# A Stunning Demonstration of Why Good Science Needs Good Math

Everyone is scientific circles is abuzz with the big news: there’s proof that dark matter exists! The paper from the scientists who made the discovered is [here][dark-matter-paper]; and a Sean Carroll (no relation) has [a very good explanation on his blog, Cosmic Variance][cv]. This discovery happens to work as a great example of just why good science needs good math.
As I always say, one of the ways to recognize a crackpot theory in physics is by the lack of math. For an example, you can look at the [electric universe][electric] folks. They have a theory, and they make predictions: but because there’s *no* math, the predictions are vague, and there’s no good way of *really* testing them, because there’s no quantifiable way of making a precise prediction – because there’s no math. So they can make predictions like “the stardust experiment will get bigger particles than they expect”; but they can’t tell you *how* big.
The dark matter result is a beautiful example of how to use good math in science.
Here’s the basic idea. The theory says that there are two kinds of matter: “dark” matter, and “light” matter. Dark matter only interacts with light matter via gravity; it does not interact with light matter via other forces. But dark matter and light matter generally clump in the same places – because gravity pulls them together. So it’s very difficult to really prove that dark matter exists – because you can’t see it directly, and it normally only appears with light matter, so you can’t really prove that the dark matter is there: any observed effect *might* be caused by the light matter behaving in a way different than our current theories claim it should.
But what if you could somehow sweep the light matter away?
What the scientists who did this work found is a collision of two galactic clusters. When these clusters collided, the light matter, mostly in the form of gas, interacted very strongly with one another, creating a shock wave pattern. But the *dark* matter passed through without interacting – the “collision” between the gas clouds didn’t affect the dark matter. So the gas clouds were swept back, while the dark matter continued moving. There’s a great animation illustrating this; in the animation, the blue is the dark matter; the red is the light matter. As the two clusters pass through each other, the light matter is swept away by the electromagnetic interactions between the gas clouds; the dark matter passes right through:

Here’s where the math comes in.
They used a combination of optical and X-ray telescope to produce maps of the gravitational fields of the clusters. This was done by computing the gravitational lensing effect distorting the images of other, more distant galaxies visible *behind* the collided clusters. By carefully computing the distortion caused by gravitational lensing, they were able to determine the distribution of *mass* in the collided clusters. And what they found was the bulk of the mass was *not* in the light matter. It was in the places that the center of gravities of the clusters would have been *without* the shock-wave effects of the collision. So the bulk of the mass of these two clusters do not appear on our telescope images; but it behaves exactly as the math predicts it would if it were dark matter.
The prediction and the result are both based on very careful computations based on the *mathematical* predictions of gravity and relativity. They were able to predict precisely what they would expect from the interaction using a mathematical model of the how the gas clouds would interact to be swept away; and how the dark matter would interact gravitationally to predict where the dark matter masses should be. Then they were able, via a *separate* computation to determine how much mass was in what location based on gravitational lensing. And finally, they were able to compare the two *separately computed* results to see if the reality matched the prediction.
Now *that* is both good math and good science! And the science could *not* have been done without the math.
[dark-matter-paper]: http://chandra.harvard.edu/photo/2006/1e0657/media/paper.pdf
[cv]: http://cosmicvariance.com/2006/08/21/dark-matter-exists/
[electric]: http://www.holoscience.com/
[animate]: http://chandra.harvard.edu/photo/2006/1e0657/media/bullet.mpg

## 0 thoughts on “A Stunning Demonstration of Why Good Science Needs Good Math”

1. Doug

Great thread! – but two questions.
How is the dark matter subject of this post different from essentially invisible neutrinos passing through planets like Earth?
How does the visible gas collision differ from Cherenkov radiation?

2. Mark C. Chu-Carroll

Doug:
You’d probably be better off heading for Cosmic Variance with questions about the physics; I’m just a math geek.
My understanding, such as it is:
(1) Neutrinos *do* interact with light matter. Not *much*, but they do interact. In something spanning the amount of space covered by gas clouds surrounding galactic clusters, they would be affected. The behavior would be noticably different than the masses passing through each other while the gas clouds were dramatically disrupted, which is what was observed.
(2) Cherenkov radiation is a strange phenomenon. It’s caused by a particle crossing a boundary between different materials where the speed of the particle is faster than the speed of light through the material. (Remember that the speed of light *in a vaccum* is an absolute maximum; the speed of light through other things can be slower.) My understanding is that what we see in collisions between different galaxies doesn’t involve particles interacting at relativistic speeds. But I could be wrong; as I said, I’m not a physicist.

Thanks for pointing out this – I hadn’t seen the original press release so I had missed this. They not only demonstrate dark matter unambigiously but also show really strong results that makes no sense from the view of the rival idea of modified gravity.
This is as Cosmic Variance (CV) points out both good and bad news. The good news is that this is the last piece in the CMBR cosmology puzzle, so now the prefered Lambda-CDM model seems robust. (CDM means after all Cold Dark Matter.) The bad news is that dark matter means a less revolutionary and helpful view on gravity and how a quantum gravity should be.
This is a good year for cosmology. Just yesterday I heard about a result that explains the observations of low lithium content compared to the expected from the primordial Big Bang Nucleosynthesis (BBN) CV mentions. Another major math feast of modelling observations and diffusion in stars show that lithium is concealed and broken down in the stars where it is. So now the BBN checks out too, which was a minor problem for big bang and Lambda-CDM. ( http://www.nature.com/nature/journal/v442/n7103/full/nature05011.html )
BTW, this is not my field but I think there are some minor mistakes in the post that should be pointed out in an effort to be as correct as possible.
– AFAIK, “light matter” is no term used. It is easily confused with heavy and light particles. “Normal matter” is probably used if it needs to be separated from the dark matter in matter.
– Dark matter may interact by more than gravity.
“The CDM theory makes no predictions about exactly what the cold dark matter particles are, and one large weakness in the cold dark matter theory is that it is unclear what the dark matter consists of.” ( http://en.wikipedia.org/wiki/Cold_dark_matter )
“In astrophysics, WIMPs, or weakly interacting massive particles, are hypothetical particles serving as one possible solution to the dark matter problem. These particles interact through the weak nuclear force and gravity, and possibly through other interactions no stronger than the weak force. Because they do not interact with electromagnetism they cannot be seen directly, and because they do not interact with the strong nuclear force they do not react strongly with atomic nuclei.” ( http://en.wikipedia.org/wiki/WIMP )
Lastly, on crackpots. My own preference is to use an operational definition ( http://math.ucr.edu/home/baez/crackpot.html ). It allows me to sort out serious crackpots from what I would like to call cranks.
I have an example of what seems to be a crank that fits right in with “the electric universe”. It is “the electric consciousness” by Glen Davidson. ( http://students.wwcc.edu/~glendavidson/website/ )
The short version, sorely needed in this long post, is that his PhD work, AFAIK only accessible in detail by buying his book (he publishes books of all sorts), is an idea in search of a theory. Ie todays work in neuroscience and nerve signals doesn’t seem to need his ideas of induction signals in the brain, so far.

Doug:
Good questions, so I will make a try. But check with CV.
1) Neutrinos are light and weakly interacting. Star produced neutrinos zip right through masses like our Earth. Even primordial neoutrinos from bigbang and BBN is probably too energetic. They are HDM (Hot DM) instead of the required CDM.
“The best candidate for hot dark matter is the neutrino. Neutrinos have very small mass, and do not partake in two of the four fundamental forces, the electromagnetic interaction, and strong interaction. They do interact with the weak nuclear force, and gravity, and are extremely difficult to detect.” ( http://www.answers.com/topic/hot-dark-matter )
In the context of the article HDM alone could have been fitted with modified gravity theories. But CDM and GR was always the most parsimonous theory.
2) Cherenkov radiation is emitted by charged particles travelling through a media faster than the media light speed. (Note: It doesn’t have to cross a boundary, contrary to what Mark says.) This EM shockwave differs from bremsstrahlung, radiation emitted by accelerated moving particles.
Here we look at intracluster X-ray emission: “However, during a merger of two clusters, galaxies behave as collisionless particles, while the fluid-like X-ray emitting intracluster plasma experiences ram pressure.” ( http://chandra.harvard.edu/photo/2006/1e0657/media/paper.pdf )
And naturally intragalactic plasmas emits by bremsstrahlung: “X-ray studies have revealed the presence of large amounts of intergalactic gas known as the intracluster medium. This gas is very hot, between 10^7K and 10^8K, and hence emits X-rays in the form of bremsstrahlung and atomic line emission.” ( http://www.answers.com/topic/galaxy-groups-and-clusters )

5. Jeremy Feifner

Xanthir: thanks but please give a URL for the video — that wasn’t a link!

6. Left_Wing_Fox

That’s incredible. 🙂 This does sound like a theoretical phoenomenon I heard described by a scientist discussing String theory on CBC radio’s Quirks and Quarks. Do you know if Dark Matter is part of string theory, and if this provides support for it? Or is this an independant branch of physics?
On a completely off-topic note, The opening still of that Video looks like it should be the jump-off point for a post on. Cognitive Daily. Whenever I shift my focus from one sphere to the other, the one I look away from looks like it’s shrinking. Nifty little optical illusion I hadn’t seen before. 🙂

7. Craig Helfgott

Neutrinos interact with ordinary matter via the weak force. Let me back up a bit. Physicists have identified 4 “fundamental” forces in nature, all other forces are expressions of these 4: gravity, electromagnetism, the weak nuclear force, and the strong nuclear force. Everyone knows the first two. The last one binds quarks together into protons and neutrons, and binds protons and neutrons together into nuclei (the latter is a less-fundamental expression of the former).
The weak force is implicated in the decay of free neutrons into a proton, an electron, and something else, which we could only originally tell was there because of conservation of energy & momentum. The something else is an anti-neutrino. It is also implicated in other nuclear processes.
Dark matter: We can’t see it directly, so it doesn’t interact via electromagnetism (this we know due to decades of research proving that it can’t be an exotic form of dust). We don’t find that one out of every 10^10+ deuterium atoms is extra-heavy (which would imply that one of the neutrons got replaced by a heavy stable particle that interacts via the strong force), so the dark matter isn’t “baryonic” (i.e. it doesn’t interact via the strong force).
But it could interact via the weak force. In fact, one of the best candidates for a dark matter particle is the theoretical LSP — Lightest Supersymmetric Particle.
Supersymmetry is a symmetry proposed to fix some of the mathematical problems that show up when you try to extend the Standard Model of particle physics to energy scales around 500 GeV — energy scales that we are first reaching in colliders after 30 years of effort. This theory proposes that for every particle we see; electrons, neutrinos, quarks, gluons, photons, etc.; for each of these particles there is a heavier counterpart with a different “spin” but the same charges.
The lightest such particle is stable up to pair annihilation against its anti-particle. In certain supersymmetry models, this LSP only interacts via the weak force — and gravity, of course.
The Large Hadron Collider is supposed to come up to speed in 2008 and is expected (according to most models) to start spitting out these super-partners almost immediately. At which point we can try to see if the LSP fits the parameters necessary to be dark matter.

8. Craig Helfgott

Neutrinos were thought to be a candidate for dark matter for a long time. However, there are some problems with that idea: 1) As far as we can tell, there aren’t enough of them (by a factor of >~10^4), 2) the current models of galaxy formation, which are very good, greatly prefer Cold (or non-relativistic) Dark Matter to Hot (relativistic) Dark Matter — and all neutrinos are so light that they would have been relativistic at the time (and still are, for that matter).
Cerenkov radiation, is, as Mark said, only produced by a charged particle moving thru a medium faster than the speed of light in that medium. While some of the gas atoms may have been accelerated to relativistic speeds in this collision, the vast majority (AFAIK) have not. What is more, Cerenkov radiation has a distinct, almost-monochromatic spectrum. The XRay radiation they observe has a broad black-body spectrum associated with heating a gas to high temperatures.
Cerenkov radiation is never important on astronomical scales; we only observe it in particle physics experiments on Earth, and occasionally, astronauts in orbit will (IIRC) see Cerenkov radiation from charged particles going thru the aquaeous humor in their eyes!

9. Craig Helfgott

Two final comments: The main differences between neutrinos and the LSP candidate for dark matter are number (#LSP > m_neutrino). Also possibly spin; neutrinos are spin 1/2 (and hence fermions), LSP — who knows? Could be a B-ino or W-ino (spin 1/2), could be a sneutrino (spin 0).
As to whether or not it’s relevant to string theory — not really. If we’re talking the LSP, we’re talking masses around 1 TeV. If we’re talking string theory, we’re at the Planck scale, so > 10^16 Gev.
That’s the problem with string theory — the only way to test it is either to figure out how effects at the Planck scale could manifest themselves in an observable way, or by applying something called the AdS/CFT correspondence. That latter technique is a little too involved to describe here, and what it gives experimentally probably doesn’t correspond to the sort of fundamental scales most string theorists talk about.

10. Craig Helfgott

Number and mass. Argh stupid html.
There are many more neutrinos than LSPs, and the LSPs are much much heavier.

11. Thony C.

The claim that dark matter has been discovered is actually not true! Measurements made of the aftermath of the galactic collision have shown a discrepancy between the measurable visible mass and the measurable gravitational effect produced by this visible mass. The dark matter hypothesis is one possible explanation for this discrepancy. There could be and probably are other possible explanations for this discrepancy. The results are a useful piece of evidence supporting the dark matter hypothesis but do not constitute a proof in a strict scientific sense!

12. Ian Tresman

1. Just because the calculations are CONSISTENT with the hypothesis, does not prove it is correct. It does prove that it is not incorrect, which is not the same thing.
2. Sure maths may allow for more accurate predictions, but not always. For example, the Electric Universe folk predicted that when Temple 1 approached Comet Shoemaker-Levy 9, there might be “a flash (lightning-like discharge) shortly before impact.” Testable? Yes. Proof? Certainly not. Consistent? Yes.
3. The Electric Universe is not devoid of maths. It supports Alfvén’s Plasma Universe hypothesis and related subjects, of which there are many peer reviewed papers, complete with maths. (References)
Regards,
Ian Tresman

13. Ian Tresman

Good maths does not imply good science. I am reminded of:
1. Dr. Simon Newcombe’s calculations in October, 1903 (2 months before the Wright Brothers’ first flight) that the only way man would fly would be with the help of a balloon.
2. Dr. Bickerton in the 1920s proved “scientifically” that it would be impossible to provide enough energy to put anything into orbit.
3. And there are other examples where scientists demonstrated that mankind could not survive the high speeds of train travel, and that bumble bees can not fly.
This is not to say that maths does not have its uses, but it has to be used in context… the correct context.
Regards,
Ian Tresman

14. Pi Guy

MarkCC:
Good stuff!
Ian:
You’re correct. If good math is applied to bad science then it’s likely to lead to bad predictions. Science provides the numbers, math turns the crank. If the numbers are bad the then the science may be useless. I suppose that that’s what you mean by correct context. Newcombe’s et al failures to predict the correct outcomes is the result of bad science – simply, not understanding the phenomena well enough to supply the right numbers.
Also, not that I’m the first to say this here or in any other forum, nothing in science is ever proven. Proof is for math and alcohol. What this discovery implies is that the new evidence and its subsequent mathematical treatment contiues to demonstrate support for the Dark Matter Hypothesis. In other words, at this stage, Dark Matter is still a reasonable concept in cosmological models.

15. Mark C. Chu-Carroll

Ian:
No one ever said or suggested that good math *necessarily* implies good science. For example, I find MOND to be a very
unconvincing theory despite the fact that it’s mathematics are absolutely spot-on.
What I did say is: without good math, you *can’t* do good science. Good math is a *necessary* condition, but not a *sufficient* one.
If we’re talking about physics, an informal prediction describing things in purely subjective terms is worthless. So, for example, the EU prediction that there would be a “flash” before the impact on the comet is a virtually worthless prediction. You don’t say *when* the flash will happen – just “shortly before”, which could mean anything from a minute to a millisecond. You don’t predict the magnitude of the flash – just “bright”. You don’t predict the wavelength/frequency distribution of the flash – you just say “lightning-like”. You don’t show a specific hypothesis for the cause – just a vague handwave about electricity and plasma.
That’s just like the “stardust” prediction. The EU folks say “the particles will be larger than they expected”. Not a prediction of *how large*. Just “larger”. Anything from 5% larger than expected to 1000× larger allows you to declare success.
A real scientific prediction is not just a bunch of informal words, but a precise specification of what your theory predicts – and that includes the valid, correct math.

16. Mark C. Chu-Carroll

Ian:
With respect to the “proof” issue. In science, proof is used in an informal way. Nothing in science can ever be one percent certain. But there are some things that are *such* precise models of observed phenomena, backed up by observation and experiment, that we consider it acceptable to call them “true” or “proven”.
There have been a variety of theories concerning the dark matter hypothesis, and a number of alternatives to it. The observed phenomena in the galactic cluster collision is a *perfect fit* to within our ability to measure for dark matter. No theory that has been proposed thus far that excludes dark matter even comes close to creating a precise model that explain these observations.
So we call it proof. Not *mathematical* proof, but *scientific* proof.

17. RS

I agreed completely with your post. You said “one of the ways to recognize a crackpot theory in physics is by the lack of math” and I’m cool with that.
But in the comments you said
What I did say is: without good math, you *can’t* do good science. Good math is a *necessary* condition, but not a *sufficient* one.
Do you mean ‘science’ or ‘physics’?
As far as I know, subjective comparison of animal forms is an important part of the discipline of evolutionary biology (I may be mistaken). Is it good science?

18. lo

there are three fundamental forces: The electroweak, the color force and gravity.
The current undertaking is to merge the color force with the electroweak force into what is known as quantum chromodynamics.
Also i am not so impressived with the results of the seeming proof for dark matter thus far. It`s a great step but will need more observations of similar scenarios in order to really drag on.
At last good science is about good math, is just plain inlogical. The fundaments of mathematics disallow anything like bad mathematics, that is what mathematical logic has been built from ground up! And science itself is based entirely on mathematical reasoning that is extended with philosophical interpretations and views etc, individually for each respective discipline.
Good science is therefore not about good math !??! about all about the scientific method, which in itself is not really about math. See Carl Propper et al.

19. lo

good or bad math is an impossibility anyways, the same goes for any abstract entitiy. You could ascribe the terms good and bad, in a similar way as flavours are used in quantum mechanics, but that doesn`t make it anything comparable to ice cream and our emotions, tastes associated with it in our mental world.

20. 601

Does anyone know how long the sequence (pre to post collision) took in real time?

Fast Facts for 1E 0657-56:

Observation Dates 2004: Aug 10, 11, 14, 15, 17, 19, 24, 25
Observation Time 140 hours

My understanding is this conclusion is based on the post mortem.

21. Xanthir

601:
Yeah, it’s completely post-mortem. We’re talking about the collision of galactic clusters, collections of objects millions of light-years across. I dont’ know how long the collision would have taken place over, but my first guess is “a really long time”. ^_^

22. RS

A couple of dumb questions.
“Among the observed phenomena consistent with the existence of dark matter are the rotational speeds of galaxies and orbital velocities of galaxies in clusters, gravitational lensing of background objects by galaxy clusters such as the Bullet cluster, and the temperature distribution of hot gas in galaxies and clusters of galaxies.”
http://en.wikipedia.org/wiki/Dark_matter
Why is the Bullet observation considered to be the clincher? Why is it considered tangible proof while the other observations listed above were not?
[Extremely dumb question–>] Before the Bullet observation, how did we know that dark matter wasn’t just regular matter that wasn’t emitting any detectable electromagnetic radiation? Aren’t there any cold, dark places in the universe?
Thanks.

23. Mark C. Chu-Carroll

RS:
The reason that the bullet observation is such a big deal is because it’s the first case where there is no alternative explanation.
There’s a theory called MOND (modified newtonian dynamics) which, while rather ad-hod, can explain things like the rotational speed of galaxies, etc. So shapes and speeds of galaxies and clusters are consistent with dark matter, but they don’t preclude alternative explanations like MOND.
But with the Bullet, the alternative explanations don’t work. You can make MOND fit the bullet observations, but to do so, you need to add dark matter. Every explanation that fits the bullet observations requires dark matter. That’s why it’s considered such a clincher.
WRT how do we know that dark matter is something different? Well, what we call light matter isn’t just matter than emits electromagnetic radiation. It’s matter *that doesn’t interact* with the electromagnetic force *at all*.
When I put my hand down on a table. what stops my hand from going through it is the electromagnetic force between the electrons in the molecules of my hand, and the electrons in the molecules of the table. If it weren’t for that, my hand could pass right through it. Even if we have a chunk of light matter so cold that it doesn’t radiate at all, it *still* interacts with other light matter via the electromagnetic force. It would obscure light coming from other galaxies; it would be able to collide with other pieces of matter, etc. Dark matter simply *does not* interact that way.
For galaxies to behave the way that they observably do, there needs to be *dramatically* more dark matter than light. But if there were that much dark matter in the halo around our galaxy, there’s no way we’d be able to not notice it at all.

24. trrll

The claim that dark matter has been discovered is actually not true! Measurements made of the aftermath of the galactic collision have shown a discrepancy between the measurable visible mass and the measurable gravitational effect produced by this visible mass. The dark matter hypothesis is one possible explanation for this discrepancy. There could be and probably are other possible explanations for this discrepancy. The results are a useful piece of evidence supporting the dark matter hypothesis but do not constitute a proof in a strict scientific sense!

Actually, it is precisely what constitutes a proof in the strict scientific sense. In science, “proof” is used according to its older meaning of “test” (as in “proving ground”). Such a test is carried out by deriving a prediction from a theory, and then testing the theory by observation. In this respect, scientific proof differs from mathematical proof in that there always remains the possibility that some other mechanism, which nobody has thought of yet, could also explain the observations.

Yesterdays comments didn’t come through, but they seem to still have some relevany:
Thanks for pointing out this – I hadn’t seen the original press release so I had missed this. They not only demonstrate dark matter unambigiously but also show really strong results that makes no sense from the view of the rival idea of modified gravity.
This is as Cosmic Variance (CV) points out both good and bad news. The good news is that this is the last piece in the CMBR cosmology puzzle, so now the prefered Lambda-CDM model seems robust. (CDM means after all Cold Dark Matter.) The bad news is that dark matter means a less revolutionary and helpful view on gravity and how a quantum gravity should be.
This is a good year for cosmology. Just yesterday I heard about a result that explains the observations of low lithium content compared to the expected from the primordial Big Bang Nucleosynthesis (BBN) CV mentions. Another major math feast of modelling observations and diffusion in stars show that lithium is concealed and broken down in the stars where it is. So now the BBN checks out too, which was a minor problem for big bang and Lambda-CDM. ( http://www.nature.com/nature/journal/v442/n7103/full/nature05011.html )
BTW, this is not my field but I think there are some minor mistakes in the post that should be pointed out in an effort to be as correct as possible.
– AFAIK, “light matter” is no term used. It is easily confused with heavy and light particles. “Normal matter” is probably used if it needs to be separated from the dark matter in matter.
– Dark matter may interact by more than gravity.
“The CDM theory makes no predictions about exactly what the cold dark matter particles are, and one large weakness in the cold dark matter theory is that it is unclear what the dark matter consists of.” ( http://en.wikipedia.org/wiki/Cold_dark_matter )
“In astrophysics, WIMPs, or weakly interacting massive particles, are hypothetical particles serving as one possible solution to the dark matter problem. These particles interact through the weak nuclear force and gravity, and possibly through other interactions no stronger than the weak force. Because they do not interact with electromagnetism they cannot be seen directly, and because they do not interact with the strong nuclear force they do not react strongly with atomic nuclei.” ( http://en.wikipedia.org/wiki/WIMP )
Lastly, on crackpots. My own preference is to use an operational definition ( http://math.ucr.edu/home/baez/crackpot.html ). It allows me to sort out serious crackpots from what I would like to call cranks.
I have an example of what seems to be a crank that fits right in with “the electric universe”. It is “the electric consciousness” by Glen Davidson. ( http://students.wwcc.edu/~glendavidson/website/ )
The short version is that his PhD work, AFAIK only accessible in detail by buying his book (he publishes books of all sorts), is an idea in search of a theory. Ie todays work in neuroscience and nerve signals doesn’t seem to need his ideas of induction signals in the brain, so far.
http://scientopia.org/blogs/goodmath/2006/08/a-stunning-demonstration-of-why-good-science-needs-good-math

Doug:
I can make a try, but also check with CV.
1) Neutrinos are light and weakly interacting. Star produced neutrinos zip right through masses like our Earth. Even primordial neoutrinos from bigbang and BBN is probably too energetic. They are HDM (Hot DM) instead of the required CDM.
“The best candidate for hot dark matter is the neutrino. Neutrinos have very small mass, and do not partake in two of the four fundamental forces, the electromagnetic interaction, and strong interaction. They do interact with the weak nuclear force, and gravity, and are extremely difficult to detect.” ( http://www.answers.com/topic/hot-dark-matter )
In the context of the article HDM alone could have been fitted with modified gravity theories. But CDM and GR was always the most parsimonous theory.
2) Cherenkov radiation is emitted by charged particles travelling through a media faster than the media light speed. (Note: It doesn’t have to cross a boundary as Mark says.) This EM shockwave differs from bremsstrahlung, radiation emitted by accelerated moving particles.
Here we look at intracluster X-ray emission: “However, during a merger of two clusters, galaxies behave as collisionless particles, while the fluid-like X-ray emitting intracluster plasma experiences ram pressure.” ( http://chandra.harvard.edu/photo/2006/1e0657/media/paper.pdf )
And naturally intragalactic plasmas emits by bremsstrahlung: “X-ray studies have revealed the presence of large amounts of intergalactic gas known as the intracluster medium. This gas is very hot, between 107K and 108K, and hence emits X-rays in the form of bremsstrahlung and atomic line emission.” ( http://www.answers.com/topic/galaxy-groups-and-clusters )

Sorry about the last link in my first comment, it was my own reference.
Thony:
As explained in other comments, currently no other theory can explain observations without using CDM and it explains the predictions best. The observation is good, the spatial offset has 8 sigma confidence. They can also show (in an earlier paper) that the DM subclusters doesn’t lose much mass by any scattering processes, another prediction for DM verified.
And the most important here is that it isn’t an isolated hypothesis but is a part of the current best cosmology. So it have other consequences too. IIRC, it helps explain the early onset of stars.
This is another difference between math and science. In math, a second proof doesn’t contribute more certainty. (Well, if it’s as long as a Perelman proof, it may. 🙂 But in science, theories and observations often support each other by giving more results and reduce remaining uncertainty.
“As far as I know, subjective comparison of animal forms is an important part of the discipline of evolutionary biology (I may be mistaken). Is it good science?”
“The fundaments of mathematics disallow anything like bad mathematics, that is what mathematical logic has been built from ground up! And science itself is based entirely on mathematical reasoning that is extended with philosophical interpretations and views etc, individually for each respective discipline.”
The answer to both questions is that math is used in most formal models of science, and science use models.
Yes, an informal or formal model may currently lack math, and still be science. But it is often bad science. A subjective comparison gives more mistakes.
Take the paper on homo floriensis released this week. The researchers measured the LB1 skull symmetry and found that it was a diseased specimen, while the original researchers have claimed it was symmetrical and so representative based on eyeballing AFAIK.
No, science isn’t build on mathematical formalisation, it is build on observations and formal or unformal theories. Math isn’t any good if it’s used in illdefined or misapplied models. I believe that is part of the reason Mark calls his blog Good Math, Bad Math.

28. James

I’ve got \$1000 to bet anyone who thinks that “dark matter” or some other similar description of the same theory will be the explanation current in 100 years time. It reminds me of nothing more than the Victorian aether, and has the smack of transient science, maths or no maths. Anyone wishing to take up the actual bet should be aware of two things: \$1000 will be worthless in 2106, and I’ll be aged 134, science permitting.

29. Xanthir

I’ll take that bet. ^_^ All I’ve read of dark matter seems to be decent science. It’s just nonbaryonic matter – it doesn’t interact with the EM and strong forces like normal matter does.

30. emil

Interesting blog Mark, I’m not sure I agree with you though.
I suspect the supposed dark-matter discovery contains /calculations/, I doubt it contains any math (i.e. proofs of theorems).
Anyway, that being said, …. Surely it’s elementary that any physics paper must contain correct calculations, and that clearly only small controversies could rage over mistakes of this kind, as they would soon be settled one way or another.
So – the questions around the dark-matter theory, the big bang, etc revolve around the observed evidence, i.e. what is used as the starting point for the mathematical models… ?
It seems to me (and I’ll confess that I regard all cosmological theories with a massive degree of skepticism) that the main question to be asked of any theory is what evidence its proponents are regarding as being primarily important. Then the math comes later.
Emil

31. Glen Davidson

I have an example of what seems to be a crank that fits right in with “the electric universe”. It is “the electric consciousness” by Glen Davidson. ( http://students.wwcc.edu/~glendavidson/website/ )
The short version, sorely needed in this long post, is that his PhD work, AFAIK only accessible in detail by buying his book (he publishes books of all sorts), is an idea in search of a theory. Ie todays work in neuroscience and nerve signals doesn’t seem to need his ideas of induction signals in the brain, so far.
Yes, Torbjoern is incapable of dealing with what I have written in a scientific fashion, and is too ignorant even to know that the binding problem in consciousness remains an outstanding problem in neuroscience. So he sneers and smears where he is incompetent to understand, much as any pseudoscientist does. It’s dishonest, but apparently it is what he does.
I responded to his incompetent attacks more fully here (after discovering his mindless attacks from a search engine, much as I did this):
Yes, unfortunately he doesn’t know that I wrote of electric fields affecting nerve flow because most channels in the nerves are indeed voltage-gated (look it up, it’s common knowledge). Perhaps I was too generous in the link in supposing that Torbjoern would trouble to learn that most “sodium channels” (the potassium channels are just as imporant, Larson, though you wouldn’t know about that) are voltage-gated, which is why I raked him for not recognizing that voltage-gated channels are indeed affected by electrical fields. Regardless, he’s obviously blundering around in a daze in these matters, and faulting someone who does understand these matters.
And of course he claims that neuroscience doesn’t need such a theory, due to his complete ignorance of the lack of a good hypothesis for consciousness in neuroscience (that is to say, my idea isn’t actually in neuroscience at present, rather it is censored for various reasons, including the fact that I am no neuroscientist (I’m the kind of generalist that is needed to come up with a hypothesis informed by my multi-disciplinary capabilities)).
Well anyhow, it is ludicrous to observe how Torbjoern faults my use of the term “mass” when it was used quite properly, his incompetence in discussing voltage-gated channels (he should know about that aspect if he’s going to fault me over it), and his lack of knowledge of the problems of consciousness. His ignorance is his excuse to fault a learned hypothesis.
Glen D
http://tinyurl.com/b8ykm

32. Glen Davidson

I have an example of what seems to be a crank that fits right in with “the electric universe”. It is “the electric consciousness” by Glen Davidson. ( http://students.wwcc.edu/~glendavidson/website/ )
The short version, sorely needed in this long post, is that his PhD work, AFAIK only accessible in detail by buying his book (he publishes books of all sorts), is an idea in search of a theory. Ie todays work in neuroscience and nerve signals doesn’t seem to need his ideas of induction signals in the brain, so far.

33. Glen Davidson

continued from above:
Yes, Torbjoern is incapable of dealing with what I have written in a scientific fashion, and is too ignorant even to know that the binding problem in consciousness remains an outstanding problem in neuroscience. So he sneers and smears where he is incompetent to understand, much as any pseudoscientist does. It’s dishonest, but apparently it is what he does.
I responded to his incompetent attacks more fully here (after discovering his mindless attacks from a search engine, much as I did this):

34. Glen Davidson

I just thought I’d add an abstract which discusses how potassium voltage-gated channels work:
Voltage-gated ion channels respond to changes in membrane potential by movement of their voltage sensors across the electric field between cytoplasmic and extracellular solutions. The principal voltage sensors in these proteins are positively charged S4 segments. The absolute magnitude of S4 movement discriminates two competing classes of gating models. In one class, the movement is 25 Å. Here, using tethered charges attached to an S4 segment, we provide evidence that the electric field falls across a distance of
http://cat.inist.fr/?aModele=afficheN&cpsidt=17197997
Pointing up once again how very poorly he understands what he sneers at.

Hum! I see Glen is turning tables here, since he complained elsewhere that I had commented on his work on a “goodmath” site without involving him.
“So he sneers and smears where he is incompetent to understand, much as any pseudoscientist does. It’s dishonest, but apparently it is what he does.”
Fact: I don’t know more about neuroscience than any interested blogger.
Fact: I have 17 years of work on voltage-controlled components, from a PhD in electronics to CMOS VLSI industry, producing, testing, constructing, patenting and using.
I expect to be able to make a reasonable discussion about EM and material properties. Identifying cranky science is another type of contribution, where I may or may not be successful. I *love* new ideas, but I am also critical of them. I see that I mention this as a PhD work, but this time I can’t find it, any peer-reviewed work of it, or citates. (Though I suck at finding these.)
To further support that todays neuroscience may not need “Electrical fields in the brain are likely to be dominated by information encoded in the nerves … consciousness as interacting electrical fields” there is this description of emergence of symbol-like processing for abstract thoughts involved in consciousness, without any connection to a wetware brain with ‘electric consciousness’ from field effects between nerves:
“recent advances in neural network modeling have rendered this criticism largely obsolete. In this article from the Proceedings of the National Academy, Rougier et al. demonstrate how a specific network architecture – modeled loosely on what is known about dopaminergic projections from the ventral tegmental area and the basal ganglia to prefrontal cortex – can capture both generalization and symbol-like processing, simply by incorporating biologically-plausible simulations of neural computation.
These include the use of distributed representations, self-organizing and error-driven learning (equivalent to contrastive hebbian learning), reinforcement learning (via the temporal differences algorithm), lateral inhibition (via k-winners-take-all), and a biologically-plausible activation function based on known properties of ionic diffusion across the neural cell membranes (via Leabra’s point-neuron activation function).”
As discussed on
http://develintel.blogspot.com/2006/10/generalization-and-symbolic-processing.html .
I think the remaining discussion may continue (or not) at the Pharyngula thread Glen provided.

36. Glen Davidson

Poor Larsson, he doesn’t even know the difference between explaining the functionality of the brain and explaining consciousness. So he brings in this irrelevant quote, something which has nothing to do with consciousness per se or what I have said about it.
It’s no better than the earlier sneers and smears. He doesn’t understand, but only wallows in his ignorance like a frantic IDist pointing out that “life really is complex”. Here he’s saying, “the brain really does have a neuroscientific basis”, the which I have always taken pains to agree with.
He has no cogent comments, however, nor any understanding of relevant subject, so what else is he going to do? He answered nothing either here or on Pharyngula, only bringing in non sequiturs.
Unsurprisingly, I never complained that Larsson “commented on his work on a “goodmath” site without involving him.” He can’t even keep that straight. Of course it’s slimy for him to do such a thing, but I didn’t say that. I wrote only this about it:
(I wouldn’t have bothered with this, Larson, if you didn’t feel the need to attack me yet again with your little learning on goodmath).
http://scienceblogs.com/pharyngula/2006/11/granpappy_was_a_neandertal.php#comment-259991
I am generally stunned at how badly he reads (not that this is important in itself, but it is yet another example of his sloppy misrepresentations produced in these discussions), or how conveniently he reinterprets things to fit his preconceptions. It goes along with the practice of his criticizing without understanding.
So I “turned the tables” on him, because I finally responded to an unprovoked and uninformed, and generally irrelevant attack? What an odd sense of justice he has.
Glen D
http://tinyurl.com/b8ykm

37. Glen Davidson

Poor Larsson, he doesn’t even know the difference between explaining the functionality of the brain and explaining consciousness. So he brings in this irrelevant quote, something which has nothing to do with consciousness per se, nor with what I have said about it.
It’s no better than the earlier sneers and smears. He doesn’t understand, but only wallows in his ignorance like a frantic IDist pointing out that “life really is complex”. Here he’s saying, “the brain really does have a neuroscientific basis”, the which I have always taken pains to agree with.
He has no cogent comments, however, nor any understanding of relevant subject, so what else is he going to do? He answered nothing either here or on Pharyngula, only bringing in non sequiturs.
Unsurprisingly, I never complained that Larsson “commented on his work on a “goodmath” site without involving him.” He can’t even keep that straight. Of course it’s slimy for him to do such a thing, but I didn’t say that. I wrote only this about the goodmath posting:
(I wouldn’t have bothered with this, Larson, if you didn’t feel the need to attack me yet again with your little learning on goodmath).
http://scienceblogs.com/pharyngula/2006/11/granpappy_was_a_neandertal.php#comment-259991

38. Glen Davidson

Continuing:
I am generally stunned at how badly he reads (not that this is important in itself, but it is yet another example of his sloppy misrepresentations produced in these discussions), or how conveniently he reinterprets things to fit his preconceptions. It goes along with the practice of his criticizing without understanding.
So I “turned the tables” on him, because I finally responded to an unprovoked and uninformed, and generally irrelevant, attack? What an odd sense of justice he has.
Glen D
http://tinyurl.com/b8ykm

39. Mark C. Chu-Carroll

Glen:
Cut the personal attacks. As I’ve said before, the two things I won’t tolerate in discussions here at GM/BM is spamming and personal attacks. Torbjorn is being polite but argumentative; you’re being abusive in return. This is the only warning I’ll give you: one more comment in the attack vein, and you’re out of here.