Tuesday, 28 May 2013

Bad Mathematics: The Perfect Cream Tea

I am not a reader of the Daily Mail, but a search engine threw up this tasty morsel;
Mathematicians formula adds perfect cream tea
A real mathematician has come up with a formula for the perfect cream tea (and let's not get into the Cornish verses Devon argument!). Not only is there the fancy graphic, but there is a paper. There is some impressive (if you are in Year 7) mathematics for the thickness of the jam and the cream, and the news media just laps it up.

In his fantastic book (READ IT!), Bad Science, Ben Goldacre bemoans these studies that regularly appear in the media, studies like the most miserable day of the year, or most perfect bottom, for a number of reasons.

Firstly, these are generally not real mathematical studies, but are often commissioned by advertisers and media groups to promote something. In this case, it is clear that this is true with our cream teas, as the Daily Mail tells us
and a quick google shows us that

That's right - it's been used by a clotted cream company to promote cream teas!

The other problem is that this is simply not the way that mathematics is done. It trivializes an important human endeavor,  one of the things that got us out of the caves and into cars, aeroplanes and space-ships. You might get an understanding that I am a big fan of mathematics, and I wish I had time to learn more. You might think I am crazy, but once you realise that mathematics is a lot more than algebra (which are all these puff formulas [yes, formulas] are) then you can see how cool it is too. I'm having a hard time convincing my son, but he is still learning algebra.

As I noted at the start, Dr Cheng who wrote the original article is a real mathematician, and she has some cool work on her webpage, including higher dimensional spaces and algebraic topology.
(Image taken from her webpage). It is also clear Dr Cheng is an advocate for bringing mathematics to a broader audience, which is, of course, an excellent thing to do. And I bet that in signing up to the cream teas story, she felt that this would be the result.

However, as invariably happens with these "perfect formula" stories, the comments quickly turn nasty.

And many, many more. There are a couple of things to note; firstly, many seem to think Eugenia Cheng is a man (perhaps they think that all mathematicians are men?) But also note the "waste of tax payers money" statement! People think this is real research, funded through a research grant! It isn't. It's a puff piece from a clotted cream company.

And when universities call for extra funding for research, the response can be "why should we? all they do is work out mathematical formula for the most perfect/depressing day/bottom/cream tea. Money should be spent on hospitals and roads...."

I know this won't be the last such puffy story we see, but it would be nice to see a little more real mathematics in the news, such as the fact that we have the first proof that there are an infinite number of prime pairs. What's that? Too complex, too esoteric, not as tasty as a cream tea?

But those in the know know that things like prime numbers provide us with the secure communication (such as RSA), and knowing the properties of primes will give us secure communications into the future. And it's not just primes, it's a whole range of mathematics that underpin modern life, and there is a wealth of untapped pure mathematics waiting in the wings to change the future (once we work out what it can be used for). Maybe it would be nice if the public understands that.

So, next time you use encryption (like when you are using a website with https), remember that it was designed by a mathematician thinking about pure numbers. They might have also been thinking about perfect/depressing days/bottoms and even cream teas, but let's not forget how important their real work is for modern life.

[Note added - the story is alive an has appeared on major news-sites in the UK and Australia, and Ben Goldacre has commented on his twitter]

Sunday, 26 May 2013

The Theory of Nothing?

There has been quite a buzz this week about a man called Weinstein.
No! Not Einstein! Weinstein!
Oh, for crying out loud - that's Ninestein, from Terrahawks.

This is Weinstein.
But with a name that sounds a bit like Einstein, he must be smart!

So, what's the buzz? It all started with an article in The Guardian - well, I say article, but the correct name is puff piece. It's a strange read, but is authored by well known mathematician, Marcus du Sautoy. I have a lot of respect for du Sautoy, firstly as he is the Simonyi Professor for the Public Understanding of Science, and for several of the TV shows he has presented, including the wonderful The Story of Maths. But this article left me scratching my head.

The title is rather provocative;
Eric Weinstein may have found the answer to physics' biggest problems
Big call! Especially when you realise that Weinstein is not a physicist. He has a PhD in mathematics and has worked as an economist. du Sautoy weaves an interesting tale about the current state of modern physics, and mysteries we have to face, such as what the heck is dark matter, and why quantum mechanics and general relativity will play together nicely.

du Sautoy description of the work contains the words you would expect to see in a solution, the concept of symmetry, and how it is broken in our low energy universe. If this is correct, then it is potentially Nobel prize territory.
But hang on! While Weinstein is clearly smart, and du Sautoy is no fool, how do we know that Weinstein's ideas are any different from the large population of "Theory of Everything" lay-researchers out there. They are not hard to find, just try google.

There is a way to find out if this is science, and it's the equivalent of "Show Me The Money". Not a piece in the Guardian, but a scientific paper, or at least a talk to your peers, so they can start to assess the success, or, more importantly, the failure of your new Theory of Everything.

And apparently this is happening with Weinstein's new theory, with him presenting a talk at Oxford University. Surely the physicists will have a chance to really get to the nuts and bolts of this secret to the running of the universe.

Such talks are dangerous, as a bright audience can slay your ideas in the space of an hour; there is a story about a famous physicist who thought they has the theory of everything back in the 60s or 70s (and for the life of me, I cannot remember who) who gave such a lecture, and the description of the lecture is that it was like watching the dying of a noble beast - it was clear this was no theory of everything.

So, what happened in Oxford? Did Weinstein's theory survive, or was it put to the sword?

Funnily, we don't really know, as while the lecture was held in the Physics Department, the particle physicists were not in attendance (as they weren't invited and were at a different lecture). This is really a little bizzarre - while I wasn't there myself and don't know the make up of the audience - it is very strange to make your splash without the particle physicists in the room.

Now, don't get me wrong. This is not meant to be a critique of Weinstein's work - basically, like most other people, I don't know what it consists of, and I probably don't have the right background to understand it fully - and he might be right, he may have solved the problems of modern physics, but is this the right way to about it, with a splash in the newspaper and a lecture without appropriate peers?

As noted by Cocktail Party Physics, this is not a good way of doing science, and getting a lot of press  who-ha before results and ideas are verified is not a good idea; we all remember the balls-up which was the Neutrinos travel after than light malarkey!

So, I wait with baited breath for the paper to appear on arxiv. Once the community get their teeth into it, we'll soon know if the Theory of Everything has been found and we will be entering a golden age of modern physics, or if it is another of a long line of damp squibs and failures. Hopefully we'll know very soon.

Sunday, 19 May 2013

A peculiar faint satellite in the remote outer halo of M31

The Pan-Andromeda Survey (PAndAS) continues to be a gold-mine for science. We're squeezing it hard to get out key results, but next year, the data will become public and everyone can have a looksie and write their own paper.

Here we have another paper by ANU astronomer, Dougal Mackey. Dougal's expertise is understanding the globular clusters orbiting the Andromeda galaxy, especially the distant clusters. He published a really nice piece of work recently which showed that these distant globulars are not just scattered randomly about Andromeda, but are more likely to be sitting on the stellar substructure we see. This substructure is the tidal debris from smaller galaxies that have fallen in and been shredded, meaning that the globulars are immigrants, having been born outside Andromeda, but joining the halo when their parent galaxy is destroyed; this is galactic cannibalism in action.

This new paper is about a particular cluster of stars orbiting Andromeda, named PAndAS-48 (who says astronomers aren't imaginative when it comes to naming things!). While this cluster was initially observed with the Canada-France-Hawaii Telescope (CFHT) as part of PAndAS, this paper presents new observations with the Hubble Space Telescope.

While the CFHT, at 3.6m, is larger than Hubble (2.5m), the lack of an atmosphere means we get much sharper images, and hence can see a lot fainter. Here's images from CFHT (left) compared to Hubble (right).
Nice! We actually observed the cluster in a couple of photometric bands with Hubble, which allowed us to make a colour-magnitude diagram; as you know, stars are not randomly scattered in such a picture, but sit on sequences that are driven by stellar evolution. What do we see?
For those in the know, yes, the faintest stars in there are around 28th magnitude!

In there, we can see the Red Giant Branch and Horizontal Branch, and that allows us to understand lots of things about the globular, such as how far away it is and what stage it is at in terms of its evolution.

We can also measure the distribution of stars, and measure the shape of the clusters.
So, what is this cluster of stars? Is it a dwarf galaxy, dominated by dark matter? or a globular cluster, which are thought not to contain dark matter? It's actually very hard to tell. This piccy illustrates the issue.
The picture is pretty self-explanatory; size is along the bottom in parsecs, and brightness is up the side. The dots are colour-coded in terms of how elliptical they are.  The squares on the right are dwarf galaxies; they tend to be big and elliptical. The dots on the left are globular clusters, which tend to be small and circular (but notice that they can be of the same brightness as the dwarfs).

Where's PAndAS-48? It's the point with a circle around it, stubbornly right between the two populations! In fact, the ultimate conclusion is that we don't know what it is. If it is one or the other, then there are problems. But that's cool too!

 It is worth noting that PAndAS-48 appears to sit on the vast thin plane of satellites orbiting Andromeda, which makes it even more intriguing, but we haven't got it's velocity so can't confirm if it is orbiting in the same sense. But if it is, it will be extra cool.

As ever, the more we learn, the more questions we have. Yay!!

Well done Dougal!

We present Hubble Space Telescope imaging of a newly-discovered faint stellar system, PAndAS-48, in the outskirts of the M31 halo. Our photometry reveals this object to be comprised of an ancient and very metal-poor stellar population with age > 10 Gyr and [Fe/H] < -2.3. Our inferred distance modulus of 24.57 +/- 0.11 confirms that PAndAS-48 is most likely a remote M31 satellite with a 3D galactocentric radius of 149 (+19 -8) kpc. We observe an apparent spread in color on the upper red giant branch that is larger than the photometric uncertainties should allow, and briefly explore the implications of this. Structurally, PAndAS-48 is diffuse, faint, and moderately flattened, with a half-light radius rh = 26 (+4 -3) pc, integrated luminosity Mv = -4.8 +/- 0.5, and ellipticity = 0.30 (+0.08 -0.15). On the size-luminosity plane it falls between the extended globular clusters seen in several nearby galaxies, and the recently-discovered faint dwarf satellites of the Milky Way; however, its characteristics do not allow us to unambiguously class it as either type of system. If PAndAS-48 is a globular cluster then it is the among the most elliptical, isolated, and metal-poor of any seen in the Local Group, extended or otherwise. Conversely, while its properties are generally consistent with those observed for the faint Milky Way dwarfs, it would be a factor ~2-3 smaller in spatial extent than any known counterpart of comparable luminosity.

Saturday, 18 May 2013

Bad Physics: Midsomer Murders

I've lived in Australia for thirteen years, but in the way that Sting was an English Man in New York, I have never quite felt "Australian", rather, I am a Welsh Man in Sydney. Anyway, I still feel very British, and am a fan of British TV (apart from a few highlights, Australian TV is generally bilge).

Anyway, I've always loved a good murder mystery, and I like Midsomer Murders, even though they have changed the lead character (and the new chief inspector was actually a criminal in a previous episode). The premise of Midsomer's is simple; a cop in the quite fictional county of Midsomer solves murders. However, the show has been running for 15 years, and there seems to have been an awful lot of murders (although the murder rate is considerably lower than Honduras!). To keep the stories going, murders are set in, quite often, bizzarre circumstances.

A recent episode, Written in the Stars, focused on the intrigue and mystery at a research observatory at Midsomer University (up until this point, I don't think there had been mention of a university in the county). With usual stereotypical fashion, we have a mean professor, who is ready to steam-roller anybody to build his reputation, and a young genius who is writing her thesis (on the Heisenberg uncertainty principle) and threatens to dethrone the evil professor.

As part of her research, she needs to look at an eclipse (go figure) and the murder mayhem ensues. That's not the bad physics (but doesn't help).

Here's the young genius at work, presenting her work in the dome of a telescope (not sure why she is not in an office or lecture room).
Someone has gone to great effort to fill the board with lots of scientific squiggles. It's not, however, gibberish. I'm not sure if they used a text book, or wikipedia, but there are some correct things there.

However,  something annoyed me. Zooming in on the board, what do we see?
Plank's constant! Argh!! You'd think that our young genius who has written a thesis on quantum mechanics and is presenting her research to evil and nasty professor could spell Planck's name correctly. But there is more! Whoever wrote the squiggles got the symbol, h, correct, and even the value, 1.054 x 10-27, correct, but they completely screwed up the units (that's too painful to go into) and what this number actually is is ħ ,which is Planck's constant divided by 2π.

Why would they bother going to the effort of writing something semi-correct, but pay so little attention that they make a mess of it? Why not just do it right? Don't they realise that professors of astrophysics might be watching?

One other thing that annoyed me is that they did the "astronomers only do their work inside telescope domes" thing
We don't. We have offices like everyone else. And even when we are at the telescope, we are in the control room, not freezing our bottoms off in the dome.

Before finishing, I think it's worth noting that the observatory actually used in the show is actually a university observatory. It is the University of London Observatory at Mill Hill
Even though I was a student at the University of London, I never used this observatory, although I did visit there when I was looking for a PhD position. However, the observatory is not in the picturesque county of Midsomer, but is next to the A1 in North West London.
Like a lot of observatories around the world, it was build outside of a city, but the cities have grown around them.

Anyway, the murderer was not the evil astrophysicist..... It was actually the friendly professor of Quantum Physics! I'm sure his knowledge of the uncertainty principle will help him in prison.

Monday, 13 May 2013

Nature doesn't care how smart you are

Random Monday Morning Thought:

Becoming a science professor sorta snuck up on me. Not getting the title, as that happened at a distinct point in time (namely the first of January 2009), but the 'separation' from being a student and then postdoctoral researcher grows somewhat slowly. A colleague of mine recently expressed surprise when he discovered his students were somewhat daunted when speaking with him (this is partly as there is the perennial fear of "looking stupid" that students have), and I'm pretty sure my fellow faculty member does not feel that different to the students he talks to.

The important point, I think, is that students should realise that you don't get smarter with age; in fact, it's probably the opposite. What you do gain is experience. When a professor speaks from authority, it is not necessarily that they are "smart", but they have gathered significant experience over the years. But it's important to realise that there is a limit to experience, and just because a particular professor makes a pronouncement, it doesn't necessarily mean it's correct. Over at Letters to Nature, Luke Barnes has a nice article on appealing to authority.

Anyway, I just wanted to add to this a marvellous quote

In high school, my two idols were Einstein and Feynman. While Einstein felt that QM must be wrong, Feynman felt it was the ultimate truth of the universe. This discrepancy bothered me, and I wasn't sure who to believe. So, about six weeks into physics X, I screwed up my courage and asked Feynman about the "dice" and Einstein.  "Dr. Feynman", I asked, "Einstein was one of the greatest geniuses of physics, and certainly a lot smarter than me. He knew more physics that I ever hope to. But, he didn't believe in quantum mechanics--so why should I?" 
Feynman paused -- which surprised all of us -- and smiled. He looked at me and said, in that wonderful Far Rockaway accent, "Nature doesn't care how smart you are. You can still be wrong." He went on to explain some background on Einstein's view of physics, and why he might feel that way. 

(from here).

"Nature doesn't care how smart you are"; I think that's an important lesson that all of us should remember.

Saturday, 11 May 2013

Bad Physics: No Energy Radio Waves

Just a little bit of Bad Physics, this time from the L. A. Times. The story was "Mysterious hydrogen clouds detected in space, puzzling scientists", a nice story.
I quote
"The clouds don't emit light or energy, but the neutral atomic hydrogen that they are made of gives off a distinct radio signal that astronomers were able to pick up using the National Science Foundation's Green Bank Telescope which measures radio waves."
Apparently, these clouds do not emit light or energy, but they do emit radio waves that we can detect with out telescopes. Aghhh!!

I know that you already know this, but radio waves are one form of electromagnetic radiation, and (in terms of quantum mechanics) are packets of energy called photons. The energy of a photon is given by
where λ is the wavelength of the radiation.

Light has a wavelength of around 550nm, and so each photon carries some energy. Radio waves, however, have wavelengths from millimetres to many hundreds of kilometres. Such long wavelengths mean each photon carries a much smaller amount of energy, but they still carry energy!

Real warp drives – can distributed computing help?

Some how, I blinked and discovered we're in mid-May. This is scary as I have some travel coming up, and need get some things out of the way. It's been a busy week (but heck, when isn't it) and part of the load is that I am on the Australian Research Council College and am ranking the current round of Future Fellowships; this is a lot of work, but is incredibly interesting, especially looking at the sheer excellence of research being undertaken in Australia. However, it's also completely confidential, and so I'm not going to talk about any details :)

However, I will say that this is the last round of Future Fellowships, removing the opportunity for mid-career researchers to focus on, well, research. This will leave a hole in research efforts in Australia.

Anyway, some stories never die, especially of it's about warp drives. A couple of years ago, my new PhD student, Brendan McMonigal, and I wrote a cool paper called "The Alcubierre warp drive: On the matter of matter". I've written about this before, but we showed that as the warp drive accelerates, it starts to gather up particles and radiation, and this is released in a burst as it decelerates, frying all your relatives who have come to meet you.

If you think you have seen Brendan recently, you're probably correct.

Anyway, we receive a steady stream of requests for comments on the paper, especially for inclusion in news stories. And here's another.
(picture taken from the article). The crux of the story is that we effectively did a 2 dimensional analysis of the warp drive, one in time and one in space, What we really want to do is do a full 4-dimensional analysis, one in time and three in space, to really understand what happens to light rays, especially those that come in obliquely. But this is computationally expensive, and we need to use big computers to do this.

The computational problem is that we need to follow the path of a particle in 4-D space-time, and to do this we use the Geodesic Equation. This looks like this
For those in the know, to integrate this, we have 8 coupled one-dimensional equations, and we have to follow the path of each particle and each bit of light. But this is a "stupidly parallel" problem - each particle and light beam is independent and so we can calculate on on one machine, and one on another machine, and pull all the results together at the end.

Anyway, you can read more about this in the article. But the point I want to make is the catch-cry of rating modern science is impact. One form of impact is easy to measure - it is citations to your work by other scientists. The harder one to quantify is "societal impact", and that is the broader impact your results have (things like science appearing in the press, or leading to a technological spin-off etc).

This is why I am happy that this story happily keeps bumbling along, with each new article highlighting our work and the science being done at the University of Sydney. It might not change the world, but at it is, at least, blooming interesting :)