i doubt most people r even familiar with Newton's first law. they might still believe in Aristotle's ideas

@ACuriousMind the source I'm watching says that Aristotle's philosophy didn't make a sharp distinction between mind and body. Descartes made a distinction (calling the separate parts body and soul) and simultaneously declared that only humans had the soul

Aristotle got spacetimes named after him :P

aristotle seems to disagree with the above, but i still dont know what he disagrees about :P

it says Plato and Aristotle each unified the Eleatian and the Heractilian philosophies

i dont think Plato and Aristotle introduced this. they may have formalised it

it says "Plato and Aristotle introduced a metaphysical ontology in which things r certain, contrary to the pre-Socratic thought". And that this metaphysical framework only worked out for the macro world

@SillyGoose this principle is only a rule of thumb. in practice, explanations have to be satisfy a lot more principles. e.g. the simplest explanation of why planets go in circles might be to say that big things in space go in circles. this is what Aristotle did.

i doubt this view because aristotle's physics lasted way too long to be positive

do u think aristotle had a net positive contribution to physics by showing "what not to do"?

i also hav an idea to model Aristotle's physics. u define the geometry of spacetime to be a 0 connection. so the geodesic eqn is $\frac{d x^{\mu}}{d\lambda}= v^{\mu} (x^{\mu})$. then we can define a sort of covariant derivative $\nabla=\frac{d}{d\lambda} - v^{\mu}$. then non geodesics r given by $\nabla (x^{\mu}(\lambda))=q^{\mu}$

Aristotle would have had a moving particle tend to come back to rest

if u go one level below Aristotle's physics, u get a 0 order differential eqn

how are we characterising Aristotle's physics here?

like Aristotle's wild guesses

perhaps there were good scientists between Galileo and Aristotle, but their work never happened to get mainstream

@Slereah Aristotle discovered the principle of least action :P

@Slereah Aristotle is a huge armchair physicist

Aristotle said that the natural motion of Earthly things is to go down

some like Zeno, Plato, Newton, Lebnitz would be thrilled to know modern physics. someone like Aristotle would ignore it

yes. i remember discussing this notion of connection while discussing Aristotle's physics

i would even say logic just rules out Aristotle's hypothesis. plain and simple

trust me. logic alone can get you very far in ruling out Aristotle's hypothesis

here is a great question : Is Aristotle's hypothesis, that more massive objecs fall faster, ruled out empirically or logically?

Aristotle's theory is more badass tho. celestial planets as the in-charge of time

@naturallyInconsistent yes, i too had this intuition about Aristotle's laws. One other huge problem is that people dont realise that Newton's second law is pretty much just the definition of force

What is the divide Aristotle made tho? Is it same natural motion vs forced motion divide he is talking about?

I think it misunderstands Aristotle. Aristotle just said that the natural motion is to be at rest wrt some absolute space. This is the part that no physics theory agrees with.

But i myself dont find this a justified assumption in itself. Becuz it rules out Aristotle for no reason. This is y I prefer the metric approach. It's shorter and rules out Aristotle @Amit

When i was trying to rule out Aristotle's relativity, I took this same approach. Assuming the metric gives u the relativity of constant velocity frames, rather than constant rest frames

@naturallyInconsistent i dont care about Aristotle. I just want to know why equivalence of "constant velocity frames" is more natural than equivalence of "rest frames related by affine transformations"

Yes. So I believe we need two principles to get rid of Aristotle in principle : 1. A metric-ful theory 2. Lack of such an absolute vector field

Then I think we r really close to breaking the mystery. Assuming a metric gets us very close to the equivalence of "constant velocity frames" in flat space theories @ACuriousMind I'm thinking the metric underlies Newton's first law and puts a coffin on Aristotle's law

I think it's a misconception that Aristotle meant $F=mv$. His law can be second order. It's very hard to know what Aristotle meant

@Slereah Hello. I think Aristotle's model need not b first order differential eqns. E.g. we can hav $\frac{dx}{dt}=\frac{p}{m}$ $\frac{dp}{dt}=-p$. These r second order

Is there no Aristotle algebra?

@Slereah this Aristotle universe has principle of relativity for rest frames

My real question : y is this Aristotle universe not very natural to have

This wud give a translationally invariant Aristotle theory

I hav an idea : the current state is determined by initial positions of everything in the Aristotle universe. The law of physics maps this state to a 0-connection. Then the particles follow that flow. And then we rinse and repeat in small time-steps @Slereah @ACuriousMind

The metric gives u a connection which is not a vector field like what Aristotle wants

I'm not as interested in what exactly Aristotle had in mind, as I'm interested in first order laws diff eqn vs second order diff eqn laws :P

@Slereah Once we assume a metric, the metric-compatible connection is the Christoffel symbols instead of a 0-connection like Aristotle vector field. So the metric compatible connection can b a deep reason for Newton's first law, rather than Aristotle's law

@ACuriousMind yeah. Becuz Aristotle did not hav a model in mind

To go full Aristotle, u wud hav to define separate flows for separate elements like fire, water, dust

I was thinking we cud make a translationally invariant aristotle theory by using Coulomb's law formula

Ooh then this is ugly. But i think we can easily make translationally invariant Aristotle formulas

Yes. We can define the connection stuff so that the parallel transport and hence geodesic equation obeys Aristotle's law I guess. Is this it? @Slereah

I was just wondering how one could define Aristotle stuff using manifolds. Is the spacetime in this theory defined using a metric? @Slereah

Y is Newton's first law prettier than Aristotle's law that moving objects come to rest?