"Astronomers sometimes say that space is curved or that the universe is finite but unbounded
Whatever they're talking about...
And what's more, has witnessed a greeting coming from his insides
A voice from within
He surely is getting a little worried about his sanity
The three dimensional creature is unhappy about being considered a psychological aberration
And so he descends to actually enter Flatland
But the three dimensional creature exists in Flatland only partially
Only a plane, a cross-section through him can be seen
So, when the three dimensional creature first reaches Flatland
It's only the points of contact which can be seen
Well, represent that set of objects who mysteriously appear from nowhere inside a closed room
And change their shape dramatically
His only conclusion could be that he's gone bonkers
Well, the apple might be a little annoyed of this conclusion, so
We imagine our universe to be flat in three dimensions but maybe it's curved into a fourth
We can talk about a fourth dimension but we can't experience it
But maybe more interesting is the other direction in dimensionality
What about the fourth dimension? To touch that let's consider a cube
Now if we look at the shadow of a three dimensional object in two dimensions
We see that in this case not all the lines appear equal, not all the angles are right angles
A three dimensional object has not been perfectly represented in its projection in two dimensions
But that's part of the cost of losing a dimension in the projection
Now let's take this three dimensional cube and project it through a fourth physical dimension
Not that way... But at right angles to those three directions
I can't show you what direction that is but imagine that there's a physical fourth dimension
In that case we would generate a four dimensional hypercube which is also called a tesseract
I cannot show you a tesseract because I and you are trapped in three dimensions
But what I can show you is the shadow in three dimensions of a four dimensional hypercube or tesseract This is it!
And now the real tesseract in four dimensions would have all the lines of equal lenght
And all the angles right angles.
That's not what we see here but that's the penalty of projection"
Madame Spectrum - The Penalty of Projection Lyrics
Madame Spectrum - The Penalty of Projection Lyrics
Official
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"Astronomers sometimes say that space is curved or that the universe is finite but unbounded
Whatever they're talking about...
And what's more, has witnessed a greeting coming from his insides
A voice from within
He surely is getting a little worried about his sanity
The three dimensional creature is unhappy about being considered a psychological aberration
And so he descends to actually enter Flatland
But the three dimensional creature exists in Flatland only partially
Only a plane, a cross-section through him can be seen
So, when the three dimensional creature first reaches Flatland
It's only the points of contact which can be seen
Well, represent that set of objects who mysteriously appear from nowhere inside a closed room
And change their shape dramatically
His only conclusion could be that he's gone bonkers
Well, the apple might be a little annoyed of this conclusion, so
We imagine our universe to be flat in three dimensions but maybe it's curved into a fourth
We can talk about a fourth dimension but we can't experience it
But maybe more interesting is the other direction in dimensionality
What about the fourth dimension? To touch that let's consider a cube
Now if we look at the shadow of a three dimensional object in two dimensions
We see that in this case not all the lines appear equal, not all the angles are right angles
A three dimensional object has not been perfectly represented in its projection in two dimensions
But that's part of the cost of losing a dimension in the projection
Now let's take this three dimensional cube and project it through a fourth physical dimension
Not that way... But at right angles to those three directions
I can't show you what direction that is but imagine that there's a physical fourth dimension
In that case we would generate a four dimensional hypercube which is also called a tesseract
I cannot show you a tesseract because I and you are trapped in three dimensions
But what I can show you is the shadow in three dimensions of a four dimensional hypercube or tesseract This is it!
And now the real tesseract in four dimensions would have all the lines of equal lenght
And all the angles right angles.
That's not what we see here but that's the penalty of projection"
Whatever they're talking about...
And what's more, has witnessed a greeting coming from his insides
A voice from within
He surely is getting a little worried about his sanity
The three dimensional creature is unhappy about being considered a psychological aberration
And so he descends to actually enter Flatland
But the three dimensional creature exists in Flatland only partially
Only a plane, a cross-section through him can be seen
So, when the three dimensional creature first reaches Flatland
It's only the points of contact which can be seen
Well, represent that set of objects who mysteriously appear from nowhere inside a closed room
And change their shape dramatically
His only conclusion could be that he's gone bonkers
Well, the apple might be a little annoyed of this conclusion, so
We imagine our universe to be flat in three dimensions but maybe it's curved into a fourth
We can talk about a fourth dimension but we can't experience it
But maybe more interesting is the other direction in dimensionality
What about the fourth dimension? To touch that let's consider a cube
Now if we look at the shadow of a three dimensional object in two dimensions
We see that in this case not all the lines appear equal, not all the angles are right angles
A three dimensional object has not been perfectly represented in its projection in two dimensions
But that's part of the cost of losing a dimension in the projection
Now let's take this three dimensional cube and project it through a fourth physical dimension
Not that way... But at right angles to those three directions
I can't show you what direction that is but imagine that there's a physical fourth dimension
In that case we would generate a four dimensional hypercube which is also called a tesseract
I cannot show you a tesseract because I and you are trapped in three dimensions
But what I can show you is the shadow in three dimensions of a four dimensional hypercube or tesseract This is it!
And now the real tesseract in four dimensions would have all the lines of equal lenght
And all the angles right angles.
That's not what we see here but that's the penalty of projection"
Writer: Carl Sagan
Copyright: Lyrics © O/B/O DistroKid
Copyright: Lyrics © O/B/O DistroKid