 10; 46 +- 9 degrees F
week 11; 42 +- 12 degrees F
week 12; 49 +- 3 degrees F
That +-7 degrees F for week 9 has some very important implications, and it's terribly imprecise at the moment. Is that 1-, 2-, or 3-sigma standard deviation? Did you include the systematic corrections? Did you account for all of the errors? How did you calculate this 7 degrees?
I just threw out a bunch of terms that may not be familiar. Let me define one of them. What is standard deviation? It's a measure of the variability of the observations. You have a ~68.3% confidence that any of your measurements are one standard deviation away from the mean value. Let's say that everyone was so careful in their measurements and calibration that the +-7 degrees F for week 9 is the 3-sigma standard deviation. That means that 99.7% of the neighborhood measurements were within 7 degrees of the mean value, 45 degrees F. If you only reported 1-sigma, only 68.3% of your measurements were within 7 degrees of the mean.
If you were to continue these measurements over a decade, you'd be able to say something about the long-term change and the short-term variability of the temperatures in your neighborhood. If you do this right, you might notice a pattern. Here's a good discussion of long-term change vs. short-term variability; I think it's written by someone who knows how to educate people.
What's the point of this terribly long and boring discussion? Well, scientists report the errors/uncertainty in their data as a method of limiting the strength of their conclusions. When they report that 99.7% of their measurements fall within a range and that range indicates such-and-such, that means there's only a 3/1000 chance of something outside that range being important to their conclusions.
Lots of people willingly or ignorantly seem to see scientific "uncertainty" or "error" or any other scientific language as a way to wiggle out of doing anything they don't want to do.
Obviously, scientists are only human; some may be sloppy and some may be dishonest. That's what peer-review and reproduction of results is about. Sometimes fraud slips through (and it's always reported as if this happens regularly), sometimes mistakes are made, but those are usually corrected rather quickly and are an embarrassment to the journal publishing the incorrect results. Often models are only approximations to reality. That's fine; they give us a way of understanding complex situations, not as a way of saying exactly what will happen.
Let's go back to measuring temperatures. Let's say that you were told that over the past 100 years, the mean temperature of the earth's lower atmosphere has increased by 0.75 degrees C, and that the data plotted here are plotted with a 95% confidence interval. (Note that these are just measurements, not models or approximations. The error bars are from the kinds of errors I discussed above.)
You are also told that this increase is very likely (>90% to >99%) to have been caused by human activity.
What does this mean?
First, what does that 95% confidence interval mean? It means that those little grey bars on the plot here are 2-sigma error bars. It essentially means that 19 of 20 observations were within the range of the bar-ends. Notice that while the errors were relatively large early in the measurements, the old measurements rarely overlap with the new measurements. That is, even if you were to take the warmest measurements from 1850 and the coldest measurements from 2000, we're still significantly warmer.
What is the meaning that there's a 90% probability that human activity has caused this warming? It means that after all the known errors in the measurements and in the models have been accounted for, we're virtually certain that this warming is due to human activity. It means that all of the other possible sources of error account for less than a 10% chance that global climate change is not mostly human-induced. It means that those who advocate doing nothing to slow down CO2 emissions are counting on a--at best--1 in 10 chance of being right.
When scientists speak in terms of uncertainty, they're being careful to note that there is noise associated with all measurements. When laypeople glom on to this language as a way to avoid doing anything because "there's uncertainty" or "there are errors in the data", they're being the opposite of careful. They're claiming that a 1 in 10 chance of not causing 1000 or more years of difficulties for our posterity is the right bet to make.
By the way, there is not a single climate model out there that can reproduce the observed mean temperature increases without including anthropogenic sources. None. There is no controversy among scientists. There may be controversy among politicians, media, and special interests, but no honest climate scientist thinks that humans are not a major cause of global climate change.
Who would take their children or grandchildren on a flight with an airline if they knew that it had a record of crashing nine times for every ten flights it operated? Who would take a flight with an airline if it even had a 1 in 10 chance of crashing?
So, why are we doing this with the future?
Monday, March 9, 2009
Vertebral wedge and compression fractures, a follow-up
So, the most common google search used to find this blog is about wedge fractures in the vertebrae. I thought I'd send everyone on to much better resources than I could possibly provide.
Obviously, you can find these links via google, but this blog seems to be bumping some of them off the top page (and will probably bump some more after I post this)...
Links follow:
University of Maryland explanation on the causes and treatments of compression fractures.
American Family Physician journal article about compression fractures in people with osteoporosis.
SpineUniverse discussion by a professor from the University of Wisconsin, re: treatment.
Another article at the same website by the same professor.
And yet another (of course, you could just follow the links at the bottom of the articles).
American Journal of Roentgenology paper on diagnosing vertebral fractures.
X-rays of vertebral fractures from the above paper.
Discussion of vertebroplasty, a method of treating a wedge fracture by injecting bone cement into the affected vertebra.
Another article about injecting bone cement into a fractured vertebra, in the journal Spine. This article shows mixed results w.r.t. recovered behavior of the bones.
Article on how to deal with osteoporosis, including exercises that should help.
A few paragraphs about wedge fractures.
Google Books preview of a book called Practical Fracture Treatment.
Paragliders are likely to break their backs, apparently...
Google Books preview of The Osteoporosis Book.
Another discussion of vertebroplasty and kyphoplasty.
Google Books preview of Tidy's Physiotherapy, a book for students of...physiotherapy.
American Journal of Neuroradiology article on kyphosis correction and vertebroplasty.
Article from Rice University about testing spinal stability.
Anyway, obviously I cannot reproduce the google results pages.
Here are some of the search terms I used.
wedge fracture vertebrae recovery T6 osteoporosis vertebroplasy kyphosis kyphoplasty treatment
Good luck on your recovery!
Obviously, you can find these links via google, but this blog seems to be bumping some of them off the top page (and will probably bump some more after I post this)...
Links follow:
University of Maryland explanation on the causes and treatments of compression fractures.
American Family Physician journal article about compression fractures in people with osteoporosis.
SpineUniverse discussion by a professor from the University of Wisconsin, re: treatment.
Another article at the same website by the same professor.
And yet another (of course, you could just follow the links at the bottom of the articles).
American Journal of Roentgenology paper on diagnosing vertebral fractures.
X-rays of vertebral fractures from the above paper.
Discussion of vertebroplasty, a method of treating a wedge fracture by injecting bone cement into the affected vertebra.
Another article about injecting bone cement into a fractured vertebra, in the journal Spine. This article shows mixed results w.r.t. recovered behavior of the bones.
Article on how to deal with osteoporosis, including exercises that should help.
A few paragraphs about wedge fractures.
Google Books preview of a book called Practical Fracture Treatment.
Paragliders are likely to break their backs, apparently...
Google Books preview of The Osteoporosis Book.
Another discussion of vertebroplasty and kyphoplasty.
Google Books preview of Tidy's Physiotherapy, a book for students of...physiotherapy.
American Journal of Neuroradiology article on kyphosis correction and vertebroplasty.
Article from Rice University about testing spinal stability.
Anyway, obviously I cannot reproduce the google results pages.
Here are some of the search terms I used.
wedge fracture vertebrae recovery T6 osteoporosis vertebroplasy kyphosis kyphoplasty treatment
Good luck on your recovery!
Saturday, March 7, 2009
Pluto: A planet? a plutoid? a minor planet? a dwarf planet?
So, DS occasionally corrects his books on planets that were written before the latest IAU renaming event. That's fine. It's good for him to think about how science happens and why we need to sometimes reclassify things when new information comes to light.
Here's the basic history of the naming of the planets:
1) Etymology of the word planet:
late O.E., from O.Fr. planete (Fr. planète), from L.L. planeta, from Gk. (asteres) planetai "wandering (stars)," from planasthai "to wander," of unknown origin. So called because they have apparent motion, unlike the "fixed" stars. Originally including also the moon and sun; modern scientific sense of "world that orbits a star" is from 1640.
2) That "modern scientific sense" is not quite accurate any more. Here are some reasons:
A) Ganymede, one of Jupiter's moons is larger in radius than Mercury by about 200 km.
B) Pluto's orbit is very strange compared with the eight other planets; Pluto sometimes is closer to the sun than Neptune. No, they're not likely ever to hit each other.
C) There are objects outside of Pluto's orbit that are larger than Pluto; should they be called planets? If so, we're going to end up with a few hundred or more planets in our solar system; we'll never come up with a reasonable mnemonic to remember their names. ;)
Here's the resolution by the IAU, the body responsible for naming objects in space:
So, this is really just taxonomy.
Here's the deal. Nearly every planetary scientist I know refers, in casual conversation, to the larger objects they study as planets: Ganymede is a planet, Io is a planet, Mars is a planet, Pluto is a planet. This isn't out of some kind of misguided rebellion, it's just easier. When we write technical manuscripts, we use the correct taxonomy when necessary. This is because we like to have a reliable and predictable method of categorizing things.
So, some people feel bad for Pluto and think it should be re-instated as a planet. Who cares? It was still the ninth large object discovered orbiting our sun (as opposed to orbiting an object orbiting our sun). Some people have taken it pretty far.
Here's how far it's gone:
The Illinois State Senate has:
Here's a graphic that shows the current taxonomy of our solar system's objects:
Here's the basic history of the naming of the planets:
1) Etymology of the word planet:
late O.E., from O.Fr. planete (Fr. planète), from L.L. planeta, from Gk. (asteres) planetai "wandering (stars)," from planasthai "to wander," of unknown origin. So called because they have apparent motion, unlike the "fixed" stars. Originally including also the moon and sun; modern scientific sense of "world that orbits a star" is from 1640.
2) That "modern scientific sense" is not quite accurate any more. Here are some reasons:
A) Ganymede, one of Jupiter's moons is larger in radius than Mercury by about 200 km.
B) Pluto's orbit is very strange compared with the eight other planets; Pluto sometimes is closer to the sun than Neptune. No, they're not likely ever to hit each other.
C) There are objects outside of Pluto's orbit that are larger than Pluto; should they be called planets? If so, we're going to end up with a few hundred or more planets in our solar system; we'll never come up with a reasonable mnemonic to remember their names. ;)
Here's the resolution by the IAU, the body responsible for naming objects in space:
RESOLUTIONSResolution 5A is the principal definition for the IAU usage of "planet" and related terms.
Resolution 6A creates for IAU usage a new class of objects, for which Pluto is the prototype. The IAU will set up a process to name these objects.
IAU Resolution: Definition of a "Planet" in the Solar System
Contemporary observations are changing our understanding of planetary systems, and it is important that our nomenclature for objects reflect our current understanding. This applies, in particular, to the designation "planets". The word "planet" originally described "wanderers" that were known only as moving lights in the sky. Recent discoveries lead us to create a new definition, which we can make using currently available scientific information.
RESOLUTION 5A
The IAU therefore resolves that planets and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way:
(1) A "planet" [1] is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.
(2) A "dwarf planet" is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape [2], (c) has not cleared the neighbourhood around its orbit, and
(d) is not a satellite.
(3) All other objects [3], except satellites, orbiting the Sun shall be referred to collectively as "Small Solar-System Bodies".
IAU Resolution: Pluto
RESOLUTION 6A
The IAU further resolves:
Pluto is a "dwarf planet" by the above definition and is recognized as the prototype of a new category of trans-Neptunian objects.
So, this is really just taxonomy.
Here's the deal. Nearly every planetary scientist I know refers, in casual conversation, to the larger objects they study as planets: Ganymede is a planet, Io is a planet, Mars is a planet, Pluto is a planet. This isn't out of some kind of misguided rebellion, it's just easier. When we write technical manuscripts, we use the correct taxonomy when necessary. This is because we like to have a reliable and predictable method of categorizing things.
So, some people feel bad for Pluto and think it should be re-instated as a planet.
Here's how far it's gone:
The Illinois State Senate has:
RESOLVED, BY THE SENATE OF THE NINETY-SIXTH GENERALHmm... More legislative meddling in the affairs of science a la the Indiana attempt in 1897 to legislate the value of Pi? I'm not sure. This is not exactly a bill requiring that Pluto be called a planet; it's a resolution stating that the Illinois senate would like to make March 13 "Pluto Day" in the state of Illinois (and also that they would like to see Pluto reinstated as a planet, but it's not like they can do anything about that). This is certainly not binding; the science books in Illinois are not necessarily going to be any different from those in the rest of the US because of this resolution. Also, during the same legislative session, the Illinois Senate encouraged the state citizens to recognize that age 50 is a great and wondorous mark of wisdom (I'm not saying it isn't!).
ASSEMBLY OF THE STATE OF ILLINOIS, that as Pluto passes
overhead through Illinois' night skies, that it be
reestablished with full planetary status, and that March 13,
2009 be declared "Pluto Day" in the State of Illinois in honor
of the date its discovery was announced in 1930.
Here's a graphic that shows the current taxonomy of our solar system's objects:
Sunday, March 1, 2009
Magnetism: What is attracted to a magnet?
My son's school is having its science fair this week (okay, two weeks ago now; I'm late). My son is in kindergarten. His teacher made participation in the fair a required activity (have I mentioned how much I like her?).
So, DS wanted to play with magnets for his project.
His question: What sticks to a magnet.
His methodology: Get a bunch of different kinds of things and test whether they stick to a magnet by trying to pick them up with a magnet. He tested plastic objects, metal objects, coins, paper, and some other things. If an object responded at all to the pull of the magnet, he considered it to have stuck.
His results: Metal sticks to a magnet. However, not all metals do; coins, for example, do not stick to magnets. No non-metal objects stuck to the magnet.
He asked how do magnets work. His mom answered, "magic." Seriously. She thinks magnets are magical. /sigh Two steps forward, 1.5 steps back. Okay, maybe she doesn't seriously think that, but come on...
So. How do magnets work?
Actually, it's a little difficult, so my DW has a good excuse for explaining it away with magic.
Before I go any further, I need to confess that I slept through most of my magnetohydrodynamics class in graduate school; I only earned a B. The fundamentals of magnetism is a difficult subject for me so most of what I tell you is just scratching the surface and may not be entirely accurate.
First, a magnetic field is essentially an area of influence caused by an electric current. An electric current can travel through wires, such as your computer, or microscopically when individual electrons move in their orbit around an atom's nucleus. Now, it's not just the flow of electrons that creates a magnetic field. Electrons "spin" in a particular direction. In normal materials, the electron spin is pretty much randomly distributed, but in a magnet, the spin is aligned such that the flowing electrons all have the same spin.
This flow of spin-aligned electrons causes magnet(ic field)s to be dipolar. That is, a magnet has a "north" and a "south" pole. (dipolar, not bipolar; magnets are not manic-depressive.). By convention, electrons flow from the north pole to the south pole. You can see this by putting a bar magnet under a piece of paper with a bunch of iron fileings on the top; they'll align along the field lines.
When spin-aligned electrons encounter other spin-aligned electrons going in the opposite direction, they're repelled from each other. Thus when you put the north (or south) poles of two magnets together, they'll push each other apart. If you put the north and south poles together, they'll attract each other.
So, why do non-metal objects not display magnetic properties? Because their electrons' spins are randomly distributed. Most metals also have more randomly distributed electron spins. Ferrous iron and a few other metals have highly ordered electrons and are magnetic (or even are magnets). ALL materials will respond to a strong enough magnetic field because every electon with spin (every electron) is basically a little magnet. At some (very large) magnetic field strength, a piece of paper will respond as though it were magnetic because the average spin of its electrons will be slightly greater in one spin direction than another.
Relativity requires that both electricity and magnetism be two expressions of the same thing; if either one is neglected, the other is inconsistent with relativity.
So, it's magic. ;)
links:
hyperphysics
http://en.wikipedia.org/wiki/Magnetism
Drexel university
So, DS wanted to play with magnets for his project.
His question: What sticks to a magnet.
His methodology: Get a bunch of different kinds of things and test whether they stick to a magnet by trying to pick them up with a magnet. He tested plastic objects, metal objects, coins, paper, and some other things. If an object responded at all to the pull of the magnet, he considered it to have stuck.
His results: Metal sticks to a magnet. However, not all metals do; coins, for example, do not stick to magnets. No non-metal objects stuck to the magnet.
He asked how do magnets work. His mom answered, "magic." Seriously. She thinks magnets are magical. /sigh Two steps forward, 1.5 steps back. Okay, maybe she doesn't seriously think that, but come on...
So. How do magnets work?
Actually, it's a little difficult, so my DW has a good excuse for explaining it away with magic.
Before I go any further, I need to confess that I slept through most of my magnetohydrodynamics class in graduate school; I only earned a B. The fundamentals of magnetism is a difficult subject for me so most of what I tell you is just scratching the surface and may not be entirely accurate.
First, a magnetic field is essentially an area of influence caused by an electric current. An electric current can travel through wires, such as your computer, or microscopically when individual electrons move in their orbit around an atom's nucleus. Now, it's not just the flow of electrons that creates a magnetic field. Electrons "spin" in a particular direction. In normal materials, the electron spin is pretty much randomly distributed, but in a magnet, the spin is aligned such that the flowing electrons all have the same spin.
This flow of spin-aligned electrons causes magnet(ic field)s to be dipolar. That is, a magnet has a "north" and a "south" pole. (dipolar, not bipolar; magnets are not manic-depressive.). By convention, electrons flow from the north pole to the south pole. You can see this by putting a bar magnet under a piece of paper with a bunch of iron fileings on the top; they'll align along the field lines.
When spin-aligned electrons encounter other spin-aligned electrons going in the opposite direction, they're repelled from each other. Thus when you put the north (or south) poles of two magnets together, they'll push each other apart. If you put the north and south poles together, they'll attract each other.
So, why do non-metal objects not display magnetic properties? Because their electrons' spins are randomly distributed. Most metals also have more randomly distributed electron spins. Ferrous iron and a few other metals have highly ordered electrons and are magnetic (or even are magnets). ALL materials will respond to a strong enough magnetic field because every electon with spin (every electron) is basically a little magnet. At some (very large) magnetic field strength, a piece of paper will respond as though it were magnetic because the average spin of its electrons will be slightly greater in one spin direction than another.
Relativity requires that both electricity and magnetism be two expressions of the same thing; if either one is neglected, the other is inconsistent with relativity.
So, it's magic. ;)
links:
hyperphysics
http://en.wikipedia.org/wiki/Magnetism
Drexel university
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