lmao i was just about to comment that

"... i don't fucking care what happens when you turn a figure 8 into a circle, i don't give a flying fuck about avoiding sharp bends, why are you avoiding me? ..."

*way too nerdy

@@SweetRollTheif **squints** thats a typo

I mean. With a healthy dose of vsauce and… apparently huggbees? Im pretty sure ive become omnipotent

@@simpli_A ahhhhhhhhhhh AHHHHHHH *AHHHHHHHHHHHHH* OMNIPOTENTENCE HAS BEEN ACHIEVED

It had to have been an accident lmao

what about megacube? or even rampagecube

And a supercube for 6-cubes.

No

@@ThoughtThrill365you have a great voice!

Your subjective view of complexity does not necessarily correspond with everyone else's. I imagine the average person on the street can't even tell you what a tesseract, a hypercube, or a polytope is.

I'm glad you injected your comment with unnecessary vulgarity for absolutely no reason, all in favor of your unabashed display of wrongness. All the other middle schoolers think you are very cool. Anyway, this is not the standard definition of dimension in mathematics. In order to understand that definition, we have to think about degrees of freedom. Imagine a space consisting only of the points on a line. Now, imagine a creature living within this space. It's all they've ever known, just like our universe is the only space we've ever known. If the creature can move forward and backward within this space, how many directions do they need to be able to face in order to freely traverse the space? Of course, the answer is 1. So the number of degrees of freedom in this space is 1, meaning the line has dimension 1. Alright, so now, imagine a space consisting only of the points on a circle, the set of points a given distance from a given center point in 2-dimensional Euclidean space. Imagine a creature living within this space. If they can move forward and backward within this space, how many directions do they need to be able to face in order to freely traverse the space? Once again, the answer is 1, since that's all you need to be able to get anywhere you want along the circle. So the number of degrees of freedom in this space is 1, meaning the circle has dimension 1. It's a bit of an unusual space, since you can loop back on yourself by just continuously walking forward within it, but it's a valid space nonetheless. We can keep going with other objects. A plane has dimension 2. A disk, the plane region enclosed by a circle, also has dimension 2. A sphere, the set of all points a given distance form a given point in 3-dimensional Euclidean space, has dimension 2-imagine traversing the surface of Earth, except that the surface is actually its own space that you're inhabiting. Of course, this definition admits only nonnegative integers as dimension numbers. However, an extended definition comes from the measure of objects. Just like a line segment, scaling the distances in a circle by a factor of s scales its measure (in this case, its length, or circumference) by a factor of s. The same is true of every other object of dimension 1. This is not a coincidence; it's just how dimension, scaling, and measure work. Similarly, scaling an object of dimension 2 by a factor of s scales its measure (in this case, its area) by a factor of s^2. In general, if an n-dimensional object is scaled by a factor of s, its measure is scaled by a factor of s^n. This is the motivation behind the definition of Hausdorff dimension. If you feel personally offended by this, as you seem to be, I recommend looking yourself in the mirror and asking yourself why this is how you are spending your life.

XD

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