Rob just told me--
There's something about going through the math classes that gives you a sense of when there are holes in someone's argument. You may not know exactly where the holes are, but you know that you're not totally convinced.
The classes themselves may not give me the most pertinent knowledge-- some of the math I'm doing right now, I will never use. But he's right-- I am learning when to say "Wait a minute, something's fishy." And that's what's fundamental to scientific reasoning and discussion.
It's somewhat astonishing how my ability to find these holes has improved over the past few years. Just ask my study buddies-- I have a bad reputation for destroying their ideas that they were done with the homework...
20 February 2009
04 September 2008
innumeracy
Yesterday I saw Janet Hyde speak about her article in science magazine about gender similarities in math performance. Her meta-analyses of other people's studies on gender and math performance show that performance is about the same except in advanced problem solving skills for advanced students, where men have performed better.
The most interesting discussion of performance, though, was that if white men are better than white women by a couple of points, Asian men and women wallop whites by tens of points. When an audience member asked Professor Hyde to comment on this, she gave her opinion that we have a dangerous cultural problem with mathematics: Firstly, she suggested that with the advent of IQ scores and the like, white cultures tended to give accolades for ability more than for hard work. This is not true in other cultures, and a subject like mathematics does require perseverance in order to develop a good intuition and understanding. Secondly, she made a very good point that it is somehow acceptable for even very educated adults to say something like "Oh I am SO bad at math!" She asked what would you think if a medical professional said "Oh I just cannot read!" And what's the difference? I heard the same thing mentioned in an introduction for a Mathematics and Biology symposium that I attended yesterday as well. This speaker recommended the book Innumeracy: Mathematical Illiteracy and its Consequences. It's now on my to-read list.
The most interesting discussion of performance, though, was that if white men are better than white women by a couple of points, Asian men and women wallop whites by tens of points. When an audience member asked Professor Hyde to comment on this, she gave her opinion that we have a dangerous cultural problem with mathematics: Firstly, she suggested that with the advent of IQ scores and the like, white cultures tended to give accolades for ability more than for hard work. This is not true in other cultures, and a subject like mathematics does require perseverance in order to develop a good intuition and understanding. Secondly, she made a very good point that it is somehow acceptable for even very educated adults to say something like "Oh I am SO bad at math!" She asked what would you think if a medical professional said "Oh I just cannot read!" And what's the difference? I heard the same thing mentioned in an introduction for a Mathematics and Biology symposium that I attended yesterday as well. This speaker recommended the book Innumeracy: Mathematical Illiteracy and its Consequences. It's now on my to-read list.
20 August 2008
Chicago Guide to your Academic Career
I've started reading this book which discusses the choice of getting a PhD and going into an academic career. So far it's reasonably interesting, though I am wary that it may not be applicable for the engineering career because the authors are all in social sciences and humanities. Still, they have some interesting ideas about the required personality traits of an academic.
One of the authors suggests some things to think about and questions to ask yourself before and throughout your graduate career:
"Original research requires much self-reliance, perseverance, and intelligence as well as creativity. You also need self-discipline to complete the monotonous tasks that inevitably accompany even the most exciting research project. Do you have enough of these qualities to succeed?
"Self-questioning is, of course, an important quality to nurture in yourself, but it certainly requires practice to be effective. One cannot develop such critical skills overnight. Do you know yourself well enough? ... Are you able to judge yourself without making excuses? Do you rationalize your mistakes, so you cannot learn from them? You can improve your forecasts about yourself by consciously updating your information... How have you erred in the past, and what can you learn from these errors about your true abilities and about your expectations? Are the goals you are about to set for yourself reasonable in light of your past performance? Are you getting closer to formulating a reasonable strategy for solving problems?"
Here is a quote from the female professor about the particular issues she faces with family care:
"A generation ago, ...some relief on at least the domestic side was possible-- if you were male. Most professors were male (if female, they were generally single and/or childless), and they were mostly married, with wives who did not work outside the home when the children were young. These wives made possible the devotion of their husbands to their work, as they handled all the shopping, cooking, child care, doctor's appointments, and entertainment of colleagues and students. I know there must be a few cases out there today where the roles are flipped and the husband is 'Mr. Mom,' but they are few and far between. Even in the households where tasks are divided up 50-50 (as they have been in mine and in some others I know), there is an extra layer of responsibility that somehow gravitates to the female in the household. She's the one who seems to be responsible for keeping the system running, for knowing what nonroutine things have to be done when, for initiating the conversation about dividing up tasks, for anticipating when the schedule will need to change, and for locating the backup help when the system flounders ... From time to time it surfaces that underneath it all, my husband still fantasizes occasionally about a life where I would do all this stuff, just as his upbringing prepared him for. Good thing we can laugh about it."
A quote on the mentor relationship:
"The best students coming into graduate school are not only intelligent-- they are also independent-minded, and that independence has been encouraged for years, inside school and out. Of these, the very best will very likely think that they know what they want out of school. Many of them may think (often rightly) that they are smarter, or at least quicker, than any of their teachers in college.
"When they come to the point of having to submit themselves... to both a specific discipline and a particular mentor, many students find themselves unable to do so. ... It may come out as a dissatisfaction on the student's part or an inability to work comfortably with any of the faculty members in the department. But graduate education requires... a submission of the ego to that of the mentor... This student-mentor relationship is fundamental to becoming a successful researcher.
"Central to the relationship is your common and joint research. In general, what is shared is the research interests of the professor; in a more unusual circumstance, the student may bring a special research interest and involve the professor in it... The student gets to see, for the first time, what it means for knowledge to arise out of confusion and ignorance. That, after all, is the meaning of research; it is the patient struggle to achieve comprehension where there was none before."
An interesting point about your faculty recommendation writers:
"[The] mentor's responsibilities are, to some extent, split, involving responsibility to the student who may be looking for a first job and responsibility to the field (that is, to colleagues at another university who need hoenst and frank letters of appraisal). To balance these commitments is not always an easy task."
On choosing a dissertation topic:
"Some professors are reluctant to suggest thesis topics, either out of a philosophical conviction that that is the student's job or out of a concern about the commitment and responsibility that go with such advice... There are those who argue for a sink-or-swim approach on the assumption that the student will learn these skills by being forced to choose a dissertation topic. This point of view is surely reasonable, but my own experience leads me to urge you to err on the side of caution if you have the opportunity unless you have reason to think that you have already mastered such skills: the risk of sinking is too great at this stage."
On working through peripheral issues:
"One of the most difficult challenges you will face is the temptation to work on ancillary issues during the course of your research. ... Any original research will bring to the surface dozens of peripheral issues that have not been explored in the past. You will have to consciously avoid being attracted by them. Just tell yourself that you will come back to those questions later, and, of course, these are potential dissertation topics that you can suggest to your future students. Avoid at any cost falling into the trap of thinking that answering these questions is a precondition to completing the dissertation. ...you need to develop skills that will enable you to avoid boxing yourself in on particular issues. Argue by analogy, argue by order of magnitude, or suggest that your conclusions are tentative and are subject to revision with further research. There is nothing to be ashamed of in admitting the limitations of your work. On the contrary, it is wise to do so, since it is hardly your fault that insufficient research has been done in your field."
One of the authors suggests some things to think about and questions to ask yourself before and throughout your graduate career:
"Original research requires much self-reliance, perseverance, and intelligence as well as creativity. You also need self-discipline to complete the monotonous tasks that inevitably accompany even the most exciting research project. Do you have enough of these qualities to succeed?
"Self-questioning is, of course, an important quality to nurture in yourself, but it certainly requires practice to be effective. One cannot develop such critical skills overnight. Do you know yourself well enough? ... Are you able to judge yourself without making excuses? Do you rationalize your mistakes, so you cannot learn from them? You can improve your forecasts about yourself by consciously updating your information... How have you erred in the past, and what can you learn from these errors about your true abilities and about your expectations? Are the goals you are about to set for yourself reasonable in light of your past performance? Are you getting closer to formulating a reasonable strategy for solving problems?"
Here is a quote from the female professor about the particular issues she faces with family care:
"A generation ago, ...some relief on at least the domestic side was possible-- if you were male. Most professors were male (if female, they were generally single and/or childless), and they were mostly married, with wives who did not work outside the home when the children were young. These wives made possible the devotion of their husbands to their work, as they handled all the shopping, cooking, child care, doctor's appointments, and entertainment of colleagues and students. I know there must be a few cases out there today where the roles are flipped and the husband is 'Mr. Mom,' but they are few and far between. Even in the households where tasks are divided up 50-50 (as they have been in mine and in some others I know), there is an extra layer of responsibility that somehow gravitates to the female in the household. She's the one who seems to be responsible for keeping the system running, for knowing what nonroutine things have to be done when, for initiating the conversation about dividing up tasks, for anticipating when the schedule will need to change, and for locating the backup help when the system flounders ... From time to time it surfaces that underneath it all, my husband still fantasizes occasionally about a life where I would do all this stuff, just as his upbringing prepared him for. Good thing we can laugh about it."
A quote on the mentor relationship:
"The best students coming into graduate school are not only intelligent-- they are also independent-minded, and that independence has been encouraged for years, inside school and out. Of these, the very best will very likely think that they know what they want out of school. Many of them may think (often rightly) that they are smarter, or at least quicker, than any of their teachers in college.
"When they come to the point of having to submit themselves... to both a specific discipline and a particular mentor, many students find themselves unable to do so. ... It may come out as a dissatisfaction on the student's part or an inability to work comfortably with any of the faculty members in the department. But graduate education requires... a submission of the ego to that of the mentor... This student-mentor relationship is fundamental to becoming a successful researcher.
"Central to the relationship is your common and joint research. In general, what is shared is the research interests of the professor; in a more unusual circumstance, the student may bring a special research interest and involve the professor in it... The student gets to see, for the first time, what it means for knowledge to arise out of confusion and ignorance. That, after all, is the meaning of research; it is the patient struggle to achieve comprehension where there was none before."
An interesting point about your faculty recommendation writers:
"[The] mentor's responsibilities are, to some extent, split, involving responsibility to the student who may be looking for a first job and responsibility to the field (that is, to colleagues at another university who need hoenst and frank letters of appraisal). To balance these commitments is not always an easy task."
On choosing a dissertation topic:
"Some professors are reluctant to suggest thesis topics, either out of a philosophical conviction that that is the student's job or out of a concern about the commitment and responsibility that go with such advice... There are those who argue for a sink-or-swim approach on the assumption that the student will learn these skills by being forced to choose a dissertation topic. This point of view is surely reasonable, but my own experience leads me to urge you to err on the side of caution if you have the opportunity unless you have reason to think that you have already mastered such skills: the risk of sinking is too great at this stage."
On working through peripheral issues:
"One of the most difficult challenges you will face is the temptation to work on ancillary issues during the course of your research. ... Any original research will bring to the surface dozens of peripheral issues that have not been explored in the past. You will have to consciously avoid being attracted by them. Just tell yourself that you will come back to those questions later, and, of course, these are potential dissertation topics that you can suggest to your future students. Avoid at any cost falling into the trap of thinking that answering these questions is a precondition to completing the dissertation. ...you need to develop skills that will enable you to avoid boxing yourself in on particular issues. Argue by analogy, argue by order of magnitude, or suggest that your conclusions are tentative and are subject to revision with further research. There is nothing to be ashamed of in admitting the limitations of your work. On the contrary, it is wise to do so, since it is hardly your fault that insufficient research has been done in your field."
14 August 2008
From Krulwich's Caltech Commencement address
Robert Krulwich, correspondent for NPR science desk, was invited to Caltech to give the commencement address this year. The speech was put on the Radiolab podcast a few weeks ago and I finally got a chance to listen.
The topic he discussed was the duty of scientists to explain their work and tell their stories in a way that a non-scientists will understand. The speech was outstanding. Here are some of my favorite quotes.
4:05
So here's my question, when you are asked "What are you working on?" should you think: There's no way I can talk about my science with this guy, because I don't have the talent, I don't have the words, I don't have the patience to do it. It's too hard. And anyway what's the point?
Which is, by the way, not an unusual position. No less than Isaac Newton, I mean Sir Isaac Newton, when asked, Why did you make the Principia Mathematica, your earthshaking book about gravity and laws of motion, so impossibly hard to read, he said well I considered writing a popular version that people might understand, but, and I am quoting Newton here, "to avoid being baited by little smatterers in mathematics" he intentionally wrote a book in dense scholarly latin with lots of math so that only scholars could follow. In other words, Isaac Newton didn't care to be understood by average folks.
But here's the argument I want to make to you guys this morning. You aren't going to hear this advice often; I suggest you may never hear it again.
When asked about your work, do not do what Isaac Newton did. When a cousin, or an uncle, or a buddy comes up and asks, "So what are you working on?" even if it's hard to explain, even if you know they don't really want to hear it, not really, I urge you to give it a try; Because, talking about science, telling stories to regular folks is not a trivial thing. Scientists need to tell stories to non-scientists, because science stories-- and you know this-- have to compete with other stories about how the universe works and how the universe came to be.
8:47
Your teachers [at Caltech] ... were giving you values. A deep respect for curiosity, for doubt, for open-mindedness. For going wherever the data lead no matter how uncomfortable. For honesty, for discipline. And most of all, the belief that anybody no matter where they're from, no matter what their language, no matter what their religion, no matter what their politics, no matter what their age or their temperament -- I mean this place has seen monstrous egos, and bongo players, and people who dress in viking hats-- but if you can learn how to sit down in a laboratory and think in an orderly way, and if you have the patience to stare and stare and stare, looking for a pattern in nature, you are welcome here. It may be boring, it may be sometimes very exhausting, but there's a freedom, there's a freedom in this way of looking that is precious in the world, and that freedom can be attacked or defended with stories.
11:00
Unlike Newton, Galileo wanted to tell people what was on his mind. Unlike Newton, he thought that people could understand him-- that's why he got in so much trouble. ... He wrote [The Dialogues] in Italian for a mass audience. ... So, because Galileo's book was so easy to read, and such a page turner, it so threatened the established order that Galileo, as you know, was put under house arrest. And it wasn't just the science that was alarming, I think it was the power of his storytelling.
17:55
But the job that we face is to put more stories out there about nature that are true and complex-- not dumbed down-- but still have the power to enthrall, to excite, to remind people that there's a deep beauty, a many-leveled beauty in the world. And what scientists say is not their offhand opinion, it's hard-won information, it's carefully hewn from the world. It's not a bunch of ideas from a tribe of privileged intellectuals who look down on everybody. It's my sense that if more scientists wanted to, they could learn how to tell their stories with words and pictures and metaphor, and people will hear and remember those stories, and not be as willing to accept the other folks stories-- or at least there will be a tug of war.
24:46
You are part of and you are celebrating something very rare and very precious and very fragile in our world. This place celebrates freedom. And because you are now free men and women, you have to protect what you've been given, by helping others who haven't been here, who are never coming here to understand the value of what you do, and what your teachers do, and what their predecessors have done.
The topic he discussed was the duty of scientists to explain their work and tell their stories in a way that a non-scientists will understand. The speech was outstanding. Here are some of my favorite quotes.
4:05
So here's my question, when you are asked "What are you working on?" should you think: There's no way I can talk about my science with this guy, because I don't have the talent, I don't have the words, I don't have the patience to do it. It's too hard. And anyway what's the point?
Which is, by the way, not an unusual position. No less than Isaac Newton, I mean Sir Isaac Newton, when asked, Why did you make the Principia Mathematica, your earthshaking book about gravity and laws of motion, so impossibly hard to read, he said well I considered writing a popular version that people might understand, but, and I am quoting Newton here, "to avoid being baited by little smatterers in mathematics" he intentionally wrote a book in dense scholarly latin with lots of math so that only scholars could follow. In other words, Isaac Newton didn't care to be understood by average folks.
But here's the argument I want to make to you guys this morning. You aren't going to hear this advice often; I suggest you may never hear it again.
When asked about your work, do not do what Isaac Newton did. When a cousin, or an uncle, or a buddy comes up and asks, "So what are you working on?" even if it's hard to explain, even if you know they don't really want to hear it, not really, I urge you to give it a try; Because, talking about science, telling stories to regular folks is not a trivial thing. Scientists need to tell stories to non-scientists, because science stories-- and you know this-- have to compete with other stories about how the universe works and how the universe came to be.
8:47
Your teachers [at Caltech] ... were giving you values. A deep respect for curiosity, for doubt, for open-mindedness. For going wherever the data lead no matter how uncomfortable. For honesty, for discipline. And most of all, the belief that anybody no matter where they're from, no matter what their language, no matter what their religion, no matter what their politics, no matter what their age or their temperament -- I mean this place has seen monstrous egos, and bongo players, and people who dress in viking hats-- but if you can learn how to sit down in a laboratory and think in an orderly way, and if you have the patience to stare and stare and stare, looking for a pattern in nature, you are welcome here. It may be boring, it may be sometimes very exhausting, but there's a freedom, there's a freedom in this way of looking that is precious in the world, and that freedom can be attacked or defended with stories.
11:00
Unlike Newton, Galileo wanted to tell people what was on his mind. Unlike Newton, he thought that people could understand him-- that's why he got in so much trouble. ... He wrote [The Dialogues] in Italian for a mass audience. ... So, because Galileo's book was so easy to read, and such a page turner, it so threatened the established order that Galileo, as you know, was put under house arrest. And it wasn't just the science that was alarming, I think it was the power of his storytelling.
17:55
But the job that we face is to put more stories out there about nature that are true and complex-- not dumbed down-- but still have the power to enthrall, to excite, to remind people that there's a deep beauty, a many-leveled beauty in the world. And what scientists say is not their offhand opinion, it's hard-won information, it's carefully hewn from the world. It's not a bunch of ideas from a tribe of privileged intellectuals who look down on everybody. It's my sense that if more scientists wanted to, they could learn how to tell their stories with words and pictures and metaphor, and people will hear and remember those stories, and not be as willing to accept the other folks stories-- or at least there will be a tug of war.
24:46
You are part of and you are celebrating something very rare and very precious and very fragile in our world. This place celebrates freedom. And because you are now free men and women, you have to protect what you've been given, by helping others who haven't been here, who are never coming here to understand the value of what you do, and what your teachers do, and what their predecessors have done.
causality
"Causal inference is one of the most important, most subtle, and most neglected of all the problems of Statistics." -- Philip Dawid, 1979
24 July 2008
Mirrors
Here is an interesting science article from the New York Times. I've been reading a lot lately about how mirrors can help psychological disorders that no medications can help-- like getting rid of phantom limbs or phantom pains in amputees.
The main point of the article is to explain the fact that, when you look in a mirror, no matter how far you are from the mirror, your image on the mirror's surface will remain the same size. This is due to the fact that the mirror is always half-way between you and your reflected image.
There are other interesting things in the article: there is research that people are more self-aware when mirrors are around. If you are in a room with a mirror, you are less likely to cheat or judge people and more likely to help others.
On a separate note, the article says that when people are presented with photos of themselves which are airbrushed to look better, worse, or left the same, people identify the best photograph as the one untouched. But they only did that with their own photos-- for other people's photos they could identify the unairbrushed image.
The main point of the article is to explain the fact that, when you look in a mirror, no matter how far you are from the mirror, your image on the mirror's surface will remain the same size. This is due to the fact that the mirror is always half-way between you and your reflected image.
There are other interesting things in the article: there is research that people are more self-aware when mirrors are around. If you are in a room with a mirror, you are less likely to cheat or judge people and more likely to help others.
On a separate note, the article says that when people are presented with photos of themselves which are airbrushed to look better, worse, or left the same, people identify the best photograph as the one untouched. But they only did that with their own photos-- for other people's photos they could identify the unairbrushed image.
08 July 2008
a science journalist answers some questions
From Dennis Overbye of the NY times:
There really isn't any such thing as a silly question in science, where the best people often are those who are free enough to think up a really outlandish question. Einstein said his success was due to the fact that he kept asking a child's questions when he was an adult. I am reminded of what Niels Bohr once said, "We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct."
There really isn't any such thing as a silly question in science, where the best people often are those who are free enough to think up a really outlandish question. Einstein said his success was due to the fact that he kept asking a child's questions when he was an adult. I am reminded of what Niels Bohr once said, "We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct."
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