A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.
Its not really that physical, haven’t read the article but the way “dimensions” are used is best explained via algebra:
Say you have a formula x=6, you can visualise the value on a number line from 0 to 10, with a little mark at the 6. That’s one dimension, a line.
Bringing the next dimension in you can add a new variable/unknown like y. Given the formula x-y=6, often formatted as y=x-6, you can now visualise the value or the solution with a graph, the number line for x horizontally and y vertically (2D). Now instead of marking a dot on the number line you draw a line through the graph where y=x-6, e.g at coordinates (x=6,y=0).
In a similar way you can add a variable z, which you can draw as a new line perpendicular to the other two, turning the plane into a three dimensional space with 3 number lines, one for each variables.
This is where things get complicated, you add the fourth variable, bringing things into the fourth dimension. As you eluded to, it can sometimes be represented as time, so the contents of the 3D space from before can change with time, a bit harder to imagine but think of the new 4th dimension of time as being a slider like on a video player, dragging it around to “play the video” in the other three dimensions. Instead of the 4th dimension being time though, you can also think of it as another number line added to the graph with the other 3, the problem is that it’s impossible to visualise, we can’t draw a fourth line perpendicular to the other three. So we just say its there and keep solving the algebra as if it was there.
That’s the basics anywho, theres a bunch of material online, both text and videos if you wanna dive further, khan academy being a good place to start, or maybe brilliant.org.
Its not really that physical, haven’t read the article but the way “dimensions” are used is best explained via algebra:
Say you have a formula x=6, you can visualise the value on a number line from 0 to 10, with a little mark at the 6. That’s one dimension, a line.
Bringing the next dimension in you can add a new variable/unknown like y. Given the formula x-y=6, often formatted as y=x-6, you can now visualise the value or the solution with a graph, the number line for x horizontally and y vertically (2D). Now instead of marking a dot on the number line you draw a line through the graph where y=x-6, e.g at coordinates (x=6,y=0).
In a similar way you can add a variable z, which you can draw as a new line perpendicular to the other two, turning the plane into a three dimensional space with 3 number lines, one for each variables.
This is where things get complicated, you add the fourth variable, bringing things into the fourth dimension. As you eluded to, it can sometimes be represented as time, so the contents of the 3D space from before can change with time, a bit harder to imagine but think of the new 4th dimension of time as being a slider like on a video player, dragging it around to “play the video” in the other three dimensions. Instead of the 4th dimension being time though, you can also think of it as another number line added to the graph with the other 3, the problem is that it’s impossible to visualise, we can’t draw a fourth line perpendicular to the other three. So we just say its there and keep solving the algebra as if it was there.
That’s the basics anywho, theres a bunch of material online, both text and videos if you wanna dive further, khan academy being a good place to start, or maybe brilliant.org.