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Fitting an elephant with four non-zero parameters

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Re: Fitting an elephant with four non-zero parameters

#121

Post by zellyn »

pharmacy7766 wrote: post #28

One parameter is enough: https://aip.scitation.org/doi/10.1063/1.5031956

From the paper:

> Paintadosi [4] argues that one parameter is always enough. He constructed a function that, through a single parameter, can depict any shape. However, in essence, this work is a form of encoding, mapping the shape into a real number with precision extending to hundreds or even thousands of decimal places. For our problem, this is meaningless, although the paper’s theme is that “parameter counting” fails as a measure of model complexity

Re: Fitting an elephant with four non-zero parameters

#122

Post by slashdave »

tobias2014 wrote: post #51
edflsafoiewq wrote: post #48

Earlier quoted context omitted.

Isn't the form of an equation really just another sort of parameter?

This is why I think that modeling elementary physics is nothing else than fitting data. We might end up with something that we perceive as "simple", or not. But in any case all the fitting has been hidden in the process of ruling out models. It's just that a lot of the fitting process is (implicitly) being done by theorists; we come up with new models and that are then being falsified. For example, how many parameter…

You are using the word "fitting" rather loosely. We usually "fit" models of fixed function form and fixed number of parameters.

You are also glossing over centuries of precedent that predate high-energy physics, namely quantum field theory, special relativity, and foundational principles such as conservation of energy and momentum.

Re: Fitting an elephant with four non-zero parameters

#123

Post by nyssos »

karmakaze wrote: post #119
adrian_b wrote: post #90

Earlier quoted context omitted.

"Seeing" is indeed a poorly chosen word. The problem with dark matter is that there does not exist any second relationship from which to verify its existence, like in the case of normal matter, which takes part in a variety of interactions that lead to measurable effects, which can be compared. The amount and the location of dark matter is computed from the gravitational forces that explain the observed movements of…

> The problem with dark matter is that there does not exist any second relationship from which to verify its existence. This is exactly it! Dark matter is strictly defined by its effects. The only 'theory' part is a belief that it's caused by yet to be found particle that's distributed to fit observations. Take all the gravitational anomalies that we can't explain with ordinary matter, then arbitrarily distribute an…

> Dark matter is strictly defined by its effects

All physical entities are defined by their effects! Suppose we found axions and they had the right mass to be dark matter. Would that mean we now "really knew" what dark matter was, in your sense? No, it would just push the defining effects further back - because all an axion is is a quantum of the (strong CP-violation term promoted to a field).

Just like the electromagnetic field is the one that acts on charged particles in such and such a way, and a particle is charged if the electromagnetic field acts on it in that way. There's no deeper essence, no intuitive "substance" with some sort of intrinsic nature. All physical properties are relational.

Re: Fitting an elephant with four non-zero parameters

#124

Post by aeneasmackenzie »

fiddlerwoaroof wrote: post #95
edflsafoiewq wrote: post #50

Earlier quoted context omitted.

It's easy to say "Epicycles! Epicycles!", but people are going to continue using their epicycles until a Copernicus comes along.

Well, the funny thing is Copernicus posits just about as many epicycles in his theory as previous geocentric theories. Only Kepler’s discovery of the equal area law and elliptical orbits successfully banishes epicycles.

The history of these discoveries is fascinating and shows that Kuhn’s scientific revolutions idea is wrong but it’s always rounded off to “Copernicus and Galileo” and doesn’t even get them right

Re: Fitting an elephant with four non-zero parameters

#125

Post by karmakaze »

nyssos wrote: post #69
karmakaze wrote: post #43

Earlier quoted context omitted.

That's how I feel about dark matter. Oh this galaxy is slower than this other similar one. The first one must have less dark matter then. What can't be fit by declaring the amount of dark matter that must be present fits the data? It's unfalsifiable, just because we haven't found it, doesn't mean it doesn't exist. Even worse than string/M-theory which at least has math.

> What can't be fit by declaring the amount of dark matter that must be present fits the data? Tons of things - just like there are tons of things that can't be fit by declaring the amount of electromagnetically-interacting matter that must be present fits the data. You can fit anything you like by positing new and more complicated laws of physics, but that's not what's going on here. Dark matter is ordinary mass gra…

> Dark matter is ordinary mass gravitating in an ordinary way: the observed gravitational lensing needs to match up with the rotation curves needs to match up with the velocity distributions of galaxies in clusters

Those are all the same thing, the shape of spacetime. The only thing DM adds is a backstory that this shaping comes from hypothetical undiscovered particles with properties that match observations.

Re: Fitting an elephant with four non-zero parameters

#126

Post by andrewflnr »

karmakaze wrote: post #120
andrewflnr wrote: post #83

Earlier quoted context omitted.

Dark matter is constrained by, among other things, dynamical simulations. For instance, here's an example of reproducing real world observations, that previously didn't have great explanations, using simulations with dark matter: https://www.youtube.com/live/8rok8E_tz8k?si=Q7vmQYpZr_6K7--m . And that's not even getting into the cosmology that has to (and mostly does) fit together.

Interesting that you should link that video. Its title card says "Angela Collier". Here's a more recent video by the physicist[0]. Re: where it says "using simulations with dark matter", we can't simulate DM because it doesn't have any properties beyond our observations. All we do is distribute amounts of it to match observations. It could be "Dyson spheres with EM shields" and the results would be the same. [0] http…

Yes, and I think that video is stupid. She doesn't use the term that way in her own talk, and neither does any scientist I've ever heard. I think she's trying to make some abstract point about science in general and muddying the water in the process. Her takes on terminology are often bad IMO.

That doesn't take away the fact that when you work with the slightly more specific theory of "particle dark matter" it produces real results. And I believe there's a lot more work over the years in similar areas. It doesn't get talked about because it's not sexy, so people who only follow cosmology when there's drama don't hear about it. That was just the example at the top of my mind because I'd seen it recently, and the result is really quite spectacular. Did you watch it through?

Re: Fitting an elephant with four non-zero parameters

#128

Post by aqme28 »

nyssos wrote: post #76
aqme28 wrote: post #34

> It only satisfies a weaker condition, i.e., using four non-zero parameters instead of four parameters. Why would that be a harder problem? In the case that you get a zero parameter, you could inflate it by some epsilon and the solution would basically be the same.

> In the case that you get a zero parameter, you could inflate it by some epsilon and the solution would basically be the same. Not everything is continuous. Add an epsilon worth of torsion to GR and you don't get almost-GR, you get a qualitatively different theory in which potentially arbitrarily large violations of the equivalence principle are possible.

That's not relevant here though, because their function is continuous and they're fitting to an arbitrary shape. It's not a "perfect science," so there would be wiggle room.

Re: Fitting an elephant with four non-zero parameters

#129

Post by Dylan16807 »

jampekka wrote: post #115
Dylan16807 wrote: post #97

Earlier quoted context omitted.

I don't see how those resources are fungible with each other.

Research funding is very competitive and scarce.

Building a physics machine, and thinking about how the equations might work, are so very different.

Does the latter even get funding?

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