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Who’s worried about the Hubble Constant?

Posted in The Universe and Stuff with tags , , , , on January 11, 2018 by telescoper

One of the topics that is bubbling away on the back burner of cosmology is the possible tension between cosmological parameters, especially relating to the determination of the Hubble constant (H0) by Planck and by “traditional” methods based on the cosmological distance ladder; see here for an overview of the latter.

Before getting to the point I should explain that Planck does not determine H0 directly, as it is not one of the six numbers used to specify the minimal model used to fit the data. These parameters do include information about H0, however, so it is possible to extract a value from the data indirectly. In other words it is a derived parameter:

Planck_parameters

The above summary shows that values of the Hubble constant obtained in this way lie around the 67 to 68  km/s/Mpc mark, with small changes if other measures are included. According to the very latest Planck paper on cosmological parameter estimates the headline determination is H0 = (67.8 +/- 0.9) km/s/Mpc.

About 18 months I blogged about a “direct” determination of the Hubble constant by Riess et al.  using Hubble Space Telescope data quotes a headline value of (73.24+/-1.74) km/sec/Mpc, hinting at a discrepancy somewhere around the 3 sigma level depending on precisely which determination you use. A news item on the BBC hot off the press reports that a more recent analysis by the same group is stubbornly sitting around the same value of the Hubble constant, with a slight smaller error so that the discrepancy is now about 3.4σ. On the other hand, the history of this type of study provides grounds for caution because the systematic errors have often turned out to be much larger and more uncertain than the statistical errors…

Nevertheless, I think it’s fair to say that there isn’t a consensus as to how seriously to take this apparent “tension”. I certainly can’t see anything wrong with the Riess et al. result, and the lead author is a Nobel prize-winner, but I’m also impressed by the stunning success of the minimal LCDM model at accounting for such a huge data set with a small set of free parameters.

If one does take this tension seriously it can be resolved by adding an extra parameter to the model or by allowing one of the fixed properties of the LCDM model to vary to fit the data. Bayesian model selection analysis however tends to reject such models on the grounds of Ockham’s Razor. In other words the price you pay for introducing an extra free parameter exceeds the benefit in improved goodness of fit. GAIA may shortly reveal whether or not there are problems with the local stellar distance scale, which may reveal the source of any discrepancy. For the time being, however, I think it’s interesting but nothing to get too excited about. I’m not saying that I hope this tension will just go away. I think it will be very interesting if it turns out to be real. I just think the evidence at the moment isn’t convincing me that there’s something beyond the standard cosmological model. I may well turn out to be wrong.

Anyway, since polls seem to be quite popular these days, so let me resurrect this old one and see if opinions have changed!

 

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Maynooth joins the Euclid Community

Posted in Euclid, Maynooth, The Universe and Stuff with tags , , , on January 10, 2018 by telescoper

There’s a nice webpage showing all the institutions around the world who belong to the consortium behind the European Space Agency’s Euclid Mission. Here’s a screen grab that shows all the logos of all the institutions involved in this very large Consortium:

There are so many that it’s hard to see them all, but if you look very closely about half way down, among the Ms, you will see Maynooth University among them. This is the first institution in Ireland to have joined the Euclid Consortium and it has just been officially added thanks to yours truly moving there later this year. Ireland is a member state of the European Space Agency, by the way.

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Crunch time for Dark Matter?

Posted in The Universe and Stuff with tags , , on January 9, 2018 by telescoper

Gratuitous picture of the cluster Abel 2218, showing numerous gravitational lensing arcs

I was reading through an article by Philip Ball in the Grauniad this morning about likely breakthroughs in science for the forthcoming year. One of the topics discussed therein was dark matter. Here’s an excerpt:

It’s been agreed for decades that the universe must contain large amounts of so-called dark matter – about five times as much as all the matter visible as stars, galaxies and dust. This dark matter appears to exert a gravitational tug while not interacting significantly with ordinary matter or light in other ways. But no one has any idea what it consists of. Experiments have been trying to detect it for years, but all have drawn a blank. The situation is becoming grave enough for some researchers to start taking more seriously suggestions that what looks like dark matter is in fact a consequence of something else – such as a new force that modifies the apparent effects of gravity. This year could prove to be crunch time for dark matter: how long do we persist in believing in something when there’s no direct evidence for it?

It’s a good question, though I have to say that there’s very little direct evidence for anything in cosmology: it’s mostly circumstantial, i.e. evidence that relies on an inference to connect it to a conclusion of fact…

Anyway, I thought it would be fun to do a totally unscientific poll of the sort that scientists find  fun to do, so here’s one. It’s actually quite hard to make this the topic of a simple question, because we know that there is ordinary (baryonic) matter that we can’t see, and there is known to be some non-baryonic dark matter in the form of a cosmic neutrino background. What the question below should be interpreted to mean, therefore, is  `is there a dominant component of non-baryonic dark matter in the Universe in the form of some as-yet undiscovered particle?’ or something like that.

For the record, I do think there is dark matter but less convinced that it is simple cold dark matter. On the other hand, I regard its existence as a working hypothesis rather than an article of faith and do not lose any sleep about the possibility of that hypothesis turning out to be wrong!

 

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Hamiltonian Poetry

Posted in Poetry, The Universe and Stuff with tags , , , , , , on January 8, 2018 by telescoper

I posted a couple of items last week inspired by thoughts of the mathematician William Rowan Hamilton. Another thing I thought I might mention about Hamilton is that he also wrote poetry, and since both science and poetry feature quite regularly on this blog I thought I’d share an example.

In fact during the `Romantic Era‘ (in which Hamilton lived) many scientists wrote poetry related either to their work or to nature generally. One of the most accomplished of these scientist-poets was chemist and inventor Humphry Davy who, inspired by his friendship with the poets Wordsworth and Coleridge, wrote poems throughout his life. Others to do likewise were: physician Erasmus Darwin; and astronomer William Herschel (who was also a noted musician and composer),

William Rowan Hamilton interests me because seems to have been a very colourful character as well as a superb mathematician, and because his work relates directly to physics and is still widely used today. Interestingly, he was a very close friend of William Wordsworth, to whom he often sent poems with requests for comments and feedback. In the subsequent correspondence, Wordsworth was usually not very complimentary, even to the extent of telling Hamilton to stick to his day job (or words to that effect). What I didn’t know was that Hamilton regarded himself as a poet first and a mathematician second. That just goes to show you shouldn’t necessarily trust a man’s judgement when he applies it to himself.

Here’s an example of Hamilton’s verse – a poem written to honour Joseph Fourier, another scientist whose work is still widely used today:

Hamilton-for Fourier

If that’s one of his better poems, then I think Wordsworth may have had a point!

The serious thing that strikes me is not the quality of the verse, but how many scientists of the 19th Century, Hamilton included, saw their scientific interrogation of Nature as a manifestation of the human condition just as the romantic poets saw their artistic contemplation. It is often argued that romanticism is responsible for the rise of antiscience. I’m not really qualified to comment on that but I don’t see any conflict at all between science and romanticism. I certainly don’t see Wordsworth’s poetry as anti-scientific. I just find it inspirational:

I HAVE seen
A curious child, who dwelt upon a tract
Of inland ground, applying to his ear
The convolutions of a smooth-lipped shell;
To which, in silence hushed, his very soul
Listened intensely; and his countenance soon
Brightened with joy; for from within were heard
Murmurings, whereby the monitor expressed
Mysterious union with its native sea.
Even such a shell the universe itself
Is to the ear of Faith; and there are times,
I doubt not, when to you it doth impart
Authentic tidings of invisible things;
Of ebb and flow, and ever-during power;
And central peace, subsisting at the heart
Of endless agitation.

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Hamilton and the “Light-Bulb” Moment

Posted in Biographical, The Universe and Stuff with tags , , , , , , on January 5, 2018 by telescoper

In yesterday’s post I mentioned in passing the bridge (Broom Bridge) beside which William Rowan Hamilton first wrote down the fundamental result of quaternions after having a flash of genius while walking from Dunsink Observatory into Dublin.

That reminded me last night that a while ago I read a piece in Physics World (which you can read here, but only if you have a subscription) about whether breakthroughs in physics occur very often in the way of Hamilton’s – through sudden flashes of inspiration or, as they are called in the article,  “light-bulb moments” –  or are more often the result of solid hard graft, sweat and spadework? In other words, how much is inspiration and how much perspiration?

The piece includes some interesting comments from distinguished scientists about their own “Eureka” moments, which I’m sure will resonate with many researchers, not only physicists. Incidentally, the article refers to such moments as “claritons”, a word I’d never heard before, presumably intended to evoke solitons. It is interestin, though just how strongly the light-bulb has become so strongly associated with this sort of brainwave. You can find a short discussion of this here.

Anyway, I’m pretty sure that  most scientists – even the eminent individuals interviewed for the Physics World piece – have spent a large part of their time “stuck”. I know I have, but then I’m not really eminent anyway. In the long run it’s probably good to go through such periods as I think they’re essential for intellectual development, but they’re undoubtedly extremely frustrating at the time. How you get “unstuck” is a very mysterious process. I’m not a neuroscientist, but it seems to me that when you get really immersed in, say, a research problem, your subconscious brain gets drawn into what you think is a fully conscious process, to the extent that even when you’re apparently not thinking about something you really are. I’ve had ideas come to me in all kinds of weird situations: watching ducks paddling on a pond, listening to music, walking in a park, and even pushing a trolley around a supermarket. Often it seems that it’s precisely when you’re not thinking that you have your best ideas. It’s not always clear what acted as the trigger, but and when it is it is often something quite abstract. In the case I mentioned of the ducks on the pond it was just a question of thinking about reference frames. It was a nudge in the right direction, but I still had to do quite a lot of work to finish the calculation. Come to think of it, it’s usually at that conceptual level that such things happen rather than in the detailed working, at least in my case.

The Physics World piece also talks about ideas coming through dreams. That has happened to me too, but I think it’s basically the same phenomenon that I’ve just discussed. It seems to me that dreams are a product of your brain sorting through recent events or experiences and trying to make sense of them in terms of others it has filed away. This can help with a research problem by flagging up a connection with something else hidden away. I can remember at least two occasions when I’ve woken up from a dream with an exact understanding of what I’d been doing wrong and how I could fix it. It’s great to wake up in the morning with that kind of feeling!

I know it’s wrong to draw inferences about other people from one’s own particular experiences, but I do feel that there are some general lessons. One is that if you are going to be successful at research you have to have a sense of determination that borders on obsession. You have to immerse yourself in it and be prepared to put long hours in. When things are going well you will be so excited that you will find it as hard to stop as it is when you’re struggling. I’m writing as a physicist, but I imagine it is the just same for other disciplines.

The other, equally important, lesson to be learned is that it is essential to do other things as well as doing science. Being “stuck” on a problem is an essential part of mathematics or physics research, but sometimes battering your head against the same thing for days on end just makes it less and less likely you will crack it. The human brain is a wonderful thing, but it can get stuck in a rut. One way to avoid this happening is to have more than one thing to think about.

I’ve lost count of the number of times I’ve been stuck on the last clue in a crossword, which usually means that my facility for thinking laterally, which is so essential for solving cryptic puzzles, is not operating well. What I always do in that situation is put it down and do something else for a bit. It could even be something as trivial as making a cup of tea, just as long as I don’t think about the clue at all while I’m doing it. Nearly always when I come back to it and look at it afresh I can solve it. I have a large stack of prize dictionaries to prove that this works!

It can be difficult to force yourself to pause in this way. I’m sure that I’m not the only physicist who has been unable to sleep for thinking about their research. I do think however that it is essential to learn how to effect your own mental reboot. In the context of my research this involved simply turning to a different research problem, but I think the same purpose can be served in many other ways: taking a break, going for a walk, playing sport, listening to or playing music, reading poetry, doing a crossword, or even just taking time out to socialize with your friends. Time spent sitting at your desk isn’t guaranteed to be productive, and you should never feel guilty about taking a thinking break.

I’d be interested to receive examples of other “light-bulb” moments through the comments box. I’d also welcome comments from neuroscientists on my extremely naïve comments about how the brain works in such situations.

 

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The Expanding Universe: An Introduction

Posted in The Universe and Stuff with tags , , on January 5, 2018 by telescoper

For those of you reading this blog who feel they need an up-to-date primer for the basics of modern cosmology without too much technical detail, I found a paper on the arXiv that might give you what you want. It’s over a hundred pages long but does not use much complicated mathematics but has some nice illustrations. The author is Markus Pössel; the abstract reads

An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various distance concepts and the generalized redshift-luminosity relation, among other topics.

This paper focusses on the basics of the standard framework founded on general relativity, especially how cosmological distances are defined and measured, rather than on trendy modern topics like dark energy and the cosmic microwave background. I’d say any first-year physics student should be able to cope with it, but it’s not for someone who hasn’t learned calculus. On the other hand, it’s free to download so you don’t have much to lose by having a look!

You can download a PDF here.

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The Winter Solstice

Posted in The Universe and Stuff with tags , , , , , on December 21, 2017 by telescoper

The winter solstice in the Northern hemisphere happens today, Thursday 21st December 2017, at 16.28 GMT (16.28 UTC). This marks the shortest day of the year: days will get longer from now until the Summer Solstice next June.  In fact the interval between sunrise and sunset tomorrow will be a whole two seconds longer tomorrow than it is today. Yippee!

Anyway, in advance of this forthcoming celestial event I thought I’d present some solstitial facts for your entertainment and edification or so you can bore people with them in the pub later on.

As we were discussing in the office today, however, this does not mean that sunrise will happen earlier tomorrow than it did this morning. In fact, sunrise will carry on getting later until the new year. This is because there is a difference between mean solar time (measured by clocks) and apparent solar time (defined by the position of the Sun in the sky), so that a solar day does not always last exactly 24 hours. A description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767:

Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time.

The discrepancy between mean time and apparent time arises because of the Earth’s axial tilt and the fact that it travels around the Sun in an elliptical orbit in which its orbital speed varies with time of year (being faster at perihelion than at aphelion).

In fact if you plot the position of the Sun in the sky at a fixed time each day from a fixed location on the Earth you get a thing called an analemma, which is a sort of figure-of-eight shape whose shape depends on the observer’s latitude. Here’s a photographic version taken in Edmonton, with photographs of the Sun’s position taken from the same position at the same time on different days over the course of a year:

maxresdefault

The winter solstice is the lowermost point on this curve and the summer solstice is at the top. The north–south component of the analemma is the Sun’s declination, and the east–west component is the so-called equation of time which quantifies the difference between mean solar time and apparent solar time. This curve can be used to calculate the earliest and/or latest sunrise and/or sunset.

Using a more rapid calculational tool (Google), I found a table of the local mean times of sunrise and sunset for Cardiff (where I live) around the 2016 winter solstice. The table shows that today is indeed the shortest day (with a time between sunrise and sunset of 7 hours 49 minutes and 59 seconds).  The table also shows that sunset already started occurring later in the day before the winter solstice (although the weather has been too overcast to notice this), and sunrise will continue to happen later for a few days after the solstice. In fact the earliest sunset this year in Cardiff was on 12th December, and the latest sunrise will be on 30th December.

I hope this clarifies the situation.

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The Taste and Tincture of Another Education

Posted in Education, Literature, The Universe and Stuff with tags , on December 17, 2017 by telescoper

This is what a University education meant to the poet and theologian Thomas Traherne (1636-1674), according to his Centuries of Meditations. In this astonishing book describing his own voyage of spiritual discovery, Traherne celebrates, among many other things, the beauty and complexity of creation as a manifestation of the power of God. Even  a non-religious person like myself can find much to appreciate in his words about the wonder of the natural world and the joy of learning for learning’s sake:

Having been at the University, and received there the taste and tincture of another education, I saw that there were things in this world of which I never dreamed; glorious secrets, and glorious persons past imagination. 

There I saw that Logic, Ethics, Physics, Metaphysics, Geometry, Astronomy, Poesy, Medicine, Grammar, Music, Rhetoric all kinds of Arts, Trades, and Mechanisms that adorned the world pertained to felicity; at least there I saw those things, which afterwards I knew to pertain unto it: and was delighted in it. 

There I saw into the nature of the Sea, the Heavens, the Sun, the Moon and Stars, the Elements, Minerals, and Vegetables. All which appeared like the King’s Daughter, all glorious within; and those things which my nurses, and parents, should have talked of there were taught unto me.

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Trees, Graphs and the Leaving Certificate

Posted in Biographical, mathematics, Maynooth, The Universe and Stuff with tags , , , , , , on December 15, 2017 by telescoper

I’m starting to get the hang of some of the differences between things here in Ireland and the United Kingdom, both domestically and in the world of work.

One of the most important points of variation that concerns academic life is the school system students go through before going to University. In the system operating in England and Wales the standard qualification for entry is the GCE A-level. Most students take A-levels in three subjects, which gives them a relatively narrow focus although the range of subjects to choose from is rather large. In Ireland the standard qualification is the Leaving Certificate, which comprises a minimum of six subjects, giving students a broader range of knowledge at the sacrifice (perhaps) of a certain amount of depth; it has been decreed for entry into this system that an Irish Leaving Certificate counts as about 2/3 of an A-level for admissions purposes, so Irish students do the equivalent of at least four A-levels, and many do more than this.

There’s a lot to be said for the increased breadth of subjects undertaken for the leaving certificate, but I have no direct experience of teaching first-year university students here yet so I can’t comment on their level of preparedness.

Coincidentally, though, one of the first emails I received this week referred to a consultation about proposed changes to the Leaving Certificate in Applied Mathematics. Not knowing much about the old syllabus, I didn’t feel there was much I could add but I had a look at the new one and was surprised to see a whole `Strand’, on Mathematical Modelling with netwworks and graphs.

The introductory blurb reads:

In this strand students learn about networks or graphs as mathematical models which can be used to investigate a wide range of real-world problems. They learn about graphs and adjacency matrices and how useful these are in solving problems. They are given further opportunity to consolidate their understanding that mathematical ideas can be represented in multiple ways. They are introduced to dynamic programming as a quantitative analysis technique used to solve large, complex problems that involve the need to make a sequence of decisions. As they progress in their understanding they will explore and appreciate the use of algorithms in problem solving as well as considering some of the wider issues involved with the use of such techniques.

 

Among the specific topics listed you will find:

  • Minimal Spanning trees applied to problems involving optimising networks and algorithms associated with finding these (Kruskal, Prim);  
  • Bellman’s Optimality Principal to find the shortest paths in a weighted directed network, and to be able to formulate the process algebraically;
  •  Dijkstra’s algorithm to find shortest paths in a weighted directed network; etc.

 

For the record I should say that I’ve actually used Minimal Spanning Trees in a research context (see, e.g., this paper) and have read (and still have) a number of books on graph theory, which I find a truly fascinating subject. It seems to me that the topics all listed above  are all interesting and they’re all useful in a range of contexts, but they do seem rather advanced topics to me for a pre-university student and will be unfamiliar to a great many potential teachers of Applied Mathematics too. It may turn out, therefore, that the students will end up getting a very superficial knowledge of this very trendy subject, when they would actually be better off getting a more solid basis in more traditional mathematical methods  so I wonder what the reaction will be to this proposal!

 

 

 

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A Python Toolkit for Cosmology

Posted in The Universe and Stuff with tags , , , , on December 14, 2017 by telescoper

The programming language Python has established itself as the industry standard for researchers in physics and astronomy (as well as the many other fields, including most of those covered by the Data Innovation Research Institute which employs me part-time). It has also become the standard vehicle for teaching coding skills to undergraduates in many disciplines. In fact it looks like the first module I will be teaching in Maynooth next term is in Computational Physics, and that will be delivered using Python too. It’s been a while since I last did any significant hands-on programming, so this will provide me with a good refresher. The best way to learn something well is to have to teach it to others!

But I digress. This morning I noticed a paper by Benedikt Diemer on the arXiv with the title COLOSSUS: A python toolkit for cosmology, large-scale structure, and dark matter halos. Here is the abstract:

This paper introduces Colossus, a public, open-source python package for calculations related to cosmology, the large-scale structure of matter in the universe, and the properties of dark matter halos. The code is designed to be fast and easy to use, with a coherent, well-documented user interface. The cosmology module implements FLRW cosmologies including curvature, relativistic species, and different dark energy equations of state, and provides fast computations of the linear matter power spectrum, variance, and correlation function. The large-scale structure module is concerned with the properties of peaks in Gaussian random fields and halos in a statistical sense, including their peak height, peak curvature, halo bias, and mass function. The halo module deals with spherical overdensity radii and masses, density profiles, concentration, and the splashback radius. To facilitate the rapid exploration of these quantities, Colossus implements about 40 different fitting functions from the literature. I discuss the core routines in detail, with a particular emphasis on their accuracy. Colossus is available at bitbucket.org/bdiemer/colossus.

The software can be downloaded here. It looks a very useful package that includes code to calculate many of the bits and pieces used by cosmologists working on the theory of large-scale structure and galaxy evolution. It is also, I hope, an example of a trend towards greater use of open-source software, for which I congratulate the author! I think this is an important part of the campaign to create truly open science, as I blogged about here.

An important aspect of the way science works is that when a given individual or group publishes a result, it should be possible for others to reproduce it (or not, as the case may be). At present, this can’t always be done. In my own field of astrophysics/cosmology, for example, results in traditional scientific papers are often based on very complicated analyses of large data sets. This is increasingly the case in other fields too. A basic problem obviously arises when data are not made public. Fortunately in astrophysics these days researchers are pretty good at sharing their data, although this hasn’t always been the case.

However, even allowing open access to data doesn’t always solve the reproducibility problem. Often extensive numerical codes are needed to process the measurements and extract meaningful output. Without access to these pipeline codes it is impossible for a third party to check the path from input to output without writing their own version assuming that there is sufficient information to do that in the first place. That researchers should publish their software as well as their results is quite a controversial suggestion, but I think it’s the best practice for science. There isn’t a uniform policy in astrophysics and cosmology, but I sense that quite a few people out there agree with me. Cosmological numerical simulations, for example, can be performed by anyone with a sufficiently big computer using GADGET the source codes of which are freely available. Likewise, for CMB analysis, there is the excellent CAMB code, which can be downloaded at will; this is in a long tradition of openly available numerical codes, including CMBFAST and HealPix.

I suspect some researchers might be reluctant to share the codes they have written because they feel they won’t get sufficient credit for work done using them. I don’t think this is true, as researchers are generally very appreciative of such openness and publications describing the corresponding codes are generously cited. In any case I don’t think it’s appropriate to withhold such programs from the wider community, which prevents them being either scrutinized or extended as well as being used to further scientific research. In other words excessively proprietorial attitudes to data analysis software are detrimental to the spirit of open science.

Anyway, my views aren’t guaranteed to be representative of the community, so I’d like to ask for a quick show of hands via a poll…

…and you are of course welcome to comment via the usual box.

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