Pushed Around by the Stars • Hacker News Board

Re: Pushed Around by the Stars

#11

Post by antognini » Thu, Dec 02, 2021, 7:02 AM UTC

pfdietz wrote: post #10

antognini wrote: post #7

Earlier quoted context omitted.

I don't think there's the exponential dependence they claim. I think a more correct derivation would look like this: Let's suppose that we place a 1 g mass at 4 ly. How does this affect the internal dynamics of a helium balloon? The relevant change is the tidal acceleration induced by the 1 g mass: a_tide ~ GMl/r^3 where l is the mean free path in the balloon (l ~ 1 / n sigma), where n is the number density and sigma…

I think the dependence is clearly exponential. The discrepancy in the scattering angle should grow by a factor of O(mean free path/radius of scatterer) per scattering event.

I think that for extremely small perturbations the discrepancy will be linear until it reaches a critical threshold, at which point the trajectories diverge exponentially. Basically, you need to get to the point where the path of one atom diverges by ~atomic radius. But until that happens, there is no non-linear mechanism to increase the divergence.

For example, if you just consider a billiard ball bouncing between two walls, the divergence in trajectories will only ever grow linearly. But for very small perturbations, the case of collisions between atoms is effectively the same as collisions between walls --- the curvature of the scattering atom can be neglected. After all, the curvature here is a second order term, and when the perturbation is of the order of 10^-68, the non-linear factor will be (10^-68)^2 ~ 10^-136.

Re: Pushed Around by the Stars

#12

Post by pfdietz » Thu, Dec 02, 2021, 12:57 PM UTC

antognini wrote: post #11

pfdietz wrote: post #10

Earlier quoted context omitted.

I think the dependence is clearly exponential. The discrepancy in the scattering angle should grow by a factor of O(mean free path/radius of scatterer) per scattering event.

I think that for extremely small perturbations the discrepancy will be linear until it reaches a critical threshold, at which point the trajectories diverge exponentially. Basically, you need to get to the point where the path of one atom diverges by ~atomic radius. But until that happens, there is no non-linear mechanism to increase the divergence. For example, if you just consider a billiard ball bouncing between t…

> I think that for extremely small perturbations the discrepancy will be linear until it reaches a critical threshold

An error of epsilon on the angle of a path toward the scatter will cause an error of ~(distance to scatter/size of scatter) epsilon in the angle from the center of the scatterer to the "impact point". So the errors should grow exponentially in the number of scatterings.

The (effective) curvature of the scatterer CANNOT be neglected -- it is crucial. Modeling this with large flat reflectors is not appropriate.

Re: Pushed Around by the Stars

#13

Post by dsizzle » Thu, Dec 02, 2021, 1:31 PM UTC

perl4ever wrote: post #9

dsizzle wrote: post #3

> Everything affects everything else, and the correct questions to ask are how much? I don't think this is true. It's true that interstellar mass movements affect atomic motions on earth (the theory is well understood!), but it's not true that the movements affect, say, whether a particular computer program correctly meets a given spec: they're simply at different levels of explanation. One can't even imagine a theor…

>One can't even imagine a theory that connects them. You are saying that atomic motions on earth cannot affect computer programs? Or are you saying that some atomic motions on earth cannot affect computer programs? If the latter, then how, theoretically, would you divide them into those that can and those that can't?

The distinction I'm making is not between different types of atomic motions, but between properties of an algorithm (eg whether it meets a spec) and the physical instantiation of the algorithm running on some computer: ie software vs hardware. Hardware is subject to physics (cosmic rays etc), but software is not. There are lots of examples like this where the subject of interest occurs at different levels of emergence/analysis.

I wouldn't be going down this tangent if the author didn't make such strong, overbroad statements that amount to "everything affects everything," and instead said something like "small, distant phenomena can have surprisingly non-negligible effects" or something, but I get the impression the author would argue against this change on fundamental (vs pedantic) grounds.

For what it's worth, I like the story referenced in the blog's name https://eighteenthelephant.com/2013/08/02/167/

Re: Pushed Around by the Stars

#14

Post by r_parthasarathy » Thu, Dec 02, 2021, 3:40 PM UTC

antognini wrote: post #11

pfdietz wrote: post #10

Earlier quoted context omitted.

I think the dependence is clearly exponential. The discrepancy in the scattering angle should grow by a factor of O(mean free path/radius of scatterer) per scattering event.

I think that for extremely small perturbations the discrepancy will be linear until it reaches a critical threshold, at which point the trajectories diverge exponentially. Basically, you need to get to the point where the path of one atom diverges by ~atomic radius. But until that happens, there is no non-linear mechanism to increase the divergence. For example, if you just consider a billiard ball bouncing between t…

pfdietz is correct. The key thing is that divergences always multiply, leading to an exponential dependence on number of scattering events. There isn't a transition between a linear and an exponential dependence. I think where you're getting confused is that an exponential can be initially approximated by a linear function (i.e. exp(x) ~= 1 + x), but that doesn't mean that the process is linear.

The dominance of the exponential growth is also why the tidal correction, as massive as it seems, gets swamped and ends up not mattering much.

-- Raghu Parthasarathy

Re: Pushed Around by the Stars

#15

Post by r_parthasarathy » Thu, Dec 02, 2021, 3:46 PM UTC

dsizzle wrote: post #13

perl4ever wrote: post #9

Earlier quoted context omitted.

>One can't even imagine a theory that connects them. You are saying that atomic motions on earth cannot affect computer programs? Or are you saying that some atomic motions on earth cannot affect computer programs? If the latter, then how, theoretically, would you divide them into those that can and those that can't?

The distinction I'm making is not between different types of atomic motions, but between properties of an algorithm (eg whether it meets a spec) and the physical instantiation of the algorithm running on some computer: ie software vs hardware. Hardware is subject to physics (cosmic rays etc), but software is not. There are lots of examples like this where the subject of interest occurs at different levels of emergenc…

Your comment is a good one, and I don't have time for a long reply, but I'll point out that the motivation for my being a bit "overblown" is the unfortunate and very common tendency of many people to have a nonsensical "null hypothesis" that there's precisely zero effect of something on something else, as if it's at all sensible that there are zero connections. I work, for example, on microbiome research, and there's an unending stream of papers testing the "hypothesis" of "the gut microbiome affects X" rather than "what's the magnitude of the effect of the gut microbiome on X". I'm writing quickly, but hopefully this makes sense.

Glad you like the blog name, by the way!

Re: Pushed Around by the Stars

#16

Post by perl4ever » Thu, Dec 02, 2021, 4:35 PM UTC

dsizzle wrote: post #13

perl4ever wrote: post #9

Earlier quoted context omitted.

>One can't even imagine a theory that connects them. You are saying that atomic motions on earth cannot affect computer programs? Or are you saying that some atomic motions on earth cannot affect computer programs? If the latter, then how, theoretically, would you divide them into those that can and those that can't?

The distinction I'm making is not between different types of atomic motions, but between properties of an algorithm (eg whether it meets a spec) and the physical instantiation of the algorithm running on some computer: ie software vs hardware. Hardware is subject to physics (cosmic rays etc), but software is not. There are lots of examples like this where the subject of interest occurs at different levels of emergenc…

>strong, overbroad statements that amount to "everything affects everything,"

Perhaps the author did not mean to include abstractions as "things" in this context?

I think you're discussing metaphysics and I don't see the connection to the article.

I guess gravity doesn't affect faith, hope, or charity, but is that news, or actionable?

Re: Pushed Around by the Stars

#17

Post by dsizzle » Thu, Dec 02, 2021, 4:36 PM UTC

r_parthasarathy wrote: post #15

dsizzle wrote: post #13

Earlier quoted context omitted.

The distinction I'm making is not between different types of atomic motions, but between properties of an algorithm (eg whether it meets a spec) and the physical instantiation of the algorithm running on some computer: ie software vs hardware. Hardware is subject to physics (cosmic rays etc), but software is not. There are lots of examples like this where the subject of interest occurs at different levels of emergenc…

Your comment is a good one, and I don't have time for a long reply, but I'll point out that the motivation for my being a bit "overblown" is the unfortunate and very common tendency of many people to have a nonsensical "null hypothesis" that there's precisely zero effect of something on something else, as if it's at all sensible that there are zero connections. I work, for example, on microbiome research, and there's…

Thanks for the reply. I would be interested in your longer reply, if you get the chance!

I get where you're coming from now that you mention the microbiome. That similarly reminds me of headlines like "antidepressants alter the brain," specifically variations that imply something groundbreaking; on some level it IS impressive that physical effects can be observed, but on another, it's almost trivially true that it affects the brain, because where else do thoughts originate? In fact, speaking of depression, there's probably studies exactly like what you described where depression is X.

I think this could be usefully tied back to the software/hardware distinction I raised. Some might say that, in a lot of cases, depression is due to faults in "software" -- negative thinking, assuming the worst, etc, -- or at least is better treated as though it were. This is opposed to faults in "hardware" -- insufficient production of serotonin, or whatever (and I'm sure there cases where this is the best explanation/treatment).

So maybe a certain microbiome state is like a computer running on the Mars rover where its hardware is subjected to fault-inducing radiation? The software/hardware distinction probably isn't as clean in the brain compared to our silicon-based computers! We know so little in this area that it probably does make sense to proceed as though everything affects everything, as you say -- but I also think it's important to allow that it may not.

Re: Pushed Around by the Stars

#18

Post by dsizzle » Thu, Dec 02, 2021, 5:00 PM UTC

perl4ever wrote: post #16

dsizzle wrote: post #13

Earlier quoted context omitted.

The distinction I'm making is not between different types of atomic motions, but between properties of an algorithm (eg whether it meets a spec) and the physical instantiation of the algorithm running on some computer: ie software vs hardware. Hardware is subject to physics (cosmic rays etc), but software is not. There are lots of examples like this where the subject of interest occurs at different levels of emergenc…

>strong, overbroad statements that amount to "everything affects everything," Perhaps the author did not mean to include abstractions as "things" in this context? I think you're discussing metaphysics and I don't see the connection to the article. I guess gravity doesn't affect faith, hope, or charity, but is that news, or actionable?

First, I'd say it'd be an impoverished scientific worldview that excludes algorithms just because it's not a "thing" per se!

But I could have just as well chosen a "thing"-ier example. For example, do quarks/the strong nuclear force affect the melting point of metals? There's probably a large "parameter space" where it literally has zero effect (in some part of parameter space atoms cease to exist, so it is a leaky abstraction!). But you can have melting phenomena in substrates that don't even have quarks. In fact, to bring it back to software, you can get melting phenomena in a pure algorithm like the Ising model.

(I won't comment on what the author meant to include -- he responded to me earlier, and maybe he'll respond to this too.)

Re: Pushed Around by the Stars

#19

Post by perl4ever » Thu, Dec 02, 2021, 5:15 PM UTC

dsizzle wrote: post #18

perl4ever wrote: post #16

Earlier quoted context omitted.

>strong, overbroad statements that amount to "everything affects everything," Perhaps the author did not mean to include abstractions as "things" in this context? I think you're discussing metaphysics and I don't see the connection to the article. I guess gravity doesn't affect faith, hope, or charity, but is that news, or actionable?

First, I'd say it'd be an impoverished scientific worldview that excludes algorithms just because it's not a "thing" per se! But I could have just as well chosen a "thing"-ier example. For example, do quarks/the strong nuclear force affect the melting point of metals? There's probably a large "parameter space" where it literally has zero effect (in some part of parameter space atoms cease to exist, so it is a leaky a…

You sound like you are champing at the bit to get into the argument about whether there is a difference between rain in "reality" and rain in a simulation.

All I have to say about the question of whether there is a difference between physics and metaphysics is to quote "Reality is that which, when you stop believing in it, doesn’t go away".

Which is really the same thing as Samuel Johnson kicking a stone: "I refute it thus."

Whether or not you like the distinction, it remains.

And while only the author can say what they intended, I didn't see any hint in the article of this topic.

Re: Pushed Around by the Stars

#20

Post by dsizzle » Thu, Dec 02, 2021, 5:35 PM UTC

perl4ever wrote: post #19

dsizzle wrote: post #18

Earlier quoted context omitted.

First, I'd say it'd be an impoverished scientific worldview that excludes algorithms just because it's not a "thing" per se! But I could have just as well chosen a "thing"-ier example. For example, do quarks/the strong nuclear force affect the melting point of metals? There's probably a large "parameter space" where it literally has zero effect (in some part of parameter space atoms cease to exist, so it is a leaky a…

You sound like you are champing at the bit to get into the argument about whether there is a difference between rain in "reality" and rain in a simulation. All I have to say about the question of whether there is a difference between physics and metaphysics is to quote "Reality is that which, when you stop believing in it, doesn’t go away". Which is really the same thing as Samuel Johnson kicking a stone: "I refute i…

Conversely you now seem focused on getting into an argument about simulations -- I gave an example of what I meant that doesn't involve simulations and is purely physical but you didn't comment on that.

It's true I've focused on something that wasn't the meat of the original post -- but it's also true that I challenged a direct quote that is arguably the most profound claim in the post, and that's what I'm most interested in ¯\_(ツ)_/¯