It means just that, it is flat in four dimensions. It’s the middle ground between an open and a closed universe.
Those are closed, open and flat universes, respectively. To be clear, these are three-dimensional representations of four-dimensional objects.
A closed universe would eventually stop expanding and then start contracting.
An open universe would expand forever.
In a flat universe expansion would slow down, but never quite stop.
Watch this for more information.
I know about the proposed shapes of the universe. You’re saying that the universe is geometrically flat then say that the universe is non-Euclidean.
These are mutually exclusive terms.
What? You can’t even use Euclidean geometry to describe the earth… You know, a triangle on the earth’s surface not being 180° total and all that…
There’s a HD version of that lecture on YouTube somewhere… Forgot the link though. I like that guy.
“Flat” is a Euclidean term and, apparently, only exists in Euclidean geometry. If space is curved, then anything in it will exhibit this curve, even if it’s so gradual that it’s completely imperceptible. Therefore, “geometrically flat” cannot be used to describe the universe if the universe is non-Euclidean. In non-Euclidean space, you can have a closed triangle with two right angles, the interior angles adding up to greater than 180 degrees: Simply place two points on a globe’s equator and a third point on the pole and draw a line segment between them all and the two segments going to the pole will be at right angles to the segment on the equator, but both “parallel” lines will meet at the pole.
Flat and straight cannot exist in a non-Euclidean universe.
Euhm, yes it can. “Flat” is not a term reserved to Euclidean geometry, only your interpretation of it is.
It is four-dimensionally flat. The space-time continuum is geometrically flat. Euclidean geometry cannot make any statements about four-dimensional geometry. Ergo four-dimensionally flat is non-Euclidean by definition.
Also, there isn’t just “Euclidean geometry” and “non-Euclidean geometry”. Non-Euclidean can entail a range of geometry systems.
Also also, “you can have a closed triangle with two right angles” etc., I believe I just said that.
Btw, if you know about the proposed shapes of the universe, why are we arguing about this? A flat universe is one of the proposed shapes…
Yeah, I have it in my bookmarks, but the one I linked is more complete, because he ran out of time in the youtube one.
I know that a flat universe is one of the proposed shapes, but I don’t believe that the universe is shaped that way. See, the problem with 4-dimensional objects such as tesseracts is that they appear to ‘live’ in the world of mathematics alone and do not come into our 3-dimensional world. We know that 1D is a single dimensionless point dragged along (left-right) to create a line, 2D is that line dragged along (up-down) to create a square, and 3D is that square dragged along (in-out) to create a cube.
The fourth dimension, however, supposedly moves that cube along (???-???) to create a tesseract…but tesseracts have not been shown to exist in real life, have they? All “real life tesseracts” appear to only be a projection (much like a 3D projection on a 2D surface of a computer screen). What is that “along” direction?
The math might work, but is there evidence that a tesseract (or other 4th dimensional objects) exist? As I said, all representations of a tesseract are merely representations and it cannot be constructed…so, is it real?
Currently, our observational reality is reliant on all three dimension (up-down, left-right, in-out). A three-dimensional object can travel in three dimensions (I take my spindle of blank DVDs and slide it across the table), but is that the fourth dimension? I say no because it is simply moving in 3D space.
So, long story short (too late!), is there a such thing as a tesseract or 4D space?
Oh, and 1D and 2D space appears to also be simply a mathematical construct because there’s no such thing as a 2D object, right?
When I took a shitload of drugs I sort of started figuring it out, the universe doesn’t actually have a shape, and it wasn’t created just so that living things could see it, the universe exists to prove the logic that random non-existing numbers being used in equations with other random numbers create SPECIFIC numbers and the universe is calculating every possible combination forever, which results in data. non-logical data has a shorter equation so it disappears quickly, while other results like the cellular organism are always ongoing, with humanity absorbing information all the time, we could be effectively preventing the end of this particular chain of equations, where in another universe where life didn’t exist, all the calculations were done and it collapsed on itself.
You can say we cannot know either way if there is a god or not, but you can’t say the “odds” are the same. It is like saying the odds of gravity existing are the same that the odds of gravity not existing. I think you should have at least a good argumentation to believe that God exists. Do you have one?
In any case, your theory is a lot less of a pushover than the religious theories I’ve heard of, it is a simple theory without many assumptions. Or are there more things that you believe?
Euhm, yes, four-dimensional physics (relativity, quantum physics, etc. included) fits perfectly with what we observe, mathematics included. It’s the whole basis of the proposed shapes…
I also believe Life is just a single blanket force that creates many living things from one source, meaning we are all one.
So, which direction do we move a cube to create a tesseract? What is the name of the direction? What word(s) should be used to describe this motion in the 4th dimension?
time, bscly…
No, really, the space-time continuum (which is 4D) is essential to relativity…
So, if I have a cube on my desk, and I slide it from one side of my desk to another, am I creating a tesseract, connecting where the cube was to where the cube is now? Are cubes just sitting on my desk also tesseracts because they’re moving through spacetime (as the table, which is on the floor which is on the foundation which is on the Earth, which is speeding through the cosmos)?
I don’t know what a tesseract is. I do know that every moment is connected to the previous and the next moment.
4D space/geometry is very real in both physics and mathematics. I suggest you read up a bit (and watch the video I posted) before continuing to draw oversimplified comparisons.
A tesseract (4D) is to cube (3D) as cube (3D) is to square (2D) as square (2D) is to line (1D).
By the way, I know it works in mathematics. But, let’s “oversimplify” a bit to show the limitations of mathematics. You have three apples. You cut one apple in half and discard/eat one of the halves. Now, take three more apples and cut one apple in half, discarding/eating one of the halves. Now, place four whole apples on the table, then a half apple from each group on the table.
So, let the first group of apples be “A” and let the second group of apples be “B”.
Group A is two and a half apples (2.5)
Group B is two and a half apples (2.5)
How many apples are on the table? Mathematics would suggest five.
2.5+2.5
(2+2)+(0.5+0.5)
4+1=5
But this suggests five whole apples because the idea was you took the integers to represent whole apples and the fractions to represent the NOT-whole apples. Is it five whole apples? Or is it four whole apples and two halves of two different apples? You can’t combine two half-apples into one whole apple.
It’s like the question my elementary math teacher posed to the class: If you have five white balloons and five red balloons, how many pink balloons do you have? The answer is 0 because you can’t (generally) combine balloons.
Also, I can’t get the video to work. I tried multiple times and it gets through the (very long) list of sponsors and such and I get to the guy that states that the “future is depressing” and that the lecture should be called “We’re all screwed”, but then the video fails. I can’t get beyond these introductory portions.
First you would have to define a unit of time and a unit of space. For instance, you say that one inch corresponds to one second. Then, if you cube has edges of 2 inches, you would have to create the cube, then destroy the cube after exact 2 seconds without moving it (at least from the perspective of your reference frame). That is a tesseract.
If you let it to exist for more than 2 seconds, you will obtain a 4-dimensional “parallelepiped”. If you move it, you will obtain an “inclined” 4D cube or parallelepiped.
To imagine this, think of the 2D space as one dimension of position and one dimension of time. A square means a line of 1 unit of length stopped from time 0 to time 1, then ceasing to exist after that.
That is a problem of your model, not a limitation of Mathematics. A better way to deal with this situation would be to create sets of apples and half-apples. Then you would say that in group A you have two apples and one half-apple, same for group 2, and the union would have four apples and two half-apples.
guga: Thanks for, I guess, ‘dumbing it down’ for me. However, don’t the laws of thermodynamics now come into play about “creation” and “destruction” of matter/energy? Aren’t tesseracts and other 4th-dimensional objects conjectural and not “theoretical” (that is, they have no practical usage)?
I don’t know exactly how Physics models the world in 4 dimensions, I just know the math. I would say that there are no “tesseracts” as much as there isn’t any “perfect cube”. A tesseract is a set of points (a “place”) in the 4D universe, it consists of the points that are enclosed by a cube in an interval of time, not a real object.
I personally think of the universe as a set of particles, each particle being a continuous function with time as a domain and the 3 dimensional space as co-domain. The graph of this function, then, is a line in a 4D space. That is how I see things, I’m not sure if that is how Physicians model the universe.
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