It depends on where you draw the line (heh) on "straightness" and "flatness". Some planes on gems or geodes are pretty flat, but probably not perfectly flat. Another example is a spider's web between two points. That's a pretty straight line if it's taut, but again, probably not exactly perfect.
Nothing is perfectly flat, neither in nature nor man made. It's purely a mathematical concept as every surface has some form of texture if you look close enough.
Well, yes. My point exactly.
Right, atoms are not flat
Lines and planes in the mathematical sense are 1 and 2 dimensional. They don't have any height (and lines also no width). So they can't exist as a physical object made out of atoms as they are already 3 dimensional.
They only exist as a concept.
The fact that something isn't a 3d object doesn't mean it doesn't exist. Does a line of contrast between 2 colors exist? Does a movie projected at a wall exist?
Does a line of contrast between 2 colors exist?
I'd say no. And even if it did, those colours are made out a material that consists of atoms that reflect light, both of which are "fuzzy" and 3D and can't make a proper line.
Does a movie projected at a wall exist?
Sure. There is photons bouncing of a wall and the information they carry we call "the movie". I guess that counts. But the relevant bit is the wall and again it's made out of atoms and therefore is not a proper flat 2D surface.
So yeah, I'd say not being 3D does mean something can't exist in the physical world.
Then, o pedant, do straight or flat objects (thus linelike, planelike) exist?
Short answer, depends on perspective. For example surface of perfectly still lake could be considered flat, but on macro level it follows curvature of the earth. But we still use water to level our buildings, because radius of a planet is so big. On microscopic level it's anything but flat.
Someone else mentioned spider silk danging. It's also another great example, but the same perspective clause applies. But usually crystals and some geological features tend to have flat features.
maybe somebody else pointed this out:
Light ALWAYS travels in its idea of a straight-line.
Always.
It doesn't matter whether it is bent by gravity or refraction, from its perspective, it kept going straight.
Only an "outside viewer" sees any non-straight-line-ness being done, but the outside-viewer isn't seeing the curved-space or the curved-refractive-index that the photon saw.
Well, kinda, but the trajectory of the photon is contracted into a single point from its POV. Whatever destination is has, it's already there as far as it's concerned. It doesn't experience time given that it's moving at the speed of light.
You really have to declare to what degree you are asking. You could take a very carefully grown crystal and define a plane based on its lattice structure. But the atoms are not all perfectly placed on the lattice once you zoom in far enough. There's even gaps between the atoms! A "plane" of carbon looks more like a net to an observer on the scale of those atoms.
Is an electron a perfect sphere? Scientists probably thought so in 1900 but now ask a physicist and they will say "No, probably not".
And yes, as others have stated, our space time is not perfectly Euclidean so that's another level of uncertainty. How do you measure the small imperfections in a Euclidean model when actual space time isn't Euclidean?
As a professor used to tell my class, there are no 0s.
No, they are mathematical constructs. Everything in nature is composed of matter and the like, so there are no perfectly straight lines or flat planes.
Even a beam of light curves and refracts as it interacts with matter and space over a long enough distance.
Light is going straight from it's point of view . It is following the shortest path between two points. The transform from different reference frames is why we see it as curved.
But if that's your definition, then there are no straight lines in mathematics either because you could transform the straight line from one system into a curved line in another system.
Yes, nature is not objective - it is relative. Mathematics is a discipline that is based around an objective framework. Lines and planes are mathematical constructs. Mathematics gives us an objective framework that can be used to model a natural world, but they are just models.
Some things are "line-like" or "plane-like," in that modeling them as lines or planes is helpful to describe them. You can measure a distance "as the bird flies" because birds fly in lines compared to how humans travel along roads and paths. You can describe a dense, heavy, falling object as traveling in a straight line, because air resistance may be negligible over short distances.
A model is only useful insofar as it accurately represents reality. Lines and planes are mathematical constructs, and they may be incorporated into models that describe real things. "A beam of light crossing a room travels in a straight line" is probably a useful construct because the effects of gravity and refraction of the air are probably negligible for nearly all purposes. "The surface of a pond is a plane" is probably an acceptable model for a cartographer, since the height of ripples and the curvature of the earth are negligible at that scale.
The initial question was not "Do straight lines and flat planes model anything in nature," but whether they exist in nature. They do not. They only exist in mathematics.
Unless the light is in a vacuum like space
Light bends in space all the time. Our sun has enough gravity to bend light.
There is no perfect vacuum, even in deep space. In the space of our Solar System, there is on average 5 atoms in every cubic centimeter. In interstellar space, there is on average 1 atom every cubic centimeter. In intergalactic space, there is on average 1 atom every 100 cubic centimeters. It's a gradient, but much like the perfectly straight lines and flat planes in the original question, perfect vacuum is a theoretical construct that is impossible to achieve in our reality.
Space is not empty
Depending on scale. Is the surface of the lake flat?
Once you experience true level you will never go back.
True level must be like true symbols (like, in the idea that there are true names and words. Like a divine language).
If you have a true level or symbol then you have something, just as good as reality, but manipulable like language. The best of both worlds.
And even better, you need never leave the confines of the inside of your mind ever again. You can live, within your construct of perfect god-language, and interact with the world from there. Safe and powerful.
Man… are you good? You sound like a guy who showed up at my house and started saying that the pyramids and stars would aline and tell us the meaning of the universe. Also that açaí berries were the ultimate nutrition. Hope you’re doing okay there.
Neutrinos travel in a straight line.
Unfortunately (fortunately?) the space they're traveling through is curved. It was a good attempt though neutrinos.
Edwin A. Abbott has entered the chat...
The neutrino neither knows that nor does it care about it.
In it's reality, the line remains perfectly straight.
Not to mention quantum fuzzing
They don't, although they
do not"rarely" interact with other particles, they move as waves, like all other energy in the universe.“I want to emphasize that light comes in this form-particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I’m telling you the way it does behave- like particles.”
Richard Feynman, “QED The Strange Theory of Light and Matter.” Introduction, Page 15.
Cubed pyrite is one of my favorite examples of this.
That's very cool, I see why you like it
According to mathematical platonism, yes.
Otherwise we have no idea. We have some models of physics, none perfectly describing our universe. We don't know the structure of space, or the structure of time.
Even if we did: what would it mean for a line or a plane to exist? There could be equivalent descriptions of our universe, some including those as objects and some only as emergent properties.
A lot of people talk about straightness and flatness as mathematical concepts. But I think OP means it in a technical sense, as in flat like your phone screen or straight as the edges of the screen but in nature. In this sense, flatness or straightness is defined as a finite number of measured points on a surface of which the coordinates all lie between 2 mathematicaly flat/straight parallel tolerance planes/lines. By that definition, depending on what a person would consider flat, say 0.002 mm between the planes/lines, there are definetly naturally occurring crystals that would pass that test.
A frozen lake.
A spider's thread when it's climbing downwards.
Aaaaactchhhually a frozen lake would follow the local curvature of the earth, even assuming ideal conditions and crystal formation and so on
Simple answer: no
Is the Higgs Field a flat plane?
Right after they mow, otherwise it's rather fluffy.
I think we've got enough evidence (proof?) that the universe is flat, and straight lines will continue straight forever and never intersect.
Whether there's an actual thing that exists that does this? Dunno. Two parallel particles I guess?
I am pretty sure we have no such evidence of the sort. Last i checked the universe being torus/donut shaped was still in the cards.
Wikipedia, https://en.m.wikipedia.org/wiki/Shape_of_the_universe
"As of 2023 current observational evidence suggests that the observable universe is spatially flat with an unknown global structure."
I don't fully understand this stuff, so I dunno.
Wut? Spacetime is anything but flat.
Sorry. Straight parallel like never intersect
Right, my bad.
