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I can remember that I was introduced to sine and cosine through game programming before it was discussed in school. Particularly I was trying to make games wit

I can remember that I was introduced to sine and cosine through game programming before it was discussed in school. Particularly I was trying to make games with Pascal and Assembly on an 80386. Asphyxia tutorials. No Stack Overflow, no Khan Academy, Wikipedia, in fact no Internet or even BBS at all. I feel nostalgic towards this time, but I guess that those feelings are more attached to the curiosity of an analog child being introduced to the digital magic.

deepaksurti 7y ago
I really liked your phrase: "analog child being introduced to the digital magic". I don't know if children in today's generation can at all be called as 'analog children'? And that plausibly is not good, overall.
- tempguy9999 7y ago
  That's quite an assumption. I really don't know if they are any better, worse or just different because their environment is different. I really don't like dissing things just because they've changed. Can you really summarise an entire generation so easily?
  - deepaksurti 7y ago
    Sorry, my intent was neither to diss nor to summarise trivially; thanks for pointing it out and I need to put my thoughts in a better way.
- bayesian_horse 7y ago
  It's inevitable that children today have more contact to digital technology in all its forms. This may have disadvantages. But it's certainly not avoidable. The best that parents can do is to try and teach and encourage children to focus on healthier stuff. To not be slaves to their mobile phones. To have empathy. Easier said than done though.
  - GuiA 7y ago
    > But it's certainly not avoidable. It certainly is avoidable. The difference between my friends who are very conscious of the exposure they give their children to TV, phones, tablets, etc vs those who don’t is striking. Case study A: a friend who lives with her 6 year old son in a tiny Paris apartment. She has a laptop for work and an old phone she uses for WhatsApp/basic tasks, and that’s it. When I spent a few days at her place last winter, the kid helped us cook, we played board games after dinner, and he was really excited to go to the park the next day. Case study B: San Francisco friends who let their kid use an iPad pretty much any time there is any chance the kid might be bored, moody, etc. She is pretty much addicted, and it’s quite hard to get her excited about anything else.
    - bayesian_horse 7y ago
      The 6 year is probably in kindergarden or starting elementary school. You can bet his class mates / potential friends will soon all have smart phones and converse mainly through online groups. It's hard to say if at some point the disadvantages of limiting screen use is outweighing the benefits. Worse, if children already use social media heavily, stripping them of access during the school hours (or longer) will actually increase their anxiety levels. Children's social dynamics are tricky, especially for adults, and a lot can go wrong. In my youth I wasn't spending so much time with a computer because it was my free choice. I lacked the social skills to make friends and was bullied heavily through my entire school life. Next problem: To entertain a child without iPads requires a lot of time and conscious effort, which not all parents can spare, despite their best efforts. Instead of iPads, especially with preschool children, you'll see parents give them some food item when they need to be still for a time (bus, train etc). That's not necessarily a better solution. Nor is letting them cry all the time because children at such ages can't control their focus and impulses for a meaningful amount of time.
TeMPOraL 7y ago
> I can remember that I was introduced to sine and cosine through game programming before it was discussed in school. I was introduced to it slightly after I was in school, but unlike school, gamedev is what made me actually understand it. Then the whole trigonometry, and basics of vector arithmetic and matrices. School for me was boring repetition of arbitrary tasks forced top-down by unpleasant people. Wanting to make my own game, that gave me huge motivation. (Then I went to university, and on the first year's physics lab, I was asked to solve something on a whiteboard. It was a simple thing involving a vector cross product, so I proceeded to write out the formula and calculate the result. TA looked bewildered and asked me what the hell am I doing? Turns out, I was supposed to first do a whole dance around base vectors and 3x3 matrices to derive the appropriate formula, which I simply memorized when I was 14, having implemented it in C++ half a dozen times. Turns out, gamedev-driven education can leave you with holes in theory.)
- xamuel 7y ago
  Re your parenthetical story, So like, the TA asked you to compute <1,2,3>X<4,5,6> and you jumped straight to <2x6-3x5, -(1x6-3x4), 1x5-2x4>, without the intermediate step of | i j k | | 1 2 3 | | 4 5 6 |? Or did you begin by computing the angle between the two vectors, so as to use the sine formula for cross product? Either way, I can certainly understand how your classmates (and TA) would be bewildered (especially if the two vectors were such that it wasn't immediately obvious what the angle between them was).
  - TeMPOraL 7y ago
    The first one. I jumped straight to the component-wise formula. TA expected to see the matrix you wrote above (except AFAIR transposed, but I might recall wrong). I understand why TA didn't like it, though back then I wasn't happy that my short and "obvious" solution wasn't received well.
animal531 7y ago
Same here. First to try and get your own sine scroller working, and then to figure out 2d and 3d rotations.
roel_v 7y ago
"analog child being introduced to the digital magic." In high school, my electricity teacher made us draw the sine waves of monophasic and tri-phasic (if that's what it's called in English?) voltages manually by drawing into a Cartesian arrangement and projecting onto a line diagram, much like the animation about halfway through the article. It was tedious and it seemed very repetitive to draw the various variations, but in later years I started to understand its relevance (also with regards to the relation between current, voltage and power). Just in general it gave me such a good example of the relationship between the geometry, trigonometry and calculus involved, much better than the canonical speed/distance example ever did (for me). There are only a few core concepts I learned in high school that I still use often, and this is definitely one of them.
- tigerlily 7y ago
  That'll be single-phase and three-phase for your enkelfasig en driefasig :)
  - roel_v 7y ago
    Yeah that makes much more sense, I knew something was off :)
Sharlin 7y ago
I remember playing around with these weird sin and cos functions whose return values seemed to lack any readily discernible pattern. After some experimenting I ended up plotting something like x=a*sin(t) y=a*cos(t) and was delighted to realize that the coordinates traced the arc of a circle! Not a long time earlier I had wondered how to write a program that displays an analog clock… The connection to right-angled triangles was revealed to me only later, although in retrospect they are obviously two sides of the same coin.
- cellular 7y ago
  I made a whiteboard robot to teach/experiment those equations. It's fun to fill a whiteboard with patterns and let people wonder how they were made: https://sites.google.com/view/wbr https://sites.google.com/view/wbr
- lakkal 7y ago
  That's my story, too - learned about sine and cosine by playing around with plotting the results in Applesoft Basic. Wasn't until the following year that I learned what they're for in Trigonometry class.
cmroanirgo 7y ago
I remember making a simple inlined asm function that called a little known x87 function fsincos that returns the sine and cosine of an angle. I seem to remember that it only took a few extra clock cycles to get both answers. This was really helpful when building matrices (in the mid '90s).
acollins1331 7y ago
What an interesting and strange childhood you must have had to be writing games in Pascal before you heard about cosine. Either your schooling was great or terrible!
- CodeMage 7y ago
  Maybe it's not the schooling. I went through a similar experience, because I started programming when I was 7 years old. By the time I had learned enough to want to try to make a game, I had taught myself Turbo Pascal, but I still wasn't of an age to learn trigonometry in school.
- bayesian_horse 7y ago
  I had undiagnosed ADHD and was bullied all throughout my school years. So I had plenty of time. And it really doesn't take much to learn programming in class 5 or 6... I believe my teachers were pretty good, overall. At least as good as can be expected.
  - acollins1331 7y ago
    The first sentence is the same for me but to just pick up programming when you're 11 or 12 by yourself seems crazy! I'm sure you had a mentor or an older friend or some adult that at least exposed you to the concept.
    - bayesian_horse 7y ago
      I remember vaguely a course on Basic on Amigas. But other than that, I didn't really have mentors or peers. I believe I learnt QBasic from a book, later Turbo Pascal from another book and assembly from yet another.
      - acollins1331 7y ago
        That would probably have been enough to spark my creativity. We had a class on using word and powerpoint and typing in grade 8. America is GREAT /s
deleted 7y ago
[deleted]
ben7799 7y ago
Denthor of Asphyxia! I didn't remember what it was by read those back in the early 90s as well, learning to program on a 486 with an early SVGA card. I think I downloaded them on a trial of AOL, my parents wouldn't/couldn't pay for AOL but I sucked all those tutorials down when I had a chance. I was taking Pascal in school but learned a ton more from those tutorials. I wrote an asteroids type game and got tons of eye rolls from the teacher as the other students were playing my game after I shared the source. I had done the whole years curriculum in a month or two and then sat there and wrote games in class. The teacher didn't really care as I'd just about matched his knowledge by the middle of the year. He was a great teacher, had a PhD in math which was pretty darn rare for high school. Those tutorials had a significant effect on my chosen career path.
teamonkey 7y ago
I ended up deriving sin and cos myself. I was trying to make a Spacewar-style game and knew I needed to make the ship move depending on how it was rotated. Plotted a circle on squared paper and tried to figure out the coordinates at the circumference for all the angles I was using. Quite a surprise when I was finally introduced to trig at school and found out it had a name!
- xamuel 7y ago
  I was utterly confused by trigonometry in junior high, it seemed to be some kind of secret language I had missed the sacred initiation rites into. And everyone seemed to treat it as exactly that--meaningless esoterica. And then one day someone explained the high-level point to me: "Of the six quantities of a triangle (three angles and three sides), given any three of them, at least one of which is a side, the other three are automatically nailed down." Suddenly a switch was flipped. After that, the rest is just details that write themselves.
- SamBam 7y ago
  Indeed, anytime I move something on the screen at an angle for a distance, I have to do a quick check to remember whether the horizontal distance is sin or cos. I do this probably half a dozen times a month. (I'm not a quick learner.) I was kind of surprised that the article used circular motion as its main motivating point, since I feel like just moving at some angle is so much more common.
CodeMage 7y ago
Wow, that takes me back down the nostalgia lane! Denthor's tutorials, PCGPE, Ralf Brown's Interrupt List...

deepaksurti 7y ago

I really liked your phrase: "analog child being introduced to the digital magic". I don't know if children in today's generation can at all be called as 'analog children'? And that plausibly is not good, overall.

tempguy9999 7y ago
That's quite an assumption. I really don't know if they are any better, worse or just different because their environment is different. I really don't like dissing things just because they've changed. Can you really summarise an entire generation so easily?
- deepaksurti 7y ago
  Sorry, my intent was neither to diss nor to summarise trivially; thanks for pointing it out and I need to put my thoughts in a better way.
bayesian_horse 7y ago
It's inevitable that children today have more contact to digital technology in all its forms. This may have disadvantages. But it's certainly not avoidable. The best that parents can do is to try and teach and encourage children to focus on healthier stuff. To not be slaves to their mobile phones. To have empathy. Easier said than done though.
- GuiA 7y ago
  > But it's certainly not avoidable. It certainly is avoidable. The difference between my friends who are very conscious of the exposure they give their children to TV, phones, tablets, etc vs those who don’t is striking. Case study A: a friend who lives with her 6 year old son in a tiny Paris apartment. She has a laptop for work and an old phone she uses for WhatsApp/basic tasks, and that’s it. When I spent a few days at her place last winter, the kid helped us cook, we played board games after dinner, and he was really excited to go to the park the next day. Case study B: San Francisco friends who let their kid use an iPad pretty much any time there is any chance the kid might be bored, moody, etc. She is pretty much addicted, and it’s quite hard to get her excited about anything else.
  - bayesian_horse 7y ago
    The 6 year is probably in kindergarden or starting elementary school. You can bet his class mates / potential friends will soon all have smart phones and converse mainly through online groups. It's hard to say if at some point the disadvantages of limiting screen use is outweighing the benefits. Worse, if children already use social media heavily, stripping them of access during the school hours (or longer) will actually increase their anxiety levels. Children's social dynamics are tricky, especially for adults, and a lot can go wrong. In my youth I wasn't spending so much time with a computer because it was my free choice. I lacked the social skills to make friends and was bullied heavily through my entire school life. Next problem: To entertain a child without iPads requires a lot of time and conscious effort, which not all parents can spare, despite their best efforts. Instead of iPads, especially with preschool children, you'll see parents give them some food item when they need to be still for a time (bus, train etc). That's not necessarily a better solution. Nor is letting them cry all the time because children at such ages can't control their focus and impulses for a meaningful amount of time.

TeMPOraL 7y ago

> I can remember that I was introduced to sine and cosine through game programming before it was discussed in school. I was introduced to it slightly after I was in school, but unlike school, gamedev is what made me actually understand it. Then the whole trigonometry, and basics of vector arithmetic and matrices. School for me was boring repetition of arbitrary tasks forced top-down by unpleasant people. Wanting to make my own game, that gave me huge motivation. (Then I went to university, and on the first year's physics lab, I was asked to solve something on a whiteboard. It was a simple thing involving a vector cross product, so I proceeded to write out the formula and calculate the result. TA looked bewildered and asked me what the hell am I doing? Turns out, I was supposed to first do a whole dance around base vectors and 3x3 matrices to derive the appropriate formula, which I simply memorized when I was 14, having implemented it in C++ half a dozen times. Turns out, gamedev-driven education can leave you with holes in theory.)

xamuel 7y ago
Re your parenthetical story, So like, the TA asked you to compute <1,2,3>X<4,5,6> and you jumped straight to <2x6-3x5, -(1x6-3x4), 1x5-2x4>, without the intermediate step of | i j k | | 1 2 3 | | 4 5 6 |? Or did you begin by computing the angle between the two vectors, so as to use the sine formula for cross product? Either way, I can certainly understand how your classmates (and TA) would be bewildered (especially if the two vectors were such that it wasn't immediately obvious what the angle between them was).
- TeMPOraL 7y ago
  The first one. I jumped straight to the component-wise formula. TA expected to see the matrix you wrote above (except AFAIR transposed, but I might recall wrong). I understand why TA didn't like it, though back then I wasn't happy that my short and "obvious" solution wasn't received well.

animal531 7y ago

Same here. First to try and get your own sine scroller working, and then to figure out 2d and 3d rotations.

roel_v 7y ago

"analog child being introduced to the digital magic." In high school, my electricity teacher made us draw the sine waves of monophasic and tri-phasic (if that's what it's called in English?) voltages manually by drawing into a Cartesian arrangement and projecting onto a line diagram, much like the animation about halfway through the article. It was tedious and it seemed very repetitive to draw the various variations, but in later years I started to understand its relevance (also with regards to the relation between current, voltage and power). Just in general it gave me such a good example of the relationship between the geometry, trigonometry and calculus involved, much better than the canonical speed/distance example ever did (for me). There are only a few core concepts I learned in high school that I still use often, and this is definitely one of them.

tigerlily 7y ago
That'll be single-phase and three-phase for your enkelfasig en driefasig :)
- roel_v 7y ago
  Yeah that makes much more sense, I knew something was off :)

Sharlin 7y ago

I remember playing around with these weird sin and cos functions whose return values seemed to lack any readily discernible pattern. After some experimenting I ended up plotting something like x=a*sin(t) y=a*cos(t) and was delighted to realize that the coordinates traced the arc of a circle! Not a long time earlier I had wondered how to write a program that displays an analog clock… The connection to right-angled triangles was revealed to me only later, although in retrospect they are obviously two sides of the same coin.

cellular 7y ago
I made a whiteboard robot to teach/experiment those equations. It's fun to fill a whiteboard with patterns and let people wonder how they were made: https://sites.google.com/view/wbr https://sites.google.com/view/wbr
lakkal 7y ago
That's my story, too - learned about sine and cosine by playing around with plotting the results in Applesoft Basic. Wasn't until the following year that I learned what they're for in Trigonometry class.

cmroanirgo 7y ago

I remember making a simple inlined asm function that called a little known x87 function fsincos that returns the sine and cosine of an angle. I seem to remember that it only took a few extra clock cycles to get both answers. This was really helpful when building matrices (in the mid '90s).

acollins1331 7y ago

What an interesting and strange childhood you must have had to be writing games in Pascal before you heard about cosine. Either your schooling was great or terrible!

CodeMage 7y ago
Maybe it's not the schooling. I went through a similar experience, because I started programming when I was 7 years old. By the time I had learned enough to want to try to make a game, I had taught myself Turbo Pascal, but I still wasn't of an age to learn trigonometry in school.
bayesian_horse 7y ago
I had undiagnosed ADHD and was bullied all throughout my school years. So I had plenty of time. And it really doesn't take much to learn programming in class 5 or 6... I believe my teachers were pretty good, overall. At least as good as can be expected.
- acollins1331 7y ago
  The first sentence is the same for me but to just pick up programming when you're 11 or 12 by yourself seems crazy! I'm sure you had a mentor or an older friend or some adult that at least exposed you to the concept.
  - bayesian_horse 7y ago
    I remember vaguely a course on Basic on Amigas. But other than that, I didn't really have mentors or peers. I believe I learnt QBasic from a book, later Turbo Pascal from another book and assembly from yet another.
    - acollins1331 7y ago
      That would probably have been enough to spark my creativity. We had a class on using word and powerpoint and typing in grade 8. America is GREAT /s

deleted 7y ago

[deleted]

ben7799 7y ago

Denthor of Asphyxia! I didn't remember what it was by read those back in the early 90s as well, learning to program on a 486 with an early SVGA card. I think I downloaded them on a trial of AOL, my parents wouldn't/couldn't pay for AOL but I sucked all those tutorials down when I had a chance. I was taking Pascal in school but learned a ton more from those tutorials. I wrote an asteroids type game and got tons of eye rolls from the teacher as the other students were playing my game after I shared the source. I had done the whole years curriculum in a month or two and then sat there and wrote games in class. The teacher didn't really care as I'd just about matched his knowledge by the middle of the year. He was a great teacher, had a PhD in math which was pretty darn rare for high school. Those tutorials had a significant effect on my chosen career path.

teamonkey 7y ago

I ended up deriving sin and cos myself. I was trying to make a Spacewar-style game and knew I needed to make the ship move depending on how it was rotated. Plotted a circle on squared paper and tried to figure out the coordinates at the circumference for all the angles I was using. Quite a surprise when I was finally introduced to trig at school and found out it had a name!

xamuel 7y ago
I was utterly confused by trigonometry in junior high, it seemed to be some kind of secret language I had missed the sacred initiation rites into. And everyone seemed to treat it as exactly that--meaningless esoterica. And then one day someone explained the high-level point to me: "Of the six quantities of a triangle (three angles and three sides), given any three of them, at least one of which is a side, the other three are automatically nailed down." Suddenly a switch was flipped. After that, the rest is just details that write themselves.
SamBam 7y ago
Indeed, anytime I move something on the screen at an angle for a distance, I have to do a quick check to remember whether the horizontal distance is sin or cos. I do this probably half a dozen times a month. (I'm not a quick learner.) I was kind of surprised that the article used circular motion as its main motivating point, since I feel like just moving at some angle is so much more common.

CodeMage 7y ago

Wow, that takes me back down the nostalgia lane! Denthor's tutorials, PCGPE, Ralf Brown's Interrupt List...