A Newtonian physics simulator simulates infinitely small conceptual points and/or quantum-cubes in an euclidean space at fixed positions. Not “billiard balls”, AFAIK. I’ve always found the “balls” concept supremely absurd and immediately assumed they were talking about conceptual zero-space point entities.
Otherwise, it seemed very inconsistent to me that the smallest indivisible pieces of reality would have a measurable curved surface and measurable volume (whether physically possible to make these measurements or not). The idea of anything statically perfectly circular or spherical existing in nature was, to my young 13-year-old-mind, obviously inconsistent with the idea that the shortest possible route between two points is a line and that pi happens to be an irrational number (“I mean, infinitely non-regular! How the hell could that happen an infinite amount of times for each surface of a potential infinity of tiny objects bouncing around?!”, would I have said back then). It also seemed like it would fuck up gravity somehow, though I can’t recall the exact train of thought I had back then.
Of course, this is just for the “billiard balls” thing. I agree that it was (and still is in some cases) a very useful model and even the balls make it simpler to explain because it is simplex to most human minds, so on that part I think it’s a fair example. I would, however, have been thoroughly surprised and shaken to learn that it was truly how-things-are that there were tiny literal spheres/balls moving about, rather than conceptual concentrations that represent zero-volume points in space.
A Newtonian physics simulator simulates infinitely small conceptual points and/or quantum-cubes in an euclidean space at fixed positions. Not “billiard balls”, AFAIK. I’ve always found the “balls” concept supremely absurd and immediately assumed they were talking about conceptual zero-space point entities.
How old were you when you learned this part of science? I got the “billiard ball” diagram and analogy when I was fairly young, before I knew a whole lot of science, or the art of questioning what my teacher told me. Looking back, it seems implausible to me to ever “immediately assume” she was talking about “conceptual zero-space point entities”.
After all, isn’t that one reason why some biases and mental images are so hard to grow past? They help form our basis of reality, they’re working deep in our understanding and aren’t easily rooted out just because we’ve updated some aspects of our thinking.
I learned about the actual atomic model, what with how atoms form molecules and all the standard model descriptions, fairly late. I can’t remember the age, but I had already fully learned arithmetic and played a lot with real numbers, and the number zero being what it is, I had already spent a fair amount of time philosophizing over “the nature of nothingness” and what a true zero might really represent, and come to the conclusion that there’s an infinity of “zero” numbers in-between any nonequal real numbers, and as applied to geometry this would translate to an infinity of infinitely small points.
Before learning the actual model as described in classrooms, all my knowledge of atoms came from hearsay and social osmosis and modern culture and various popular medias (TV, pop-sci magazines, etc.)
All I remember was that I had already been told atoms were “the tiny lego blocks of the world” and “so infinitely tiny that they’re impossible to see no matter how big a microscope you make”. From the terms “infinitely”, “tiny”, “impossible”, and “blocks”, and armed with my knowledge about zero applied to geometry, I found natural to infer that the tiny building blocks of the smallest possible size were tiny zero-space points that only have “position” by way of somehow “measuring” their relative distance to other tiny zero-space points. Now that I think about it, that “measuring” term was my first-ever use of a mental placeholder for “THIS IS MAGIC, I HAVE NO IDEA HOW IT WORKS! LET’S DO SCIENCE!”
In retrospect, spending so much time thinking philosophically about the “zero” number and the careless wordings of those that told me about the Atomic Model are probably what made me think this way.
Thanks for sharing. I’m going to have to spend a while trying to envision how that kind of upbringing and pacing would change the way I currently view the world and learn. It certainly seems different from my own. ^_^
A Newtonian physics simulator simulates infinitely small conceptual points and/or quantum-cubes in an euclidean space at fixed positions. Not “billiard balls”, AFAIK. I’ve always found the “balls” concept supremely absurd and immediately assumed they were talking about conceptual zero-space point entities.
Otherwise, it seemed very inconsistent to me that the smallest indivisible pieces of reality would have a measurable curved surface and measurable volume (whether physically possible to make these measurements or not). The idea of anything statically perfectly circular or spherical existing in nature was, to my young 13-year-old-mind, obviously inconsistent with the idea that the shortest possible route between two points is a line and that pi happens to be an irrational number (“I mean, infinitely non-regular! How the hell could that happen an infinite amount of times for each surface of a potential infinity of tiny objects bouncing around?!”, would I have said back then). It also seemed like it would fuck up gravity somehow, though I can’t recall the exact train of thought I had back then.
Of course, this is just for the “billiard balls” thing. I agree that it was (and still is in some cases) a very useful model and even the balls make it simpler to explain because it is simplex to most human minds, so on that part I think it’s a fair example. I would, however, have been thoroughly surprised and shaken to learn that it was truly how-things-are that there were tiny literal spheres/balls moving about, rather than conceptual concentrations that represent zero-volume points in space.
There are ways to derive radii of elementary particles—I’m not sure to what extent classical physicists thought these numbers represented actual radii of actual spheres.
How old were you when you learned this part of science? I got the “billiard ball” diagram and analogy when I was fairly young, before I knew a whole lot of science, or the art of questioning what my teacher told me. Looking back, it seems implausible to me to ever “immediately assume” she was talking about “conceptual zero-space point entities”.
After all, isn’t that one reason why some biases and mental images are so hard to grow past? They help form our basis of reality, they’re working deep in our understanding and aren’t easily rooted out just because we’ve updated some aspects of our thinking.
I learned about the actual atomic model, what with how atoms form molecules and all the standard model descriptions, fairly late. I can’t remember the age, but I had already fully learned arithmetic and played a lot with real numbers, and the number zero being what it is, I had already spent a fair amount of time philosophizing over “the nature of nothingness” and what a true zero might really represent, and come to the conclusion that there’s an infinity of “zero” numbers in-between any nonequal real numbers, and as applied to geometry this would translate to an infinity of infinitely small points.
Before learning the actual model as described in classrooms, all my knowledge of atoms came from hearsay and social osmosis and modern culture and various popular medias (TV, pop-sci magazines, etc.)
All I remember was that I had already been told atoms were “the tiny lego blocks of the world” and “so infinitely tiny that they’re impossible to see no matter how big a microscope you make”. From the terms “infinitely”, “tiny”, “impossible”, and “blocks”, and armed with my knowledge about zero applied to geometry, I found natural to infer that the tiny building blocks of the smallest possible size were tiny zero-space points that only have “position” by way of somehow “measuring” their relative distance to other tiny zero-space points. Now that I think about it, that “measuring” term was my first-ever use of a mental placeholder for “THIS IS MAGIC, I HAVE NO IDEA HOW IT WORKS! LET’S DO SCIENCE!”
In retrospect, spending so much time thinking philosophically about the “zero” number and the careless wordings of those that told me about the Atomic Model are probably what made me think this way.
Thanks for sharing. I’m going to have to spend a while trying to envision how that kind of upbringing and pacing would change the way I currently view the world and learn. It certainly seems different from my own. ^_^