Archive for November, 2013

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Would Scottish Independence be Good for English Science?

Posted in Politics, Science Politics with tags , , , , on November 13, 2013 by telescoper

On Monday the Minister for Universities and Science, David Willetts, visited Edinburgh where he took in, among other things, the UK Astronomy Technology Centre and was treated to an explanation of how adaptive optics work. There being less than a year to go before the forthcoming referendum on Scottish independence, the visit was always likely to generate political discussion and this turned out to be the case.

According to a Guardian piece

Scientists and academics in Scotland would lose access to billions of pounds in grants and the UK’s world-leading research programmes if it became independent, the Westminster government has warned.

David Willetts, the UK science minister, said Scottish universities were “thriving” because of the UK’s generous and highly integrated system for funding scientific research, winning far more funding per head than the UK average.

Unveiling a new UK government paper on the impact of independence on scientific research, Willetts said that despite its size the UK was second only to the United States for the quality of its research.

“We do great things as a single, integrated system and a single integrated brings with it great strengths,” he said.

Overall spending on scientific research and development in Scottish universities from government, charitable and industry sources was more than £950m in 2011, giving a per capita spend of £180 compared to just £112 per head across the UK as a whole.

It is indeed notable that Scottish universities outperform those in the rest of the United Kingdom when it comes to research, but it always struck me that using this as an argument against independence is difficult to sustain. In fact it’s rather similar to the argument that the UK does well out of European funding schemes so that is a good argument for remaining in the European Union. The point is that, whether or not a given country benefits from the funding system, it still has to do so by following an agenda that isn’t necessarily its own. Scotland benefits from UK Research Council funding, but their priorities are set by the Westminster government, just as the European Research Council sets (sometimes rather bizarre) policies for its schemes. Who’s to say that Scotland wouldn’t do even better than it does currently by taking control of its own research funding rather than forcing its institutions to pander to Whitehall?

It’s also interesting to look at the flipside of this argument. If Scotland were to become independent, would the “billions” of research funding it would lose (according to Willetts) benefit science in what’s left of the United Kingdom? There are many in England and Wales who think the existing research budget is already spread far too thinly and who would welcome an increase south of the border. If this did happen you could argue that, from a very narrow perspective, Scottish independence would be good for English science.

For what it’s worth, I am a complete agnostic about Scottish independence – I really think its for the Scots to decide – but I don’t think it would benefit the rest of the UK from the point of view of science funding. I think it’s much more likely that if Scotland were to leave the United Kingdom then the part of the science budget it currently receives would be cancelled rather than redistributed, which would leave us no better off at all.

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The Curse of P-values

Posted in Bad Statistics with tags , , , on November 12, 2013 by telescoper

Yesterday evening I noticed a news item in Nature that argues that inappropriate statistical methodology may be undermining the reporting of scientific results. The article focuses on lack of “reproducibility” of results.

The article focuses on the p-value, a frequentist concept that corresponds to the probability of obtaining a value at least as large as that obtained for a test statistic under the null hypothesis. To give an example, the null hypothesis might be that two variates are uncorrelated; the test statistic might be the sample correlation coefficient r obtained from a set of bivariate data. If the data were uncorrelated then r would have a known probability distribution, and if the value measured from the sample were such that its numerical value would be exceeded with a probability of 0.05 then the p-value (or significance level) is 0.05.

Anyway, whatever the null hypothesis happens to be, you can see that the way a frequentist would proceed would be to calculate what the distribution of measurements would be if it were true. If the actual measurement is deemed to be unlikely (say that it is so high that only 1% of measurements would turn out that big under the null hypothesis) then you reject the null, in this case with a “level of significance” of 1%. If you don’t reject it then you tacitly accept it unless and until another experiment does persuade you to shift your allegiance.

But the p-value merely specifies the probability that you would reject the null-hypothesis if it were correct. This is what you would call making a Type I error. It says nothing at all about the probability that the null hypothesis is actually a correct description of the data. To make that sort of statement you would need to specify an alternative distribution, calculate the distribution based on it, and hence determine the statistical power of the test, i.e. the probability that you would actually reject the null hypothesis when it is correct. To fail to reject the null hypothesis when it’s actually incorrect is to make a Type II error.

If all this stuff about p-values, significance, power and Type I and Type II errors seems a bit bizarre, I think that’s because it is. It’s so bizarre, in fact, that I think most people who quote p-values have absolutely no idea what they really mean.

The Nature story mentioned above argues that in fact that results quoted with a p-value of 0.05 turn out to be wrong about 25% of the time. There are a number of reasons why this could be the case, including that the p-value is being calculated incorrectly, perhaps because some assumption or other turns out not to be true; a widespread example is assuming that the variates concerned are normally distributed. Unquestioning application of off-the-shelf statistical methods in inappropriate situations is a serious problem in many disciplines, but is particularly prevalent in the social sciences when samples are typically rather small.

While I agree with the Nature piece that there’s a problem, I don’t agree with the suggestion that it can be solved simply by choosing stricter criteria, i.e. a p-value of 0.005 rather than 0.05. While it is true that this would throw out a lot of flaky `two-sigma’ results, it doesn’t alter the basic problem which is that the frequentist approach to hypothesis testing is intrinsically confusing compared to the logically clearer Bayesian approach. In particular, most of the time the p-value is an answer to a question which is quite different from that which a scientist would want to ask, which is what the data have to say about a given hypothesis. I’ve banged on about Bayesian methods quite enough on this blog so I won’t repeat the arguments here, except that such approaches focus on the probability of a hypothesis being right given the data, rather than on properties that the data might have given the hypothesis. If I had my way I’d ban p-values altogether.

Not that it’s always easy to implement a Bayesian approach. Coincidentally a recent paper on the arXiv discussed an interesting apparent paradox in hypothesis testing that arises in the context of high energy physics, which I thought I’d share here. Here is the abstract:

The Jeffreys-Lindley paradox displays how the use of a p-value (or number of standard deviations z) in a frequentist hypothesis test can lead to inferences that are radically different from those of a Bayesian hypothesis test in the form advocated by Harold Jeffreys in the 1930’s and common today. The setting is the test of a point null (such as the Standard Model of elementary particle physics) versus a composite alternative (such as the Standard Model plus a new force of nature with unknown strength). The p-value, as well as the ratio of the likelihood under the null to the maximized likelihood under the alternative, can both strongly disfavor the null, while the Bayesian posterior probability for the null can be arbitrarily large. The professional statistics literature has many impassioned comments on the paradox, yet there is no consensus either on its relevance to scientific communication or on the correct resolution. I believe that the paradox is quite relevant to frontier research in high energy physics, where the model assumptions can evidently be quite different from those in other sciences. This paper is an attempt to explain the situation to both physicists and statisticians, in hopes that further progress can be made.

Rather than tell you what I think about this paradox, I thought I’d invite discussion through the comments box…

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Astronomy Look-alikes, No. 88

Posted in Astronomy Lookalikes with tags , on November 12, 2013 by telescoper

At a meeting of the Royal Astronomical Society on Friday I was struck by the resemblance between Scottish comic actor John Sessions and space scientist Professor Mark Burchell of the University of Kent. I wonder if by any chance they might be related?

 

Lookalike

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Strange Meeting – A Poem for Armistice Day

Posted in History, Poetry on November 11, 2013 by telescoper

I’ve been travelling all morning, but managed to observe the Armistice Day minute’s silence, standing outside the station in the pouring rain, while I was waiting for a connecting train.

Anyway, this poem, Strange Meeting was written by Wilfred Owen, who died just a few days before the Armistice came into effect in 1918. It’s a poem that needs to be read repeatedly to be fully appreciated, but there is one line that is utterly devastating straight away: “I am the enemy you killed, my friend”..

 It seemed that out of the battle I escaped
Down some profound dull tunnel, long since scooped
Through granites which Titanic wars had groined.
Yet also there encumbered sleepers groaned,
Too fast in thought or death to be bestirred.
Then, as I probed them, one sprang up, and stared
With piteous recognition in fixed eyes,
Lifting distressful hands as if to bless.
And by his smile, I knew that sullen hall;
By his dead smile, I knew we stood in Hell.
With a thousand fears that vision’s face was grained;
Yet no blood reached there from the upper ground,
And no guns thumped, or down the flues made moan.
“Strange, friend,” I said, “Here is no cause to mourn.”
“None,” said the other, “Save the undone years,
The hopelessness. Whatever hope is yours,
Was my life also; I went hunting wild
After the wildest beauty in the world,
Which lies not calm in eyes, or braided hair,
But mocks the steady running of the hour,
And if it grieves, grieves richlier than here.
For by my glee might many men have laughed,
And of my weeping something has been left,
Which must die now. I mean the truth untold,
The pity of war, the pity war distilled.
Now men will go content with what we spoiled.
Or, discontent, boil bloody, and be spilled.
They will be swift with swiftness of the tigress,
None will break ranks, though nations trek from progress.
Courage was mine, and I had mystery;
Wisdom was mine, and I had mastery;
To miss the march of this retreating world
Into vain citadels that are not walled.
Then, when much blood had clogged their chariot-wheels
I would go up and wash them from sweet wells,
Even with truths that lie too deep for taint.
I would have poured my spirit without stint
But not through wounds; not on the cess of war.
Foreheads of men have bled where no wounds were.
I am the enemy you killed, my friend.
I knew you in this dark; for so you frowned
Yesterday through me as you jabbed and killed.
I parried; but my hands were loath and cold.
Let us sleep now . . .”

Lest we forget.

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The Number 1 Scientist from the North

Posted in History, The Universe and Stuff on November 10, 2013 by telescoper

This morning I was glancing through an old book called Science since 1500, which was written by H.T. Pledge and published in 1939 by Her Majesty’s Stationery Office on behalf of the Ministry of Education.

The map shows the distribution of birthplaces of famous British scientists (from about 1800 to about 1900). This map is restricted to the “exact” sciences, and I’m not exactly sure what that means, but judging by the names, it includes physics, astronomy and chemistry. Clustering is apparent, especially in Edinburgh and Glasgow but also in Ireland.

Note, however, the relative dearth of such scientists from the North of England. In fact there is only one (appropriately enough labelled ‘1’), though there are several born in the Midlands, especially near Manchester..

I have scanned the legend which reveals the names, and will post it in due course, but I thought it would be fun to have a small competition to see who knows the identity of the Number 1 Scientist from the North.

If you’d like to guess any of the others please feel free too. Just to give an example, No. 7 is Arthur Stanley Eddington (who was born in 1882 in Kendal, in what is now Cumbria).

Answers through the comments box please!

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Alms for Oblivion

Posted in Literature with tags , on November 9, 2013 by telescoper

When I posted the great St Crispian’s Day from Henry V a while ago, a colleague of mine mentioned another great speech from Shakespeare that I might like to share. This is froma much less familiar play, Troilus and Cressida, which interweaves a love story between the title characters, with an account of the siege of Troy. This speech, from Act III, finds Ulysses trying to persuade the legendary warrior Achilles, who is sulking in his tent, to enter the fray and help his struggling army.

What Ulysses says, in a nutshell, is that all of Achilles’ past deeds, great though they were, will soon be forgotten and count for nothing. All that matters is what he does now, so he should stop resting on his laurels, get off his backside and come to the aid of his comrades.

It’s an important message for those in any field, including academia, who try to trade on past glories without making a contribution at the present moment. Honour goes to those who persevere. In other words, do it now or push off…

Time hath, my lord, a wallet at his back,
Wherein he puts alms for oblivion,
A great-sized monster of ingratitudes:
Those scraps are good deeds past; which are devour’d
As fast as they are made, forgot as soon
As done: perseverance, dear my lord,
Keeps honour bright: to have done is to hang
Quite out of fashion, like a rusty mail
In monumental mockery. Take the instant way;
For honour travels in a strait so narrow,
Where one but goes abreast: keep then the path;
For emulation hath a thousand sons
That one by one pursue: if you give way,
Or hedge aside from the direct forthright,
Like to an enter’d tide, they all rush by
And leave you hindmost;
Or like a gallant horse fall’n in first rank,
Lie there for pavement to the abject rear,
O’er-run and trampled on: then what they do in present,
Though less than yours in past, must o’ertop yours;
For time is like a fashionable host
That slightly shakes his parting guest by the hand,
And with his arms outstretch’d, as he would fly,
Grasps in the comer: welcome ever smiles,
And farewell goes out sighing. O, let not
virtue seek
Remuneration for the thing it was;
For beauty, wit,
High birth, vigour of bone, desert in service,
Love, friendship, charity, are subjects all
To envious and calumniating time.
One touch of nature makes the whole world kin,
That all with one consent praise new-born gawds,
Though they are made and moulded of things past,
And give to dust that is a little gilt
More laud than gilt o’er-dusted.
The present eye praises the present object.
Then marvel not, thou great and complete man,
That all the Greeks begin to worship Ajax;
Since things in motion sooner catch the eye
Than what not stirs. The cry went once on thee,
And still it might, and yet it may again,
If thou wouldst not entomb thyself alive
And case thy reputation in thy tent;
Whose glorious deeds, but in these fields of late,
Made emulous missions ‘mongst the gods themselves
And drave great Mars to faction.

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Sweet Lorraine

Posted in Jazz, LGBTQ+ with tags , , , on November 8, 2013 by telescoper

I bought the album You’re Looking at Me (A Collection of Nat King Cole Songs by Carmen McCrae on vinyl when it came out way back in 1983, and I thought I’d share one of my favourite tracks from it on here. One of the reviews of the album that came out at the time asked why she sang Sweet Lorraine without changing any of the lyrics, presumably because it’s a love song directed at a woman and the critic thought that it didn’t work when sung by another woman. Thirty years on it’s quite possible that there’s a lady somewhere (perhaps even a lady called Carmen) looking forward to marrying her Sweet Lorraine next April when such a marriage will be legal in the United Kingdom!

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The Shadow of Newton

Posted in History, The Universe and Stuff with tags , , , , , , , on November 7, 2013 by telescoper

Yesterday I overheard some Electrodynamics students talking about the fact that all the famous names attached to pioneering laws or theorems in that subject seem to be either French (Biot-Savart, Laplace, Poisson..) or German (Gauss, Helmholtz…). Why are there no British names in this list?

Well, there was Faraday, of course. But Michael Faraday was primarily an experimentalist rather than a theorist, which sets him apart from the others already mentioned. So why is it that British theoretical was behind continental Europe in the early part of the 19th Century when all this important work on electricity and magnetism was being done.

There was also Maxwell, but he came along a bit later; he published his theory of electromagnetism in 1861/2. So why were the British so slow to enter this field?

Well, my theory of this is that it’s all the fault of Isaac Newton. I came to this conclusion when reading about the work of British mathematician and physicist George Green, who lived from 1793 until 1841, and who left a substantial legacy for modern theoretical physicists, in Green’s theorems and Green’s functions. George Green is also credited as being the first person to use the word “potential” in electrostatics. Green was the son of a Nottingham miller who, amazingly, taught himself mathematics and did most of his best work, especially his remarkable Essay on the Application of mathematical Analysis to the theories of Electricity and Magnetism (1828) before starting his studies as an undergraduate at the University of Cambridge (which he did at the age of 30, after his father died, and he leased out the mill he consequently inherited, to pay for his studies).

Extremely unusually for British mathematicians of his time, Green taught himself from books that were published in France. This gave him a huge advantage over his national contemporaries in that he learned the form of differential calculus that originated with Leibniz, which was far more elegant than that devised by Isaac Newton (which was called the method of fluxions).

Great scientist though he was, Newton’s influence on the development of physics in Britain was not entirely positive. Newton was held in such awe, especially in Cambridge, that his inferior mathematical approach was deemed to be the “right” way to do calculus and generations of scholars were forced to use it. This held back British science until the use of fluxions was phased out. Green himself was forced to learn fluxions when he went as an undergraduate to Cambridge despite having already learned the better method.

Unfortunately, Green’s great pre-Cambridge work on mathematical physics didn’t reach wide circulation in the United Kingdom until after his death. William Thomson, later Lord Kelvin, found a copy of Green’s Essay in 1845 and promoted it widely as a work of fundamental importance. This contributed to the eventual emergence of British theoretical physics from the shadow cast by Isaac Newton which reached one of its heights just a few years later with the publication a fully unified theory of electricity and magnetism by James Clerk Maxwell.

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Astronomy Look-alikes, No. 87

Posted in Astronomy Lookalikes with tags , on November 6, 2013 by telescoper

It is widely believed that Carlos the Jackal is now in prison in France, but this is in fact untrue.  He has assumed a new identity and goes by the name of Prof. Jonathan Rawlings of the Department of Physics and Astronomy at University College London. You have been warned.

CTJ_JR

P.S. Please blame Matt Griffin for this one!

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Why is Astronomy Important?

Posted in The Universe and Stuff with tags , , , , on November 5, 2013 by telescoper

There’s an interesting and unusual article on the arXiv today entitled Why is Astronomy Important? Here is the abstract:

For a long time astronomers and other scientists believed that the importance of their work was evident to society. But in these difficult days of financial austerity, even the most obvious benefits of science have to undergo careful scrutiny. Eradicating poverty and hunger is a worldwide priority, and activities that do not directly attempt to resolve these issues can be hard to justify and support. However, several studies have told us that investing in science education, research and technology provides a great return not only economically, but culturally and indirectly for the population in general and has helped countries to face and overcome crises. The scientific and technological development of a country or region is closely linked to its human development index a statistic that is a measure of life expectancy, education and income.

The full text of the paper can be found on the IAU website here.

The article focusses on matters relating to the transfer of technology between astronomy and, e.g. industry, aerospace, and medicine, its effect on technology we are familiar with in everyday life, on astronomy as an exemplar of international collaboration and on its wider cultural and philosophical impact. Many of the points made in this article can also be found in the Royal Astronomical Society‘s free publication Beyond the Stars: Why Astronomy Matters which is available for free online here.

I recommend you read the full article and make your own mind up about why astronomy is important. I have just two comments, which are partly questions. The first is that I’ve always had a bit of a problem with the interpretation of correlations like that mentioned in the last sentence of the abstract (between technological development and the human development index). The issue is the basic one that correlation of two phenomena does not necessarily imply that one causes the other. Is it really possible to establish rigorously a causal link between spending money on astronomy and wider societal benefits? I’m not saying that there isn’t such a link, just that it’s difficult to interpret evidence which is dependent on so many factors. Could one not argue instead that more developed countries spend more money on astronomy because they can afford to?

The other thing that troubles me with arguments of the type presented in the paper is that there is a danger that  emphasizing the transfer of knowledge to other disciplines as the rationale for funding astronomy implicitly negates the argument that astronomy has intrinsic worth of its own. In other words, answering the question “Why is Astronomy important?” seems to accept at the outset that it isn’t.  If it is indeed the case that we can only justify astronomy because it has produced spin-offs in, e.g., medicine, why not just spend more money on medicine and forget the astronomy?

I’m not saying that the technology transfer arguments carry no weight, just that they are definitely double-edged and should be used with caution. For the record, I think we should fund Astronomy (and other sciences) primarily because they are an essential part of the fabric of our culture and civilization; all the rest is icing on the cake. In other words, I support state funding for the sciences for very much the same reasons as for the arts.  I’m fully aware, however, that this unlikely to persuade the powers that be as effectively as an appeal to economic benefits; that’s why science funding has fared so much better than arts funding in this age of austerity.

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