While it stands on its own, this discussion is a continuation of this post on an essay by Errol Morris.
At the end of his essay Morris contemplates whether or not there is a limit to human knowledge. He basically frames it as considering whether or not we will ever be able to understand the structure of the universe. His own opinion seems to be that we will not, but his only justification is that he would be disappointed in the architect of creation if creatures as simple as we were able to understand it all.
I think he gets the answer right, but his rational is frankly juvenile. By way of giving a better rational, I've long been fascinated by a very simple question. Is it possible to create a mind, an organism, that can understand itself? To focus on a concrete example, let's look at man. Neglecting temporarily our ability to make sense of the universe, will we ever be able to fully understand how our own minds work? To me, the answer is clearly that we will not, at least not without genetic manipulation which renders us a new species entirely, unrecognizable as homo sapien. Hopefully I at least began to spell out why in this post.
In essence, I think that no single person will ever be able to simultaneously understand all the biochemical interactions in our brain, the way all the different centers of the brain are specialized and interact with each other, and how the physical features and processes of the brain give rise to consciousness, to the fact that there is a way that our experiences feel that seems irreducible to materialistic terms. I think it's quite possible that at some point it may be possible to assemble a thousand biochemists who between therm understand the biochemical pathways of the mind, and similarly for its physiological structure and its philosophic ramifications, but I do not believe that any single individual will ever understand the whole.
But this leads to several other layers to the question. Can mankind as a whole understand how a human's brain works? If we take those three thousand specialists, might their collective knowledge give us an understanding of how the brain works? I think the answer there again is no. If those three thousand specialists got together to try to design a genetic manipulation or a drug to affect the brain in a certain way, my experience in the pharmaceutical industry tells me that to a large degree they would still be shooting in the dark at a series of moving targets, though perhaps in a room in which they had a flashlight or two. Human beings just don't interface as smoothly as collectives like ants or bees, and of course ant collectives aren't nearly sophisticated enough to understand the human brain, or their own collective lives.
But of course, there is another avenue of thought to pursue. These specialists could catalog their knowledge on a computer. If it were a sentient computer, it may even be capable of understanding the whole of the human brain. Of course, to go back to the original question, if we were to build such a sentient computer, this wouldn't mean it understood its own mind, simply our minds. Still, would such a sentient computer be able to understand its own mind? Unfortunately, this is a question that I can't even begin to answer. I'm inclined to think it more likely simply because computer CPU's can be understood by people, whereas brains cannot be understood. But no one yet knows what a sentient computer would require, whether or not its circuits would be of a type we could even build, or perhaps might require a team of thousands each working on a small part of the whole that only they understand. Perhaps the circuits required for true learning or creativity would grow more difficult to comprehend exponentially, so that every improvement that might lead to an understanding the previous iteration couldn't understand itself.
Either way, I think it would be an incredibly bad idea to build such a computer. It could only take two views of its human creators. It could think us irrelevant, or it could think us a waste of energy and space. Best case scenario, it tolerates our existence, worst case it tries to extinguish it. No upside. At all.
So, to go back to Morris's question, while I think a single homo sapien will never understand everything in the universe, I do think we have a chance to understand the general structure of existence. Looking at something like the periodic table, for instance, there is a stunningly beautiful simplicity to its arrangement. The consequences of its structure, most relevant to us in that a molecule like water is so abundant, stable, and conducive to life, are sublime and quickly give rise to a complexity and subtlety that likewise is stunning in both its beauty and rationality. My own opinion is that current efforts in subatomic particles and quantum mechanics have gone off the track somehow. I think that whatever force created the universe created a system, like the periodic table, that is stunningly simply fundamentally, but which quickly gives rise to complexities and consequences (like evolution, consciousness, and creativity) which blossom explosively.
Tuesday, August 24, 2010
Wednesday, August 11, 2010
Knowing and Not Knowing
I want to spend some time taking about the concept of anosognosia--not knowing something you should know--developed most fully in part 4 of Morris's essay. I think this is the first place that Morris really falls down and fails to give us any kind of answer to the question of how anosognosia works in what I'd guess is an effort to make his topic seem more interesting. But I think as you actually approach an answer, the topic only gets more interesting.
To start, if we're going to talk about not knowing something we should know, we need first to think about what it means to know something. The average person knows at a minimum tens of thousands of things. Most illustrative, to me, is proper names, perhaps because I am so bad with them. Names of friends, names of relatives, names of actors, names of movies, names of books. In my experience, not infrequently in the course of conversations people want to refer to someone or something but can't remember what that thing is called. Surely this, too, is a case of anosognosia. All the more because often the name that we are searching for comes to us at some later indeterminate time, when we have no use for the name at all.
This raises the question, how do we know things at all? What is going on with these simple memory omissions? Is our brain like a computer, with each fact stored in a discrete location? If so, then when we fail to remember something, have we either forgotten where to find that location or has that location been corrupted? Both of these errors, after all, happen in computers. But neither of those seems an adequate explanation. If the location of the fact is corrupted, then how could we remember that fact later? If we've simply forgotten where that information is stored, then how do we find that location later? The latest research suggests that memories are connections between neurons and that the connections grow stronger with repetition. But to me that doesn't really address the issue. First, it is obvious. Our brain is nothing more than a bunch of connections of neurons, so of course memories have to be connections too. But further, how does the fact that a memory is a connection of neurons really explain how we know facts? What kind of connections of neurons are necessary to remember the name of my Aunt Bea? What kinds are necessary for me to remember that I like the actress Renee Zellweger and the fact that along with remembering her name a mental image of her face comes to mind. And don't even get me started on what connections are necessary to remember how to spell her name. For me, who can't spell, the answer is no connections would ever be sufficient. For me, this is the first interesting aspect of anosognosia: for all our science, picturing how memory works is still a very hazy endeavor.
So anosognosia, actually, is nothing special at all. Almost every fact in our brain is dormant for the majority of our waking moments. And it quickly gets more complicated when you start to add in all the psychological biases we display. We tend not to remember things which we don't want to remember. As much as I might rack my brain to give you some personal examples, I'm a bit too busy not remembering them now. I will assure you, though, that there are many things I've done which I'd rather not remember doing, and there are many things I'm not good at that I've long forgotten the myriad cues and signals that might indicate to me, if I chose to pay attention to them in the first place, that I wasn't good at those tasks. There are positive aspects of people I hate which I will never recall. And there's absolutely no way you could prove whether or not I know these things. In many cases if I've done a good job at repressing a memory so that there are neural connections for that memory but the memory could never ever get into my consciousness, we would really need to define a bit more clearly what we mean by "know".
But where it again starts to get really interesting is when you start to look into areas where the beliefs one holds are complicated. I believe I am a trifle on the lazy side (just a trifle), yet I've always gotten good reviews at every job I've ever worked. Somehow I have to reconcile those two contrary pieces of information. I believe that people ought to earn the lifestyle they want to lead, but I believe that we ought to make some basic provisions for those people who are not equipped by either genetics or society to earn their way, and I'm also aware that many people who do have money have done very little to earn it whether because they obtained the money illicitly, inherited it, or, perhaps, won the lottery. These competing ideas and hundreds if not thousands more are all in my head, in essence vying for dominance.
Is it really any surprise, given all this, that there are people who display varying levels of awareness, indifference, and denial regarding the fact that they've lost the use of their left arm? I don't think so, and I think in trying to persuade us that this is where the big mystery is, Morris does us a disservice.
To me, the big mystery is tied up in these complex net of beliefs. And reading, conversation and writing really bring out how tenuous our knowledge and beliefs are, really illustrate their fluidity. In the course of verbal debates, in the course of trying to present my thoughts in writing, I've often discovered that I don't believe the things I thought I believed. Sometimes I find that I don't believe something which I was going to write a passionate essay in support of, sometimes I find in writing that two ideas I thought were compatible are not, sometimes I find that I actually end up disproving the thesis of my paper. Sometimes in a debate I say something and realize how silly it sounds. Sometimes I read something that just completely and irrefutably contradicts something I had believed.
It's hard for me to describe, especially to someone who might not have occasion to write or debate a lot. Writing and debating have always seemed to me like trials. You have an idea, you need to play with it some, give it a spin, explore it. You believe an author of a book was trying to say one thing, but on talking to others who read the book, on looking more closely at the text, you see you were entirely wrong. There seems something permanently makeshift about my ideas, my beliefs, my mind. And I think that is the way it has to be. We are creatures of the moment. Our mental capacities are extremely limited. We can really only hold one thing in our mind at any time to look at it and think about it. If this is the kind of creature we are and the limitations our mind works under, then how could our beliefs and our knowledge behave any differently?
To start, if we're going to talk about not knowing something we should know, we need first to think about what it means to know something. The average person knows at a minimum tens of thousands of things. Most illustrative, to me, is proper names, perhaps because I am so bad with them. Names of friends, names of relatives, names of actors, names of movies, names of books. In my experience, not infrequently in the course of conversations people want to refer to someone or something but can't remember what that thing is called. Surely this, too, is a case of anosognosia. All the more because often the name that we are searching for comes to us at some later indeterminate time, when we have no use for the name at all.
This raises the question, how do we know things at all? What is going on with these simple memory omissions? Is our brain like a computer, with each fact stored in a discrete location? If so, then when we fail to remember something, have we either forgotten where to find that location or has that location been corrupted? Both of these errors, after all, happen in computers. But neither of those seems an adequate explanation. If the location of the fact is corrupted, then how could we remember that fact later? If we've simply forgotten where that information is stored, then how do we find that location later? The latest research suggests that memories are connections between neurons and that the connections grow stronger with repetition. But to me that doesn't really address the issue. First, it is obvious. Our brain is nothing more than a bunch of connections of neurons, so of course memories have to be connections too. But further, how does the fact that a memory is a connection of neurons really explain how we know facts? What kind of connections of neurons are necessary to remember the name of my Aunt Bea? What kinds are necessary for me to remember that I like the actress Renee Zellweger and the fact that along with remembering her name a mental image of her face comes to mind. And don't even get me started on what connections are necessary to remember how to spell her name. For me, who can't spell, the answer is no connections would ever be sufficient. For me, this is the first interesting aspect of anosognosia: for all our science, picturing how memory works is still a very hazy endeavor.
So anosognosia, actually, is nothing special at all. Almost every fact in our brain is dormant for the majority of our waking moments. And it quickly gets more complicated when you start to add in all the psychological biases we display. We tend not to remember things which we don't want to remember. As much as I might rack my brain to give you some personal examples, I'm a bit too busy not remembering them now. I will assure you, though, that there are many things I've done which I'd rather not remember doing, and there are many things I'm not good at that I've long forgotten the myriad cues and signals that might indicate to me, if I chose to pay attention to them in the first place, that I wasn't good at those tasks. There are positive aspects of people I hate which I will never recall. And there's absolutely no way you could prove whether or not I know these things. In many cases if I've done a good job at repressing a memory so that there are neural connections for that memory but the memory could never ever get into my consciousness, we would really need to define a bit more clearly what we mean by "know".
But where it again starts to get really interesting is when you start to look into areas where the beliefs one holds are complicated. I believe I am a trifle on the lazy side (just a trifle), yet I've always gotten good reviews at every job I've ever worked. Somehow I have to reconcile those two contrary pieces of information. I believe that people ought to earn the lifestyle they want to lead, but I believe that we ought to make some basic provisions for those people who are not equipped by either genetics or society to earn their way, and I'm also aware that many people who do have money have done very little to earn it whether because they obtained the money illicitly, inherited it, or, perhaps, won the lottery. These competing ideas and hundreds if not thousands more are all in my head, in essence vying for dominance.
Is it really any surprise, given all this, that there are people who display varying levels of awareness, indifference, and denial regarding the fact that they've lost the use of their left arm? I don't think so, and I think in trying to persuade us that this is where the big mystery is, Morris does us a disservice.
To me, the big mystery is tied up in these complex net of beliefs. And reading, conversation and writing really bring out how tenuous our knowledge and beliefs are, really illustrate their fluidity. In the course of verbal debates, in the course of trying to present my thoughts in writing, I've often discovered that I don't believe the things I thought I believed. Sometimes I find that I don't believe something which I was going to write a passionate essay in support of, sometimes I find in writing that two ideas I thought were compatible are not, sometimes I find that I actually end up disproving the thesis of my paper. Sometimes in a debate I say something and realize how silly it sounds. Sometimes I read something that just completely and irrefutably contradicts something I had believed.
It's hard for me to describe, especially to someone who might not have occasion to write or debate a lot. Writing and debating have always seemed to me like trials. You have an idea, you need to play with it some, give it a spin, explore it. You believe an author of a book was trying to say one thing, but on talking to others who read the book, on looking more closely at the text, you see you were entirely wrong. There seems something permanently makeshift about my ideas, my beliefs, my mind. And I think that is the way it has to be. We are creatures of the moment. Our mental capacities are extremely limited. We can really only hold one thing in our mind at any time to look at it and think about it. If this is the kind of creature we are and the limitations our mind works under, then how could our beliefs and our knowledge behave any differently?
Thursday, August 5, 2010
Dunning-Kruger: Teachers of Pre-Med Students
Continuation of this discussion on teaching pre-med students.
So I find myself in something of a conundrum. I recognize the reasons that my students are unable to obtain the scores they want on the MCAT. Broadly, they either have poor study skills or they have poor problem solving skills. But I'm left banging my head against the Dunning-Kruger effect:
Basically, in this situation what it means is that those students who are capable of realizing they are doing things poorly and improving have already realized their flaws and tried to fix them. That is the difference between the 30-to-36 student and the 24-to-28 student.
As I've come to understand these things, I've come to understand that I too am flawed. I stand at the front of the classroom and lecture on things (the facts of chemistry and biology important to know for the MCAT) that ultimately don't address the fundamental needs of these students. While it might be flattering to think that because I understand what the true needs of my students are, I'm better than the other teachers, despite my understanding I'm not really sure how to help them. I, too, am a victim of Dunning-Kruger. As a teacher, I have an obligation to help these students learn, but I am unable to figure out what to do. There are teaching techniques, ways of reaching and influencing students that I should know but which I don't know.
So I come back to these different types of questions Morris proposes in his article on anosognosia. I've asked a question that I don't know how to answer, a question I believe no one actually knows how to answer: How do you help students become better test-takers? Take problem solving skills as an example, I've done some research on the issue. It turns out that problems are solved in two steps. Before a test, one must internalize the steps necessary to solve a large number of types of problems. Then, when taking a test, one must properly categorize each particular problem as one of those types and then execute the steps we carry in our minds. But knowing that this is how we solve problems only raises other issues. Without accounting for time constraints and class sizes, how does one teach an abstract skill such as categorizing a problem as one of the hundreds of types a student ought to know, and then successfully following through on each of the steps? How, for that matter, do I teach students whose problem might be poor reading comprehension how to read better?
I'm not going to pretend I have the answers to these questions. This is kind of where I am right now, trying to figure out if anyone else has the answers or if there even are answers. I'm trying a few techniques out to see how they work. For a while I have been telling students that when they get a problem wrong, they need to understand why they got it wrong. That, in other words, practice without improvement is useless, that it doesn't matter how many questions you do if you don't learn to do any of them better. But as Dunning has suggested, I'm always frightened to find out, in one-on-one discussions, that students haven't listened to my advice and continue to plow through practice problems unreflectively, valuing quantity over quality. Of the students who do listen, many don't really understand the advice. They look for the reason they got the problem wrong, but they don't actually try to go through the right method to solve the problem step by step to get that routine in their mind. It's a subtle, but extremely important difference, knowing what you did wrong versus knowing how to do it right the next time.
I've also taken to more explicitly telling students the steps I'm taking as I solve a problem. For all MCAT questions the first step is determining if the answer was in the test passage, if it draws on things the student is expected to know, or if it is a fusion of the two. But there are more steps past that. What concept is being tested? What are the relevant equations, facts and rationalizations surrounding that concept? This technique has helped a little in that while most often a student who can't get started just can't figure out what the question is asking (a reading comprehension issue), a significant portion of the time I'll uncover that the student simply doesn't know something he ought to know. But this leads back to another thing I've had difficulty understanding. If I tell students that they ought to memorize things, why do they not memorize them? When I took a science test, I always made a list of things I ought to know (and memorized them) and things I ought to understand (and made sure I could explain them). Many students seem to lack this skill. More, as Dunning-Kruger teaches, they seem to be unaware that they ought to know this skill. Basically, every time I find a trick that seems to help, I'm brought back to the fact that these students need to learn to help themselves, my ability to help them is limited.
This need to learn to help themselves, and the centrality of reading comprehension issues in the difficulties these students face, brings me to the post I made a few days ago. Good teachers, especially early in education, are immeasurably important. While I would love to be able to address these issues, I simply can't given the format of my interaction with these students and the amount of time we have together. Typically I have students either in a one-on-one setting for eight hours or in groups of ten for twenty hours. In that time, I have to teach them material which it takes college professors 45 hours to cover, while also doing a fair number of sample problems together, discussing time management and other test strategies, and covering other logistical issues of the class and of the MCAT. Given these restrictions, how much can I really expect to do in terms of re-teaching these students how to approach a test? More broadly, if we have no restrictions, how do we teach young students or re-teach older students how to solve problems and how to read effectively?
I think the answer is we simply don't know. Good elementary school teachers and good parents teach these things, but we don't know how they do it. More, I've over-generalized in my description of students. I've seen students who come in with an initial 24 and leave scoring in the mid 30's by, among other things, re-teaching themselves how to pay more attention to the wording of questions and re-teaching themselves using the problem-solving techniques I preach that don't reach the other students. I've seen students who come in scoring a 24 and don't improve through the length of the course. I refuse to believe that the 24-to-28 students, who are literally as close as they can be to going to a quality medical school, are beyond hope. If we want to do something that will improve our society more than any scientific advance in the history of the world, all we have to do is answer one simple question: How do we raise children, how do we re-teach older students, so that they are not subject to the Dunning-Kruger effect?
So I find myself in something of a conundrum. I recognize the reasons that my students are unable to obtain the scores they want on the MCAT. Broadly, they either have poor study skills or they have poor problem solving skills. But I'm left banging my head against the Dunning-Kruger effect:
"When people are incompetent in the strategies they adopt to achieve success and satisfaction, they suffer a dual burden: Not only do they reach erroneous conclusions and make unfortunate choices, but their incompetence robs them of the ability to realize it."
Basically, in this situation what it means is that those students who are capable of realizing they are doing things poorly and improving have already realized their flaws and tried to fix them. That is the difference between the 30-to-36 student and the 24-to-28 student.
As I've come to understand these things, I've come to understand that I too am flawed. I stand at the front of the classroom and lecture on things (the facts of chemistry and biology important to know for the MCAT) that ultimately don't address the fundamental needs of these students. While it might be flattering to think that because I understand what the true needs of my students are, I'm better than the other teachers, despite my understanding I'm not really sure how to help them. I, too, am a victim of Dunning-Kruger. As a teacher, I have an obligation to help these students learn, but I am unable to figure out what to do. There are teaching techniques, ways of reaching and influencing students that I should know but which I don't know.
So I come back to these different types of questions Morris proposes in his article on anosognosia. I've asked a question that I don't know how to answer, a question I believe no one actually knows how to answer: How do you help students become better test-takers? Take problem solving skills as an example, I've done some research on the issue. It turns out that problems are solved in two steps. Before a test, one must internalize the steps necessary to solve a large number of types of problems. Then, when taking a test, one must properly categorize each particular problem as one of those types and then execute the steps we carry in our minds. But knowing that this is how we solve problems only raises other issues. Without accounting for time constraints and class sizes, how does one teach an abstract skill such as categorizing a problem as one of the hundreds of types a student ought to know, and then successfully following through on each of the steps? How, for that matter, do I teach students whose problem might be poor reading comprehension how to read better?
I'm not going to pretend I have the answers to these questions. This is kind of where I am right now, trying to figure out if anyone else has the answers or if there even are answers. I'm trying a few techniques out to see how they work. For a while I have been telling students that when they get a problem wrong, they need to understand why they got it wrong. That, in other words, practice without improvement is useless, that it doesn't matter how many questions you do if you don't learn to do any of them better. But as Dunning has suggested, I'm always frightened to find out, in one-on-one discussions, that students haven't listened to my advice and continue to plow through practice problems unreflectively, valuing quantity over quality. Of the students who do listen, many don't really understand the advice. They look for the reason they got the problem wrong, but they don't actually try to go through the right method to solve the problem step by step to get that routine in their mind. It's a subtle, but extremely important difference, knowing what you did wrong versus knowing how to do it right the next time.
I've also taken to more explicitly telling students the steps I'm taking as I solve a problem. For all MCAT questions the first step is determining if the answer was in the test passage, if it draws on things the student is expected to know, or if it is a fusion of the two. But there are more steps past that. What concept is being tested? What are the relevant equations, facts and rationalizations surrounding that concept? This technique has helped a little in that while most often a student who can't get started just can't figure out what the question is asking (a reading comprehension issue), a significant portion of the time I'll uncover that the student simply doesn't know something he ought to know. But this leads back to another thing I've had difficulty understanding. If I tell students that they ought to memorize things, why do they not memorize them? When I took a science test, I always made a list of things I ought to know (and memorized them) and things I ought to understand (and made sure I could explain them). Many students seem to lack this skill. More, as Dunning-Kruger teaches, they seem to be unaware that they ought to know this skill. Basically, every time I find a trick that seems to help, I'm brought back to the fact that these students need to learn to help themselves, my ability to help them is limited.
This need to learn to help themselves, and the centrality of reading comprehension issues in the difficulties these students face, brings me to the post I made a few days ago. Good teachers, especially early in education, are immeasurably important. While I would love to be able to address these issues, I simply can't given the format of my interaction with these students and the amount of time we have together. Typically I have students either in a one-on-one setting for eight hours or in groups of ten for twenty hours. In that time, I have to teach them material which it takes college professors 45 hours to cover, while also doing a fair number of sample problems together, discussing time management and other test strategies, and covering other logistical issues of the class and of the MCAT. Given these restrictions, how much can I really expect to do in terms of re-teaching these students how to approach a test? More broadly, if we have no restrictions, how do we teach young students or re-teach older students how to solve problems and how to read effectively?
I think the answer is we simply don't know. Good elementary school teachers and good parents teach these things, but we don't know how they do it. More, I've over-generalized in my description of students. I've seen students who come in with an initial 24 and leave scoring in the mid 30's by, among other things, re-teaching themselves how to pay more attention to the wording of questions and re-teaching themselves using the problem-solving techniques I preach that don't reach the other students. I've seen students who come in scoring a 24 and don't improve through the length of the course. I refuse to believe that the 24-to-28 students, who are literally as close as they can be to going to a quality medical school, are beyond hope. If we want to do something that will improve our society more than any scientific advance in the history of the world, all we have to do is answer one simple question: How do we raise children, how do we re-teach older students, so that they are not subject to the Dunning-Kruger effect?
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