Interesting. I also found this article extremely personally relevant. While not as big a contrast as your case, in 8th grade I got a D- in geometry and honors on the California Golden State Exam for geometry—that last much to the amazement of my teacher, who was forced to present the award to me at assembly.
I also identify with the duality from the article of being an average thinker in the moment, but having very strong reasoning skills. It seems half the smart people I know are sharper than I am, but people regard my reasoning and verbal debate skills to be very good. I’ve never quite known how to reconcile this with how g seems to work.
Geometry award notwithstanding, I’ve never been good at math, though I was always put in the gifted math classes. Everyone knows kids who didn’t study and still aced the exams—some here are those kids. Whether I studied or didn’t study, I would always get Cs and Ds. I never had enough time to finish the tests. When I took physics, the professor had a rule that you could take as long as you liked on exams; this let me get the highest grade in the class on every one.
I would love to be better at math, because it’s important, but it’s not intrinsically interesting to me. Today I’m a software developer and I learn whatever math I need, but what interests me is tools and efficiency through design and I prefer to work at the functional layer where the math I learned in high school and college isn’t the longest lever.
Recently, due to articles on Less Wrong and such, I’ve come to realize that there are math subjects I probably do have an interest in, but they weren’t the math foundations we grow up with, at least in the US. Continuous math is boring to me, but discrete math—starting with probabilities—I can find lots of programming and everyday uses for, so much so that I’m considering going back and finishing a probability and statistics degree.
Continuous math is boring to me, but discrete math—starting with probabilities—I can find lots of programming and everyday uses for, so much so that I’m considering going back and finishing a probability and statistics degree.
A word of warning: probability and statistics make heavy use of continuous math. Here Be Integrals.
He worked on both ultrafinitism and nonstandard analysis, bringing new approaches to both. He was discussed around here a couple of years ago for his claim to have proved the existence of a contradiction in Peano Arithmetic, but Terry Tao found the flaw. Unfortunately, he died last year.
In his nonstandard days, he wrote Radically Elementary Probability Theory. This is not simply redoing standard continuous probability theory with nonstandard analysis, but doing discrete probability theory with nonstandard integers. All of the useful things appear, but it all looks very different. Princeton still hosts the PDF: https://web.math.princeton.edu/~nelson/books/rept.pdf
ETA: While ultrafinitism and nonstandard analysis seem almost complete opposites as far as constructivism goes, his approaches to them are actually quite similar to one another.
Interesting. I also found this article extremely personally relevant. While not as big a contrast as your case, in 8th grade I got a D- in geometry and honors on the California Golden State Exam for geometry—that last much to the amazement of my teacher, who was forced to present the award to me at assembly.
I also identify with the duality from the article of being an average thinker in the moment, but having very strong reasoning skills. It seems half the smart people I know are sharper than I am, but people regard my reasoning and verbal debate skills to be very good. I’ve never quite known how to reconcile this with how g seems to work.
Geometry award notwithstanding, I’ve never been good at math, though I was always put in the gifted math classes. Everyone knows kids who didn’t study and still aced the exams—some here are those kids. Whether I studied or didn’t study, I would always get Cs and Ds. I never had enough time to finish the tests. When I took physics, the professor had a rule that you could take as long as you liked on exams; this let me get the highest grade in the class on every one.
I would love to be better at math, because it’s important, but it’s not intrinsically interesting to me. Today I’m a software developer and I learn whatever math I need, but what interests me is tools and efficiency through design and I prefer to work at the functional layer where the math I learned in high school and college isn’t the longest lever.
Recently, due to articles on Less Wrong and such, I’ve come to realize that there are math subjects I probably do have an interest in, but they weren’t the math foundations we grow up with, at least in the US. Continuous math is boring to me, but discrete math—starting with probabilities—I can find lots of programming and everyday uses for, so much so that I’m considering going back and finishing a probability and statistics degree.
Looking forward to the rest of this series.
A word of warning: probability and statistics make heavy use of continuous math. Here Be Integrals.
Unless you take Edward Nelson’s approach.
Sorry, I haven’t heard of him. Could you explain and/or link?
He worked on both ultrafinitism and nonstandard analysis, bringing new approaches to both. He was discussed around here a couple of years ago for his claim to have proved the existence of a contradiction in Peano Arithmetic, but Terry Tao found the flaw. Unfortunately, he died last year.
In his nonstandard days, he wrote Radically Elementary Probability Theory. This is not simply redoing standard continuous probability theory with nonstandard analysis, but doing discrete probability theory with nonstandard integers. All of the useful things appear, but it all looks very different. Princeton still hosts the PDF: https://web.math.princeton.edu/~nelson/books/rept.pdf
ETA: While ultrafinitism and nonstandard analysis seem almost complete opposites as far as constructivism goes, his approaches to them are actually quite similar to one another.