Continua are a good start, but you realize that's only one-dimensional, right? That leaves at least 2 or three just to catch up to physical dimensionality as we commonly think of it.
What would be some analogs to 2-, 3-, and 4-dimensional thinking?
Well, three points determine a plane, so triangulation would be a 2-D example.
An application of triangulation when considering an issue A would be to listen to (genuinely) and understand (from their proponents' perspectives) the ¬A narratives, the †A narratives, and the neutral/undecided narratives BEFORE coming to one's own conclusion. ("¬" = negation, "†" = affirmation, per https://en.wikipedia.org/wiki/List_of_logic_symbols -- but personally, I don't speak symbolese, lol.)
Four points define a 3-D coordinate system (width, height, depth) within a 4-D "space". Think of it like a 22nd Century version of a pad of Post-It notes capable of static 3-D renderings that you flip through to give the illusion of 3-D objects in motion. Or for that matter, a hologram that is a series of 2-D images projected onto a 3-D medium to give the illusion of 3-D objects in motion.
This implies the element of time, which has often been called the fourth dimension. But then what about motion?
A rock lying on the ground that someone picks up and throws at your head at 60 MPH (unless you're an athlete, that's about all you'd be able to manage) is the same rock, but considering the consequences those two different *velocities*, it might as well be two different rocks. Or, let's say the rock-thrower is a really bad aim. Again, a *trajectory* that will hit your head is worlds apart from a trajectory that would miss -- even if it's only by an inch.
That's a pretty big oversight, given that nothing we know of exists statically. Everything but everything is in motion.
Notice that even our most sophisticated disciplines -- even the ones that study trajectory and velocity -- do not incorporate velocity or trajectory or even recognize them *in their methodologies used as the means to study them*. In other words, before thinking about *anything*, even our premiere thinkers first translate their objects of study into static terms (which is what calculus does) and then analyze the freeze-frames. There's nothing wrong with that, but since that's all we've ever done (so far), it has left us with the impression that it's all that could ever be done. Any decent logic freshman could point out the problem in that assumption.
I'm neither mathematician nor "hard" scientist, but I dabble enough to satisfy my needs. I'm a sociologist whose interests bring me to these musings from the people side, trying to understand how we think and feel and interrelate/interact; and part of that is to identify the context and boundaries for those phenomena, and then to imagine to where we could expand them and how we could manage to do it.
Hmm... This is really interesting and I haven't ever thought about issues along anything other than 2 dimensions. Certainly, in college, I was forced to consider issues that might be more complex than triangulation, but still 2-D nonetheless. Let me try to apply 3-D and 4-D to the issue of gun control and see where it goes....
2-D: Thinking about the pros and cons of gun control and considering policies that range from a strict ban to an unregulated free market for guns. Looking at all of these policies is like examining the freeze-frames around the issue.
3-D: To get to 3-D maybe you consider time and how these policies will evolve or affect our country's future and how the past has affected how we see the issue today.
4-D: It's interesting for me to think about trajectory as a factor to consider in these decisions, but how is this not just another point to consider in 2-D "space"? This is fascinating but difficult for me to conceptualize as it applies to a real-world problem.
Yeah, just thinking out loud here too. Velocity/trajectory involve something that 3-D alone does not: not just the element of time but change over time resulting in relative motion, which entail velocity/trajectory. A 3-D space need not involve motion or time.
Continua are a good start, but you realize that's only one-dimensional, right? That leaves at least 2 or three just to catch up to physical dimensionality as we commonly think of it.
What would be some analogs to 2-, 3-, and 4-dimensional thinking?
I don't know, but I'm super curious to know if you have any ideas!
Well, three points determine a plane, so triangulation would be a 2-D example.
An application of triangulation when considering an issue A would be to listen to (genuinely) and understand (from their proponents' perspectives) the ¬A narratives, the †A narratives, and the neutral/undecided narratives BEFORE coming to one's own conclusion. ("¬" = negation, "†" = affirmation, per https://en.wikipedia.org/wiki/List_of_logic_symbols -- but personally, I don't speak symbolese, lol.)
Four points define a 3-D coordinate system (width, height, depth) within a 4-D "space". Think of it like a 22nd Century version of a pad of Post-It notes capable of static 3-D renderings that you flip through to give the illusion of 3-D objects in motion. Or for that matter, a hologram that is a series of 2-D images projected onto a 3-D medium to give the illusion of 3-D objects in motion.
This implies the element of time, which has often been called the fourth dimension. But then what about motion?
A rock lying on the ground that someone picks up and throws at your head at 60 MPH (unless you're an athlete, that's about all you'd be able to manage) is the same rock, but considering the consequences those two different *velocities*, it might as well be two different rocks. Or, let's say the rock-thrower is a really bad aim. Again, a *trajectory* that will hit your head is worlds apart from a trajectory that would miss -- even if it's only by an inch.
That's a pretty big oversight, given that nothing we know of exists statically. Everything but everything is in motion.
Notice that even our most sophisticated disciplines -- even the ones that study trajectory and velocity -- do not incorporate velocity or trajectory or even recognize them *in their methodologies used as the means to study them*. In other words, before thinking about *anything*, even our premiere thinkers first translate their objects of study into static terms (which is what calculus does) and then analyze the freeze-frames. There's nothing wrong with that, but since that's all we've ever done (so far), it has left us with the impression that it's all that could ever be done. Any decent logic freshman could point out the problem in that assumption.
I'm neither mathematician nor "hard" scientist, but I dabble enough to satisfy my needs. I'm a sociologist whose interests bring me to these musings from the people side, trying to understand how we think and feel and interrelate/interact; and part of that is to identify the context and boundaries for those phenomena, and then to imagine to where we could expand them and how we could manage to do it.
Hmm... This is really interesting and I haven't ever thought about issues along anything other than 2 dimensions. Certainly, in college, I was forced to consider issues that might be more complex than triangulation, but still 2-D nonetheless. Let me try to apply 3-D and 4-D to the issue of gun control and see where it goes....
2-D: Thinking about the pros and cons of gun control and considering policies that range from a strict ban to an unregulated free market for guns. Looking at all of these policies is like examining the freeze-frames around the issue.
3-D: To get to 3-D maybe you consider time and how these policies will evolve or affect our country's future and how the past has affected how we see the issue today.
4-D: It's interesting for me to think about trajectory as a factor to consider in these decisions, but how is this not just another point to consider in 2-D "space"? This is fascinating but difficult for me to conceptualize as it applies to a real-world problem.
Yeah, just thinking out loud here too. Velocity/trajectory involve something that 3-D alone does not: not just the element of time but change over time resulting in relative motion, which entail velocity/trajectory. A 3-D space need not involve motion or time.