6 ms·

"Utility had a strange backseat for me" I kinda took that to the extreme when I was young. Used to loathe anything practical - experiments, programming, applie

"Utility had a strange backseat for me" I kinda took that to the extreme when I was young. Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived haha.

grugagag 3y ago
I was the other way around. Only when I found utility in something could I finally grasp the subject properly. I remember how I was taught derivatives and integrals in HS, I knew how to do them but I was confused as hell. I asked the professor and once explained some uses it all clicked into place.
- cezart 3y ago
  Same. I studied derivatives and integrals twice. First time in HS, and it was just a bunch of random rules I had to learn by heart to be able to do these calculations that were required to pass the tests. Second time was during the first year at university. Here the professor explained that derivatives are needed to calculate the speed with which something changes. Since we were studying economics, interest rates and growth rates made great intuitive examples. Or that integrals permit us to calculate the area under a graph, thus making it possible to calculate for ex the total expected value of something over time. When I saw the utility out of this mathematical tools, studying how to apply them became of great interest!
- jack_pp 3y ago
  Same. There's an infinite things to learn, if you can't argue for the usefulness of any piece of information and if that use isn't related to my own goals I will stop you from communicating said information
- drorco 3y ago
  Same. I really struggle to learn anything which I can't see a practical use for. Just as an example, in high school learning trigonometry was really difficult for me, like why would I even care about finding an angle in a triangle, etc.? Only once I studied physics or game dev, this has started to become relevant, and then studying it got SO MUCH easier.
  - Solvency 3y ago
    It's mindboggling to me that every teacher doesn't just debut the subject with videogames as a reference. "Alright everyone, let's make a video game character out of triangles". "Let's make a little cannon that you can change the angle of. How do you calculate the angle? Funny you should ask.." "Now let's learn how you'd make the fireball move up and down as it travels. That's a sine wave!" Every single student understands the basic concept of a game visually, even if they don't play them regularly. It's just a perfect frame of reference and context for applying the concepts in 2D, and then in 3D. And it's so easy to help the students understand how easily those concepts get extrapolated to other things (engineering, sports, whatever).
    - grugagag 3y ago
      Back when I studied these videogames were much simpler. I was explained instead calculating areas and volumes for various functions and that was enough for me to get it. The thing is that not everyone was confused and some can take in theory without a practical application. They’re different modes of thinking and I appreciate both, I just happen to fall in the practical group.
    - drorco 3y ago
      Totally! One of the first thing I did after learning Newton's law of gravity, was to write down a small simulation of planets in orbit and how they "dance" around each other. This little exercise totally blew my mind and the code was really simple to code. There's probably an untapped opportunity here, but ed-tech is such a difficult industry.
      - 3y ago
- ConfusedDog 3y ago
  Same here. A lot of concepts seemed didn't matter if cannot be reflected in real world. That has changed for me though. Abstract things and first principle, zero knowledge actually quite interesting to me now.
  - grugagag 3y ago
    Congrats. I’ve made some progress on the abstract axis but still with some faint endgoal to make some progress in the practical realm I feel more grounded in.
- apomekhanes 3y ago
  I think the parent comment + yours (and others off parent) provides a perfect encapsulation of one of the dimensions of teaching / learning: what's often referred to as "style"*. One way to summarize, specifically, might be something like "inductive" vs. "deductive". As my experience has ... accumulated ... through the decades, I've come to feel that these sorts of differences / preferences likely don't have much impact on ultimate (potential) "level"**. And, I think you see this and related notions of "what mathematics 'actually is'" echoed (in a very fractal-like way, +1 to the universe in achieving a consistency we'll never rival) across the development of individual mathematicians as well as through the history of mathematics [1-6]. These distinctions are important in "pedagogy" - can be very helpful for teachers and students to be aware of and work at, especially at the more "basic" levels. This can make a massive difference in how an individual's arc unfolds - with extremes of "F this subject" vs. "I'm willing to accept low pay in exchange for torturing myself with this material for the rest of my life!" But, aside from trying to be mindful of the differences - and all involved, ideally, trying to USE awareness of knowledge and "EQ" and all of that in making the mutual learning enterprise work for everyone involved, many other aspects of the differences can just be outlets for time-wasting if focused on IMO (/ experience). * AFAIK, not really my field though and it has been ~15 years since I did any significant reading / study in the area - for the sake of 'full disclosure' ** The effects end up more in details of notes, problems and areas people are drawn to more or less, etc. [1] https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/comment-page-1/ https://terrytao.wordpress.com/career-advice/theres-more-to-... [2] Polya's "How to Solve It", in particular, I think of (from the intro): "The title of the very short second part is 'How to Solve It.' It is written in dialogue; a somewhat idealized teacher answers short questions of a somewhat idealized student.") - many options for accessing / buying, but, for this text, it's in the (unfortunately images) here - https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pdf https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pd... [3] https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=8f1556f607ec505a48c48bac8e226958c4a2a58a https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&d... [4] https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020748.02p0019l.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2... [5] https://en.wikipedia.org/wiki/Galois_theory#A_non-solvable_quintic_example https://en.wikipedia.org/wiki/Galois_theory#A_non-solvable_q... [6] https://en.wikipedia.org/wiki/Hilbert%27s_program https://en.wikipedia.org/wiki/Hilbert%27s_program ... and, so many more, of course...
agumonkey 3y ago
Wow, my thoughts word for word I'm still like that, albeit with some plasticity to avoid dying on my lonely rock.
- yantrams 3y ago
  I've come a long way I guess in the sense that I've learned to adult my way through things that don't necessarily excite me :| Programming in particular was a gamechanger for me and helped me see and appreciate the beauty in practical problem solving using simulations etc.
  - agumonkey 3y ago
    Can you describe what do you mean by simulations in this context ? you explore various solution configurations ?
    - yantrams 3y ago
      Yep kinda like that. I call it Answer guided monkeying around :) I try and see if I can arrive at the answer using Monte Carlo simulations and then try to work around that. Often times they give valuable insights and help uncover symmetries etc that aren’t obvious.
      - agumonkey 3y ago
        hmm seeking symmetries, the best kind of fun
importantbrian 3y ago
> I would also have a hard time processing/registering something if I'm not able to derive it analytically from first principles. This really resonates with me. I always had a really hard time with anything where I just had to memorize formulas, but I didn't have any issues if I could derive it myself. For this reason I actually struggled a lot more with algebra in HS than I did with calculus in college. I don't know if it's just the teachers I had growing up or if it's a more broad issue with how the curriculum is structured, but I didn't even realize you could derive things from first principles until I took calculus in college.
inimino 3y ago
That section was great. As soon as he said "interesting" I said "hard"! This is a real gem, there's a lot of wisdom in this short talk.
tiffanyg 3y ago
...Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived... Hello, 'undergraduate me'. "haha" indeed. The universe is still experiencing California-splitting [1], planet-slapping [2] spasms of laughter at my ... stupidity [3] (speaking only for myself, here, of course). [1] https://www.bbc.com/news/world-us-canada-48921915 https://www.bbc.com/news/world-us-canada-48921915 [2] https://en.wikipedia.org/wiki/Tunguska_event https://en.wikipedia.org/wiki/Tunguska_event [3] https://archive.org/details/novicetomasteron0000mori_w1f1 https://archive.org/details/novicetomasteron0000mori_w1f1
freetinker 3y ago
Exactly my experience! Can tell you how often I was on the brink of failing school/college because I wanted to derive as much as I could from first principles - under time pressure in an exam! I did myself no favors. I now find I learn better by being the opposite - finding a problem to solve and using math as a tool.
Tainnor 3y ago
> I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. I still find it easier to understand something if I understand it from the ground up instead of in an ad-hoc way. For example, I found it easier to reason about probability once I had seen a rigorous definition for what a probability distribution is. I guess the reason is that it gives me a way to sanity check my intuition. I still struggle with the fact that in software development, you get hundreds of technologies thrown at you and you barely have any time to understand them all fully. It makes me sometimes feel not very confident in what I do. I feel that I could understand e.g. Kubernetes better, if I had real in-depth (not just superficial) knowledge about networking. A lot of the time I'm just missing crucial information like "what problem are we trying to solve?", "why does this technology work the way it works?", etc. Something like Kafka is another example.
- hyperthesis 3y ago
  I had a hardtime remembering if I didn't understand. But I tried an experiment at uni (once...) to learn a subject solely by rote. I could typically recall about 7 out of 10 items. I was astonished I could do it at all. Unfortunately, I lost all my usual strengths in that subject: unable to generalize, unable to justify, unable to adapt. Re: software technologies: non-leaky abstractions are the way to understand without details. Algebras are a great example: arithmetic, concatenation, boolean, Kleene, relational. Although they still leak (overflow, PCRE, etc), an idealized core plus ad-hoc crap beats all-crap. jq has an algebra of , and | operators (though it doesn't call it that) \aside git: I wonder if git internals can be interpreted as an algebra (absent in UI)? TBF I tried to design a programming language around git internal operations (tree navigation and construction), but it was tedious to use. Maybe something analogous to a declarative SQL over relational algbra would solve this?

grugagag 3y ago

I was the other way around. Only when I found utility in something could I finally grasp the subject properly. I remember how I was taught derivatives and integrals in HS, I knew how to do them but I was confused as hell. I asked the professor and once explained some uses it all clicked into place.

cezart 3y ago
Same. I studied derivatives and integrals twice. First time in HS, and it was just a bunch of random rules I had to learn by heart to be able to do these calculations that were required to pass the tests. Second time was during the first year at university. Here the professor explained that derivatives are needed to calculate the speed with which something changes. Since we were studying economics, interest rates and growth rates made great intuitive examples. Or that integrals permit us to calculate the area under a graph, thus making it possible to calculate for ex the total expected value of something over time. When I saw the utility out of this mathematical tools, studying how to apply them became of great interest!
jack_pp 3y ago
Same. There's an infinite things to learn, if you can't argue for the usefulness of any piece of information and if that use isn't related to my own goals I will stop you from communicating said information
drorco 3y ago
Same. I really struggle to learn anything which I can't see a practical use for. Just as an example, in high school learning trigonometry was really difficult for me, like why would I even care about finding an angle in a triangle, etc.? Only once I studied physics or game dev, this has started to become relevant, and then studying it got SO MUCH easier.
- Solvency 3y ago
  It's mindboggling to me that every teacher doesn't just debut the subject with videogames as a reference. "Alright everyone, let's make a video game character out of triangles". "Let's make a little cannon that you can change the angle of. How do you calculate the angle? Funny you should ask.." "Now let's learn how you'd make the fireball move up and down as it travels. That's a sine wave!" Every single student understands the basic concept of a game visually, even if they don't play them regularly. It's just a perfect frame of reference and context for applying the concepts in 2D, and then in 3D. And it's so easy to help the students understand how easily those concepts get extrapolated to other things (engineering, sports, whatever).
  - grugagag 3y ago
    Back when I studied these videogames were much simpler. I was explained instead calculating areas and volumes for various functions and that was enough for me to get it. The thing is that not everyone was confused and some can take in theory without a practical application. They’re different modes of thinking and I appreciate both, I just happen to fall in the practical group.
  - drorco 3y ago
    Totally! One of the first thing I did after learning Newton's law of gravity, was to write down a small simulation of planets in orbit and how they "dance" around each other. This little exercise totally blew my mind and the code was really simple to code. There's probably an untapped opportunity here, but ed-tech is such a difficult industry.
    - 3y ago
ConfusedDog 3y ago
Same here. A lot of concepts seemed didn't matter if cannot be reflected in real world. That has changed for me though. Abstract things and first principle, zero knowledge actually quite interesting to me now.
- grugagag 3y ago
  Congrats. I’ve made some progress on the abstract axis but still with some faint endgoal to make some progress in the practical realm I feel more grounded in.
apomekhanes 3y ago
I think the parent comment + yours (and others off parent) provides a perfect encapsulation of one of the dimensions of teaching / learning: what's often referred to as "style"*. One way to summarize, specifically, might be something like "inductive" vs. "deductive". As my experience has ... accumulated ... through the decades, I've come to feel that these sorts of differences / preferences likely don't have much impact on ultimate (potential) "level"**. And, I think you see this and related notions of "what mathematics 'actually is'" echoed (in a very fractal-like way, +1 to the universe in achieving a consistency we'll never rival) across the development of individual mathematicians as well as through the history of mathematics [1-6]. These distinctions are important in "pedagogy" - can be very helpful for teachers and students to be aware of and work at, especially at the more "basic" levels. This can make a massive difference in how an individual's arc unfolds - with extremes of "F this subject" vs. "I'm willing to accept low pay in exchange for torturing myself with this material for the rest of my life!" But, aside from trying to be mindful of the differences - and all involved, ideally, trying to USE awareness of knowledge and "EQ" and all of that in making the mutual learning enterprise work for everyone involved, many other aspects of the differences can just be outlets for time-wasting if focused on IMO (/ experience). * AFAIK, not really my field though and it has been ~15 years since I did any significant reading / study in the area - for the sake of 'full disclosure' ** The effects end up more in details of notes, problems and areas people are drawn to more or less, etc. [1] https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/comment-page-1/ https://terrytao.wordpress.com/career-advice/theres-more-to-... [2] Polya's "How to Solve It", in particular, I think of (from the intro): "The title of the very short second part is 'How to Solve It.' It is written in dialogue; a somewhat idealized teacher answers short questions of a somewhat idealized student.") - many options for accessing / buying, but, for this text, it's in the (unfortunately images) here - https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pdf https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pd... [3] https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=8f1556f607ec505a48c48bac8e226958c4a2a58a https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&d... [4] https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020748.02p0019l.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2... [5] https://en.wikipedia.org/wiki/Galois_theory#A_non-solvable_quintic_example https://en.wikipedia.org/wiki/Galois_theory#A_non-solvable_q... [6] https://en.wikipedia.org/wiki/Hilbert%27s_program https://en.wikipedia.org/wiki/Hilbert%27s_program ... and, so many more, of course...

agumonkey 3y ago

Wow, my thoughts word for word I'm still like that, albeit with some plasticity to avoid dying on my lonely rock.

yantrams 3y ago
I've come a long way I guess in the sense that I've learned to adult my way through things that don't necessarily excite me :| Programming in particular was a gamechanger for me and helped me see and appreciate the beauty in practical problem solving using simulations etc.
- agumonkey 3y ago
  Can you describe what do you mean by simulations in this context ? you explore various solution configurations ?
  - yantrams 3y ago
    Yep kinda like that. I call it Answer guided monkeying around :) I try and see if I can arrive at the answer using Monte Carlo simulations and then try to work around that. Often times they give valuable insights and help uncover symmetries etc that aren’t obvious.
    - agumonkey 3y ago
      hmm seeking symmetries, the best kind of fun

importantbrian 3y ago

> I would also have a hard time processing/registering something if I'm not able to derive it analytically from first principles. This really resonates with me. I always had a really hard time with anything where I just had to memorize formulas, but I didn't have any issues if I could derive it myself. For this reason I actually struggled a lot more with algebra in HS than I did with calculus in college. I don't know if it's just the teachers I had growing up or if it's a more broad issue with how the curriculum is structured, but I didn't even realize you could derive things from first principles until I took calculus in college.

inimino 3y ago

That section was great. As soon as he said "interesting" I said "hard"! This is a real gem, there's a lot of wisdom in this short talk.

tiffanyg 3y ago

...Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived... Hello, 'undergraduate me'. "haha" indeed. The universe is still experiencing California-splitting [1], planet-slapping [2] spasms of laughter at my ... stupidity [3] (speaking only for myself, here, of course). [1] https://www.bbc.com/news/world-us-canada-48921915 https://www.bbc.com/news/world-us-canada-48921915 [2] https://en.wikipedia.org/wiki/Tunguska_event https://en.wikipedia.org/wiki/Tunguska_event [3] https://archive.org/details/novicetomasteron0000mori_w1f1 https://archive.org/details/novicetomasteron0000mori_w1f1

freetinker 3y ago

Exactly my experience! Can tell you how often I was on the brink of failing school/college because I wanted to derive as much as I could from first principles - under time pressure in an exam! I did myself no favors. I now find I learn better by being the opposite - finding a problem to solve and using math as a tool.

Tainnor 3y ago

> I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. I still find it easier to understand something if I understand it from the ground up instead of in an ad-hoc way. For example, I found it easier to reason about probability once I had seen a rigorous definition for what a probability distribution is. I guess the reason is that it gives me a way to sanity check my intuition. I still struggle with the fact that in software development, you get hundreds of technologies thrown at you and you barely have any time to understand them all fully. It makes me sometimes feel not very confident in what I do. I feel that I could understand e.g. Kubernetes better, if I had real in-depth (not just superficial) knowledge about networking. A lot of the time I'm just missing crucial information like "what problem are we trying to solve?", "why does this technology work the way it works?", etc. Something like Kafka is another example.

hyperthesis 3y ago
I had a hardtime remembering if I didn't understand. But I tried an experiment at uni (once...) to learn a subject solely by rote. I could typically recall about 7 out of 10 items. I was astonished I could do it at all. Unfortunately, I lost all my usual strengths in that subject: unable to generalize, unable to justify, unable to adapt. Re: software technologies: non-leaky abstractions are the way to understand without details. Algebras are a great example: arithmetic, concatenation, boolean, Kleene, relational. Although they still leak (overflow, PCRE, etc), an idealized core plus ad-hoc crap beats all-crap. jq has an algebra of , and | operators (though it doesn't call it that) \aside git: I wonder if git internals can be interpreted as an algebra (absent in UI)? TBF I tried to design a programming language around git internal operations (tree navigation and construction), but it was tedious to use. Maybe something analogous to a declarative SQL over relational algbra would solve this?