A Problem involving Simpson’s Rule

Posted in Cute Problems, mathematics with tags , on March 9, 2018 by telescoper

Since I’m teaching a course on Computational Physics here in Maynooth and have just been doing methods of numerical integration (i.e. quadrature) I thought I’d add this little item to the Cute Problems folder. You might answer it by writing a short bit of code, but it’s easy enough to do with a calculator and a piece of paper if you prefer.

Use the above expression, displayed using my high-tech mathematical visualization software, to obtain an approximate value for π/4 (= 0.78539816339…) by estimating the integral on the left hand side using Simpson’s Rule at ordinates x =0, 0.25, 0.5, 0.75 and 1.

Comment on the accuracy of your result. Solutions and comments through the box please.

HINT 1: Note that the calculation just involves two applications of the usual three-point Simpson’s Rule with weights (1/3, 4/3, 1/3). Alternatively you could do it in one go using weights (1/3, 4/3, 2/3, 4/3, 1/3).

HINT 2: If you’ve written a bit of code to do this, you could try increasing the number of ordinates and see how the result changes…

P.S. Incidentally I learn that, in Germany, Simpson’s Rule is sometimes called called Kepler’s rule, or Keplersche Fassregel after Johannes Kepler, who used something very similar about a century before Simpson…

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Willow Weep For Me – Mary Lou Williams

Posted in Jazz with tags , , , on March 8, 2018 by telescoper

Today is International Women’s Day, so I thought I’d post this lovely performance of the standard Willow Weep For Me, not just because it is played by the wonderfully talented pianist composer and arranger Mary Lou Williams, but because the song itself was written by Ann Ronell…

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Back to Maynooth

Posted in Biographical, Cardiff, Maynooth with tags , , , on March 7, 2018 by telescoper

So here I am back in Maynooth. The University re-opened on Monday after being closed from Wednesday last week owing to the extremely bad weather. I’m told the snow was several feet deep and the town was virtually cut off until the weekend. There is still some snow lying here and there, but the thaw has begun and you can see the effect of the meltwater on the river (the Lyreen) that flows through town, which is usually no more than a little stream:

Picture Credit: Coyne’s Family Butcher, Maynooth

It’s not quite a raging torrent, but getting there!

At the moment there’s no sign of a resolution to the industrial action that’s affecting Cardiff University (as well as others in the UK) so I decided to travel to Ireland yesterday rather than my usual Wednesday. The flight over was virtually empty and so was Dublin Airport, so I got on the bus well ahead of schedule and made it back to my flat (which was cold, but otherwise all in order) in time to buy some groceries and make dinner. The panic-buying of bread had caused a shortage, but all seems to be back to normal again.

I had arranged for someone else to do last week’s Thursday lecture and Lab session so I could attend the event the IOP event I posted about, but as the campus was closed they were cancelled anyway and I now have to find a way to catch up. Do not worry, though, I have a cunning plan.

Unless there’s an announcement in the next couple of days that next week’s strike is off I plan to stay in Ireland over the weekend, which will give me the chance to explore Dublin a bit, something that my schedule has not so far allowed. Next week will be the fourth week of industrial action and the last of the current batch of strike days, this time a full week (having escalated from two, three and four days in the preceding weeks). If there is no resolution by then I don’t know what will happen, possibly an all-out indefinite strike. Nobody wants that, but there’s no doubt in my mind who is to blame for this dispute and it’s not the Universities and Colleges Union. However, there are some signs of movement, so let’s hope for a negotiated settlement. If not, I’m seriously thinking of trying to bring forward my full-time move to Maynooth. There’s little point continuing in my post in Cardiff if I’m going to be permanently on strike.

Anyway, I have a 9am lecture to give tomorrow so I think I’ll toddle off, get some tea and have an early night.

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R.I.P. Trevor Baylis (1937-2018)

Posted in Biographical with tags , on March 6, 2018 by telescoper

I heard yesterday the sad news of the death of inventor Trevor Baylis, who was most famous for his wind-up radio device. This brought back memories of when we both appeared in a Tomorrow’s World Live event that took place 21 years ago. I didn’t get to know him very well, but seemed to me to be a nice man, and the very epitome of an old-school boffin complete with pipe and tweed jacket.

I was on the show to do an item on the Tomorrow’s World Live show – which was not broadcast but performed in front of an audience of a few hundred people in a temporary theatre. In fact there were four shows a day for the period of the event (19-23 March 1997). Each show was only about 30 minutes long, but it was quite hard work as there were many technical things to sort out in between performances.

My role was to do a little piece about the refurbished Hubble Space Telescope and then answer questions on astronomy and cosmology from the audience. I had no script for that bit, as it was impossible to know what would be asked. I answered with varying degrees of success.

Other items featured on the show, as well as Trevor’s clockwork radio, were an  electric sports car, and a device for scrambling an egg without breaking its shell. I couldn’t see the point of the last invention, as one would have to break the shell to eat the egg anyway.

The best bit about being involved in Tomorrow’s World Live was meeting so many of the presenters, all of them proper professionals (unlike me) who were very friendly and helpful although most of them seemed very nervous beforehand. I think they knew better than I did how many things might go wrong. Only two presenters were involved in each show,  and  each pair only did one or two shows, so over the five days I got to work with the whole set, including Craig Doyle, Philippa Forester, Howard Stableford, Vivienne Parry and Shahnaz Pakravan. I didn’t envy them as they had to work not only with amateurs like me, but also had to learn a detailed script and deal with the gadgets. I was relieved that I could basically just wing it.

My clearest memory of the whole event was the technical rehearsal early  in the morning before the very first show. Apart from the wind-up radio, nothing worked properly, and I was convinced that it was all going to be a complete disaster. Somehow, however, it all came together and there weren’t any major problems in any of the real shows.

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Talent versus Luck

Posted in Biographical with tags , , on March 5, 2018 by telescoper

I’ve remarked quite a number of times on the blog that I think I’ve been exceptionally lucky in my scientific career, the latest example being the good fortune that the position at Maynooth University came up precisely when it did, enabling me to relocate to Ireland.

It struck me further the other day that the people who think that science is genuinely meritocratic, tend to be those who have done well in the system rather than those who haven’t. It’s rather like the way that very rich people tend to think that they have earned their wealth and that makes them better people than those who are less well off, even when that’s demonstrably not true.

Likewise, luck plays a definite role in winning grant funding. Having been on grants panels I’m away that many very good proposals are not funded. A scoring system is generally used that introduces some level of objectivity into the process, but the fact is that a lot of proposals come out with similar scores and the ranking of these is a bit arbitrary. A slightly different panel would produce slightly different scores, but perhaps a large difference in ranking would result.

Anyway, there’s a paper on the arXiv (by Pluchino et al) with the title Talent vs Luck: the role of randomness in success and failure that
discusses the role of good fortune in scientific careers. This is the abstract:

The largely dominant meritocratic paradigm of highly competitive Western cultures is rooted on the belief that success is due mainly, if not exclusively, to personal qualities such as talent, intelligence, skills, efforts or risk taking. Sometimes, we are willing to admit that a certain degree of luck could also play a role in achieving significant material success. But, as a matter of fact, it is rather common to underestimate the importance of external forces in individual successful stories. It is very well known that intelligence or talent exhibit a Gaussian distribution among the population, whereas the distribution of wealth – considered a proxy of success – follows typically a power law (Pareto law). Such a discrepancy between a Normal distribution of inputs, with a typical scale, and the scale invariant distribution of outputs, suggests that some hidden ingredient is at work behind the scenes. In this paper, with the help of a very simple agent-based model, we suggest that such an ingredient is just randomness. In particular, we show that, if it is true that some degree of talent is necessary to be successful in life, almost never the most talented people reach the highest peaks of success, being overtaken by mediocre but sensibly luckier individuals. As to our knowledge, this counterintuitive result – although implicitly suggested between the lines in a vast literature – is quantified here for the first time. It sheds new light on the effectiveness of assessing merit on the basis of the reached level of success and underlines the risks of distributing excessive honors or resources to people who, at the end of the day, could have been simply luckier than others. With the help of this model, several policy hypotheses are also addressed and compared to show the most efficient strategies for public funding of research in order to improve meritocracy, diversity and innovation.

Comments are, as always, welcome!

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Tohguht for the Day

Posted in Uncategorized on March 4, 2018 by telescoper

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The Weather and the LGBT Physical Sciences Climate Survey.

Posted in Uncategorized on March 3, 2018 by telescoper

I wrote this post on Thursday, after a long and busy day, in a hotel near Paddington station, having long since given up the possibility of returning to Cardiff today owing to the inclement weather conditions. Fortunately I had taken my overnight things and a change of clothes in anticipation of the likelihood of getting stranded.

Unfortunately the hotel WiFi crapped out and it seems it never got posted, so I’ve updated it and here it is now. I was in London for the launch event for the LGBT Physical Sciences Climate survey.

Before going on please let me wish you a belated Dydd Gŵyl Dewi Hapus, as Thursday was St David’s Day!

I rose at 5 o’clock on Thursday morning to get the 6.26 train to London to participate in this event. It was all going well until we reached Swindon (about halfway into the journey) but then we warned that Paddington station was closed and the train would be terminating at Reading. I was a bit surprised by this as there wasn’t really very much snow at all, but it turns out that the snowy conditions had made Paddington too slippery to be safe. That’s no doubt because of the shiny floors added at great expense but very little point when the station was refurbished some years ago. At no point on the journey into London did I see more than half an inch of snow. It’s truly pathetic that such total disruption of this major transport route resulted from such a small amount of snow.

I was advised by the GWR staff at Reading to turn forget about making it to London and instead to get on the train back to Cardiff, as no trains were going into out out of London and snow was heading for Cardiff making it unlikely I would get back this evening even if I did continue on my journey.

Eschewing this advice I found that trains were leaving from Reading to Ealing Broadway, so I got one of those and took the Central Line underground from there into town. I arrived about 11am at the Institute of Physics, about two hours later than planned but I had left early in anticipation of likely delays.

Anyway, the event itself seemed to go quite well. I gave a little introductory talk, followed by four other speakers, and then chaired a panel discussion. Here’s a few pictures:

The participants (from left to right) were: Dr Ashley Spindler, Dr James Claverley, myself, Niamh Kavanagh, and Professor Dave Smith. There then followed a little drinks reception and a group of us subsequently adjourned to a local pub for drinks.

Anyway, the main point is that the survey is now live and can be found here. That link also tells you who’s eligible to complete it.

The survey is open until the end of April so I’ll probably post a few reminders over the next few weeks…

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Back to Snowy Cardiff

Posted in Biographical, Bute Park, Cardiff on March 3, 2018 by telescoper

I made it back to Cardiff yesterday. The train I was on was about half an hour late, but that was understandable. The strange bit was that most of the delay resulted from us running very slowly through the Severn Tunnel. There certainly wasn’t any snow down there!

Cardiff city centre was virtually deserted and none of the roads had been cleared of snow. I’m guessing no buses were running, as I didn’t see any on the way, and there were few cars. Many shops were closed. The M&S in the station was open but had received no deliveries that day, and was just selling what it had from the day before. I bought some groceries, mostly at a reduced price.

It was snowing quite heavily and was very cold when I walked back to my house from the station, so I didn’t take many pictures, but I couldn’t resist this one of the River Taff, frozen over by the Principality Stadium:

This was the view towards Pontcanna Fields from near the cricket ground.

Fortunately I was wearing heavy walking boots, but I’d forgotten what hard work it is to walk through snow!

This morning there’s still a lot of snow around and no sign of any attempt to clear the roads.

I wonder if there’ll be anywhere open to buy a paper?

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Cosmic Dawn?

Posted in Astrohype, The Universe and Stuff on March 2, 2018 by telescoper

I’m still in London hoping to get a train back to Cardiff at some point this morning – as I write they are running, but with a reduced service – so I thought I’d make a quick comment on a big piece of astrophysics news. There’s a paper out in this week’s Nature, the abstract of which is

After stars formed in the early Universe, their ultraviolet light is expected, eventually, to have penetrated the primordial hydrogen gas and altered the excitation state of its 21-centimetre hyperfine line. This alteration would cause the gas to absorb photons from the cosmic microwave background, producing a spectral distortion that should be observable today at radio frequencies of less than 200 megahertz1. Here we report the detection of a flattened absorption profile in the sky-averaged radio spectrum, which is centred at a frequency of 78 megahertz and has a best-fitting full-width at half-maximum of 19 megahertz and an amplitude of 0.5 kelvin. The profile is largely consistent with expectations for the 21-centimetre signal induced by early stars; however, the best-fitting amplitude of the profile is more than a factor of two greater than the largest predictions2. This discrepancy suggests that either the primordial gas was much colder than expected or the background radiation temperature was hotter than expected. Astrophysical phenomena (such as radiation from stars and stellar remnants) are unlikely to account for this discrepancy; of the proposed extensions to the standard model of cosmology and particle physics, only cooling of the gas as a result of interactions between dark matter and baryons seems to explain the observed amplitude3. The low-frequency edge of the observed profile indicates that stars existed and had produced a background of Lyman-α photons by 180 million years after the Big Bang. The high-frequency edge indicates that the gas was heated to above the radiation temperature less than 100 million years later.

The key plot from the paper is this:

I’ve read the paper and, as was the case with the BICEP2 announcement a few years ago, I’m not entirely convinced. I think the paper is very good at describing the EDGES experiment, but far less convincing that all necessary foregrounds and systematics have been properly accounted for. There are many artefacts that could mimic the signal shown in the diagram.

If true, the signal is quite a lot larger than amplitude than standard models predict. That doesn’t mean that it must be wrong – I’ve never gone along with the saying `never trust an experimental result until it is confirmed by theory’ – but it’s way too early to claim that it proves that some new exotic physics is involved. The real explanation may be far more mundane.

There’s been a lot of media hype about this result – reminiscent of the BICEP bubble – and, while I agree that if it is true it is an extremely exciting result – I think it’s far too early to be certain of what it really represents. To my mind there’s a significant chance this could be a false cosmic dawn.

I gather the EDGES team is going to release its data publicly. That will be good, as independent checks of the data analysis would be very valuable.

I’m sorry I haven’t got time for a more detailed post on this, but I have to get my stuff together and head for the train. Comments from experts and non-experts are, as usual, most welcome via the comments box.

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Maynooth in the Snow

Posted in Maynooth with tags , on February 28, 2018 by telescoper

There has been very little snow in Cardiff (so far) but there have been heavy falls in Maynooth. The above picture was tweeted by Maynooth University this morning, along with an announcement that the campus is closed today (and probably until Friday, as more snow is on the way).

Under normal circumstances I would be in Ireland from today until the weekend, but I have to be in London tomorrow (Thursday) so arranged cover for my teaching. Looks like teaching will be cancelled tomorrow anyway.

UPDATE: Maynooth University campus will be closed until Monday.

Whether I can make it to and from London, or whether the event I’m supposed to attend tomorrow will be cancelled, remains to be seen…

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