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Comment by maitola | Hacker News Reader

I love the ironic side of the article. Perhaps they should add the reason for it, from Fermi's and Neumann's. When you are building a model of reality in Physics, If something doesn’t fit the experiments, you can’t just add a parameter (or more) variate it and fit the data. The model should have zero parameters, ideally, or the least possible, or, even at a more deeper level, the parameters should emerge naturally from some simple assumptions. With 4 parameters you don’t know whether you are really capturing a true aspect of reality of just fitting the data of some experiment.

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This was mentioned in the first paragraph of the paper. The paper is mostly humoristic.

That said, the wisdom of the quip has been widely lost in many fields. In many fields data is "modeled" with huge regression models with dozens of parameters or even neural networks with billions of parameters.

> In 1953, Enrico Fermi criticized Dyson’s model by quoting Johnny von Neumann: “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”[1]. This quote is intended to tell Dyson that while his model may appear complex and precise, merely increasing the number of parameters to fit the data does not necessarily imply that the model has real physical significance.

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.

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

There will be no Copernicus if everybody just studies epicycles. E.g. there are massive resources put into the desperate WIMP hunt that could be used for finding new theories.

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?

Of course. It's called theoretical physics.

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

I used to think this, but dark matter does make useful predictions, that are hard to explain otherwise.

This is partially because there are two ways to detect dark-matter. The first is gravitational lensing. The second is the rotatinal speed of galaxies. There are some galaxies that need less Dark Matter to explain their rotational speed. We can then cross check whether those galaxies cause less gravitational lensing.

Besides that, the gravitational lensing of galaxies being stronger than the bright matter in the galaxies can justify is hard to explain without dark matter.

The problem with dark matter is that there's no (working) theory on how the dark matter is distributed. It's really easy to "explain" gravitational effects if you can postulate extra mass ad-hoc to fit the observations.

If there are two different types of observations, and one parameter can explain both, that is pretty strong evidence. Put differently, dark matter is falsifyable, and experiments have tried to falsify it without success.

Besides the idea 'not all mass can be seen optically' is not that surprising. The many theories on what that mass might be are all speculation, but they are treated as such.

It's worth noting that one dark matter explanation is just: it's cold matter we just can't see through telescopes. Or black holes without accretion disks.

Both of these are pretty much ruled out though: you can't plausibly add enough brown dwarfs, and if it's black holes then you should see more lensing events towards nearby stars given how many you'd need.

But they're both concrete predictions which are falsifiable (or boundable such that they can't be the dominant contributors).

I dunno if this is the correct way of thinking about it, but I just imagine it as a particle that has mass but does not interact with other particles (except at big-bang like energy levels?). So essentially a galaxy would be full of these particles zipping around never colliding with anything. And over time, some/most of these particles would have stable orbits (as the ones in unstable orbits would have flown off by now) around the galactic core. And to an observer, it would look like a gravitational tractor ahead of the rest of the physical mass of the galaxy (which is slower because it is affected by things like friction and collisions?). And so you'd see galaxies where the arms are spinning faster than they should be?

> I dunno if this is the correct way of thinking about it, but I just imagine it as a particle that has mass but does not interact with other particles (except at big-bang like energy levels?).

Not even anything that extreme. What's ruled out is interaction via electromagnetism (or if you want to get really nit-picky, electromagnetic interaction with a strength above some extremely low threshold).

The dark matter theory is falsifiable. Sure we can't see dark matter (it doesn't interact electromagnetically), but we can see its effects, and it has to follow the laws of physics as we understand them today.

It is actually a satisfying theory with regard to the Occam razor. We don't have to change our laws of physics to explain the abnormal rotations of galaxy, we just need "stuff" that we can't see and yet interact gravitationally. When we have stuff like neutrinos, it is not that far fetched. In fact, though unlikely given our current understanding of physics, dark matter could be neutrinos.

If, as it turn out, the invisible stuff we call dark matter doesn't follow the laws of physics as we know them, then the dark matter theory is falsified and we need a new one (or at least some tweaks). And it may actually be the case as a recent paper claims that gravitational lensing doesn't match the predictions of the dark matter theory.

The main competitor to dark matter is modified gravity, which calls for no new stuff, but changes the equations for gravity. For the Occam razor, adding some random term to an equation is not really better than adding some invisible but well characterized stuff, especially when we consider that the equation in question is extremely well tested. It is, of course, also falsifiable.

The problem right now is not that these theories are unfalsifiable, it is that they are already pretty much falsified in their current form (dark matter less than modified gravity), and some rework is needed.

> Sure we can't see dark matter (it doesn't interact electromagnetically), but we can see its effects

Even this is granting too much: "seeing it" and "seeing its effects" are the same thing. No one has ever "directly seen", in the sense that internet DM skepticism demands, anything other than a photon.

"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 bodies, but there are no additional relationships with any other data, which could corroborate the computed distribution of dark matter. That is what some people mean by "seeing".

All major DM candidates also have multiple interactions: that's the WI in WIMP, for instance. In fact I don't know that anyone is seriously proposing that dark matter is just bare mass with no other properties - aside from the practical problems, that would be a pretty radical departure from the last century of particle physics.

No interactions have been found, despite a lot of resources put into the search. So currently all dark matter particle theories apart from "non-interacting" have been falsified. And non-interacting theories are probably unfalsifiable.

Radical departure may well be needed, for other reasons too.

> 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 imaginary 'particle' that solves them: that's DM.

The problem is that the language used to talk about DM is wrong. It's not that DM doesn't interact with EM, or the presence of DM is causing the galaxies to rotate faster than by observed mass. These are all putting the cart before the horse. What we have is unexplained gravitational effects being attributed to a hypothetical particle. If we discovered a new unexplained gravitational property, we would merely add that to the list of DM's attributes rather than say "oh then it can't be DM".

> 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.

> For the Occam razor, adding some random term to an equation is not really better than adding some invisible but well characterized stuff...

You're being too kind. It's worse. Especially when (in my understanding anyway) that added term doesn't even explain all the things dark matter does.

Adding any finite number of parameters is strictly better than adding an infinity of parameters (i.e. an arbitrary distribution of dark matter chosen to match the observations).

The distribution has to be consistent forward and backwards in time. It's a lot less arbitrary than you're implying, and adding a hundred parameters (or similar finite number) to gravity is not better.

If we add an arbitrary amount of dark matter everywhere, to match the observed motions of the celestial bodies, that adds an infinity of parameters, and not even a enumerable one.

This obviously can match almost anything and it has extremely low predictive power (many future observations may differ from predictions, which can be accounted by some dark matter whose distribution was previously unknown), so it is a much worse explanation than a modified theory of gravity that would have only a finite number of additional parameters.

> to match the observed motions of the celestial bodies

The point is that even with current observational data there's no reasonable distribution of dark matter that correctly explains all evidence that we have.

Your intuition that "if I have an infinite number of degrees of freedom anything at all can be fit" is leading you astray here.

the reason this isn't true is that by the hypothesis of dark matter, it follows gravity but not electromagnetism. as such it only fits distributions recoverable from evolving gravity. e.g. if we require a certain distribution today, it fixes the distribution at all other points in time, and we can use light speed delay to look into the past to verify whether the distributions have evolved according to gravity.

All observations of individual galaxies occur at a specific point in time. We can’t use light speed delay to see the evolution of individual galaxies only completely different galaxies at some other point in time. As such each galaxy gets its own value for the amount of dark matter.

At minimum this is a ~200 billion parameter model, and more if you’re looking at smaller structures.

That's equally true of the distribution of baryonic matter. We have to assess each galaxy individually to figure out what it's made of? What a crime against science. Never mind that they're still all made of a small handful of types of parts, which can nevertheless combine to form lots of possible histories and shapes for individual objects. Just like literally everything else in the observable universe. Seriously, what part of this argument is different for computing the amount of visible mass in each galaxy?

The availability to detect visible light from stars or detect that light being blocked by baryonic matter.

With dark matter it’s two steps removed where we’re inferring the behavior of baryonic matter and then inferring the amount of baryonic matter we aren’t observing and then calculating the existence of dark matter to get that behavior after accounting for undetected baryonic matter.

Yeah, that's a pain, but calculating mass from photons is still pretty indirect. More importantly, and independently of "directness", no one pretends that galaxies having different masses introduces two billion parameters into our models of cosmology. Because that's not what a model of cosmology is.

Calculating the percentage of the universe’s observable mass is dark matter adds 200+ billion parameters because the mass fraction of each galaxy varies.

So there’s no simple way to calculate it from say looking at the Milky Way alone and extrapolating from the baryonic mass of the rest of the universe. Trying to approximate things from a representative sample is its own problem.

You're still confusing a physics model with a map of the universe. That said, it's sure a heck of a coincidence that the number they get from adding up estimated dark matter in galaxies lines up with the number they get from other cosmological measurements, isn't it? Almost like galaxy rotation curves aren't the only evidence for dark matter and haven't been for a long time. https://en.wikipedia.org/wiki/Dark_matter#Observational_evid...

Gravitational lensing, velocity dispersions, etc circles back to the total mass of galaxies. So it shows up on many of the ways we calculate the total mass fraction not just rotation anomalies.

Many of the ways? I guess that's it then, there's no reason to look at the whole picture, and especially no point in reading all the way to https://en.wikipedia.org/wiki/Dark_matter#Cosmic_microwave_b...

Your being redundant, Many in this instance obviously implied not every.

Then, in what way is it relevant to my claims here? Namely,

1. Dark matter does not meaningfully introduce billions more parameters into cosmological models than they already have, and

2. Individual galaxies' dark matter fractions are not essential to (not proving, but) strongly suggesting dark matter exists.

Something being consistent with a model is different than something being sufficient evidence on its own to support a model.

If the observed dark matter fractions of all known galaxies were 0% but the CMB was unchanged we wouldn’t assume dark matter exists. Thus your #2 is false. There’s infinite models consistent with any observation so finding something after a model was created for other reasons is useful as validation, but the chain of logic is still dependent on the prior observations not the model.

In a meaningfully different cosmos different observations would have happened and different models would exist. Trying to pick out specific experiments as sufficient on their own glosses over that particular limitation.

> If the observed dark matter fractions of all known galaxies were 0% but the CMB was unchanged we wouldn’t assume dark matter exists.

No, astrophysicists would eventually figure out something was up when they couldn't replicate the actual spectrum with dark-matter-free simulations. Why would you assume otherwise? Unless you want to dig into the assumptions of the scenario, in which case you're probably proposing a self-inconsistent universe so of course you can draw whatever conclusions you want from it.

> There’s infinite models consistent with any observation...

You can't actually believe this and still believe in science. If observations don't constrain models, then there is no point in observing. And in the long run, there's asymptotically no difference between "prior observations" and later observations. They're just observations that all go into the same model-constraining mill. Scientists are not fools, and are capable of realizing when an initial observation put them on a wrong trail.

You're still barely touching the real point. This all just sounds like rationalizations to avoid the fact that dark matter, for now at least, and for all that it genuinely sucks, is the Occam's razor explanation for the full suite of observations. Why is this so hard to accept?

'dark matter' is not a theory, it is the name of an observational problem.

There are many theories to explain dark matter observations. MOND is not a competitor with 'dark matter', because MOND is a theory and it tries to explain some aspects (spiral galaxy rotation) of what is observed as the dark matter problem, which consists of many more observations. There is no competition here. There are other theories to explain dark matter, like dark matter particle theories involving neutrinos or whatever, and these may be called competitors, but dark matter itself is not a theory, but a problem statement.

Yes and no...MOND's core proposition is that dark matter doesn't exist, and instead modified gravity does.

Whereas you can have many proposals for what dark matter is, provided it is capable of being almost entirely only gravitationally interacting, and there's enough of it.

MOND has had the problem that depending which MOND you're talking about, it still doesn't explain all the dark matter (so now you're pulling free parameters on top of free parameters).

I've seen this opinion before, but can't seem to square it with any reliable source.

Wikipedia has: "dark matter is a hypothetical form of matter that appears not to interact with light or the electromagnetic field ... Although the astrophysics community generally accepts dark matter's existence, a minority of astrophysicists, intrigued by specific observations that are not well-explained by ordinary dark matter, argue for various modifications of the standard laws of general relativity. These include modified Newtonian dynamics, tensor–vector–scalar gravity, or entropic gravity."

Even its name, "dark matter", sort of strongly implies this. If someone were just trying to refer to the observations, rather than a specific explanation for the observations, wouldn't they just say "abnormal galaxy rotation curves" rather than "dark matter"?

I'm not saying Wikipedia is an end-all-be-all source on this, I'm just asking where you're getting this alternate definition. If it is somewhere reliable then perhaps the article needs to be rephrased.

As far as I know it's from here: https://www.youtube.com/watch?v=PbmJkMhmrVI As I said elsewhere in this thread, I think she's trying to make some meta point but ends up just muddying the water.

> 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 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; you don't strictly need large scale homogeneity and isotropy but you really really want it, etc. Lambda-CDM doesn't handle everything perfectly (which in itself demonstrates that it's not mindless overfitting) but neither does anything else.

You also have to do other things like not break General Relativity.

Which MOND does: it creates huge problems fitting into GR.

Whereas dark matter as just regular mass that interacts poorly by other means does not.

There are modified gravity theories that are compatible/extensions to GR, e.g the f(R) gravity theories.

Nobody probably believes MOND as such is some fundamental theory, rather as a "theory" it's sort of a stepping stone. Also MOND is used often interchangeably (and confusingly) with modified gravity theories in general.

> 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.

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] https://www.youtube.com/watch?v=PbmJkMhmrVI

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?

> > In 1953, Enrico Fermi criticized Dyson’s model by quoting Johnny von Neumann: “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

For those who are interested, you can watch Freeman Dyson recount this conversation in his own words in an interview: https://youtu.be/hV41QEKiMlM

I think a model with zero parameters belongs more to math, because it can be derived from first principles. E.g. The surface area of a sphere is 4/3 * pi * r^3, assuming Euclidean space. Physics begins when we have at least one constant of nature to measure, like the actual curvature of space or the attraction due to gravity.

Hmm..

Hodgin and Huxley did ground-breaking work on squid's giant axon and modelled neural activity. They had multiple parameters extracted from 'curve fitting' of recorded potential and injected currents which were much later mapped to sodium channels. Similarly, another process to potassium channels.

I woudnt worry too much having multiple parameters -- even four when 3 can't just explain the model.

Neuron anatomy is the product of hundreds of millions of years of brute contingency. There are reasons why it can't be certain ways (organisms that were that way [would have] died or failed to reproduce) but no reason whatsoever why it had to be exactly this way. It didn't, there are plenty of other ways that nerves could have worked, this is just the way they actually do.

The physics equivalent is something like eternal inflation as an explanation for apparent fine-tuning - except that even if it's correct it's still absolutely nowhere near as complex or as contingent as biology.

The balance between empirical data fitting and genuine understanding of the underlying reality

Notably done for the first time irl in "Least square fitting of an elephant", James Wei (1975) Chemtech

https://demonstrations.wolfram.com/FittingAnElephant/

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

Yes, it is.

Which makes the only truly zero parameter system the collection of all systems, in all forms.

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 parameters does the Standard Model have? It's not clear what you count as a parameter. Do you count the group structure, the other mathematical structure that has been "fitted" through decades of comparisons with experiments?

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.

It tends to be a parameter that can be derived from rrasoning and assumptions. This contrasts to free parameters where you say "and we have no idea what this value should be, so we'll measure it"

Kolmogorov complexity[0] solves this loophole :)

[0] https://en.wikipedia.org/wiki/Kolmogorov_complexity

Kolmogorov complexity is an effort to wrangle it. It's impossible to fully solve.

You can change measured complexity by altering the baseline assumptions.

What do you mean by baseline assumptions? The low level computer instructions?

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