My Friend Erdös..

Posted in Biographical with tags , , , , , , on March 28, 2010 by telescoper

After one of my  lectures a few weeks ago, a student came up to me and asked whether I had an Erdős number and, if so, what it was.  I didn’t actually know what he was talking about but was yesterday reminded of it, so tried to find out.

In case you didn’t know, Paul Erdős (who died in 1996) was an eccentric Hungarian mathematician who wrote more than 1000 mathematical papers during his life but never settled in one place for any length of time. He travelled between colleagues and conference, mostly living out of a suitcase, and showed no interest at all in property or possessions. His story is a fascinating one, and his contributions to mathematics were immense and wide-ranging.  The Erdős number is a tiny part of his legacy, but one that seems to have taken hold. Some mathematicians appear to take it very seriously, but most treat it with tongue firmly in cheek, as I certainly do.

So what is the Erdős number?

It’s actually quite simple to define. First, Erdős himself is assigned an Erdős number of zero. Anyone who co-authored a paper with Erdős has an Erdős number of 1. Then anyone who wrote a paper with someone who wrote a paper with Erdős has an Erdős number of 2, and so on. The Erdős number is thus a measure of “collaborative distance”, with lower numbers representing closer connections.

I say it’s quite easy to define, but it’s rather harder to calculate. Or it would be were it not for modern bibliographic databases. In fact there’s a website run by the American Mathematical Society which allows you to calculate your Erdős number as well as a similar measure of collaborative distance with respect to any other mathematician.

A list of individuals with very low Erdős numbers (1, 2 or 3) can be found here.

Given that Erdős was basically a pure mathematician, I didn’t expect first to show up as having any Erdős number at all, since I’m not really a mathematician and I’m certainly not very pure. However, his influence is clearly felt very strongly in  physics and a surprisingly large number of physicists (and astronomers) have a surprisingly small Erdős number. According to the AMS website, mine is 5 – much lower than I would have expected. The path from me to Erdős in this case goes through G.F.R. Ellis, a renowned expert in the mathematics of general relativity (as well as a ridiculous number of other things!). I wrote a paper and a book with George Ellis some time ago.

However, looking at the list I realise that I have another route to Erdős, through the great Russian mathematician Vladimir Arnold, who has an Erdős number of 3. Arnold wrote a paper with Sergei Shandarin with whom I wrote a paper some time ago. That gives me another route to an Erdős number of 5, but I can’t find any paths  shorter than that.

I guess many researchers will have links through their PhD supervisors, so I checked mine – John D. Barrow. It turns out he also has an Erdős number of 5 so a path through him doesn’t lower my number.

I used to work in the School of Mathematical Sciences at Queen Mary, University of London, and it is there that I found some people I know well who have lower Erdős numbers than me. Reza Tavakol, for example, has an Erdős number of 3 but although I’ve known him for 20 years, we’ve never written a paper together. If we did, I could reduce my Erdős number by one. You never know….

This means that anyone I’ve ever written a paper with has an Erdős number no greater than 6. I doubt if it’s very important, but it definitely qualifies as Quite Interesting.

Alternative Logo for UKSA

Posted in Science Politics with tags on March 27, 2010 by telescoper

As you all know, this past week saw the launch of the new UK Space Agency amid much fuss and fanfares. This occasion allowed the government to trumpet the creation of the new organization as a success story in the media and thus draw attention away from the continuing devastation visited on scientific research in astronomy and space science in the United Kingdom.

I’m not the only one to have expressed reservations about the quality of the new outfit’s logo which, though clearly intended to present a thrusting, dynamic, reach-for-the-skies image, ends up looking more like something from Dad’s Army. Apparently it cost £10,000 – surprisingly cheap by the standards of graphic designers these days – which perhaps explains why it isn’t very good, although even expensive ones can be rubbish too.

In order to improve the public profile of the fledgling organisation, and out of my own deep sense of public spiritedness, I’ve decided, at no expense to the taxpayer, to commission my own alternative logo by a highly skilled graphic designer of my acquaintance. I’m proud to be able to unveil it here. I think it conveys more accurately the nature of the new agency.

The broad coloured swathe represents the red tape involved in creating yet another new quango and reorganising everything else that relates to it. This leads initially to a period of increased paperwork presenting the appearance of greater activity until, shortly after the next election, everyone realises it is achieving nothing at all, its funds are cut (along with everything else), and, overwhelmed by the weight of its own bureaucracy,  it comes crashing back to Earth.

Badges featuring the new logo can be purchased from me, at the modest price of £74.99 each.

Cut and Thrust and Nip and Tuck

Posted in Finance, Science Politics with tags , , , , , , , on March 26, 2010 by telescoper

This week we received the not-altogether-unexpected news that the budgets of Welsh universities will be cut next year. The Higher Education Funding Council for Wales (HEFCW) has announced its detailed allocations for 2010-11 and all but one institution will receive a cash cut.  Cardiff University faces a cash cut of 1.74%. Lampeter is the exception, but it gets a cash increase of only 0.32%. After taking inflation into account, even they get a real terms decrease. So it’s real cuts across the board for Welsh Higher Education, with a total of about £30 million in funding taken away.

In fact, it appears that the total amount of money available to HEFCW for next year is level in cash terms compared to last year. The total amount it has distributed in recurrent grants has, however, decreased by about 2% on last year. As far as I understand it, the discrepancy between the income and expenditure is partly explained by the diversion of some funds into a new Strategic Implementation Fund(SIF) to enable HEFCW to meet the goals outlined in the Welsh Assembly Government (WAG) document stating its vision for Higher Education, entitled For our Future. Some elements of SIF are included with the current allocation, but other’s are not, hence the  cash cuts seen here.In future, a larger proportion of the budget will move from recurrent, formula-based funding towards initiatives more closely aligned with the WAGs or, more likely, wasted on window-dressing and increased bureaucracy.

We’ll have to see what the impact of the new SIF arrangements will be in the longer term. In the short-term, however, the cuts (though obviously regrettable) are by no means a shock and will probably appear entirely insignificant after the General Election and the real cuts start, probably more like 20% than 2%…

The situation in Wales contrasts with Scotland where the Higher Education has grown by 1% for 2010/11.  Some Scottish universities, such as Edinburgh with a cash increase of 2.2%, have done pretty well. A small number of others, such as Stirling have been cut by 3.3% in cash terms.

Allocations for English universities were announced by HEFCE last week. There the situation is more mixed, partly to do with HEFCE rejigging its formula for research funding to concentrate it even more than last time (something that HEFCW – wisely, in my view – decided not to do..). It seems about half the 130 institutions in HEFCE’s remit get a cash increase, although when inflation is factored in the number with a real increase is much smaller. Among the universities with big cash cuts are Reading (-7.7%) and the London School of Economics (-6.3%).

As far as I understand the situation, these figures don’t include the fines for over-recruitment recently demanded by Lord Mandelson and may not take into account cuts in capital allowances, so things may be a lot worse than they appear at first sight.

However, to complicate things  a bit more, this week’s budget announced new funding for Science Technology Engineering and Mathematics (STEM) subjects, corresponding to an increase in numbers of about 20,000.This is only for England, as Higher Education in Wales and Scotland is not part of the remit of the Westminster government. One advantage of this for those of us in Wales is that we can’t be affected by pre-election tinkering in the same way England can.

I’m sure the news of new funding is very welcome to my colleagues across the border, but it does look to me like a bit of sticking plaster that looks likely to fall off after polling day.

Anyway, it looks to me like these results are going exactly with the form book. Scotland has always valued Higher Education more strongly than England, and Wales has usually trailed along in third place.  The real struggle hasn’t yet started, however, and we have to wait anxiously to see how hard the axe will fall once the election is over.

“Tintern Abbey”

Posted in Poetry with tags , , on March 25, 2010 by telescoper

We haven’t had any Wordsworth for a while, so here’s possibly his greatest poem. It was

Composed A Few Miles Above Tintern Abbey,
On Revisiting The Banks Of The Wye During A Tour. July 13, 1798

I’m ashamed to admit that although it’s only 30 miles or so from Cardiff, and I’ve lived here nearly three years now, I still haven’t visited Tintern Abbey. That doesn’t stop me thinking this is deeply evocative of the place.

      FIVE years have past; five summers, with the length
      Of five long winters! and again I hear
      These waters, rolling from their mountain-springs
      With a soft inland murmur.–Once again
      Do I behold these steep and lofty cliffs,
      That on a wild secluded scene impress
      Thoughts of more deep seclusion; and connect
      The landscape with the quiet of the sky.
      The day is come when I again repose
      Here, under this dark sycamore, and view                        10
      These plots of cottage-ground, these orchard-tufts,
      Which at this season, with their unripe fruits,
      Are clad in one green hue, and lose themselves
      ‘Mid groves and copses. Once again I see
      These hedge-rows, hardly hedge-rows, little lines
      Of sportive wood run wild: these pastoral farms,
      Green to the very door; and wreaths of smoke
      Sent up, in silence, from among the trees!
      With some uncertain notice, as might seem
      Of vagrant dwellers in the houseless woods,                     20
      Or of some Hermit’s cave, where by his fire
      The Hermit sits alone.
                              These beauteous forms,
      Through a long absence, have not been to me
      As is a landscape to a blind man’s eye:
      But oft, in lonely rooms, and ‘mid the din
      Of towns and cities, I have owed to them
      In hours of weariness, sensations sweet,
      Felt in the blood, and felt along the heart;
      And passing even into my purer mind,
      With tranquil restoration:–feelings too                        30
      Of unremembered pleasure: such, perhaps,
      As have no slight or trivial influence
      On that best portion of a good man’s life,
      His little, nameless, unremembered, acts
      Of kindness and of love. Nor less, I trust,
      To them I may have owed another gift,
      Of aspect more sublime; that blessed mood,
      In which the burthen of the mystery,
      In which the heavy and the weary weight
      Of all this unintelligible world,                                 40
      Is lightened:–that serene and blessed mood,
      In which the affections gently lead us on,–
      Until, the breath of this corporeal frame
      And even the motion of our human blood
      Almost suspended, we are laid asleep
      In body, and become a living soul:
      While with an eye made quiet by the power
      Of harmony, and the deep power of joy,
      We see into the life of things.
                                       If this
      Be but a vain belief, yet, oh! how oft–                        50
      In darkness and amid the many shapes
      Of joyless daylight; when the fretful stir
      Unprofitable, and the fever of the world,
      Have hung upon the beatings of my heart–
      How oft, in spirit, have I turned to thee,
      O sylvan Wye! thou wanderer thro’ the woods,
      How often has my spirit turned to thee!
        And now, with gleams of half-extinguished thought,
      With many recognitions dim and faint,
      And somewhat of a sad perplexity,                               60
      The picture of the mind revives again:
      While here I stand, not only with the sense
      Of present pleasure, but with pleasing thoughts
      That in this moment there is life and food
      For future years. And so I dare to hope,
      Though changed, no doubt, from what I was when first
      I came among these hills; when like a roe
      I bounded o’er the mountains, by the sides
      Of the deep rivers, and the lonely streams,
      Wherever nature led: more like a man                            70
      Flying from something that he dreads, than one
      Who sought the thing he loved. For nature then
      (The coarser pleasures of my boyish days,
      And their glad animal movements all gone by)
      To me was all in all.–I cannot paint
      What then I was. The sounding cataract
      Haunted me like a passion: the tall rock,
      The mountain, and the deep and gloomy wood,
      Their colours and their forms, were then to me
      An appetite; a feeling and a love,                              80
      That had no need of a remoter charm,
      By thought supplied, nor any interest
      Unborrowed from the eye.–That time is past,
      And all its aching joys are now no more,
      And all its dizzy raptures. Not for this
      Faint I, nor mourn nor murmur, other gifts
      Have followed; for such loss, I would believe,
      Abundant recompence. For I have learned
      To look on nature, not as in the hour
      Of thoughtless youth; but hearing oftentimes                    90
      The still, sad music of humanity,
      Nor harsh nor grating, though of ample power
      To chasten and subdue. And I have felt
      A presence that disturbs me with the joy
      Of elevated thoughts; a sense sublime
      Of something far more deeply interfused,
      Whose dwelling is the light of setting suns,
      And the round ocean and the living air,
      And the blue sky, and in the mind of man;
      A motion and a spirit, that impels                             100
      All thinking things, all objects of all thought,
      And rolls through all things. Therefore am I still
      A lover of the meadows and the woods,
      And mountains; and of all that we behold
      From this green earth; of all the mighty world
      Of eye, and ear,–both what they half create,
      And what perceive; well pleased to recognise
      In nature and the language of the sense,
      The anchor of my purest thoughts, the nurse,
      The guide, the guardian of my heart, and soul                  110
      Of all my moral being.
                              Nor perchance,
      If I were not thus taught, should I the more
      Suffer my genial spirits to decay:
      For thou art with me here upon the banks
      Of this fair river; thou my dearest Friend,
      My dear, dear Friend; and in thy voice I catch
      The language of my former heart, and read
      My former pleasures in the shooting lights
      Of thy wild eyes. Oh! yet a little while
      May I behold in thee what I was once,                          120
      My dear, dear Sister! and this prayer I make,
      Knowing that Nature never did betray
      The heart that loved her; ’tis her privilege,
      Through all the years of this our life, to lead
      From joy to joy: for she can so inform
      The mind that is within us, so impress
      With quietness and beauty, and so feed
      With lofty thoughts, that neither evil tongues,
      Rash judgments, nor the sneers of selfish men,
      Nor greetings where no kindness is, nor all                    130
      The dreary intercourse of daily life,
      Shall e’er prevail against us, or disturb
      Our cheerful faith, that all which we behold
      Is full of blessings. Therefore let the moon
      Shine on thee in thy solitary walk;
      And let the misty mountain-winds be free
      To blow against thee: and, in after years,
      When these wild ecstasies shall be matured
      Into a sober pleasure; when thy mind
      Shall be a mansion for all lovely forms,                       140
      Thy memory be as a dwelling-place
      For all sweet sounds and harmonies; oh! then,
      If solitude, or fear, or pain, or grief,
      Should be thy portion, with what healing thoughts
      Of tender joy wilt thou remember me,
      And these my exhortations! Nor, perchance–
      If I should be where I no more can hear
      Thy voice, nor catch from thy wild eyes these gleams
      Of past existence–wilt thou then forget
      That on the banks of this delightful stream                    150
      We stood together; and that I, so long
      A worshipper of Nature, hither came
      Unwearied in that service: rather say
      With warmer love–oh! with far deeper zeal
      Of holier love. Nor wilt thou then forget,
      That after many wanderings, many years
      Of absence, these steep woods and lofty cliffs,
      And this green pastoral landscape, were to me
      More dear, both for themselves and for thy sake!

So it doesn’t have anything to do with astronomy or cosmology, except for the “unintelligible world” (line 40) of STFC…

Space without Physics…

Posted in Uncategorized with tags , , , , , on March 24, 2010 by telescoper

I’m indebted to a colleague (Annabel Cartwright) for sending me this (coincidentally topical) sample question, illustrating the quality of a modern British school science examination.

Since it’s now clear  that there is no room for science in the new era of the UK Space Agency, I suppose we should get used to the removal of science from other things too. Starting with science exams.

This question is taken from a GCSE Physics examination.

Some people think that governments spend too much money on space research.

Which ONE of the following statements is true?

  1. Science can tell us what the planets are made of, and whether they ought to be explored.
  2. Science can tell us what the planets are made of, but not whether they ought to be explored.
  3. Science cannot tell us what the planets are made of but can tell us whether they ought to be explored.
  4. Science cannot tell us what the planets are made of, nor whether they ought to be explored.

Apparently one (and only one) answer is correct. Any offers?

Spazio Commerciale

Posted in Science Politics, The Universe and Stuff with tags , , , , , on March 23, 2010 by telescoper

So here we are then. The United Kingdom has its own brand new Space Agency, courtesy of Lords Mandelson and Drayson (or Peter and Paul as they’re known to their fans). It was launched today at a glitzy do in Westminster attended by everyone who’s anyone in space science, which obviously doesn’t include me. There’s even a new logo.

According to the BBC, the new agency will be “muscular”, but I’m not really sure what that means. Perhaps brains might be more useful than brawn in this context (unless it’s Werner Von, geddit?) In fact I’m not at all sure what the new agency is about at all. The UK is already part of the European Space Agency (ESA) and a big slice of the new agency’s budget will presumably be eaten up by the ESA subscription. Much of what we do in space exploration and astronomy is dictated by decisions at the ESA level so I don’t think the new UK Agency will have much impact on that. On the other hand, the only current UK space agency is the British National Space Centre (BNSC), which is an organisation notable only for its irrelevance. I’m not even sure whether it exists at all as anything other than a logo and an accommodation address above a chip shop in Swindon.

It’s somewhat easier to see what the new UK Space Agency isn’t about. The accompanying press release doesn’t mention astronomy at all, so it’s clearly not going to help us lowly scientists who would like to use space observatories to do interesting science. It seems that it is primarily aimed at commercial space activities, and the science bit will continue to be managed mismanaged by the Science and Technology Facilities Council.

I’ve got nothing against the commercial exploitation of space, in principle, although it did provoke my feeble attempt at an Italian joke in the title of this post. The French, Germans and Italians spend much more than we do and this is obviously an area of great potential growth. I don’t object to the government using public money to help the space sector grow, either. In principle. The problem is that in these tough times the money has to be taken from somewhere else in the budget. Many of us were still hoping that the government might intervene to reverse the awful cuts we’ve suffered in physics and astronomy recently, but hiving space science off into a separate pot will probably make life even tougher for those of us left with the rump of STFC. I fear it means even less money in future going into fundamental science, and our decline is therefore set to accelerate even further.

There have always been tensions within the astronomy and space science community. Space exploration has scored many recent triumphs – such as the joint ESA-NASA Cassini-Huygens probe – but there are always difficult questions about the scientific value for money involved in sending things pottering around our backyard in the  solar system compared to, e.g., building observatories (either in space or on the ground) that can see things across the other side of the Universe. It’s difficult to see what the implications of the new agency are for this, but it seems likelyto me  that increasing amounts of public money will go on exploration at the expense of observation. I’m biased, of course, but I think there’s a lot more interesting science in the distant universe than there is nearby. In fact there’s more of everything further away than there is nearby! We may end up killing off ground-based astronomy in order to put a British flag on the Moon. That would be very sad.

But maybe this is too pessimistic. We don’t know yet how things will be divvied up between the new agency and the old STFC. Will there be any science  in UK Space, or will it be entirely commercial? Perhaps new missions and experiments will be funded through that route while exploitation continues to be  (under)funded by STFC?

Or maybe, since the new agency comes into existence on 1st April 2010, it’s all just an elaborate joke?

And while I’m being facetious, I wonder how many of you are thinking that the new logo looks like it was taken from the opening credits of Dad’s Army? I wonder if that choice was awfully wise, Captain Mainwaring?

STFC Chief Executive Keith Mason is very keen on the new outfit and is looking forward to working with it.  I know what Private Frazer would have said. We’re doomed.

PS. Andy Lawrence was there, and invites you to pump him  in the debriefing room over at the e-astronomer.

PPS. The new agency has now got a wikipedia page. It says there that the space agency will take over responsibility for space technology and instrumentation funding from other research councils. Presumably exploitation of space missions will either remain the responsibility of STFC or there won’t be any at all, which may amount to the same thing.

Reflections on Randi

Posted in The Universe and Stuff with tags , , , , on March 22, 2010 by telescoper

Yesterday evening I chanced upon a blog post by James Randi. I guess quite a few of my readers won’t have heard of him, but he’s a really interesting character. His real name is Randall James Hamilton Zwinge and he was born in Toronto. He is a professional magician (i.e. a conjuror) who is now 81 years old, and who has spent most of the last three decades debunking psychics and exposing fraudulent claims of the paranormal. Those of you out there who remember the 1970s will remember the  “paranormalist”  Uri Geller being a household name for his numerous TV appearances bending spoons, stopping clocks and generally exhibiting supernatural powers. Randi exposed these as simple conjuring tricks, and got himself sued for his trouble.

Here’s a fairly lengthy clip in which James Randi talks about the Geller case and other examples of quackery:

There’s an interesting connection between the Uri Geller phenomenon and physics. In the 1970s, when Geller was at the height of his popularity, a physicist called John G. Taylor took great interest in him and the things that he appeared to be able to do. Professor of applied mathematics at King’s College, London, Taylor was (and remains) a very distinguished scientist and was the first to take the paranormal phenomena displayed by Geller seriously. When Uri Geller visited Britain in 1974, Taylor conducted scientific tests of Geller’s feats of metal bending using all the paraphernalia of modern science, including a Geiger counter. Taylor also experimented with some of the children and adults who claimed to manifest psychic abilities after seeing Uri Geller’s appearances on British television programs. Taylor’s interest in such phenomena was not only in its scientific validation, but also in investigation of the way in which such phenomena take place and the nature of the forces involved. He suggested the phenomena may be some low-frequency electromagnetic effect generated by human beings.

Through the 1970s Taylor was regarded as fully endorsing the paranormal metal bending of Uri Geller, but gradually has made more guarded statements; then in 1980 he largely retracted his support for Geller’s paranormal talents. In 1974 he wrote

The Geller effect—of metal-bending—is clearly not brought about by fraud. It is so exceptional it presents a crucial challenge to modern science and could even destroy the latter if no explanation became available.

Taylor then spent three years of careful investigation of such phenomena as psychokinesis, metal bending, and dowsing, but could not discover any reasonable scientific explanation or validation that satisfied him. He was particularly concerned to establish whether there is an electromagnetic basis for such phenomena. After failing to find this he did not believe that there was any other explanation that would suffice. Most of his experiments under laboratory conditions were negative; this left him in a skeptical position regarding the validity of claimed phenomena.

In contrast to the endorsement in his first book, Superminds, he published a paper expressing his doubts in a paper in Nature (November 2, 1978) titled “Can Electromagnetism Account for Extra-sensory Phenomena?” He followed this with his book Science and the Supernatural (1980) in which he expressed complete skepticism about every aspect of the paranormal. In his final chapter he stated:

We have searched for the supernatural and not found it. In the main, only poor experimentation [including his own], shoddy theory, and human gullibility have been encountered.

Taylor’s investigation of the Geller effect is interesting because it shows that physics doesn’t have all the answers all the time, particularly not when the phenomena in question involve people. Physics research proceeds by assuming that Nature is not playing tricks, and that what can be measured must represent some sort of truth. This faith can be easily exploited by a charlatan. James Randi always argued that scientists aren’t the right people to detect tricks performed by people. This is best left to tricksters. There’s no reason to believe that a theoretical physicist – no matter how brilliant – can spot the way a clever deception is carried out. The best person to see that is a magician, someone like James Randi. Set a thief to catch a thief, and all that.

Anyway, you’re probably wondering what it was about James Randi’s blog post yesterday that caught my eye. Well, at the age of 81, James Randi has finally revealed to the public that he is gay. I feel a bit sad that it’s taken him so long to step out of the closet, but it is a very personal decision and no rebuke is intended. He’s lived long enough to remember times when being open was a much tougher option than it is now. Judging by the messages of support on his blog, I’m sure it’s a decision he won’t regret.

Good for you, James Randi!

PS. I noticed that the badastronomy blog has also covered this story, and generated over 100 comments in the process!

Dark Horizons

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , , , on March 21, 2010 by telescoper

Last Tuesday night I gave a public lecture as part of  Cardiff University’s contribution to National Science and Engineering Week. I had an audience of about a hundred people, although more than half were students from the School of Physics & Astronomy rather than members of the public. I’d had a very full day already by the time it began (at 7pm) and I don’t mind admitting I was pretty exhausted even before I started the talk. I’m offering that as an excuse for struggling to get going, although I think I got better as I got into it. Anyway, I trotted out the usual stuff about the  Cosmic Web and it seemed to go down fairly well, although I don’t know about that because I wasn’t really paying attention.

At the end of the lecture, as usual, there was a bit of time for questions and no shortage of hands went up. One referred to something called Dark Flow which, I’ve just noticed, has actually got its own wikipedia page. It was also the subject of a recent Horizon documentary on BBC called Is Everything we Know about the Universe Wrong? I have to say I thought the programme was truly terrible, but that’s par for the course for Horizon these days I’m afraid. It used to be quite an interesting and informative series, but now it’s full of pointless special effects, portentous and sensationalising narration, and is repetitive to the point of torture. In this case also, it also portrayed a very distorted view of its subject matter.

The Dark Flow is indeed quite interesting, but of all the things that might threaten the foundations of the Big Bang theory this is definitely not it. I certainly have never lost any sleep worrying about it. If it’s real and not just the result of a systematic error in the data – and that’s a very big “if” – then the worst it would do would be to tell us that the Universe was a bit more complicated than our standard model. The same is true of the other cosmic anomalies I discuss from time to time on here.  

But we know our standard model leaves many questions unanswered and, as a matter of fact, many questions unasked. The fact that Nature may present us with a few surprises doesn’t mean the whole framework is wrong. It could be wrong, of course. In fact I’d be very surprised if our standard view of cosmology survives the next few decades without major revision. A healthy dose of skepticism is good for cosmology. To some extent, therefore, it’s good to have oddities like the Dark Flow out in the open.

However, that shouldn’t divert our attention from the fact that the Big Bang model isn’t just an arbitrary hypothesis with no justification. It’s the result of almost a century of  vigorous interplay between theory and observation, using an old-fashioned thing called the scientific method. That’s probably too dull for the producers of  Horizon, who would rather portray it as a kind of battle of wills between individuals competing for the title of next Einstein.

Anyway, just to emphasize the fact that I think questioning the Big Bang model is a good thing to do, here is a list of fundamental questions that should trouble modern cosmologists. Most of them are fundamental,  and we do not have answers to them. 

Is General Relativity right?

Virtually everything in the standard model depends on the validity of Einstein’s general theory of relativity (or theory of general relativity…). In a sense we already know that the answer to this question is “no”.

At sufficiently high energies (near the Planck scale) we expect classical relativity to be replaced by a quantum theory of gravity. For this reason, a great deal of interest is being directed at cosmological models inspired by superstring theory. These models require the existence of extra dimensions beyond the four we are used to dealing with. This is not in itself a new idea, as it dates back to the work of Kaluza and Klein in the 1920s, but in older versions of the idea the extra dimensions were assumed to be wrapped up so small as to be invisible. In “braneworld models”, the extra dimensions can be large but we are confined to a four-dimensional subset of them (a “brane”). In one version of this idea, dubbed the Ekpyrotic Universe, the origin of our observable universe lies in the collision between two branes in a higher-dimensional “bulk”. Other models are less dramatic, but do result in the modification of the Friedmann equations at early times.

 It is not just in the early Universe that departures from general relativity are possible. In fact there are many different alternative theories on the market. Some are based on modifications of Newton’s gravitational mechanics, such as MOND, modifications of Einstein’s theory, such as the Brans-Dicke theory, as well as those theories involving extra dimensions, such as braneworld theory, and so on

There remain very few independent tests of the validity of Einstein’s theory, particularly in the limit of strong gravitational fields. There is very little independent evidence that the curvature of space time on cosmological scales is related to the energy density of matter. The chain of reasoning leading to the cosmic concordance model depends entirely this assumption. Throw it away and we have very little to go on.

What is the Dark Energy?

In the standard cosmology, about 75% of the energy density of the Universe is in a form we do not understand. Because we’re in the dark about it, we call it Dark Energy. The question here is twofold. One part is whether the dark energy is of the form of an evolving scalar field, such as quintessence, or whether it really is constant as in Einstein’s original version. This may be answered by planned observational studies, but both of these are at the mercy of funding decisions. The second part is to whether dark energy can be understood in terms of fundamental theory, i.e. in understanding why “empty space” contains this vacuum energy.  I think it is safe to say we are still very far from knowing how vacuum energy on a cosmological scale arises from fundamental physics. It’s just a free parameter.

 

What is the Dark Matter?

Around 25% of the mass in the Universe is thought to be in the form of dark matter, but we don’t know what form it takes. We do have some information about this, because the nature of the dark matter determines how it tends to clump together under the action of gravity. Current understanding of how galaxies form, by condensing out of the primordial explosion, suggests the dark matter particles should be relatively massive. This means that they should move relatively slowly and can consequently be described as “cold”. As far as gravity is concerned, one cold particle is much the same as another so there is no prospect for learning about the nature of cold dark matter (CDM) particles through astronomical means unless they decay into radiation or some other identifiable particles. Experimental attempts to detect the dark matter directly are pushing back the limits of technology, but it would have to be a long shot for them to succeed when we have so little idea of what we are looking for.

Did Inflation really happen?

The success of concordance cosmology is largely founded on the appearance of “Doppler peaks” in the fluctuation spectrum of the cosmic microwave background (CMB). These arise from acoustic oscillations in the primordial plasma that have particular statistical properties consistent owing to their origin as quantum fluctuations in the scalar field driving a short-lived period of rapid expansion called inflation. This is strong circumstantial evidence in favour of inflation, but perhaps not strong enough to obtain a conviction. The smoking gun for inflation is probably the existence of a stochastic gravitational wave background. The identification and extraction of this may be possible using future polarisation-sensitive CMB studies even before direct experimental probes of sufficient sensitivity become available. As far as I am concerned, the jury will be out for a considerable time.

Despite these gaps and uncertainties, the ability of the standard framework to account for such a diversity of challenging phenomena provides strong motivation for assigning it a higher probability than its competitors. Part of this  is that no other theory has been developed to the point where we know what predictions it can make. Some of the alternative  ideas  I discussed above are new, and consequently we do not really understand them well enough to know what they say about observable situations. Others have adjustable parameters so one tends to disfavour them on grounds of Ockham’s razor unless and until some observation is made that can’t be explained in the standard framework.

Alternative ideas should be always explored. The business of cosmology, however,  is not only in theory creation but also in theory testing. The great virtue of the standard model is that it allows us to make precise predictions about the behaviour of the Universe and plan observations that can test these predictions. One needs a working hypothesis to target the multi-million-pound investment that is needed to carry out such programmes. By assuming this model we can make rational decisions about how to proceed. Without it we would be wasting taxpayers’ money on futile experiments that have very little chance of improving our understanding. Reasoned belief  in a plausible working hypothesis is essential to the advancement of our knowledge.

 Cosmologists may appear a bit crazy (especially when they appear on TV), but there is method in their madness. Sometimes.

Cantaloupe Island(s)

Posted in Jazz with tags , , , , , , , , , on March 20, 2010 by telescoper

It’s been a pretty exhausting few weeks, but now we’ve reached the end of teaching term. Not that I’ve got nothing to do, but I should be able to concentrate on writing up a few papers that I’ve struggling with for many months.

Anyway by way of a celebration, and to correct for the fact that I haven’t posted much music recently, here are two totally different versions of a great tune by Herbie Hancock called Cantaloupe Island. The original recording of this came (made on June 17 1964) appeared on the album Empyrean Isles which came out on the Blue Note Records label. Its instantly catchy riff and fine solo playing turned it into a big hit, and it quickly became a standard.

The first  video clip features the original personnel of Herbie Hancock (piano), Ron Carter (bass), Tony Williams (drums) and Freddie Hubbard (trumpet) but with the addition of the great tenor saxophonist Joe Henderson. It was recorded during a special concert in 1985 to celebrate the Blue Note label. It’s got a similar groove to the original version, but the live performance allows the players to stretch out a lot more than on the original, so it’s about twice as long.

The second rendition also features Herbie Hancock on piano (and other keyboards), but it’s totally different. Taken at a faster tempo, and firmly in the style of Jazz-rock Fusion that Hancock gravitated towards later in his career, it features Pat Metheney (on electric guitar), Dave Holland (bass) and Jack de Johnette on drums. They’re all great, but the drummer on this track is sensational! I saw Jack de Johnette playing years ago – at the Jazz Cafe, I think – and I couldn’t believe the speed of his hands and the immense drive he generated even while playing complicated patterns. Awesome. 

PS. I’ve used the spelling I believe to be correct, as that’s how it’s written on the original Blue Note record (of which I have a copy). I’ve seen many variants, though, including those on the youtube clips shown here.

Science’s Dirtiest Secret?

Posted in Bad Statistics, The Universe and Stuff with tags , , , on March 19, 2010 by telescoper

My attention was drawn yesterday to an article, in a journal I never read called American Scientist, about the role of statistics in science. Since this is a theme I’ve blogged about before I had a quick look at the piece and quickly came to the conclusion that the article was excruciating drivel. However, looking at it again today, my opinion of it has changed. I still don’t think it’s very good, but it didn’t make me as cross second time around. I don’t know whether this is because I was in a particularly bad mood yesterday, or whether the piece has been edited. But although it didn’t make me want to scream, I still think it’s a poor article.

Let me start with the opening couple of paragraphs

For better or for worse, science has long been married to mathematics. Generally it has been for the better. Especially since the days of Galileo and Newton, math has nurtured science. Rigorous mathematical methods have secured science’s fidelity to fact and conferred a timeless reliability to its findings.

During the past century, though, a mutant form of math has deflected science’s heart from the modes of calculation that had long served so faithfully. Science was seduced by statistics, the math rooted in the same principles that guarantee profits for Las Vegas casinos. Supposedly, the proper use of statistics makes relying on scientific results a safe bet. But in practice, widespread misuse of statistical methods makes science more like a crapshoot.

In terms of historical accuracy, the author, Tom Siegfried, gets off to a very bad start. Science didn’t get “seduced” by statistics.  As I’ve already blogged about, scientists of the calibre of Gauss and Laplace – and even Galileo – were instrumental in inventing statistics.

And what were the “modes of calculation that had served it so faithfully” anyway? Scientists have long  recognized the need to understand the behaviour of experimental errors, and to incorporate the corresponding uncertainty in their analysis. Statistics isn’t a “mutant form of math”, it’s an integral part of the scientific method. It’s a perfectly sound discipline, provided you know what you’re doing…

And that’s where, despite the sloppiness of his argument,  I do have some sympathy with some of what  Siegfried says. What has happened, in my view, is that too many people use statistical methods “off the shelf” without thinking about what they’re doing. The result is that the bad use of statistics is widespread. This is particularly true in disciplines that don’t have a well developed mathematical culture, such as some elements of biosciences and medicine, although the physical sciences have their own share of horrors too.

I’ve had a run-in myself with the authors of a paper in neurobiology who based extravagant claims on an inappropriate statistical analysis.

What is wrong is therefore not the use of statistics per se, but the fact that too few people understand – or probably even think about – what they’re trying to do (other than publish papers).

It’s science’s dirtiest secret: The “scientific method” of testing hypotheses by statistical analysis stands on a flimsy foundation. Statistical tests are supposed to guide scientists in judging whether an experimental result reflects some real effect or is merely a random fluke, but the standard methods mix mutually inconsistent philosophies and offer no meaningful basis for making such decisions. Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous, and tests of medical dangers or treatments are often contradictory and confusing.

Quite, but what does this mean for “science’s dirtiest secret”? Not that it involves statistical reasoning, but that large numbers of scientists haven’t a clue what they’re doing when they do a statistical test. And if this is the case with practising scientists, how can we possibly expect the general public to make sense of what is being said by the experts? No wonder people distrust scientists when so many results confidently announced on the basis of totally spurious arguments, turn out to be be wrong.

The problem is that the “standard” statistical methods shouldn’t be “standard”. It’s true that there are many methods that work in a wide range of situations, but simply assuming they will work in any particular one without thinking about it very carefully is a very dangerous strategy. Siegfried discusses examples where the use of “p-values” leads to incorrect results. It doesn’t surprise me that such examples can be found, as the misinterpretation of p-values is rife even in numerate disciplines, and matters get worse for those practitioners who combine p-values from different studies using meta-analysis, a method which has no mathematical motivation whatsoever and which should be banned. So indeed should a whole host of other frequentist methods which offer limitless opportunities for to make a complete botch of the data arising from a research project.

Siegfried goes on

Nobody contends that all of science is wrong, or that it hasn’t compiled an impressive array of truths about the natural world. Still, any single scientific study alone is quite likely to be incorrect, thanks largely to the fact that the standard statistical system for drawing conclusions is, in essence, illogical.

Any single scientific study done along is quite likely to be incorrect. Really? Well, yes, if it is done incorrectly. But the point is not that they are incorrect because they use statistics, but that they are incorrect because they are done incorrectly. Many scientists don’t even understand the statistics well enough to realise that what they’re doing is wrong.

If I had my way, scientific publications – especially in disciplines that impact directly on everyday life, such as medicine – should adopt a much more rigorous policy on statistical analysis and on the way statistical significance is reported. I favour the setting up of independent panels whose responsibility is to do the statistical data analysis on behalf of those scientists who can’t be trusted to do it correctly themselves.

Having started badly, and lost its way in the middle, the article ends disappointingly too. Having led us through a wilderness of failed frequentists analyses, he finally arrives at a discussion of the superior Bayesian methodology, in irritatingly half-hearted fashion.

But Bayesian methods introduce a confusion into the actual meaning of the mathematical concept of “probability” in the real world. Standard or “frequentist” statistics treat probabilities as objective realities; Bayesians treat probabilities as “degrees of belief” based in part on a personal assessment or subjective decision about what to include in the calculation. That’s a tough placebo to swallow for scientists wedded to the “objective” ideal of standard statistics….

Conflict between frequentists and Bayesians has been ongoing for two centuries. So science’s marriage to mathematics seems to entail some irreconcilable differences. Whether the future holds a fruitful reconciliation or an ugly separation may depend on forging a shared understanding of probability.

The difficulty with this piece as a whole is that it reads as an anti-science polemic: “Some science results are based on bad statistics, therefore statistics is bad and science that uses statistics is bogus.” I don’t know whether that’s what the author intended, or whether it was just badly written.

I’d say the true state of affairs is different. A lot of bad science is published, and a lot of that science is bad because it uses statistical reasoning badly. You wouldn’t however argue that a screwdriver is no use because some idiot tries to hammer a nail in with one.

Only a bad craftsman blames his tools.