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June 27[edit]

Why doesn't everyone go into eachother's Roche limit when their in crowds?[edit]

I mean, they are really close together, maybe in eachother's Roche limit! AtomicSphere 19:59, 27 June 2022 (UTC)[reply]

The simple computation of the Roche limit at Roche limit#Rigid-satellite calculation assumes that the satellite is in hydrostatic equilibrium, meaning in particular that it is held together only by its own self-gravity. That assumption is radically wrong for humans. Their self-gravity is completely negligible; they are held together by their tensile strength. --Trovatore (talk) 20:27, 27 June 2022 (UTC)[reply]

By extensional metaphor, we could model complicated behaviors using some kind of effective potential, describing the crowd's behavior in aggregate "as if" it were controlled by attractive or repulsive forces between individuals...

Such modeling methods are used in both practical- and artistic- applications. For example, big-budget motion pictures might use crowd simulation to animate large groups of people for visual effects in filmmaking. Some of these methods are specifically particle system models. If one were inclined, one could tease apart the equations and work the similarities- and differences- from an inverse-square-law model. Similar methods could be used for non-filmmaking purposes to model things like foot-traffic for architectural design, fire-safety, and so on.

But the big caveat is that the dynamics of a crowd of people are more complicated - a simple inverse square law would make for a poor and unrealistic model of the crowd. Therefore, a Roche limit-like horizon - at least, one that is a consequence of an inverse square law - would probably not emerge from a well-designed model.

Applied mathematics is full of techniques for studying complex systems - and equally so, it is full of attempts to extract simplified group-dynamics from diverse governing equations. A recurring theme is explored in chaos theory: even very simple governing equations lead to unpredictability. These emergent properties would make it hard, in any non-trivial system, to rigorously define any 'limit' analogous to the Roche limit we compute for an inverse-square-law system.

Nimur (talk) 21:01, 27 June 2022 (UTC)[reply]

Nimur, I'm not sure I've understood what you're getting at, but I don't think it's what the OP meant. As I understood it, the OP was asking why you don't get torn apart by tidal forces when you walk too close to another person. --Trovatore (talk) 21:49, 27 June 2022 (UTC)[reply]

Obviously we're in agreement that the actual force of gravity is irrelevant in these scenarios ... gravity is very weak.

But the point I was making is that we can make mathematical models for emergent behaviors - we can write relations to express whether characters walk toward- or away from each other. That is to say - we can model groups of people using methods that are normally used for particle-dynamics. Then, we can use these models to study how crowds form and dissipate. These kinds of approaches aren't (necessarily) tracking any "physical law" - the governing equations are purely synthetic, and usually selected because they make cool results. Anything we conclude from the results is only as good as our computer-model. Real human individuals don't obey simple mathematical laws governing their trajectories - but animated characters in a video-game or film might do!

Here's an example - this is a tutorial for animating crowds using Unreal Engine. Around the 1 minute mark, the animator shows "traditional" crowd simulations using targets and collision dynamics; ... around the 19 minute mark, you can see the animator/programmer playing with a particle simulator by controlling parameters like effective collision radii, which is much more performant...

These kinds of approaches can be used to model or simulate how a crowd forms (or disperses). If the collision radii is too small, the characters collide in an unrealistic way; but if that same parameter is too large, the crowd disperses!

I sort of imagine you could describe a "Roche limit" metaphor to describe the circumstances that cause a group to "disperse"...

In case it's not clear, I'll reiterate: these are not physically valid models of crowds - they're dramatic simplifications that follow simple programmed rules or equations. They're basically just simple equations that are useful for creating cool animations. If you were mathematically inclined, you could manipulate those equations ad infinitum to see how the emergent behaviors compare with other particle-dynamics models, like an n-body gravity simulation; and you could try to find analogous modalities.

Nimur (talk) 00:39, 28 June 2022 (UTC)[reply]

I 100% agree with Nimur. -- Charlesreid1 (talk) 06:12, 30 June 2022 (UTC)[reply]

We stand on planet Earth, and it doesn't tear us apart (does it?) so it's unlikely standing next to a way much smaller-mass object, such as another human, would tear us apart (physically, anyway). --←Baseball Bugs ^{What's up, Doc?} carrots→ 11:41, 30 June 2022 (UTC)[reply]

I 90% agree that Baseball Bugs' self attraction will hold. Philvoids (talk) 15:46, 30 June 2022 (UTC)[reply]

You lost me at the bakery. --←Baseball Bugs ^{What's up, Doc?} carrots→ 22:56, 30 June 2022 (UTC)[reply]