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Spiral galaxies are typically composed of a disk, which is made of normal (baryonic) matter and contains the central bulge and spiral arms, and a halo, which surrounds the disk and contains dark matter. In recent years, surveys such as THINGS (conducted by the NRAO Very Large Array) have been undertaken to analyze the distribution of hydrogen in nearby galactic disks. Last year, Dr. Chakrabarti used such surveys to investigate the way that small satellite galaxies affect the disks of larger galaxies such as M51, the Whirlpool Galaxy. But the real prize lies in investigating what astronomers cannot see. Chakrabarti remarked, “Since the 70s, we’ve known from observations of flat rotation curves that galaxies have massive dark matter halos, but there are very few probes that allow us to figure out how it’s distributed.” She has now broadened her research to do just that.

Astronomers believe that the density distribution of dark matter relies on a parameter called its *scale radius*. As it turns out, varying this parameter visibly affects the shape of the galaxy’s hydrogen disk when the influence of passing dwarf galaxies is accounted for.

“Ripples in outer gas disks serve to act like a mirror of the underlying dark matter distribution,” said Chakrabarti. By varying the scale radius of M51′s dark matter halo, Chakrabarti was able to see how it would affect the shape and distribution of atomic hydrogen in its disk. She found that large scale radii give rise to galaxies with a dark matter halo that becomes gradually more diffuse as it extends along the length of the disk. This causes the hydrogen in the disk to be very loosely wrapped around the central bulge of the galaxy. Conversely, small scale radii have density profiles that fall off much more steeply.

“Steeper density profiles are more effective at holding onto their ‘stuff’,” explained Chakrabarti, “and therefore they have a much more tightly wrapped spiral planform.”

Chakrabarti’s map of the distribution of dark matter in the halo of M51 is consistent with existing theoretical models, leading her to believe that this method may be extremely useful for astronomers trying to probe the elusive, invisible substance that makes up almost a quarter of our Universe. A preprint of her paper is available on the ArXiv.

Yo Vanessa, only friggin’

astrologers“believe”, butastronomersbelievenothing!Hey, if non-scientists can have their own definitions of words different from that of scientists (“theory” being the obvious one), then why can’t it go the other way? I’m pretty sure that “believe” in this context is understood by most readers to mean “hypothesize,” or “theorize.”

Scientists must educate the great unwashed the error of their ways!

Mmm, but risky! History shows trying that usually results in screams of ‘heresy’ and ‘sacrilege’ , shortly followed by the the permanent removal of the educator from the gene pool! :-O

Cool down! “believing” as “accepting as true”, “holding as an opinion”, “thinking”, and “supposing” is what astronomers — and generally scientists — always do, and it is okay. That “believing” also means “having (religious) faith” is sad, but that’s the way it is.

I have to agree with IVAN3MAN here. Especially observation and theory have technical definitions and special support, and that ties back to how to judge the balance of them.

“Believe” is too weak, or need a similar technical definition. Absent the latter, it is better to avoid the term to keep precision.

So, do you really, really want that science journalists do *not* use the word “believe” like Vanessa did?

An anecdote: In my country, there is a theologian and philosopher who writes essays where he seriously talks about the “faith of the atheists”, because atheists “believe” that god does not exist (as he writes). This is an annoying case of not discriminating between “accepting as true” etc. (see above) on the one hand and “having (religious) faith” on the other hand. If this man really were a philosopher he would know the difference. And that’s another reason why I call him a wanna-be-philosopher.

I’m partly on your side.

Now, has this gone off-topic enough?

I tend to agree with IVAN3MAN as well. Ordinarily I might think this is a silly issue. However, the term belief has becomes something which is used by religious fundamentalists and post modernist to claim that science is on no harder ground than theology. Scientists of course need to give appropriate qualifications for statements which are made, whether they are proofs or hard evidence, theoretical possibilities or hypothetical conjectures. However, the use of the world belief is easily seen by many as a code word for a statement of faith. It is a word which needs to be abolished or used very sparingly in a scientific context.

LC

Well, the same can be said of the term “gay”, which used to mean “bright or showy” and “having or showing a merry, lively mood”; whereas nowadays it also means, er… we all know what, but that’s the way it is.

Also, Venessa is quoting Sukanya Chakrabarti’s statement that she believes in a “method” which could lead to a scientific discovery, not in the discovery. In this case her method of probing/mapping to ultimately reveal (or not), to quote L.C. in his post, “proofs or hard evidence, theoretical possibilities or hypothetical conjectures”.

As IVANMAN3 would say, I have hat in hand, now where’s the door?

Also, Venessa is quoting Sukanya Chakrabarti’s statement that she believes in a “method” which could lead to a scientific discovery, not in the discovery. In this case her method of probing/mapping to ultimately reveal (or not), to quote L.C. in his post, “proofs or hard evidence, theoretical possibilities or hypothetical conjectures”.

As IVANMAN3 would say, I have hat in hand, now where’s the door?

Also, Venessa is quoting Sukanya Chakrabarti’s statement that she believes in a “method” which could lead to a scientific discovery, not in the discovery. In this case her method of probing/mapping to ultimately reveal (or not), to quote L.C. in his post, “proofs or hard evidence, theoretical possibilities or hypothetical conjectures”.

As IVANMAN3 would say, I have hat in hand, now where’s the door?

Enough! I believe that physical phenomena can be modeled to some arbitrary degree of accuracy using mathematics. I believe this without any independent evidence from outside physical phenomena or mathematics. I do not believe that all phenomena can be modeled perfectly by real computations. I modify my beliefs as I learn of new physical evidence or new mathematics. I suspect you do too.

“Belief” is a good and useful word in its current sense. It does not help to restrict the meaning of “belief” to “belief in the supernatural”, just as it does not help to restrict the meaning of “sound” to “sound heard by a person” so your trees can fall over in a forest without noise.

But as soon as you admit to modeling instead of philosophical axiomatizing, you need testing to verify usefulness. How we do proof, how mathematicians agree on the proof steps and what objects they use are all heuristic constructions.

The first two claims are obvious. For an example of the latter, you can do counting (addition and subtraction) in finite groups, but that doesn’t generalize. So we agree to use “natural numbers” et cetera.

QED.

Ah. Now it gets deep rather quickly…

We do notice that some assumptions yield more than others. If we assume we have a set of ‘positive integers’ starting with a number 0 with a unique successor; and each additional number has a unique predecessor and successor; and the successor is not already in the set; then we get all of integer mathematics. If we allow zero to have a predecessor then we get negative numbers, If we allow the successor to be a member of the set we get cycles and set theory. These all seem to be ‘good’ assumptions that exist irrespective of the properties of our universe. Indeed, someone who comes up with something new in mathematics is usually termed a ‘discoverer’ rather than an ‘inventor’.

However, we – the engines that are doing this mathematical reasoning – are physical phenomena if we are anything. The way we handle mathematics often involves the invention and manipulation of typographical rules to mimic and embody the mathematical processes we are discussing. We use symbols and rules to model mathematics, we use symbols to describe physical phenomena, and we sometimes notice that patterns in mathematical symbols can be applied to physical phenomena, and sometimes in less abstract mathematics, we go the other way. It all ends up being modeling, and pattern matching. All the really ‘good’ assumptions are not abstractly perfect, though they may seem so, but are ‘good’ because they can be applied to so many other things.

Can you imagine a universe that contained sophisticated intelligence, but not have the structure to inspire the intelligence to invent integers? I can’t. But if it could exist, then integers would be just a locally useful system. In the end, we come back to belief again.

And then, there is the other sort of belief…

http://amultiverse.com/2011/12/28/irreducible-complexity/

You may be surprised, but as a mathematician I’m not quite with you.

I’m one of those mathematicians — yes, there are more like me — who see mathematics as (short version) something we humans construct in a cultural process — including the numbers 1, 2, 3, etc. This implies, that it is appropriate to say that mathematics is invented, but not discovered. Over and above that, mathematicians like me would not call mathematics the language of nature, but part of our own language.

Mathematics works in reality out there because we keep those inventions we are able to apply successfully, and we discard other inventions (I know, except some mathematicians have fun with it and get some money for doing it — mostly from the dumb taxpayer).

Well, mathematicians don’t always agree about mathematics

My objection to the use of the term “believe” stems from ‘debates’ I’ve had with creationists and “Electric Universe” nutters who both accuse biologists/cosmologists of having a “belief” in their respective “religion”.

Astronomers aren’t necessarily nihilists.

A

nihilistis someone who is indenialof existence, whereas abelieveris some who has absolute confidence in the existence of something without absolute proof of it.And you can’t all agree on the rules and definitions as well, which thoroughly frustrates those of us that have not been nurtured through the academic maze.

As for belief, it’s the driving force within that moves us to a better understanding of where we are and why the hell we’re here.

Well since you’re delving into the realm of soft sciences like Anthropology and Psychology, please explain why distinct and separate societies outside of Western European cultures managed to independently “invent” mathematics instead of “discover” the rules of such. Basic geometry and trigonometry have been discovered by civilizations completely separate from Greco-Roman society in ancient times, for example, even if the bulk of modern mathematics emerged from Western Europe.

For me belief (take any meaning from the comments here) is not the driving force within that moves me — believe it or not

So, I don’t belong to those “us” in your comment. I tend to say (without any hostility, of course): too much generalizing on your side.

Point taken, personal points of view should be restricted as per site policy.

Regarding the site policy: in the forum rules (I cannot find anything else) there is no statement about personal points of view being restricted (whatever it means), and these comments are full of personal views. I honestly don’t know what you mean.

I did not say anything about “distinct and separate societies outside of Western European cultures”. But anyway, I will give a short version of an answer (anything else is not possible here; and pardon my bad English):

As an example, in old Egypt people had the problem that each year the river Nile swamps their fields *and* the landmarks indicating the boundaries of the fields different families, clans, tribes, villages, etc. use.

The solution is to have landmarks more distant from the river and to invent some geometric methods — e.g. for the construction of right angles — which make it possible to reconstruct the landmarks mentioned above and the boundaries of the fields.

This solves organisational and social problems, and mathematics was used as a tool. Of course, there were more pertinent organisational and social problems in old Egypt and more pertinent mathematical solutions (not only geometrical ones). In the long run the old Egyptians kept those methods which worked.

As we know from history, other cultures had just the same problems — regarding especially water management: remember the various cultures in Mesopotamia, China, middle and south America — and they converged to the same solutions.

Now, why “invented” and not “discovered”?

The first part of the answer is given on a level different from the above. If the “things” belonging to mathematics are “discovered”, then a necessary precondition is, that there are mathematical things “out there anywhere” not depending on us (I hope you get it). This is a hypothesis, and nobody has shown (so far) that this hypothesis is true. There are only statements about mathematics being “discovered” without giving any piece of evidence. What scientists do in order to handle such a situation is to reject the hypothesis.

The second part of the answer goes like the following. When we examine the mathematical literature, and when we observe how mathematicians work, we see that, in order to solve problems, indeed the mathematicians have ideas, construct mathematical concepts, propose and try this and that solution, perhaps make some abstraction, and formulate something verbally and written. There is not a single piece of evidence, that mathematicians get *new* ideas, concepts, etc. from anywhere outside of their mind, from nature, a Platonian realm, or whatever, that there are any “rules as such”.

Of course, another question may come to our mind: Why do some mathematicians think, that mathematical things are “discovered”. I have several answers, which I won’t tell here. But I want to say this: When practicing mathematics, in most cases it doesn’t matter whether “invented” or “discovered”. If someone just likes to believe — out of whatever reason or without reason –, that mathematical things are “discovered”, that they exist “out there”, etc., then this is no problem in most cases. And, of course, I don’t have a low opinion of someone who likes to believe this.

I suppose I generalized again, I lumped personal points of view together with personal theories.

Anyway, I was originally trying to convey that Chakrabarti’s method of probing/mapping was what she believed in. I used “driving force” as confidence in one’s self.

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