Many physicists and astronomers consider Galileo Galilei to be the father of modern science. He was probably the first to suggest that the laws of nature could be understood with mathematics. Famously, his observations of the heavens put him in conflict with the church and he almost lost his head over the matter.
This year marks the 400th anniversary of Galileo's demonstration of the telescope (it was actually invented by a Dutchman, but after reading a report of it, Galileo managed to reproduce the device and improve it substantially). Because of this anniversary, 2009 has been declared the international year of astronomy.
But this blog entry is not about Galileo the astronomer. This entry is about another astronomer named Brian who started studying physics in the 1960s and finally obtained his PhD in astrophysics in 2008. This is not because he was slow, but rather because he took a long hiatus to do something else with his life. Nonetheless, he may be one of the world's best known astronomers now.
The reason I was thinking about Brian is that he has recently co-authored a successful popular book called "Bang!, the complete history of the universe" with an astronomy postdoc ("Junior Research Fellow") at Oxford and Somerville named Chris.
"Brian", is Brian May, from the amazing rock group "Queen". He left graduate school to have a career as one of the greatest rock guitar players of all time. I guess that worked out pretty well for him. But after years of rockin' out -- he decided to go back, at age 60, to finish up what he started. You can find his PhD thesis here. I haven't read it, but I'm told it is pretty solid. Here's a picture of him at the graduation ceremony.
"Galileo! Galileo! Galileo, Figaro! "
A thousand years ago this year a horde of Vikings led by Sweyn Forkbeard torched the city of Oxford to the ground as retribution for the ethnic cleansing of Danes ordered by King Ethelred the Unready of England (Needless to say, he was termed unready because of his rather stupid orders that brought destruction to his own kingdom).
About a hundred years later Oxford began to be considered a center of higher learning of some reputation, with literally thousands of students even in those early times. But violence was never far away with blood often flowing in the streets one way or the other.
Exactly eight hundred years ago this year, the situation became so bad that the university had to suspend all studies. Here is a short history of the conflict of that year (from here)
“ An Oxford clerk kills a woman—accidentally, as it is afterwards said. But the culprit flees. The town authorities search the dwelling wherein he lodged, and, in his absence, arrest two or three of his companions, who are perfectly innocent of the offence, if such it be. King John, however, is in the middle of his famous quarrel with the pope, and is ready to wreak his vengeance on any clerk. On the king’s instructions, the innocent prisoners are hanged. In combined fear and indignation, the Oxford masters proclaim a suspension of studies; and the scholars scatter.”
The university was reinstated five years later, but conflict between town and gown continued on and off, with riots occurring into the late 1800s.
There is a rather vocal band of history minded Oxonians that feel like we should re-enact the torching of the city (See here). For my money though, I’d rather see a re-enactment of the scholars fleeing the city. It happens between terms anyway.
A few minor updates:
* Congratulations to Fiona Burnell, who was indeed awarded the All-Souls fellowship (that is rather a big deal).
* My replacement bed is scheduled to be delivered tomorrow – I’m preparing myself for three more hours with a screwdriver, cursing the name of the bed company.
Added: I finally have a bed. About $!@%# time. I bought the thing on January 10th.
* I've discovered that Philip Pullman lives somewhere within a few blocks of me. One of my friends at Somerville just "happened" to have dinner with him this weekend. This will be one of my objectives.
* My webpage at Oxford finally went live here. It is horribly ugly and has a bunch of typos too. But it took two months for me to get anything up at all, so I'm not too eager to try to fix it.
About a hundred years later Oxford began to be considered a center of higher learning of some reputation, with literally thousands of students even in those early times. But violence was never far away with blood often flowing in the streets one way or the other.
Exactly eight hundred years ago this year, the situation became so bad that the university had to suspend all studies. Here is a short history of the conflict of that year (from here)
“ An Oxford clerk kills a woman—accidentally, as it is afterwards said. But the culprit flees. The town authorities search the dwelling wherein he lodged, and, in his absence, arrest two or three of his companions, who are perfectly innocent of the offence, if such it be. King John, however, is in the middle of his famous quarrel with the pope, and is ready to wreak his vengeance on any clerk. On the king’s instructions, the innocent prisoners are hanged. In combined fear and indignation, the Oxford masters proclaim a suspension of studies; and the scholars scatter.”
The university was reinstated five years later, but conflict between town and gown continued on and off, with riots occurring into the late 1800s.
There is a rather vocal band of history minded Oxonians that feel like we should re-enact the torching of the city (See here). For my money though, I’d rather see a re-enactment of the scholars fleeing the city. It happens between terms anyway.
A few minor updates:
* Congratulations to Fiona Burnell, who was indeed awarded the All-Souls fellowship (that is rather a big deal).
* My replacement bed is scheduled to be delivered tomorrow – I’m preparing myself for three more hours with a screwdriver, cursing the name of the bed company.
Added: I finally have a bed. About $!@%# time. I bought the thing on January 10th.
* I've discovered that Philip Pullman lives somewhere within a few blocks of me. One of my friends at Somerville just "happened" to have dinner with him this weekend. This will be one of my objectives.
* My webpage at Oxford finally went live here. It is horribly ugly and has a bunch of typos too. But it took two months for me to get anything up at all, so I'm not too eager to try to fix it.
This week, for the first time, I actually needed to go find a particularly arcane book in the library. With so much information on line, needing a real book is becoming a rather rare occurrence. Nonetheless , it does happen from time to time. Going into the Oxford library was quite an experience. Being away from the university setting for over a decade, I admit I was a bit blown away by the sheer size of the collection.
It has been a long time since I actually haunted the stacks of a real library. In grad school, the Cabot Science library (a rather ugly building) was a place I spent countless hours studying. My favorite desk was situated next to a stack of NASA documents from 1960. When I got frustrated with my work, I would go to the shelves and entertain myself with the records of all the failed attempts to build a better rocket. (It is amazing that they actually made it to the moon only a few years later).
Originally the Oxford science collection lived in the rather stunning Radcliffe Camera (built sometime in the 1700s) but it moved to the new Radcliffe Science library a few blocks away over a hundred years ago now. Wings have since been added to accommodate the ever increasing collection - and apparently they have continued to dig deeper underground to make more room. Currently, you enter the library on the fourth, albeit ground, floor. Since Oxford is extremely touchy about its skyline (with good reason, considering the beautiful architecture around here) digging deep below ground seems a good way to make more space. (See footnote *)
In addition to the main library, each of the constituent colleges of Oxford also has its own library. And it seems that each college has also decided that the best place for books is underground. Like the halls of Moria, the entire university seems to be permeated with ancient underground tunnels. But perhaps more important than the books, another precious resource is kept in underground tunnels - the wine.
Oxford takes wine very seriously. Each college has its own wine Steward who is entrusted to stash away piles of the best stuff for future generations of fellows. Some of the ancient (and filthy rich) colleges have done an exceptional job of this. (The best port I have ever tasted was when I had the fortune to visit All Souls College a few month ago). Somerville, unfortunately, is merely passable in this respect.
So deep below ground the colleges store the books and the wine. And what else lurks down there? As far as I know there are no Goblins, no Elves, no Trolls. No, I fear there are things far more frightenting – graduate students and the occasional college fellow haunting the stacks.
* Footnote: The physics department is thinking about building a new building next to the Clarendon lab with several levels of basements filled with labs. Unfortunately, it turns out that if you dig a hole too deep next to an existing building, you risk having the existing building fall into the hole.
It has been a long time since I actually haunted the stacks of a real library. In grad school, the Cabot Science library (a rather ugly building) was a place I spent countless hours studying. My favorite desk was situated next to a stack of NASA documents from 1960. When I got frustrated with my work, I would go to the shelves and entertain myself with the records of all the failed attempts to build a better rocket. (It is amazing that they actually made it to the moon only a few years later).
Originally the Oxford science collection lived in the rather stunning Radcliffe Camera (built sometime in the 1700s) but it moved to the new Radcliffe Science library a few blocks away over a hundred years ago now. Wings have since been added to accommodate the ever increasing collection - and apparently they have continued to dig deeper underground to make more room. Currently, you enter the library on the fourth, albeit ground, floor. Since Oxford is extremely touchy about its skyline (with good reason, considering the beautiful architecture around here) digging deep below ground seems a good way to make more space. (See footnote *)
In addition to the main library, each of the constituent colleges of Oxford also has its own library. And it seems that each college has also decided that the best place for books is underground. Like the halls of Moria, the entire university seems to be permeated with ancient underground tunnels. But perhaps more important than the books, another precious resource is kept in underground tunnels - the wine.
Oxford takes wine very seriously. Each college has its own wine Steward who is entrusted to stash away piles of the best stuff for future generations of fellows. Some of the ancient (and filthy rich) colleges have done an exceptional job of this. (The best port I have ever tasted was when I had the fortune to visit All Souls College a few month ago). Somerville, unfortunately, is merely passable in this respect.
So deep below ground the colleges store the books and the wine. And what else lurks down there? As far as I know there are no Goblins, no Elves, no Trolls. No, I fear there are things far more frightenting – graduate students and the occasional college fellow haunting the stacks.
* Footnote: The physics department is thinking about building a new building next to the Clarendon lab with several levels of basements filled with labs. Unfortunately, it turns out that if you dig a hole too deep next to an existing building, you risk having the existing building fall into the hole.
Voldemort?
Last week I was sitting in a meeting of the Education Committee of Somerville College. Although most meeting are rather dull, I actually learned quite a few interesting things in this meeting. One of the things that gets discussed in the education committee is the students who are in trouble for one reason or another. If they are in trouble, academic or not, they are put on report. If they are in more trouble, it escalates to probation. After that they get kicked out. There are really very few students who fall into this category, and really one only needs to "get your work up from miserable to mediocre" in order to get off of report. But after hearing the status of these all of these troubled students, there was then a long discussion of "how many students are being desummoned".
Desummoned? Sounds like they are being banished to the great beyond. After being completely confused for a while, I finally asked what on earth they were talking about. It turns out that "Desummoned" is the fancy word for "Rejected". They were talking about undergraduate admissions.
The admissions situation is apparently quite a topic of conversation around here (for good reason). The system is pretty complicated, and I'm sure I will know much more about it once I go through the process in detail in the fall. But here is the rough story.
First thing to realize is that students are admitted to "read" a single subject. So you are admitted as a physicist, a chemist, or whatever. There is no concept of liberal arts. Because of this the physicists all get together and discuss the physics applicants. On the other hand, you are also admitted to a single college. So you also apply to the specific college. So in essence, next year, I will be choosing from the applicant pool some 6 or 7 students a year who will come to somerville college, and I will be their tutor. As people like to say around here, "you get to choose your own mistakes."
One issue is that students get to decide which college to apply to, but in some cases they end up at other colleges because there just isn't enough room at the really popular places. One of the things Somerville worries about is that we have a lot of "hand-me-down" students.
Within the physics community, the big issue du-jour is how much we should pay attention to the entrance exam in admissions. Just in the last few years they have started keeping track of how students have been rated in the interviews versus how they have performed once they get here and several years later. What was found is that there is essentially no correlation with the interview -- but there is very high correlation with the entrance exam. So does this mean we should only pay attention to the entrance exam? That doesn't sound like such a good idea either, since the entrance exam is likely to test more how well you are prepared (i.e., how good a school you went to) rather than how smart you are. Nonetheless (given various caveats about the quality of our data) our current belief is that the entrance exam is probably the best indicator of success in physics at Oxford. The main reason people want to keep the interview right now is that a few candidates (typically overseas) take the entrance exam in "uncontrolled" conditions, and then when they get to the interview it is quite clear that they were not the ones who actually took the exam since they know none of the material. So the interview does function to weed out cheaters, but this appears to be its main purpose. These people are "desummoned" rather quickly.
Last week I was sitting in a meeting of the Education Committee of Somerville College. Although most meeting are rather dull, I actually learned quite a few interesting things in this meeting. One of the things that gets discussed in the education committee is the students who are in trouble for one reason or another. If they are in trouble, academic or not, they are put on report. If they are in more trouble, it escalates to probation. After that they get kicked out. There are really very few students who fall into this category, and really one only needs to "get your work up from miserable to mediocre" in order to get off of report. But after hearing the status of these all of these troubled students, there was then a long discussion of "how many students are being desummoned".
Desummoned? Sounds like they are being banished to the great beyond. After being completely confused for a while, I finally asked what on earth they were talking about. It turns out that "Desummoned" is the fancy word for "Rejected". They were talking about undergraduate admissions.
The admissions situation is apparently quite a topic of conversation around here (for good reason). The system is pretty complicated, and I'm sure I will know much more about it once I go through the process in detail in the fall. But here is the rough story.
First thing to realize is that students are admitted to "read" a single subject. So you are admitted as a physicist, a chemist, or whatever. There is no concept of liberal arts. Because of this the physicists all get together and discuss the physics applicants. On the other hand, you are also admitted to a single college. So you also apply to the specific college. So in essence, next year, I will be choosing from the applicant pool some 6 or 7 students a year who will come to somerville college, and I will be their tutor. As people like to say around here, "you get to choose your own mistakes."
One issue is that students get to decide which college to apply to, but in some cases they end up at other colleges because there just isn't enough room at the really popular places. One of the things Somerville worries about is that we have a lot of "hand-me-down" students.
Within the physics community, the big issue du-jour is how much we should pay attention to the entrance exam in admissions. Just in the last few years they have started keeping track of how students have been rated in the interviews versus how they have performed once they get here and several years later. What was found is that there is essentially no correlation with the interview -- but there is very high correlation with the entrance exam. So does this mean we should only pay attention to the entrance exam? That doesn't sound like such a good idea either, since the entrance exam is likely to test more how well you are prepared (i.e., how good a school you went to) rather than how smart you are. Nonetheless (given various caveats about the quality of our data) our current belief is that the entrance exam is probably the best indicator of success in physics at Oxford. The main reason people want to keep the interview right now is that a few candidates (typically overseas) take the entrance exam in "uncontrolled" conditions, and then when they get to the interview it is quite clear that they were not the ones who actually took the exam since they know none of the material. So the interview does function to weed out cheaters, but this appears to be its main purpose. These people are "desummoned" rather quickly.
It would be a gross misrepresentation to say that anyone at Oxford is “poor”. Nonetheless, there is clearly a gap between those who are fairly well-off and those who are filthy rich. Looking down the list of colleges of Oxford, one notices that the endowment of the different colleges differ by an order of magnitude. Do the colleges with huge endowments provide higher quality education? This is a good question that many people here keep asking.
One datum that is easy to point to is the famous Norrington table which basically ranks how well each college does on the final exams. My college, Somerville, was down near the bottom last year, although in previous years we have been more or less in the middle. There are plenty of reasons to distrust this table – there are all sorts of systematic biases that make this particular data in some sense unfair. But ignoring these problems for a moment, one notes immediately a high correlation between endowment and scoring well on the Norrington table.
(Disclaimer: I’m not saying that any oxford college is providing a bad education. If you look into the details of the Norrington table you realize that the differences in actual performance between the colleges is pretty small. Nonetheless, each college wants to be able to claim it is better than the others).
Here is an article (a few years old) studying the discrepancy in how the varying level of resources effect the college experience. Yes, it is true. The rich colleges have more resources, and can buy more personal attention for their students, can buy better libraries, more computers, and so forth. It is even plausible that the rich colleges are able to do more to keep their best faculty (although looking around the university it seems that at least to some extent the superstars are well distributed). But around here people think that these things are not the major factor on the Norrington table. The major factor (most people seem to think) is that the rich colleges simply are able to attract the best students – and these best students naturally score higher four years later.
Why would the best students choose to go to the rich colleges? There are a few obvious reasons: better resources, better academic reputation on that Norrington table, better food at High table, nicer rooms, manicured lawns, and so forth. But no one really seems to think that these things are too important. The one thing that people do think is important is simply the pocketbook. The rich colleges can cost less.
Apparently, a few years ago, St. John’s college thought it might be a good idea to start spending some of its money instead of swimming around in it like Scrooge McDuck (no offense intended). So they announced that they intended to stop charging tuition for a while. Now THAT is a really good reason to try to get into St. John’s. As it turned out, this announcement caused an uproar across the university and people screamed that the university could not have a two-tiered system where the elite go for free. In the end St John’s tabled this plan – but they do have some really hefty scholarships available to their students, and they guarantee housing for all of their students – which many colleges cannot.
One datum that is easy to point to is the famous Norrington table which basically ranks how well each college does on the final exams. My college, Somerville, was down near the bottom last year, although in previous years we have been more or less in the middle. There are plenty of reasons to distrust this table – there are all sorts of systematic biases that make this particular data in some sense unfair. But ignoring these problems for a moment, one notes immediately a high correlation between endowment and scoring well on the Norrington table.
(Disclaimer: I’m not saying that any oxford college is providing a bad education. If you look into the details of the Norrington table you realize that the differences in actual performance between the colleges is pretty small. Nonetheless, each college wants to be able to claim it is better than the others).
Here is an article (a few years old) studying the discrepancy in how the varying level of resources effect the college experience. Yes, it is true. The rich colleges have more resources, and can buy more personal attention for their students, can buy better libraries, more computers, and so forth. It is even plausible that the rich colleges are able to do more to keep their best faculty (although looking around the university it seems that at least to some extent the superstars are well distributed). But around here people think that these things are not the major factor on the Norrington table. The major factor (most people seem to think) is that the rich colleges simply are able to attract the best students – and these best students naturally score higher four years later.
Why would the best students choose to go to the rich colleges? There are a few obvious reasons: better resources, better academic reputation on that Norrington table, better food at High table, nicer rooms, manicured lawns, and so forth. But no one really seems to think that these things are too important. The one thing that people do think is important is simply the pocketbook. The rich colleges can cost less.
Apparently, a few years ago, St. John’s college thought it might be a good idea to start spending some of its money instead of swimming around in it like Scrooge McDuck (no offense intended). So they announced that they intended to stop charging tuition for a while. Now THAT is a really good reason to try to get into St. John’s. As it turned out, this announcement caused an uproar across the university and people screamed that the university could not have a two-tiered system where the elite go for free. In the end St John’s tabled this plan – but they do have some really hefty scholarships available to their students, and they guarantee housing for all of their students – which many colleges cannot.
Saturday, February 14, 2009
Britney Spears, Christina Aguilera, Semiconductors, and Magnesium Boride.
Labels:
General Nonsense,
Physics,
Physics for Poets
My students often ask me for good books, or web sites, to read on this or that topic. In my solid state physics course, they wanted a reference on semiconductor physics. Rather sheepishly I told them to google “Britney Spears”. That’s right, Britney Spears – teen idol turned train wreck. It turns out that the best reference on semiconductor physics on the web is called the Britney Spears’ Guide to Semiconductor Physics, and it mixes lessons in hard core physics with comments about Britney’s lip gloss. Some very bored students (yes they are in the UK) realized there was a need for a semiconductor guide and thought it would be entertaining to mix in some pop culture. To be honest, they really did a nice job with the science. And back when they made this site, Britney was just a cute young thing, rather than the celebrity Icarus that she is now. (I really like the picture of her next to Einstein here)
Well, it didn’t stop there. The Princeton chemist, Bob Cava, liked Christina Aguilera better (with good reason, she’s got an awesome voice). Anyway, Bob was apparently just itching for a chance to make a similar homage to her.
Along comes Magnesium Boride – a chemical compound made of only two elements, Magnesium and Boron. There are only so many elements on the periodic table (about one hundred of them), and so the number of compounds you can make with only two elements is rather limited. With hundreds of thousands of chemists in the world mixing things up constantly, you would think that something as simple as Magnesium Boride would have been studied to death by this time. Well, by some fluke of history, it had not been. It turns out that MgB2 (as it is now known) has a really stunning property – it superconducts at a temperature much higher than anything except a very very few extremely complex compounds. No one had noticed this until 2001 when a Japanese group announced their discovery in perhaps the shortest paper ever written in one of the premier scientific journals, Nature.
Cava, as a prominent chemist in the field, was asked to write a blurb (News and Views) in Nature to accompany the announcement. Somehow or other, he managed to get Nature to title his article “Genie in a Bottle”. Apparently none of the editors at the journal Nature listen to pop music.
Us nerds is easily amused.
Well, it didn’t stop there. The Princeton chemist, Bob Cava, liked Christina Aguilera better (with good reason, she’s got an awesome voice). Anyway, Bob was apparently just itching for a chance to make a similar homage to her.
Along comes Magnesium Boride – a chemical compound made of only two elements, Magnesium and Boron. There are only so many elements on the periodic table (about one hundred of them), and so the number of compounds you can make with only two elements is rather limited. With hundreds of thousands of chemists in the world mixing things up constantly, you would think that something as simple as Magnesium Boride would have been studied to death by this time. Well, by some fluke of history, it had not been. It turns out that MgB2 (as it is now known) has a really stunning property – it superconducts at a temperature much higher than anything except a very very few extremely complex compounds. No one had noticed this until 2001 when a Japanese group announced their discovery in perhaps the shortest paper ever written in one of the premier scientific journals, Nature.
Cava, as a prominent chemist in the field, was asked to write a blurb (News and Views) in Nature to accompany the announcement. Somehow or other, he managed to get Nature to title his article “Genie in a Bottle”. Apparently none of the editors at the journal Nature listen to pop music.
Us nerds is easily amused.
No this is not a medical procedure.
This week, postdoctoral candidate Fiona Burnell came to Oxford to interview for the prestigious All-Souls fellowship. (The last physicist to win this fellowship was Austen Lamacraft, who apparently reads this blog, at least once in a while). I’ve been working with Fiona on and off for much of the last year and I always learn something new from talking to her. While she was here this week, I finally grokked the mathematical idea of Dehn surgery – and actually it is very simple, I had just never seen it explained clearly anywhere before (although in retrospect, the Wikipedia entry on Dehn Surgery is actually not too bad).
First, let us think about a two dimensional surface, like the surface of a sphere. Cut two holes (disks) out of the sphere and throw them away. The boundary of the cutting region is two circles. Now, if I want to patch up these holes to get a smooth surface again, I need to find something that also has a boundary with two circles – and there are now two options. (1) The set of two disks has a boundary which is two circles (and if I sew them back in, I just get the original sphere). OR, (2) a hollow tube (circle cross interval, for those keeping track) also has a boundary which is two circles. If I instead sew on the hollow tube, connecting the two holes in the sphere, I end up getting a sphere with a “handle” attached, which is topologically a torus. This is a simple example of what mathematicians call surgery (for obvious reasons).
OK, now it gets a bit harder. Consider a smooth three-dimensional manifold, like the space around us (mathematicians like to add a “point at infinity” to change R3 into S3 but this is just to assure that we have a closed topology rather than an open topology). Draw some closed circle (usually called an S1) in this space. Then take a tubular neighborhood of this circle, so you have a solid torus (S1 cross disk. Disk is usually called D2 so this is S1 cross D2). Now remove this solid torus from the manifold. The boundary of what was removed is the torus surface (S1 cross S1) so if we want to sew something back in here, we need to find something whose boundary is S1 cross S1. There are two options (1) S1 cross D2. In this case we are sewing back in exactly the solid torus that we removed and we get back the original manifold. OR (2) D2 cross S1 also has the same boundary, and we can sew this back in instead along the same surface and get a new manifold! The key here is to realize that for a torus surface, the two S1’s (longitude and meridian) are on equal footing, but when we think about a solid torus, one S1 has been filled in and the other has not. Choosing a torus in a three manifold and switching which S1 is filled in is a surgery on the 3-manifold, known as Dehn surgery. Don’t try too hard to imagine it in detail, because you can’t put the result easily into our three dimensional space, and that tends to make your head explode if you think too hard about it.
Now to make life more interesting still, the torus we do surgery on may not be trivially embedded into our three manifold. In other words, when we started by drawing a closed circle in the manifold, it need not be a simple open circle, but could be knotted circle, like a trefoil. Further, we can give the original circle a “framing” meaning that the torus is embedded with a twist around its meridian before we do the surgery.
A theorem that strikes me as rather remarkable is that any closed three manifold can be obtained, starting from S3 (or any other simple three manifold) and doing successive Dehn surgeries of this type. This is known as the Lickorish-Wallace theorem and dates from the early 1960s. A relatively simple proof is provided by Rourke
J. London Math. Soc. (2) 31 (1985), no. 2, 373–376. (Sadly this probably requires a library subscription to have access – Project Euclid, has not yet put this on its list of freely available math journals)
“relatively simple” means that it is simple enough that more or less I can follow it and it doesn’t make my head explode. I found it rather entertaining that Witten, in his famous Field's medal winning paper on the Jones polynomial, refers to this theorem as “a not too deep result”. I suppose if you are Ed Witten, or a topologist, maybe that is true.
So you can describe any three manifold as successive Dehn surgeries starting with any other three manifold. However, it is possible to have more than one Dehn surgery give you the same result. Nonetheless, it is known exactly which combination of Dehn surgeries are equivalent to which other combination. The identification is given by some very very simple rules known as Kirby Calculus.
Added: Throughout, I'm assuming an orientable manifold.
This week, postdoctoral candidate Fiona Burnell came to Oxford to interview for the prestigious All-Souls fellowship. (The last physicist to win this fellowship was Austen Lamacraft, who apparently reads this blog, at least once in a while). I’ve been working with Fiona on and off for much of the last year and I always learn something new from talking to her. While she was here this week, I finally grokked the mathematical idea of Dehn surgery – and actually it is very simple, I had just never seen it explained clearly anywhere before (although in retrospect, the Wikipedia entry on Dehn Surgery is actually not too bad).
First, let us think about a two dimensional surface, like the surface of a sphere. Cut two holes (disks) out of the sphere and throw them away. The boundary of the cutting region is two circles. Now, if I want to patch up these holes to get a smooth surface again, I need to find something that also has a boundary with two circles – and there are now two options. (1) The set of two disks has a boundary which is two circles (and if I sew them back in, I just get the original sphere). OR, (2) a hollow tube (circle cross interval, for those keeping track) also has a boundary which is two circles. If I instead sew on the hollow tube, connecting the two holes in the sphere, I end up getting a sphere with a “handle” attached, which is topologically a torus. This is a simple example of what mathematicians call surgery (for obvious reasons).
OK, now it gets a bit harder. Consider a smooth three-dimensional manifold, like the space around us (mathematicians like to add a “point at infinity” to change R3 into S3 but this is just to assure that we have a closed topology rather than an open topology). Draw some closed circle (usually called an S1) in this space. Then take a tubular neighborhood of this circle, so you have a solid torus (S1 cross disk. Disk is usually called D2 so this is S1 cross D2). Now remove this solid torus from the manifold. The boundary of what was removed is the torus surface (S1 cross S1) so if we want to sew something back in here, we need to find something whose boundary is S1 cross S1. There are two options (1) S1 cross D2. In this case we are sewing back in exactly the solid torus that we removed and we get back the original manifold. OR (2) D2 cross S1 also has the same boundary, and we can sew this back in instead along the same surface and get a new manifold! The key here is to realize that for a torus surface, the two S1’s (longitude and meridian) are on equal footing, but when we think about a solid torus, one S1 has been filled in and the other has not. Choosing a torus in a three manifold and switching which S1 is filled in is a surgery on the 3-manifold, known as Dehn surgery. Don’t try too hard to imagine it in detail, because you can’t put the result easily into our three dimensional space, and that tends to make your head explode if you think too hard about it.
Now to make life more interesting still, the torus we do surgery on may not be trivially embedded into our three manifold. In other words, when we started by drawing a closed circle in the manifold, it need not be a simple open circle, but could be knotted circle, like a trefoil. Further, we can give the original circle a “framing” meaning that the torus is embedded with a twist around its meridian before we do the surgery.
A theorem that strikes me as rather remarkable is that any closed three manifold can be obtained, starting from S3 (or any other simple three manifold) and doing successive Dehn surgeries of this type. This is known as the Lickorish-Wallace theorem and dates from the early 1960s. A relatively simple proof is provided by Rourke
J. London Math. Soc. (2) 31 (1985), no. 2, 373–376. (Sadly this probably requires a library subscription to have access – Project Euclid, has not yet put this on its list of freely available math journals)
“relatively simple” means that it is simple enough that more or less I can follow it and it doesn’t make my head explode. I found it rather entertaining that Witten, in his famous Field's medal winning paper on the Jones polynomial, refers to this theorem as “a not too deep result”. I suppose if you are Ed Witten, or a topologist, maybe that is true.
So you can describe any three manifold as successive Dehn surgeries starting with any other three manifold. However, it is possible to have more than one Dehn surgery give you the same result. Nonetheless, it is known exactly which combination of Dehn surgeries are equivalent to which other combination. The identification is given by some very very simple rules known as Kirby Calculus.
Added: Throughout, I'm assuming an orientable manifold.
On of the funniest cartoons ever made is a Far-Side cartoon by Gary Larson where the sign outside the building says “Midvale school for the gifted” and the sign on the door says pull, but the kid in the cartoon is pushing on the door. (You can see the cartoon here at this time, but I’m pretty sure this picture won’t stay up long. Larson has been pretty strict about going around the web and making sure that his cartoons are not illegally posted like this one).
In the United States, in any public building, the doors open outwards. I think this is a law – the idea being that in the case of an emergency where everyone runs for the door at the same time, the first person won’t get smashed into the door and be unable to open an inwards-opening door. Without even realizing it though, one gets very used to pushing on doors when you are leaving a building and pulling on doors when you are going into buildings.
In the UK, there is no such law dictating which way doors should open. (Why?, I don't know, it seems like it would be a good idea). Doors open in or out seemingly randomly. I find myself constantly pushing on pull doors and pulling on push doors. It is so strongly ingrained that you should pull on a door going into a building, that I will still sit there yanking and yanking on the door when it obviously is not going to budge in that direction. Last week I even buzzed the receptionist in one building and she yelled back “PUSH”. Oops. Every time this happens I think “Midvale School for the Gifted”.
A similar gut reaction is which way to look when crossing a street. Fortunately, I don't have to cross many streets on my way to work.
In the United States, in any public building, the doors open outwards. I think this is a law – the idea being that in the case of an emergency where everyone runs for the door at the same time, the first person won’t get smashed into the door and be unable to open an inwards-opening door. Without even realizing it though, one gets very used to pushing on doors when you are leaving a building and pulling on doors when you are going into buildings.
In the UK, there is no such law dictating which way doors should open. (Why?, I don't know, it seems like it would be a good idea). Doors open in or out seemingly randomly. I find myself constantly pushing on pull doors and pulling on push doors. It is so strongly ingrained that you should pull on a door going into a building, that I will still sit there yanking and yanking on the door when it obviously is not going to budge in that direction. Last week I even buzzed the receptionist in one building and she yelled back “PUSH”. Oops. Every time this happens I think “Midvale School for the Gifted”.
A similar gut reaction is which way to look when crossing a street. Fortunately, I don't have to cross many streets on my way to work.
Today is VG day: Victory over garbage. Since moving in, I’ve had this problem that every time I leave trash outside for the trash collectors, they somehow ignore it. I asked around and people told me that I have to be careful what kind of trash I leave out on what days. Recycling is big here, so there is the blue bin, the green bin, the big green bin, and the large dark green trash can. “So how do I know which day to leave which trash?” The response was “oh, just google it”. Well, this is not as easy as it sounds. It took me several days to figure out that I had to google “Waste” not “Trash” or “Garbage”. Finally, I got the list of what goes in which bin, and which days they collect which type of “waste”. Unfortunately, the schedule I looked at was apparently outdated, so my attempts to get rid of my waste continued to fail. Finally, I just started peeking in my neighbor’s trash – and today, with great fanfare and angels blowing trumpets, they took some of it away. So I think I now know the scheme. About time – it was really starting to pile up in here.
The Bed: One of the first things I did when moving to the UK was to go and buy a decent bed. Even though I had scarlet fever at the time, the first weekend I was here, I still schlepped out to a local bed store (called “Dreams”) and bought one. Much to my dismay, it took three weeks to have the thing delivered. In the meantime I’ve been sleeping on little more than an army cot. Finally today the bed was delivered – in a bunch of pieces. I admit that I was a bit out of it when I bought the thing (my excuse also for buying a truly ugly bed) but I’m pretty sure no one ever told me that it was an assemble yourself kind of thing. Nonetheless, I’m usually pretty brave with this self-assembly stuff, so I started putting it together. After about three hours, I finally called their customer service line and yelled at them. They concluded that this particular bed is defective (there is no slot B to screw into tab A) and they will have to replace it. I’ll keep you updated. Fortunately, the mattress appears to work. I’ll report back after sleeping on it for a night – I can’t imagine it will be worse than the army cot.
Added: After one night sleep on the mattress, I'm debating whether it is too soft. (Although I actually tried to buy the firmest mattress available).
The Bed: One of the first things I did when moving to the UK was to go and buy a decent bed. Even though I had scarlet fever at the time, the first weekend I was here, I still schlepped out to a local bed store (called “Dreams”) and bought one. Much to my dismay, it took three weeks to have the thing delivered. In the meantime I’ve been sleeping on little more than an army cot. Finally today the bed was delivered – in a bunch of pieces. I admit that I was a bit out of it when I bought the thing (my excuse also for buying a truly ugly bed) but I’m pretty sure no one ever told me that it was an assemble yourself kind of thing. Nonetheless, I’m usually pretty brave with this self-assembly stuff, so I started putting it together. After about three hours, I finally called their customer service line and yelled at them. They concluded that this particular bed is defective (there is no slot B to screw into tab A) and they will have to replace it. I’ll keep you updated. Fortunately, the mattress appears to work. I’ll report back after sleeping on it for a night – I can’t imagine it will be worse than the army cot.
Added: After one night sleep on the mattress, I'm debating whether it is too soft. (Although I actually tried to buy the firmest mattress available).
Today it snowed a bit. And everyone had a complete nervous breakdown. I guess they don't get a whole lot of snow that sticks around here. It was huge news in London where they basically shut down the city. But to be fair to the Brits, this was apparently the heaviest snow in 18 years. In Oxford the snow was somewhat lighter -- but enough to be pretty. You can see Somerville College in the snow here. Later in the day, there were snowball fights and snowmen. Am I an old curmudgeon for not participating in the snowball fights?
Update: Two days later we actually had about four inches -- and the city came to a halt. People recalled back to "that great snow of 1947" and "that time it snowed a foot in 1962". I guess it really is pretty rare around here.
Update: Two days later we actually had about four inches -- and the city came to a halt. People recalled back to "that great snow of 1947" and "that time it snowed a foot in 1962". I guess it really is pretty rare around here.
Since I am somewhat allergic to formal events I had been avoiding the high table dinners at Somerville College. However, a few people recommended that I might want to go to this week because it was something a bit out of the ordinary.
This week was a celebration of Burns Night – the birthday of the Scottish poet Robert Burns (he wrote Auld Lang Syne among other things). In fact, this year would be his 250th birthday. Although the actual holiday is January 25th, our college celebrated it on Tuesday the 27th , as Tuesday is the day we usually have high table dinners.
As is typical for high table dinners, there are drinks before dinner in the senior common room. I went with the sherry, which was decent, although not exceptional (Note to self: get invited to the filthy rich colleges for dinner more often so I can get some of that 80 year old wine).
The fellows walk into the great hall led by a bagpiper and everyone stands until the latin grace is said by the Principal of the College. The undergrads were dressed very well, perhaps better than most the faculty. A few were even in black tie. As usual, the dopey American physicist (that would be me) was underdressed. I was wearing a tweed jacket a white shirt and to quote my ex-girlfriend “those pants that you think are nice, but they aren’t”. I had asked whether I needed a tie, and the response was “Well, you can get away without”, so I went without – then realized this was a mistake. The phrase “you can get away without” might have meant, “well, you might get away without, but I would never dream of going without a tie”. There was only one other tieless guy in the room of over a hundred – a mathematician.
As I have mentioned in previous posts, Somerville is considered “modern” because we do not eat in academic robes. But this has the disadvantage, that people actually see what you are wearing. All told, I think I am happy we do not eat in robes, as I cannot imagine how I could possibly not get the sleeves in my soup.
Many of the people who showed up for this dinner were Scottish. By the grace of the seating chart (not sure who makes it up) I was placed next to a Scottish woman (who was actually a guest of said tieless mathematician who sat across from me). She explained to me that the Scotts Scots around would probably go to five or six different Burns Night celebrations each year. She had two to go to just that evening.
This web site has a pretty good description of the traditional Burns Night supper and all the traditions. The highlight, without doubt, is the Addressing of the Haggis. An enormous Haggis is brought into the great hall with much fanfare (led by the bagpiper again), and placed on the table. The Burns poem “Address to a Haggis” is read as if speaking to the Haggis, a knife is plunged into the object, and a toast is made with Scottish whiskey (the Scotts Scots woman next to me was mortified that it was a blend rather than a single malt Scotch).
The addressing of the Haggis was done by one of the college fellows who is extremely Scottish and has a very hard Glaswegian accent. I then realized that in normal conversation she works very hard to speak in an understandable way, but her natural Glaswegian is almost incomprehensible. Of course, Burns’ poem itself is not so easy to understand to begin with. In fact, one really needs a translation from Scottish to English (one is given here). Even though many in the room (including me) had no idea what she was saying, the address was given with great fanfare and great Scottish gusto.
Dinner itself was, of course, Haggis, along with the traditional neeps and tatties. Tatties, of course are just mashed potatoes. Neeps are mashed swede (rutabaga or yellow turnip) which tastes half way in between a potato and a squash.
I admit that I feared that Haggis. I’d only eaten Haggis once, years ago when I was up in Scotland – and it was pretty awful – tasted too much like liver. But this Haggis was actually pretty good (and served without the sheep's stomach) – pretty much like a decent meatloaf– which I guess is more or less what it is (although the “loaf” is traditionally oats, as compared to usual loaf). They also had vegetarian Haggis (soy loaf, I guess) for those who preferred. I didn’t try that, but I’m told it wasn’t half bad. Dessert was oatmeal and honey ice cream. Very tasty, but by this time in the meal, something as heavy as oatmeal didn’t sound like a very good idea.
Of course after dinner the “adults” return to the senior common room for more wine, fruit, chocolate, coffee, tea and socializing. I stuck around for a bit, but couldn’t stay too late as I had homeworks to grade for my students by the next day.
This week was a celebration of Burns Night – the birthday of the Scottish poet Robert Burns (he wrote Auld Lang Syne among other things). In fact, this year would be his 250th birthday. Although the actual holiday is January 25th, our college celebrated it on Tuesday the 27th , as Tuesday is the day we usually have high table dinners.
As is typical for high table dinners, there are drinks before dinner in the senior common room. I went with the sherry, which was decent, although not exceptional (Note to self: get invited to the filthy rich colleges for dinner more often so I can get some of that 80 year old wine).
The fellows walk into the great hall led by a bagpiper and everyone stands until the latin grace is said by the Principal of the College. The undergrads were dressed very well, perhaps better than most the faculty. A few were even in black tie. As usual, the dopey American physicist (that would be me) was underdressed. I was wearing a tweed jacket a white shirt and to quote my ex-girlfriend “those pants that you think are nice, but they aren’t”. I had asked whether I needed a tie, and the response was “Well, you can get away without”, so I went without – then realized this was a mistake. The phrase “you can get away without” might have meant, “well, you might get away without, but I would never dream of going without a tie”. There was only one other tieless guy in the room of over a hundred – a mathematician.
As I have mentioned in previous posts, Somerville is considered “modern” because we do not eat in academic robes. But this has the disadvantage, that people actually see what you are wearing. All told, I think I am happy we do not eat in robes, as I cannot imagine how I could possibly not get the sleeves in my soup.
Many of the people who showed up for this dinner were Scottish. By the grace of the seating chart (not sure who makes it up) I was placed next to a Scottish woman (who was actually a guest of said tieless mathematician who sat across from me). She explained to me that the
This web site has a pretty good description of the traditional Burns Night supper and all the traditions. The highlight, without doubt, is the Addressing of the Haggis. An enormous Haggis is brought into the great hall with much fanfare (led by the bagpiper again), and placed on the table. The Burns poem “Address to a Haggis” is read as if speaking to the Haggis, a knife is plunged into the object, and a toast is made with Scottish whiskey (the
The addressing of the Haggis was done by one of the college fellows who is extremely Scottish and has a very hard Glaswegian accent. I then realized that in normal conversation she works very hard to speak in an understandable way, but her natural Glaswegian is almost incomprehensible. Of course, Burns’ poem itself is not so easy to understand to begin with. In fact, one really needs a translation from Scottish to English (one is given here). Even though many in the room (including me) had no idea what she was saying, the address was given with great fanfare and great Scottish gusto.
Dinner itself was, of course, Haggis, along with the traditional neeps and tatties. Tatties, of course are just mashed potatoes. Neeps are mashed swede (rutabaga or yellow turnip) which tastes half way in between a potato and a squash.
I admit that I feared that Haggis. I’d only eaten Haggis once, years ago when I was up in Scotland – and it was pretty awful – tasted too much like liver. But this Haggis was actually pretty good (and served without the sheep's stomach) – pretty much like a decent meatloaf– which I guess is more or less what it is (although the “loaf” is traditionally oats, as compared to usual loaf). They also had vegetarian Haggis (soy loaf, I guess) for those who preferred. I didn’t try that, but I’m told it wasn’t half bad. Dessert was oatmeal and honey ice cream. Very tasty, but by this time in the meal, something as heavy as oatmeal didn’t sound like a very good idea.
Of course after dinner the “adults” return to the senior common room for more wine, fruit, chocolate, coffee, tea and socializing. I stuck around for a bit, but couldn’t stay too late as I had homeworks to grade for my students by the next day.
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