1. I've just about used up every 125 x 125 Hayley Williams avatar out there and have thus been constricted to using this prehistoric size.
2. I really love the feel of those flat mac keyboards. They feel so good and every time I use one, I just want to type and type. Not to mention, the amount of typos I make with them is reduced by 77% because of how smooth they are. I wish I had on right now.
3. OK so hm
ok so.
so like
uh let's start off with this:
In a 3 dimensional world, there are 3 dimensions. We call the first dimension length; the second, width; and the third, depth. It doesn't matter so much as what we call them, we just use these words to describe the number of dimensions. Really the first dimension could be called 'depth' and the second and third 'length' and 'width'. It's just simply more efficient to maintain consistency and so we refer to the 1st, 2nd, and 3rd dimensions as length, width, and depth. Therefore, when I state that an object has depth, it must follow that it has length and width as well. Fore you cannot have a third dimension without the first and second.
In a 2 dimensional world, there are 2 dimensions: Length and Width.
In a 1 dimensional world, there is 1 dimension: Length. (As mentioned earlier, we could also refer to this dimension as width or depth, but for consistency we refer to a single dimension as length).
Now then let's talk about the perceptions of beings inhabiting each of these dimensional worlds:
In the third dimension, a being may observe the 2 dimensional world in its fullest. That is, a third-dimensional being is able to fully observe a world that exist solely on Length & Width. We, as 3rd-dimensional beings are able to view 2-dimensional worlds.
We are able to observe them to their fullest. However, how does a 2-dimensional being perceive its own world? Well, while they live in a 2-dimensional world, they are only able to see 1 dimension. Let is use the same picture as before. How would the two stick figures looking at each other, perceive each other? Something like this.
(It is, however, impossible for us 3 dimensional beings to fully image what a single dimension would like like, as we ourselves have never perceived such. The example above still contains width so it is not a perfect representation of a single dimension/2-dimensional perspective).
(The closest we can get to imagining the single dimension is by imagining the width infinitely getting smaller).
(By our 3-dimensional way of "seeing", a single dimension would appear invisible to us).
Now then, let's move onto a single dimensional world and attempt to apply the relationships found between the 3-dimensional world and a 2-dimensional world to that of the 2-dimensional world and a 1-dimensional world. We found that a 3rd-dimensional being is able to fully observe the 2-dimensional world. It would follow then, that a 2-dimensional being would be able to fully observe the 1-dimensional world. A 1-dimensional being itself would not even be able to observe any aspect of its dimension at all! From the 3-D to 2-D relationship we found that a being can observe
M-1 (M minus 1) dimensions, where 'M' is the number of dimensions the being itself exists in. Therefore, a 1-D being would be able to observe 1 minus 1 dimensions. That is, 0, or no dimensions.
But wait, this can't be right. We are 3-Dimensional beings. Don't we perceive OUR world in 3-D, not 3-1=2 dimensions? The answer is no. We are unable to fully perceive our own 3-dimensional world. At any given time, we are only able to to fully view 2 dimensions at once. This concept is hard to grasp at first. It appears that we do observe our 3 dimensional world. But let us again look to the dimensional world. In the picture of the two stick figures above, is there any part of the figures that we cannot see at any given time? No, we are able to fully perceive them from every side they have: their length and their width. We see everything they are made up of. No matter how hard we try however, there is no 3 dimensional object, no matter how small, that we are able to fully see every side, that is, every dimension at once.
4th-Dimension
From the pattern thus far then, we would gather that it would take a 4th dimensional being to be able to observe the 3rd dimension in its fullest. That is, In the fourth dimension all sides of a 3-dimensional figure would be able to be observed at once! In a 4th-dimensional world, one would see the front of a 3-D figure's face and the back of their head along with the sides of their head all at one time!
So then, what does the fourth dimension look like? Well, we can't even fully observe our own 3-D world, nonetheless a 4-D world. Here is the closest we can get to imagining such.
The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.
Some Questions I've been thinking about
As a 3-D being we are unable to image the view of a 2-D being or 1-D being. Would a 4-D being thus not be able to imagine the perspective of a 3-D being or less?
