[watsisname]

What do you mean an object is "in fact" spherical? Did you ask it, and it replied, "yeah, I'm spherical, congrats here are 10 points for your correct answer"?

Are all points on the surface of a non-rotating neutron star the same distance from the center (to a good approximation) only if something is observing it?  Is there ever a time when it just decides to ignore the laws of physics and become angular? 

I have an object that is approximately cubic in front of me too.  See?  Here it is!



Is it only in my head that this thing has approximately planar surfaces, each of the eight vertices a union of three orthogonal planes, each of the edges approximately the same length?

Topology is an empirical concept with deep roots in mathematics, and therefore I find it very difficult to agree with your claim that "shape" exists only in our heads, since you seem to have the same definition of shape as I do.  That's like saying that math and physics suddenly breaks down if nobody's looking.

edit:  I understand you're saying that there are no platonic solids in nature, simply because you can always find a deviation from perfection if you zoom in enough.  And this I agree with.  The event horizon of a solitary non-rotating black hole would probably be the closest thing to a perfect sphere in nature.  But my point is that just as a perfect sphere is a mathematical entity, any random object has a topology that is also capable of being defined in the same way.  One of the beauties of the principle of superposition is that any object can be represented by a sum of multiple equations.  And that makes shape a concept that is not just an artifact of human perception.

[General Battuta]

Agreed, shape is an objective property that can be mathematically defined. It does not require a cipher.

[Luis Dias]

Are all points on the surface of a non-rotating neutron star the same distance from the center (to a good approximation) only if something is observing it?  Is there ever a time when it just decides to ignore the laws of physics and become angular? 

Do objects follow the laws that our descendents wrote in a paper, otherwise they go to jail or smth? There is a lot of lack of rigor in our language, stemming from the fact that science "began" with a christian perspective that the universe obeyed the "laws of god", and it would be pretty cool for us to find such "laws", as if a celestial court existed that punished these and those particles if they dared disobey.

But I'm diggressing, flame me at will. Back to your point, no I'm not saying that things stop existing the moment you close your eyes. I'm saying that they don't care what you call them or what you decide they should do while calling it a "law". Is earth spherical, or not? Are the atoms of the surface (And what exactly constitutes the surface?) of the neutron star (and where is this "non-rotating" neutron star exactly located, apart from inside your own abstractions?) exactly placed in a spherical position?

No, you yourself agree they are not. They could as well be defined fractally, it depends upon what we want to study, to inform, etc.

I have an object that is approximately cubic in front of me too.  See?  Here it is!

[awkwardly intimate image of a cube trying to make a point]

Is it only in my head that this thing has approximately planar surfaces, each of the eight vertices a union of three orthogonal planes, each of the edges approximately the same length?

Read what I wrote. Abstract concepts that were invented by humans are very useful to categorize stuff that we see out there. I agree that if you choose to categorize your object as a "cube" then you are speaking english correctly and you are conveying useful information to me.

Topology is an empirical concept with deep roots in mathematics, and therefore I find it very difficult to agree with your claim that "shape" exists only in our heads, since you seem to have the same definition of shape as I do.  That's like saying that math and physics suddenly breaks down if nobody's looking.

edit:  I understand you're saying that there are no platonic solids in nature, simply because you can always find a deviation from perfection if you zoom in enough.  And this I agree with.  The event horizon of a solitary non-rotating black hole would probably be the closest thing to a perfect sphere in nature.  But my point is that just as a perfect sphere is a mathematical entity, any random object has a topology that is also capable of being defined in the same way.  One of the beauties of the principle of superposition is that any object can be represented by a sum of multiple equations.  And that makes shape a concept that is not just an artifact of human perception.

Topology is an abstract concept that has certain needs that you can't guarantee on your objects. I'm not saying that math and physics aren't useful. I'm saying they are constructs, they are not reality. They are models. Models do not "exist out there" as "objects".

This is an ancient mistake, like saying that things "exist in themselves".

I have a question for you. Does an orbit of a planet "really exists" outside the human mind?

[Luis Dias]

Agreed, shape is an objective property that can be mathematically defined. It does not require a cipher.

So you don't need mathematics to decypher it? What the hell are you talking about, you're not making any sense.

[General Battuta]

Mathematics is an objective truth, not a construct. It is not a cipher with arbitrarily assigned meaning, like color.

[Luis Dias]

Mathematics is an objective truth, not a construct. It is not a cipher with arbitrarily assigned meaning, like color.

Said like a true religious! May the faith in the absolute absolve you from your uncertainties .

I will spare myself of the impossible mission to deconvert you from that kind of religious belief.

[General Battuta]

Because mathematics is completely divorced from the empirical it is not constrained by the need for evidence. While mathematical axioms must be stated, altering the axioms simply leads to new mathematical approaches. No mathematical system will ever be complete, but mathematical constructs are objectively real in the way the charge on the electron is real - they are not constructs the way color is.

[Mustang19]

While mathematical axioms must be stated, altering the axioms simply leads to new mathematical approaches. No mathematical system will ever be complete, but mathematical constructs are objectively real in the way the charge on the electron is real - they are not constructs the way color is.

But to establish what is objectively real one must prove it with axioms.

wikipedia.com/Infinite_regression

[General Battuta]

Sure, but that's just philosophical fluffery. Color and shape (or other mathematical traits) are clearly on two different levels of existence; the latter could be easily derived even by an alien civilization with very different neural wiring. Math is for all intents and purposes objective common ground, and anyone who tries to argue that color is comparable is clearly Luis Dias.

[Mustang19]

Its philosophical fluffery but it disproves the certainty of everything you've ever said 

Whats a cipher?

[General Battuta]

No it doesn't, it demonstrates that mathematics is objectively available in exactly the way I've said all along.

A cipher is something like a language or, well, a cipher which cannot be determined from observation, it has to be transmitted along. An alien could not perceive color the way humans do without either examining a human brain or being given a description of how lights interact to produce color. On the other hand an alien can figure out what a sphere is without any help.

[Mustang19]

No it doesn't, it demonstrates that mathematics is objectively available in exactly the way I've said all along.

State your axioms. Come on, all of them. And the axioms behind those axioms. We can do this all day...

The arguments not over till its over, and until you post an infinitely regressive explanation without getting banned for crashing the board the answer will remain uncertain.

A cipher is something like a language or, well, a cipher which cannot be determined from observation, it has to be transmitted along. An alien could not perceive color the way humans do without either examining a human brain or being given a description of how lights interact to produce color. On the other hand an alien can figure out what a sphere is without any help.

The alien would first have to share our concept space or a similar one to understand shapes no less than they would have to understand the brain and eyes to understand color. I'm not sure what definition of "color" you're using so I'm just going by neurology.

[castor]

Universe has patterns.
Humans observe the patterns and organize the data by giving them names.
End of story,

[General Battuta]

No it doesn't, it demonstrates that mathematics is objectively available in exactly the way I've said all along.

State your axioms. Come on, all of them. And the axioms behind those axioms. We can do this all day...

They're not even necessary, the whole argument is 'what is in our head' vs. 'what could an alien come up with' and there is a clear difference between color and shapes there.

The alien would first have to share our concept space or a similar one no less than they would have to understand the brain and eyes to understand color. I'm not sure what definition of "color" you're using so I'm just going by neurology.

No it wouldn't, even the weirdest ****off alien is going to fall into one of two spaces:

1) has no concepts whatsoever
2) has a concept of 'all points at a fixed distance from a point'

There are a zillion ways to formulate the latter but mathematically they will all boil down to the same thing. You can't say the same about color, it cannot be derived without a human to explain it or a human brain to dissect.

[Mustang19]

They're not even necessary, the whole argument is 'what is in our head' vs. 'what could an alien come up with' and there is a clear difference between color and shapes there.

Again, present the assumptions you use to justify that statement...

No it wouldn't, even the weirdest ****off alien is going to fall into one of two spaces:

1) has no concepts whatsoever
2) has a concept of 'all points at a fixed distance from a point'

There are several concepts an alien could understand such as points (or shucks, color) without understanding distance. Being able to picture all points at a fixed distance alone is not necessarily sufficient for understanding all but one dimensional "shapes".

[General Battuta]

Again, present the assumptions you use to justify that statement...

It's an empirical argument, not a logical one. We know color only exists inside our head because you need a human head to make any sense out of it. The same can't be said of mathematics.

There are several concepts an alien could understand such as points (or shucks, color) without understanding distance. Being able to picture all points at a fixed distance alone is not necessarily sufficient for understanding all but one dimensional "shapes".

Man, the definition of a sphere is a mathematical concept and does not require any shared cipher to decrypt. I don't see how it can go any farther than that.

[Mustang19]

It's an empirical argument, not a logical one. We know color only exists inside our head because you need a human head to make any sense out of it. The same can't be said of mathematics.

Okay dude but Im still waiting on those axioms.

Man, the definition of a sphere is a mathematical concept and does not require any shared cipher to decrypt. I don't see how it can go any farther than that.

Sure but color can be established as a mathematical concept as well through modeling of neurological processes.

[General Battuta]

It can, but to do that you need to model something, which is the cipher.

Anyone who exists in the material world can derive the concept of a sphere. They don't need to find the Sphere Species and dissect their brains and model them.

[Mustang19]

It can, but to do that you need to model something, which is the cipher.

It's possible to model hypothetical concepts which were not transmitted to you.

ed:

Anyone who exists in the material world can derive the concept of neurons firing in some way to create color. They don't need to find the Color Species and dissect their brains and model them.

[General Battuta]

There's a clear difference between creating some hypothetical brain for no reason and the basic geometric concept of a sphere.