So this reminds me of something that has always intrigued me. Historically in the USA and much of Asia, video was always presented at 29.97 frames per second... or you could say "sides" of a visual moment. Film and most video in other parts of the world was always presented at 24 frames per second because it gave a more artistic look (often described as"cinematic") though broadcast format capabilities had something to do with it (NTSC vs PAL). But that has shifted over time as things went from analog to digital and most entertainment anywhere in the world is now presented at 24 fps. but formatted for 60p (it gets super techy but it's kind of a side point in what I'm getting at). Except sports and news, which are now often presented at approximately 60 fps. And surveillance camera footage. Objectively, 60 fps is the most accurate to how humans perceive motion, but our brain appreciates the feel of 24 fps more on an enjoyment level. And most, except me, think 60 fps is great for sports and news. I almost always prefer the more cinematic look in about anything I watch, except maybe security camera footage. But I'm weird. Or maybe I'm not, but this is how video is presented much like your circle example if you were to compare "uncircles" made of 24, 29.97, and 60 sides. I don't really have a question, but I think this "less is more for the brain's perception" idea is really interesting.
Yeah, I've been really interested in this phenomenon as well, but more from a consumer's perspective. Hearing it from someone who has worked extensively in the industry helps clarify what's going on.
I feel the same way, for what it's worth. The super duper fast frames are just awful for TV shows and movies, IMO. I prefer a slower moving picture.
I think the actual max number of what even registers with the brain is like 57.78 fps or something, but engineers gonna engineer I guess lol. But how our brain interprets things is a completely different scale I think. I think the minimum speed for our brain to turn separate images into motion is like 16 fps. Could be an interesting dive for you.
It also kinda reminds me of hearing about people in between 1930 and 1970 mostly dreamed in B&W. Color before and after with the thought that entertainment influenced our brains for dreams. We are watching “head movies” like Simple Jack spoke of so beautifully.
Upon seeing the word "100-sided Polygon," thousands of D&D fans cried out in unison, imagining in horror what the die version of that would look like.
I used to be pretty good at math in school / high-school, although I opted to take mid-level math during my International Baccalaureat to instead take high level Economics and Physics, from what I remember.
Well, I guess I liked economics enough to go on to finish a B. Sc. in Internatioinal Business and then M. Sc. in International Marketing & Management at the Copenhagen Business School. That is to say, not a whole lot.
As for physics, it's all very hazy now, but I recall being pretty good at all the lab assignments and reports. I did (and still do) enjoy understanding how the world works, but most of the details are buried deep inside my head now, under layers of random computer game and TV show trivia.
I think I was exposed to the wonder of physics at a young age. My dad's strongest subjects were math and science, and I probably watched Sagan's Cosmos on TV at some point as a young'un. We would also enjoy stuff like Star Trek together, so it was one of those areas where my dad and I could kind of enjoy thinking together a little bit. I'm sure that helped.
Economics, by contrast, is endlessly fascinating to me today, but it certainly wasn't until maybe 10 years ago, and I've been down a pretty intense learning rabbit hole this past decade, just catching up.
Math never spoke to me. However, I am intrigued by the concept of Pi, which may have some connection to what you reference (circles and infinitesimals).
I do think pi is a great example of a need for infinitesimals! You can think of a circle as "about 3 diameters around", and that works to a degree, but then you need to take like a quarter of a diameter to make it all the way around. Then, you're a little too far, so you end up having to do all these very slight nudges.
In freshman calculus, as we all gathered in a big hall collectively emoting dread for the final, my professor told a joke to break the tension: Why should’ve you sit between twins on the calculus final? Because you won’t be able to differentiate between them.
Why *shouldn’t*. Yeah the diff between loving a subject and hating it, learning a subject or not, comes down to how good the teacher is. And to answer your question - no I never understood calculus.
Does the idea of infinitesimals help a bit? To my understanding, what I have described is at least the nucleus of calculus. There's a bit more to it, of course, but if you get the idea of incrementally smaller slices that never really add up to wherever you're going (but kind of do), I think you have way more than I had when I was a math whiz.
It does help. After I dumped physics for computer science I didn't have much use for calculus, so I just carry that joke with me and trust the science.
Here's another adjunct calculus joke from a great English teacher I had in high school. He wanted us to understand how sex sells and showed us an advert with a chalkboard visual. It was covered with mathematical formulas reflecting the science behind some great product and there was a prominent, yet small integral of e to the x in the corner which spells ... well you know.
So this reminds me of something that has always intrigued me. Historically in the USA and much of Asia, video was always presented at 29.97 frames per second... or you could say "sides" of a visual moment. Film and most video in other parts of the world was always presented at 24 frames per second because it gave a more artistic look (often described as"cinematic") though broadcast format capabilities had something to do with it (NTSC vs PAL). But that has shifted over time as things went from analog to digital and most entertainment anywhere in the world is now presented at 24 fps. but formatted for 60p (it gets super techy but it's kind of a side point in what I'm getting at). Except sports and news, which are now often presented at approximately 60 fps. And surveillance camera footage. Objectively, 60 fps is the most accurate to how humans perceive motion, but our brain appreciates the feel of 24 fps more on an enjoyment level. And most, except me, think 60 fps is great for sports and news. I almost always prefer the more cinematic look in about anything I watch, except maybe security camera footage. But I'm weird. Or maybe I'm not, but this is how video is presented much like your circle example if you were to compare "uncircles" made of 24, 29.97, and 60 sides. I don't really have a question, but I think this "less is more for the brain's perception" idea is really interesting.
Yeah, I've been really interested in this phenomenon as well, but more from a consumer's perspective. Hearing it from someone who has worked extensively in the industry helps clarify what's going on.
I feel the same way, for what it's worth. The super duper fast frames are just awful for TV shows and movies, IMO. I prefer a slower moving picture.
We are old.
Interesting to know 60fps is whats most natural. I just always figured the more fps the better - like most things tech - but I forgot about our brains
I think the actual max number of what even registers with the brain is like 57.78 fps or something, but engineers gonna engineer I guess lol. But how our brain interprets things is a completely different scale I think. I think the minimum speed for our brain to turn separate images into motion is like 16 fps. Could be an interesting dive for you.
I prefer to think I have refined tastes. 🤣
Good point. We learned taste back when it was a thing.
It also kinda reminds me of hearing about people in between 1930 and 1970 mostly dreamed in B&W. Color before and after with the thought that entertainment influenced our brains for dreams. We are watching “head movies” like Simple Jack spoke of so beautifully.
https://youtu.be/nuh01mBMOtg?si=FTr07_pzLQfO3Nv0
Upon seeing the word "100-sided Polygon," thousands of D&D fans cried out in unison, imagining in horror what the die version of that would look like.
I used to be pretty good at math in school / high-school, although I opted to take mid-level math during my International Baccalaureat to instead take high level Economics and Physics, from what I remember.
How did you like the economics stuff? And, what sort of physics did you study in school?
Well, I guess I liked economics enough to go on to finish a B. Sc. in Internatioinal Business and then M. Sc. in International Marketing & Management at the Copenhagen Business School. That is to say, not a whole lot.
As for physics, it's all very hazy now, but I recall being pretty good at all the lab assignments and reports. I did (and still do) enjoy understanding how the world works, but most of the details are buried deep inside my head now, under layers of random computer game and TV show trivia.
I think I was exposed to the wonder of physics at a young age. My dad's strongest subjects were math and science, and I probably watched Sagan's Cosmos on TV at some point as a young'un. We would also enjoy stuff like Star Trek together, so it was one of those areas where my dad and I could kind of enjoy thinking together a little bit. I'm sure that helped.
Economics, by contrast, is endlessly fascinating to me today, but it certainly wasn't until maybe 10 years ago, and I've been down a pretty intense learning rabbit hole this past decade, just catching up.
Math never spoke to me. However, I am intrigued by the concept of Pi, which may have some connection to what you reference (circles and infinitesimals).
Yes, “The Devil is in the details, but so is salvation.” ―Hyman G. Rickover
I do think pi is a great example of a need for infinitesimals! You can think of a circle as "about 3 diameters around", and that works to a degree, but then you need to take like a quarter of a diameter to make it all the way around. Then, you're a little too far, so you end up having to do all these very slight nudges.
In freshman calculus, as we all gathered in a big hall collectively emoting dread for the final, my professor told a joke to break the tension: Why should’ve you sit between twins on the calculus final? Because you won’t be able to differentiate between them.
My high school calculus teacher used humor to teach as effectively as I've ever seen it done. I was super duper lucky to be in his class.
Why *shouldn’t*. Yeah the diff between loving a subject and hating it, learning a subject or not, comes down to how good the teacher is. And to answer your question - no I never understood calculus.
Does the idea of infinitesimals help a bit? To my understanding, what I have described is at least the nucleus of calculus. There's a bit more to it, of course, but if you get the idea of incrementally smaller slices that never really add up to wherever you're going (but kind of do), I think you have way more than I had when I was a math whiz.
It does help. After I dumped physics for computer science I didn't have much use for calculus, so I just carry that joke with me and trust the science.
Here's another adjunct calculus joke from a great English teacher I had in high school. He wanted us to understand how sex sells and showed us an advert with a chalkboard visual. It was covered with mathematical formulas reflecting the science behind some great product and there was a prominent, yet small integral of e to the x in the corner which spells ... well you know.
That's a terrible (but also great) joke! Ouch, and ha!
Makes me think of a certain circular orifice. Take your pick.