6 ms·

Guessing the Teacher's Password

54 points by t0pj 18y ago

aneesh 18y ago
This sadly is how the world works. In school, even in high school and college, the students who guess the teacher's password are rewarded. The (few) students who make an effort to discover and think through something on their own are criticized for wandering from the beaten path, even on the occasions when they're actually right. High school science competitions (school science fairs, all the way upto Siemens-Westinghouse and Intel STS) particularly guilty of this.
- boredguy8 18y ago
  "The (few) students who make an effort to discover and think through something on their own are criticized for wandering from the beaten path, even on the occasions when they're actually right." I remember I just -couldn't- accept that we can't take square roots of negative numbers. I mean, sure, two negatives multiplied together is a positive, but...there HAS to be a way! Numbers, to my 6th grade mind, weren't arbitrarily going to deny your ability to manipulate them. Fortunately for me, I happened to be reading a book on Mandlebrot and in the course of discussing his work the author introduces the concept of imaginary numbers. So the next day in class I asked: "Are you suuuure?" "Yes, I'm sure." "Well, I was reading in this book and so-and-so says you can take the square root of negative numbers, you get 'i' for the root of -1 and..." "Why don't you go wait outside." Where I got told that although I move to the beat of a different drummer, when I'm in her class, I really just need to be quiet. That's when public education and I had a falling out from which our relationship has never recovered. All of that to say: I think part of the 'problem' is that kids who do try to think on their own are often in a situation where they're challenging accepted rules without the social grace to do so constructively. But rather than being taught the social skills, they're just shut down. Very sad, actually. They could be taught how to 'wander well'.
  - Prrometheus 18y ago
    Isn't sqrt(-1) = i an axiom though, and not a theorem? In other words, if you just started with the integers and the basic rules of arithmetic, you will never run into the need for imaginary numbers. It's only after you posit their existence that a lot of cool results flow from it. Am I wrong there?
    - boredguy8 18y ago
      I don't really know how to interpret your sentence. Complex numbers are a field in which you do 'basic rules of arithmetic'. You can't do the 'basic rules of arithmetic' on integers. i is defined as sqrt(-1), if that answers your question.
      - Prrometheus 18y ago
        I should have said "Real Numbers" instead of "Integers", sorry. My point is that sqrt(-1) = i is an extra assumption that you don't need to make in order to derive the math you do in school. If you don't make that assumption, you can still derive a lot of math. If you do make that assumption, then you can also derive the theorems of complex analysis. I think that's true, anyway. I could be wrong. It just seems strange to me that someone would be bothered by the lack of negative square roots, since their existence is never derived, only assumed. But then again, people's minds work very differently, especially in Mathematics. I was the opposite in Math class. I fought accepting "i" when they tried to teach it to us since it seemed so arbitrary and contrived to me. This was before I discovered that all Math is arbitrary and that there is no "real math", anyway.
        ashu 18y ago
        As the "Road to Reality" explains, if you study Quantum mechanics, complex numbers become every bit as "real" as the integers or real numbers. You just can't explain some of the quantum mechanical phenomena or concepts without using complex numbers at all.
        tokipin 18y ago
        it's as you say. it is contrived. but no more contrived than the basic integers. these are abstract systems that we have contrived in ways that are most useful to us. the natural numbers just seem more "real" because everyone in most cultures deals with "quantity" and "magnitude"
Alex3917 18y ago
Someone should write a book like the little schemer but for physics. One of the best classes I took in college was somewhat like this. We measured the period of the pendulum using our heartbeats, and we also measured how long it took things to roll down differently sloped ramps. From this we derived the period of the pendulum and the relationship between slope and speed. Eventually we used this to derive the universal law of gravitation using the period of the moon's orbit as the only given. It was pretty cool because there was no math involved. Instead of using calculus to derive the equations, we instead found them inductively by iterating over a couple thousand lines in excel and then looking for the pattern. The idea of the class was to understand physics by deriving all the equations the same way the people who discovered them did. It was pretty cool.
- deleted 18y ago
  [deleted]
  - jfoutz 18y ago
    If you look here http://en.wikipedia.org/wiki/Inductive_reasoning http://en.wikipedia.org/wiki/Inductive_reasoning you will see inductive reasoning is all about drawing broad conclusions from limited evidence. In this context, the tens or thousands of experiments are generalized to support some "theory" Every time i touch ice it is cold. By induction, all ice is cold. that's not "proof" but it's a great theory of ice.
    - xlnt 18y ago
      If you read Hume or Popper you will see that inductive reasoning is logically impossible, and therefore can't actually be what people do.
      - deleted 18y ago
        [deleted]
      - jfoutz 18y ago
        I think we do this, or something very much like it: http://en.wikipedia.org/wiki/Bayesian_inference http://en.wikipedia.org/wiki/Bayesian_inference I'll agree that we can set up a game we play with symbols and rules that doesn't permit inductive reasoning as valid. I can't agree that "what people do" has anything to do with logic.
DaniFong 18y ago
Only tangentially related, but years ago, in elementary school, I decided to guess the password after the school restricted access to SimCity. I got it right on the first try, it was just the school name, but I told everyone 'I hacked it', for major props.
boredguy8 18y ago
I spend some of my time teaching at a private university. During a discussion with one student he said, "All I really know about Plato is that he thought the forms were transcendent whereas Aristotle thought the forms were immanent." "Oh," said I, "that's interesting. What does it mean for a form to be transcendent or immanent?" "I don't know, I just know that's what they thought." We then had a discussion about whether or not he really knew that, and whether or not he was OK with paying over $25k a year to learn how to be a parrot. The sad thing: he was OK with it, and probably rightly so. He realized that mostly what people want are parrots and you can get paid quite a decent amount of money for being a good parrot. Not a bad gig if you're fine being a cog. There are certain comforts it provides.
noonespecial 18y ago
I remember the first time I got an F on an assignment even though I'd gotten the correct answer to every problem. I hadn't reached my correct answers the "right" way.
- boredguy8 18y ago
  I loved calculus because about 4 weeks of teaching provided the foundation for everything else. My tests usually involved me having to derive something that was apparently derived in the book and then 'applied' on practice questions that got the 'right' way of doing things in by rote. I lost points for that. I would also lose points for "not showing my work", but if you can't factor, say, x^2-9 in your head, maybe you have deeper issues.
- xlnt 18y ago
  Ugh I hate that. I got marked down a letter grade on a math test once for not showing enough intermediate steps even though my answers were correct. I also once got an answer marked wrong because the teacher couldn't understand my intermediate steps, even though the answer (and steps) were actually correct. When I showed him, he refused to change my grade. That was at University.
- cdr 18y ago
  If the teacher was teaching a process, and looking for evidence that you understood that process, it seems entirely reasonable to not count your work.
  - noonespecial 18y ago
    I had simply taken shortcuts I'd seen later in the book for factoring quadratics. They wanted to see it written exactly as it appeared in the current examples. I realized that math in school was more like one of those simon games where you just mindlessly press the arbitrary sequence of lights you just saw, than actual mathematics. This analogy helped me suffer through "school math" while I perused real math on my own.
cdr 18y ago
I've been thinking along similar lines since I've been interviewing; far too many interviewers are only looking for the password.
nsrivast 18y ago
overcomingbias is one of those websites you should read every article in, like paul graham's essays
- jsomers 18y ago
  yeah, although you'd have a lot more work to do. Not only are there multiple posts a day but some of Elizer's have dependency trees reaching months back!

54 points by t0pj 18y ago

This sadly is how the world works. In school, even in high school and college, the students who guess the teacher's password are rewarded. The (few) students who make an effort to discover and think through something on their own are criticized for wandering from the beaten path, even on the occasions when they're actually right. High school science competitions (school science fairs, all the way upto Siemens-Westinghouse and Intel STS) particularly guilty of this.

boredguy8 18y ago
"The (few) students who make an effort to discover and think through something on their own are criticized for wandering from the beaten path, even on the occasions when they're actually right." I remember I just -couldn't- accept that we can't take square roots of negative numbers. I mean, sure, two negatives multiplied together is a positive, but...there HAS to be a way! Numbers, to my 6th grade mind, weren't arbitrarily going to deny your ability to manipulate them. Fortunately for me, I happened to be reading a book on Mandlebrot and in the course of discussing his work the author introduces the concept of imaginary numbers. So the next day in class I asked: "Are you suuuure?" "Yes, I'm sure." "Well, I was reading in this book and so-and-so says you can take the square root of negative numbers, you get 'i' for the root of -1 and..." "Why don't you go wait outside." Where I got told that although I move to the beat of a different drummer, when I'm in her class, I really just need to be quiet. That's when public education and I had a falling out from which our relationship has never recovered. All of that to say: I think part of the 'problem' is that kids who do try to think on their own are often in a situation where they're challenging accepted rules without the social grace to do so constructively. But rather than being taught the social skills, they're just shut down. Very sad, actually. They could be taught how to 'wander well'.
- Prrometheus 18y ago
  Isn't sqrt(-1) = i an axiom though, and not a theorem? In other words, if you just started with the integers and the basic rules of arithmetic, you will never run into the need for imaginary numbers. It's only after you posit their existence that a lot of cool results flow from it. Am I wrong there?
  - boredguy8 18y ago
    I don't really know how to interpret your sentence. Complex numbers are a field in which you do 'basic rules of arithmetic'. You can't do the 'basic rules of arithmetic' on integers. i is defined as sqrt(-1), if that answers your question.
    - Prrometheus 18y ago
      I should have said "Real Numbers" instead of "Integers", sorry. My point is that sqrt(-1) = i is an extra assumption that you don't need to make in order to derive the math you do in school. If you don't make that assumption, you can still derive a lot of math. If you do make that assumption, then you can also derive the theorems of complex analysis. I think that's true, anyway. I could be wrong. It just seems strange to me that someone would be bothered by the lack of negative square roots, since their existence is never derived, only assumed. But then again, people's minds work very differently, especially in Mathematics. I was the opposite in Math class. I fought accepting "i" when they tried to teach it to us since it seemed so arbitrary and contrived to me. This was before I discovered that all Math is arbitrary and that there is no "real math", anyway.
      - ashu 18y ago
        As the "Road to Reality" explains, if you study Quantum mechanics, complex numbers become every bit as "real" as the integers or real numbers. You just can't explain some of the quantum mechanical phenomena or concepts without using complex numbers at all.
      - tokipin 18y ago
        it's as you say. it is contrived. but no more contrived than the basic integers. these are abstract systems that we have contrived in ways that are most useful to us. the natural numbers just seem more "real" because everyone in most cultures deals with "quantity" and "magnitude"

Alex3917 18y ago

Someone should write a book like the little schemer but for physics. One of the best classes I took in college was somewhat like this. We measured the period of the pendulum using our heartbeats, and we also measured how long it took things to roll down differently sloped ramps. From this we derived the period of the pendulum and the relationship between slope and speed. Eventually we used this to derive the universal law of gravitation using the period of the moon's orbit as the only given. It was pretty cool because there was no math involved. Instead of using calculus to derive the equations, we instead found them inductively by iterating over a couple thousand lines in excel and then looking for the pattern. The idea of the class was to understand physics by deriving all the equations the same way the people who discovered them did. It was pretty cool.

deleted 18y ago
[deleted]
- jfoutz 18y ago
  If you look here http://en.wikipedia.org/wiki/Inductive_reasoning http://en.wikipedia.org/wiki/Inductive_reasoning you will see inductive reasoning is all about drawing broad conclusions from limited evidence. In this context, the tens or thousands of experiments are generalized to support some "theory" Every time i touch ice it is cold. By induction, all ice is cold. that's not "proof" but it's a great theory of ice.
  - xlnt 18y ago
    If you read Hume or Popper you will see that inductive reasoning is logically impossible, and therefore can't actually be what people do.
    - deleted 18y ago
      [deleted]
    - jfoutz 18y ago
      I think we do this, or something very much like it: http://en.wikipedia.org/wiki/Bayesian_inference http://en.wikipedia.org/wiki/Bayesian_inference I'll agree that we can set up a game we play with symbols and rules that doesn't permit inductive reasoning as valid. I can't agree that "what people do" has anything to do with logic.

DaniFong 18y ago

Only tangentially related, but years ago, in elementary school, I decided to guess the password after the school restricted access to SimCity. I got it right on the first try, it was just the school name, but I told everyone 'I hacked it', for major props.

boredguy8 18y ago

I spend some of my time teaching at a private university. During a discussion with one student he said, "All I really know about Plato is that he thought the forms were transcendent whereas Aristotle thought the forms were immanent." "Oh," said I, "that's interesting. What does it mean for a form to be transcendent or immanent?" "I don't know, I just know that's what they thought." We then had a discussion about whether or not he really knew that, and whether or not he was OK with paying over $25k a year to learn how to be a parrot. The sad thing: he was OK with it, and probably rightly so. He realized that mostly what people want are parrots and you can get paid quite a decent amount of money for being a good parrot. Not a bad gig if you're fine being a cog. There are certain comforts it provides.

noonespecial 18y ago

I remember the first time I got an F on an assignment even though I'd gotten the correct answer to every problem. I hadn't reached my correct answers the "right" way.

boredguy8 18y ago
I loved calculus because about 4 weeks of teaching provided the foundation for everything else. My tests usually involved me having to derive something that was apparently derived in the book and then 'applied' on practice questions that got the 'right' way of doing things in by rote. I lost points for that. I would also lose points for "not showing my work", but if you can't factor, say, x^2-9 in your head, maybe you have deeper issues.
xlnt 18y ago
Ugh I hate that. I got marked down a letter grade on a math test once for not showing enough intermediate steps even though my answers were correct. I also once got an answer marked wrong because the teacher couldn't understand my intermediate steps, even though the answer (and steps) were actually correct. When I showed him, he refused to change my grade. That was at University.
cdr 18y ago
If the teacher was teaching a process, and looking for evidence that you understood that process, it seems entirely reasonable to not count your work.
- noonespecial 18y ago
  I had simply taken shortcuts I'd seen later in the book for factoring quadratics. They wanted to see it written exactly as it appeared in the current examples. I realized that math in school was more like one of those simon games where you just mindlessly press the arbitrary sequence of lights you just saw, than actual mathematics. This analogy helped me suffer through "school math" while I perused real math on my own.

cdr 18y ago

I've been thinking along similar lines since I've been interviewing; far too many interviewers are only looking for the password.

nsrivast 18y ago

overcomingbias is one of those websites you should read every article in, like paul graham's essays

jsomers 18y ago
yeah, although you'd have a lot more work to do. Not only are there multiple posts a day but some of Elizer's have dependency trees reaching months back!