Do circles exist in nature? when i look at the moon, the wheel, the patterns in sand...

Here it is

We observe stuff. We aren't capable of observing every quality of stuff. Stuff is hard to observe (sub-atomic pieces of particles).

There are more general qualities of things that become apparent through observation. Those qualities are used to build abstracts which more or less approximate the real qualities of things. They aren't actually those qualities, because we cannot ever completely observe anything.

That's how reality works. You can't look at everything all at once. Even if you're trying to look at one thing, it's made of countless smaller things.

You can't draw a perfect circle. They don't exist.

A field is only known by its effect, interactions. The relations are not the field. The definitions are abstract.

Both center and radius are abstracts.

That's a 148.9 jpg, fag.

No wildberger. We can use irrational numbers all we want on paper but in the real world there are two possibilities

1) Irrationals don't exist
2) Irrationals do exist (as lengths/areas/volumes/etc. of some real objects I mean) but then that would require an infinite precision measuring tool which cannot exist which means that we would never be able to "touch" an irrational number so they might as well not exist.

But if you do believe irrationals do exist out there then all I could say is take out your ruler, measure the square root of 2 and then go get your Nobel prize in physics for developing the infinite precision measuring tool.

>What defines nature and our model such that they are disjoint?

Words aren't shit. Shit ain't words.

YOU are a 148.9 jpg you fucking autist piece of shit

Damn, I never knew. Guess I'll just have to accept i--fuck your noise, weak troll.

then what the fuck is reality? what is the totality that you are getting this information from if it isn't even possible to fully understand it with a full perspective? how can a circle just be an abstraction when we are looking at what we're trying to model and can't get anything more than the properties it has? if it leads to it being circular and nothing else, is it not a circle? how can something exist as anything more than its properties we measure?

But seriously. Explain why pic related instrument can't draw a perfect circle. Of course it has a different "line thickness", but it should still allow an absolutely flawless circle to be seen. You can microscope in all you want, you will always see a circle. Because it follows the same mathematical laws as the very definition of a circle.

Reality exists regardless of one person's observations. There's no "totality", because no one person looks at every damn thing.

You're on some good drugs.

There isn't any full perspective. There's no full understanding. Those are imaginary. Being alive means knowing only subjective experience and abstract representations.

The compass has a rounded point formed from ridiculous amounts of electrons. Because those electrons' fields of charge are opposed to the fields of charge of any given surface's electrons, the compass will always pivot from its original center point when a circle is drawn.

It's inevitable. Reality does not exist to suit the ideas humans have concerning it. Nobody can understand where and how the center of that compass's circle will travel, but a sufficiently accurate measurement will find that it only produces incomplete spirals.

you are contradicting yourself. you're saying that there is a collection of observations but that they cannot sum to a total observation.

I responded with "How so?", but that ain't cutting it.

There's no contradiction, collections of observations have nothing to do with total observations. There is no total observation, if you're thinking about defining something.

Reality is fucking recursive, and words aren't. You can only go so far with describing something with definite articles.

what do you mean by recursive? and doesn't first order logic allow for enough definition to mitigate its need?

Reality is recursive in that observed objects affect each other continually, and so "recursively" redefine themselves. Consider that light strikes objects, delivering energy, and that this energy disperses through adjacent objects. That never stops, and the individual effect on every object involved is not observable, though a general effect can be approximated in a fashion.

Logic is useful, but it doesn't determine what's happening in an observation. It can only describe it. Cause and effect can only be described, never exactly determined.

>reality is not our models
>but your idea conflicts with reality because *model*

Why do electrons displacing themselves get priority over the notion of circle?

Curves dont exist in nature

probably because that guy was talking about creating a mathematically perfect circle with a compass and a sheet of paper. The compass and the paper interact entirely through the weak force. The compass isn't perfectly rigid, the point isn't infinitely sharp, the point doesn't stay perfectly stationary with respect to any point on the paper, and the paper isn't perfectly flat. The lead in the compass isn't infinitely sharp either and if your eye can see the mark it means the "circle" it draws is actually a ring. Zoom in on the edge of the ring until you can see individual carbon atoms bonded to the surface of the paper and you will see that the extreme edge of the ring is jagged as all hell. Hypothetically if your pencil was sharp enough and you had some tricks up your sleeve to make the compass pivot 360 degrees on top of a single atom on paper meticulously engineered to be almost perfectly flat, you could draw a ring only one atom thick. It would still be jagged. Such is life.

I don't think he's saying your concept of a circle is invalid. He's taking the platonic stance and saying you can't possibly create a perfect circle in the physical universe, only increasingly close approximations to the concept, which exists only as a construct of your mind. It's almost not worth talking about these things because these horses were beaten to death almost two millennia ago by people with no microscopes who drank leaded wine and fucked their second cousins.

"Priority" is only in the mind, not reality.

I was hoping that dumbing things down to "seeing shit and saying stuff about said shit are different piles of shit" would be good enough, but this guy is kinda doped out.

*e'hem*

What is the trajectory of any projectile for 500

Are fields not circles?

I meant ontological priority. "electrons" exist but "circle" doesn't because it's "abstract"? Plato, incidentally, would say that the only thing that truly exists is the circle and the world we live in in which we try to make circles is a mere shadow

A circle is defined as the set of points equidistant from another fixed point.

A circle is not defined as the shape generated from a protractor.

Creating a perfect circle physically would violate heisenberg uncertainty principle, so they cannot exist.

so you are proposing that the concept of a perfect circle that literally every human has in their mind just doesn't exist? It obviously exists
>but concepts aren't reality
Yes they are, in fact it's the only thing we can use to even consider reality in any of its forms. Heisenberg's uncertainty principle is also a concept yet you seem to have no trouble claiming its existence.

>but then that would require an infinite precision measuring tool which cannot exist which means that we would never be able to "touch" an irrational number so they might as well not exist.
This problem applies equally to rational measurements though. You're just choosing to cut off the measurement at the closest rational on some scale, but you could do the same with an irrational scale.

Or if you can measure rationals with infinite precision then you can measure algebraic irrationals as well through construction.

>Creating a perfect circle physically would violate heisenberg uncertainty principle
you're a fucking retard

Again, I'm talking about the physical creation of a circle, not whether or not the idea of a circle exists. If you want to go down that road, then I argue that ideas/thoughts as physical objects (qualia,electrons,whatever) is independent of the information contained within it. If I showed you an eeg scan of one person thinking about porn and another thinking about a circle, you wouldn't know which is which.

The idea of a circle is distinct from the physical existence of the circle. You were probably trolling, but if not, I hope this helps.

If we could create a perfect circle at stp, then we would know both the position and momenta of all of the atoms in the circle exactly.

I'm just saying that its existence as an idea puts it on equal grounds with physical existence. Goes for all of mathematics.

That would be true if your circle's border was only a few atoms wide. With a protractor you can create a "perfect" circle as long as you consider the perimeter to lie somewhere between the inner and outer edge of your line. Taking any jagged edges or stray marks into consideration is pointless.

That's wrong. A circle is the set of points equidistant from another point. If the perimeter consisting of points is more than 1 point deep, or if the points aren't all equidistant, it's not a circle.

That's fine. Just remember that physicalness of ideas of things are distinct from the things themselves. Otherwise all of modern logic and science falls apart. Because then to prove god exists, I only need to think of his existence and to think of the idea that a proof of his existence exists.

This question is about the underlying nature of energy and space, as well as quantization in nature. Even infinite subdivision doesn't afford smooth edges though, it's just infinitely adding points.

Don't know.

Why did I lose to this

>as you consider the perimeter to lie somewhere between the inner and outer edge of your line

If I draw and fill in a square with an empty spot in the middle then a circle still lies in its perimeter.

I'm talking exclusively about the space covered by pen/pencil/whatever. If you use a protractor, you would be able to create a perfect circle using just one rotation and a (very, very) small eraser. Think of the Squeeze Theorem for limits; within the space covered by pen or pencil, you can imagine two non-perfect circles (the inner and outer borders) sandwiching a perfect circle. The space this circle covers would indeed be equidistant from a single point in the center.

your application is wrong

kek

I'm not saying to literally use the theorem to prove it. I was just trying to come up with a quick explanation for how to visualize it. Two lines you can ignore sandwich the line you're focusing on. It's just a superficial analogy; limits and proofs have nothing to do with it.

it's a wrong analogy, what you're saying isn't true. an arbitrary region does not contain a circle.

if the two perimeter circles are imperfect how would they ever form a perfect circle

>Protractor
Shit, I meant compass.

It's not arbitrary if it's a thick enough line created by rotating a compass. Realistically you'll get a lot of oval shapes that can't properly accommodate the perfect circle, but my point is that it's *possible*.

I made a picture. It looks right to me, but maybe not.

But the red line is actually just a bunch of pixels, not a circle.

The point you should be making is that since 'circle' is an idea, it exists by itself and you can impose it into any shape that you see it in, as long as it makes sense

If you're defining a circle between two arbitrary areas, the permiters of those areas dont need to be any specific shape, provided that you could draw a circle in that area.

you're assuming your region is "nice" enough that it contains a region. I'm telling you that's a very strong assumption to make.

That's mostly what I was getting at, but I wanted to point out that this logic could also be demonstrated intuitively in a real life scenario. It's possible not just philosophically, but practically as well. That's why I said >Taking any jagged edges or stray marks into consideration is pointless.
because I wanted to emphasize that you can create a shape that is, for all intents and purposes, a real perfect circle - just one that is obscured by an extremely similar imperfect shape.

>Provided that you could draw a circle in that area.
Pretty much. But very few people are going to draw a fat triangular surface with a compass. Most people would get an oval with some stray marks that could nonetheless be treated as perfect in every regard.

The black shape I drew seems nice enough, doesn't it? If it doesn't, can't it be made arbitrarily nice by drawing with a thicker pencil?

you're assuming a pencil covers a (small) area completely. it doesn't.

electrons exist because "electron" is a name for a thing which physically exists and you can actually interact with them in the real world
the circle exists in the sense that it is the name of an abstract concept. the unit circle is a regular apeirogon with an area of pi. but you can't build an apeirogon in the physical universe for obvious reasons.

but you can interact with it and manipulate it in a very real, concrete, tangible way. it is an abstract concept in the same way that lots of the things that you need to invoke before you arrive at the differentiated notion of electron (disregarding what specific terms you use) are concepts.

the very idea that you can partition existence in such a way as to make 'models' sensical is a concept. a remarkably useful concept, just like mathematical ones.

return to the original question "do circles exist in nature?"
the answer has to be no because you can't physically construct a circle. Whether or not you can interact with a conceptual circle is irrelevant. Whether or not you can 'partition existence' (although I'm not even sure what that means) in a way that makes models make sense is also irrelevant. There are models and there are observations. Your model is better the closer it approximates observations. I have a cube. I roll it 600 times. I should get 100 instances of each side, according to the probabilistic model of fair dice. But that's not how it happens because the number of times each side appears is an integer, and with only 600 rolls it's likely that I will see one side more than 100 times. The more times I roll it the closer the observed frequency of a side will approximate 1/6 of total rolls. But it's astronomically unlikely to be perfect.

now that you're thinking about the difference between a model of reality (math) and what reality actually is (what you can observe) it should be clear that you can't ever build a perfect circle. There can be objects so round that you think they're circles but something must be imperfect about each one of them.

a circle can't exist because atoms aren't fixed points, if you zoom in close enough they are made of electrons and protons. The edges of anything made of matter will just be just a big field of a bunch of forces and bosons and empty space with electrons and protons inside. If you zoom in further it's just empty space

How do you sum incompatible models?

What if pi has an end and therefore you could make a circle in plankton scale

>plankton scale
huh?

Perfect, euclidean geometry exists no where but your imagination.

>You can't draw a perfect circle. They don't exist.
but perfect girls don't exist either yet you can draw them

B L A C K
H
O
L
E
S

You know, the smallest possible unit: the size of a plankton.

>Reality exists regardless of one person's observations. There's no "totality", because no one person looks at every damn thing.
Which means that what they do look at is subjective.
>There isn't any full perspective. There's no full understanding
Which means there's no objective reality.
>Consider that light strikes objects, delivering energy, and that this energy disperses through adjacent objects. That never stops, and the individual effect on every object involved is not observable, though a general effect can be approximated in a fashion
In quantum physics the effect of the light is part of unitary evolution, that is to say it has a deterministic effect on the wavefunction. When someone measures the effect the light has had, they make a measurement which is a 100% accurate description of the state the system is now in. This works precisely because there is no objective reality in quantum mechanics, only your subjective information about observations you have performed.

>Perfect, euclidean geometry exists no where but your imagination.
THIS
The whole point of geometry is that we use imaginary shapes in an imaginary universe to represent real numbers.
The fact that these imaginary shapes (and the imaginary universe they exist in) roughly correspond to the real world is a nice coincidence, and it makes it easy to figure out how much paint it will take to paint the den, but the axioms of geometry do not apply to the real world in an absolute sense.

Wouldn't the event horizon of a black hole be a perfect sphere? It isn't an actual physical object, but it is found in nature, and depending on it's rate of rotation it would approach a perfect sphere as it's rotational period increases. Or am I just wrong

i was talking about "are circles real" and my definition of reality is not restricted to "observations". i was also trying to make a point that "pure observations" divorced from all conceptualization can't happen

atoms are like pixelated stuff.

yeah maybe
no one who has ever lived would be able to say for sure

Everything in nature composed of perfect spheres

Actual event horizons have spin and charge and can actually take very strange shapes. Some suggest that they may get so strange that, should you get enough in a proper configuration, one could expose a naked singularity (at least temporarily).

I suppose an event horizon sitting in very isolated space, say the result of a collapsed galactic causal cluster, would be pretty damned spherical, but it still wouldn't be a perfect sphere - especially not once you were close enough to observe and measure the thing. It'd have to remain hypothetical, and probably have to exit beyond the point where the CMB could interact with it. In the end, it may not be possible for a perfect sphere to exist and be observed. There's a lot of objects that are immeasurably close, but you'll never quite get there, so long as there's mass involved.

How, with indivisible particles (regardless of size) would you create an irrational number?

If you can measure 1, then can construct [math] \sqrt{2} [/math]. Fuck off back to /x/.

>Do circles exist

What a stupid question.

You mean: Do circles exist physically.
Answer is no.

>perfect orthogonality in euclidean space
where?