Statistics is hard because humans are not mentally structured to think in combinatorial ways. Calculus is easy because as soon as you grasp the idea of a limit the consequences are obvious. We subconsciously do calculus in our heads when we throw rocks at a target, just as birds compute trajectories literally on the fly when they eff…
Statistics is hard because humans are not mentally structured to think in combinatorial ways. Calculus is easy because as soon as you grasp the idea of a limit the consequences are obvious. We subconsciously do calculus in our heads when we throw rocks at a target, just as birds compute trajectories literally on the fly when they effortlessly flash from one branch to another, avoiding all obstacles in between. Diffequations is hard only because you have to habituate yourself to the patterns and resemblances of trigonometric identities and infinite expansions, but the basis is fundamentally as simple as tracing a line from here to there.
Adding a post note. I speculate one reason Americans are not only innumerate but in many respects almost anti-numerate is they don't want to grow up and admit that life guidance should not be through instantaneous emotional impulses. Part of that comes I think from the American tradition of salvation through an emotional purgation of sin that happens without effort, like an orgasm. You don't have to think, you have only to believe. Once you believe you are saved and it's all simple.
Ha, all greek to me ....( I stopped after Algebra II...had all I needed to get into college and as a liberal arts major, didn't think I needed more than what I already had...Math is the only subject that I really struggled with at times ( hated geometry, but, loved Algebra ( think it might be a right brain/left brain thing...lol) ...and I use math for a living now, but, the lower ends of it...as a bookkeeper...lol
I am sorry for that... I thought I hated math, because I was so good at language skills I thought everything should be like the falling off a log that reading and writing was.
But worst of all I had great language/history teachers and truly terrible math teachers. My 9th grade algebra teacher was a true asshole whose ambition was to be a footbal coach and who in retrospect I now see hated his job and went out of his way to make his students see the subject with the loathing he felt for his own pathetic life. And maybe also he literally was afraid that any student who was actually interested in the subject would try to engage with him on it, and show his own lack of ability or knowledge. Somehow I got through several terms of high school algebra but can't recall giving a damn. The instructors were at best nonentities.
I always loved and was fascinated by science. But I went through college without taking a single math course -- graduate courses in literature, history, poli-sci but no math -- and only later signed up for a calc course after my graduation because I wanted to understand what was wrong with Zeno's paradoxes (I was a philosophy major).. And that was the most amazing wonderful class I ever had, like fireworks going off. The incredible beauty of the idea totally captivated me. It worked because (maybe I'd grown up a little) but also because the instructor was as enthusiastic about it and burned with a fire to share that ecstasy with his students. And then I took physics and it was even better.
I still remember in second or third term calc not paying attention to whatever the instructor was actually working through but suddenly seeing the amazing, totally mind blowing way that any smooth and continuous function can be represented to an arbitrarily perfect approximation by a sum of sin and cosine functions. And jumping out of my seat and shouting that it was beautiful. It was better than seeing God. It was like for a moment almost being Johann Sebastian Bach. and the instructor, instead of summoning the police and having me ejected for causing the disturbance, asked what that was about and we spent the rest of the class diverted onto that topic. He was as enthused as I was.
We don't show kids how exquisitely beautiful the ideas are. So they go out into the world like the Romanian orphans who never knew what it is to have a loving caregiver. Or growing up and never seeing the glory of a sunset.
Well… I’m an old guy and the last time I really tried to use the maths I used to use so easily it seemed my head was full of cotton. I was putting together a simple model to calculate hardness concentration in a cooling tower given a few inputs, heat rejection due to evaporation, hardness of makeup, dilution due to blowdown… frustrating. Probably mostly lack of practice but also I’m sure brain ossification.. but I never will forget the numinous experience of seeing the few glimpses I’ve been vouchsafed of a tiny sliver of a part of a portion of a subset of a fragment of how reality works. Even though today I’m just another mud brain chimpanzee who saw a sunset once and that is all he gets.
When Newton and Leibniz first saw it, they must have imagined they had been given the keys to eternity. I treasure my own glimpse of that infinite landscape. It extends beyond what we see with the mind. It is also what we find in the Odyssey of Homer or the story of the Monkey King in the journey to the West or the statue of David in Florence or the dome of the Hagia Sophia.. or the brown eyes of my little firstborn child and her somber brown eyes looking at me, her hopelessly inadequent father, six hours after emerging from the body of my dear dear wife who for whatever reason, not that I deserve it, still claims to love me a half century after I assured her I would be her best friend forever and am today as ever since that day striving to fulfill that promise.
What our teachers need to do is raise the gaze of our young young chimpanzee progeny above the tiny horizon of their stupid phones and iPads up to the vast sky overarching their heads, and the wide range of visible frequencies our biological eyes cannot see but our minds have revealed to us. And all the further vistas beyond that we don’t even yet know await us.
By the way, despite her father she turned out to be awesome. And married into a family of amazingly marvelous people.
So go figure. Joy does not follow desert. If the arc of history truly bended toward justice in every case, why am I showered with blessings?
Very well stated Craig...I am old now too, and forgetting things I know I know is frustrating..it usually comes to me, but, long after I needed it ....sigh
Statistics is hard because humans are not mentally structured to think in combinatorial ways. Calculus is easy because as soon as you grasp the idea of a limit the consequences are obvious. We subconsciously do calculus in our heads when we throw rocks at a target, just as birds compute trajectories literally on the fly when they effortlessly flash from one branch to another, avoiding all obstacles in between. Diffequations is hard only because you have to habituate yourself to the patterns and resemblances of trigonometric identities and infinite expansions, but the basis is fundamentally as simple as tracing a line from here to there.
Adding a post note. I speculate one reason Americans are not only innumerate but in many respects almost anti-numerate is they don't want to grow up and admit that life guidance should not be through instantaneous emotional impulses. Part of that comes I think from the American tradition of salvation through an emotional purgation of sin that happens without effort, like an orgasm. You don't have to think, you have only to believe. Once you believe you are saved and it's all simple.
Ha, all greek to me ....( I stopped after Algebra II...had all I needed to get into college and as a liberal arts major, didn't think I needed more than what I already had...Math is the only subject that I really struggled with at times ( hated geometry, but, loved Algebra ( think it might be a right brain/left brain thing...lol) ...and I use math for a living now, but, the lower ends of it...as a bookkeeper...lol
I am sorry for that... I thought I hated math, because I was so good at language skills I thought everything should be like the falling off a log that reading and writing was.
But worst of all I had great language/history teachers and truly terrible math teachers. My 9th grade algebra teacher was a true asshole whose ambition was to be a footbal coach and who in retrospect I now see hated his job and went out of his way to make his students see the subject with the loathing he felt for his own pathetic life. And maybe also he literally was afraid that any student who was actually interested in the subject would try to engage with him on it, and show his own lack of ability or knowledge. Somehow I got through several terms of high school algebra but can't recall giving a damn. The instructors were at best nonentities.
I always loved and was fascinated by science. But I went through college without taking a single math course -- graduate courses in literature, history, poli-sci but no math -- and only later signed up for a calc course after my graduation because I wanted to understand what was wrong with Zeno's paradoxes (I was a philosophy major).. And that was the most amazing wonderful class I ever had, like fireworks going off. The incredible beauty of the idea totally captivated me. It worked because (maybe I'd grown up a little) but also because the instructor was as enthusiastic about it and burned with a fire to share that ecstasy with his students. And then I took physics and it was even better.
I still remember in second or third term calc not paying attention to whatever the instructor was actually working through but suddenly seeing the amazing, totally mind blowing way that any smooth and continuous function can be represented to an arbitrarily perfect approximation by a sum of sin and cosine functions. And jumping out of my seat and shouting that it was beautiful. It was better than seeing God. It was like for a moment almost being Johann Sebastian Bach. and the instructor, instead of summoning the police and having me ejected for causing the disturbance, asked what that was about and we spent the rest of the class diverted onto that topic. He was as enthused as I was.
We don't show kids how exquisitely beautiful the ideas are. So they go out into the world like the Romanian orphans who never knew what it is to have a loving caregiver. Or growing up and never seeing the glory of a sunset.
That sounds awesome...
Well… I’m an old guy and the last time I really tried to use the maths I used to use so easily it seemed my head was full of cotton. I was putting together a simple model to calculate hardness concentration in a cooling tower given a few inputs, heat rejection due to evaporation, hardness of makeup, dilution due to blowdown… frustrating. Probably mostly lack of practice but also I’m sure brain ossification.. but I never will forget the numinous experience of seeing the few glimpses I’ve been vouchsafed of a tiny sliver of a part of a portion of a subset of a fragment of how reality works. Even though today I’m just another mud brain chimpanzee who saw a sunset once and that is all he gets.
When Newton and Leibniz first saw it, they must have imagined they had been given the keys to eternity. I treasure my own glimpse of that infinite landscape. It extends beyond what we see with the mind. It is also what we find in the Odyssey of Homer or the story of the Monkey King in the journey to the West or the statue of David in Florence or the dome of the Hagia Sophia.. or the brown eyes of my little firstborn child and her somber brown eyes looking at me, her hopelessly inadequent father, six hours after emerging from the body of my dear dear wife who for whatever reason, not that I deserve it, still claims to love me a half century after I assured her I would be her best friend forever and am today as ever since that day striving to fulfill that promise.
What our teachers need to do is raise the gaze of our young young chimpanzee progeny above the tiny horizon of their stupid phones and iPads up to the vast sky overarching their heads, and the wide range of visible frequencies our biological eyes cannot see but our minds have revealed to us. And all the further vistas beyond that we don’t even yet know await us.
By the way, despite her father she turned out to be awesome. And married into a family of amazingly marvelous people.
So go figure. Joy does not follow desert. If the arc of history truly bended toward justice in every case, why am I showered with blessings?
Very well stated Craig...I am old now too, and forgetting things I know I know is frustrating..it usually comes to me, but, long after I needed it ....sigh
you responded before I was finished. Feeling sorry for myselfI guess. You seem like someone it would be great to talk to.
I'm sorry, it showed up in my email as a finished post, so I didn't know it wasn't
I am easy to talk to, one of my gifts...I don't mind and am a good listener
However, I going to take a nap , my eyes are drooping, I will be back later if you wish to leave me a post and I will respond when I come back....
Feel free to email. Cbutcher@umich.edu.
Thanks, sending