Question: What is the volume and area of a 2,5-dimensional "cube"

>>8679841
Well, dimension is a mathematical concept. That means that dimension means what you want it to mean. We define it.

You can have objects with 2.5 dimension, if you define dimension to be "fractal dimension". But you can't have a cube of 2.5 fractal dimension because in fractal dimension you first draw a curve and then quantify its dimension.

In the definition of dimension in which cubes make sense, dimension can only be integral. Because a cube is a regular parallelepiped, and we can only talk about parallelepipeds in the usual definition of dimension.

Buuuuuuuuuuuuuuut.................................

That is the geometric definition of a cube. You could also simply redefine a cube for fractal dimensions.

For example, define a 2.5 dimensional cube as being:
A 2.5 fractal-dimensional curve that looks kinda like a cube if you "zoom-out" a lot.

There you go. Now go play and find the area of the different 2.5 dimensional cubes you will find.

>>8679869
>>8679841
https://en.wikipedia.org/wiki/Menger_sponge
Here, this could possibly be a cube in fractal dimension

It is of dimension 2.726833 so close enough and it kinda looks like a cube, so define it to be a fractal-cube.

As for surface area and volume, it has infinite surface area and 0 volume. There you go.

>>8679869
>Dimension is a mathematical concept... we define it
Nature defined it; we just happened to observe it. But could life exist in 2,5 dimensional world? Or 8,1123124151 dimensional world? Or "red, dog dog bark" -dimensional world?

Okay so I got a way to have 2,5 dimensional object in fractal dimensions. Now I want to have either
>2,5 dimensional object not using fractal dimensions
>OR proof that no such object can be constructed with using atoms and molecules

>>8679915
No, math defines dimension, you brainlet.

>>8679915
>Nature defined it; we just happened to observe it.

That was maybe before set theory. Basically, when we were beast. But we are civilized now. Dimension has a rigorous definition, much more powerful than anything we could naively observe.

>>2,5 dimensional object not using fractal dimensions


Well, here is another definition of dimension:

Let dimension be the sum of the lengths of the segment of a shape.

Now a square of side length 0.625 has dimension 2.5. Easy.

>>8679917
There is not a single mathematical concept that we didn't originally found by observing the work of God called Nature. Even infinity and multi-dimensional objects. Mathematics is just writing down work of God.

>>8679928
If you'd apply yourself, you'd be more imaginative.

>A point requires 2 numbers to define in 2 dimensional field
>A point requires 3 numbers to define in 3 dimensional field
>A point requires 2,5 numbers to define in 2,5 dimensional field

>Cube is a collection of points with rules XYZ

Now let's try to define '2,5 numbers'

>>8679947
Well, you will have to find what is a "half point".

>>8679930
Differential geometry existed long before relativity, so no, you're dead wrong.

>>8679950
Sure in human history. But whatever humans want to know about "mathematics and logic" is already done by the Nature by the hands of God. We are just rediscovering what God has made us.

If God had made the world 2 dimensional, we would discover it and say "world is 2 dimensional".
If God had made 1+1=3, we would say "1+1=3"
If God had formulated Pythagoream theorem a^2 + b^2 = c^2 + 1; we would say "a^2 + b^2 = c^2 + 1"

There are no concepts in math that haven't been decided by the whims of God's dice

>>8679949
Not only "half point", but also "0,77 point", "dog point", "sqrt(2) point", "point point point", and "that feeling when you cum inside your gf -point"

Or. Fundamental physical proof why such constructions cannot exist.

>>8679958
God can't make 1+1=3, it's impossible. Otherwise he could make a rock so heavy he can't lift it. God is beholden to reason and as such, to mathematics. Math is super to God and only a brainlet can't see that.

>>8679968
God can make a rock so heavy he/she/it can't lift it. It's flawed human logic that God would be bound by such feeble concepts as "truth" and "false". God lives in a world where literally everything is possible. In God's world 1+1=0 and 1+1=1, and 1+1=2 and 1+1=dog... He/she/it created us humans are world where many constrictions apply, such as being restricted to think 1+1=2.

For some reasons humans think it to be some cosmic truths that two things that contradict each other can't exist simultaneously. Even quantum mechanisms knows that such things can exist.

>>8679983
So if God is not beholden to reason, then why should i? Its possible then for god to have lied, because as you have said, he is not beholden. Im sure you have some hand-wave "but i know he didnt :-)", secretly implying god actually is beholden to his own word, thus contradicting yourself and avoiding the entire problem, but whatever, the point is youre demonstrably wrong about math.

>>8679930
>brainlets literally can't comprehend that math is all in our heads

>>8680010
It appears to us we can't construct a 2,5 dimensional object. But do we have a proof that we cannot do so regardless of what axioms we choose for our mathematical language?

>>8680019
We can, though.