Yeah, the visualization is where I get hung up. Sounds like I need to stop that.
Given your response, is it fair to say time as the 4th dimension is just a sci-fi concoction?
Given your response, is it fair to say time as the 4th dimension is just a sci-fi concoction?
But "dimension" is something mathematical. I would say it doesn't quite make sense to say "is the fourth dimension time" in the same way as it wouldn't make sense to say "is the fifth an apple?" The same way that numbers can refer to different things in different contexts (including in the context of different scientific theories), dimensions can correspond to different things in different contexts. For example, statistics and machine learning heavily use "high dimensional" mathematics, but there the "dimensions" would correspond to different variables you are trying to predict or explain. E.g. if you were trying to predict chance of heart attack from 1000 different factors, then you would have 1000+1 total "dimensions," and in that case the "fourth dimension" might be "cigarettes smoked per week" (rather than time).
there's an old joke about a mathematician teaching an engineer about thirteen-dimensional spaces. "What do you think," the mathematician asks. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?"
"Well, it's not so hard. All I do is visualize the situation in arbitrary N-dimensional space and then set N = 13."
"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it."