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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