Posts Tagged ‘thinking’


June 26, 2021

In his famous essay on ‘The Two Cultures” CP Snow pointed to the yawning divide in British Culture between Science and the Humanities. It’s still there, just as crippling as it was 60 years ago.

I was reminded of this when I started reading “The Boundless Sea – a human history of the oceans” by David Abulafia a professor of history at Cambridge University (Penguin 2019), a book which has attracted extravagant praise as well as The Wolfson History Prize for 2020. It’s a subject that has fascinated me since, as a boy, I read Thor Heyerdahl’s account of the Kon Tiki expedition — his raft trip across the Pacific in 1947 to explore his hypothesis that Polynesia might have been settled from South America.

That hypothesis gradually sank into disrepute following accumulating anthropological and genetic evidence suggesting that Polynesia was in fact settled not from the East but from the North by navigators of Asian descent. But then in 2020 came better DNA evidence showing that at least some South Americans had arrived in the Marquesas with their plants around 1150 AD. What has Abulafia to say about this evidence? On p 29 he writes that it:”… indicates that Polynesians from the Marquesas interbred with people from Columbia around 1150, most plausibly suggesting that Polynesians reached and returned from South America bringing Columbians and their seeds and tubers along with them.”

Heyerdahl’s balsa raft Kon Tiki sailing West from South America to Polynesia down the West Wind Drift powered by the Coriolis Force . Notice she’s got the wind behind her, as well as a current of 50 miles a day driven by the wind. Courtesy the Heyerdahl Museum in Norway.

What? Doesn’t Abulafia understand the winds and currents which would make such a hypothetical voyage thousands of times more difficult than Heyerdahl’s journey? Surely he understands the Coriolis Force which drives the Great West Wind Drift and indeed nearly all the voyages of exploration and trade around the globe in the days of sail?

So I skip to the Index, all of 63 pages long containing no less than 9,500 entries . No mention of Coriolis Force, and only one brief one to Trade winds, but not in the Pacific Ocean. But what about the maps, of which there are dozens and dozens? The Oceanic waters are entirely blank, no sign of the all-important currents and winds which drove and circumscribed all navigators in the days of sail.

One can only conclude that Abulafia either doesn’t know, or doesn’t understand the bearing of Science on the Oceans, a bit steep when he is writing a “Human history of the Oceans”. It’s like a geography text-book which omits all mention of mountains and rivers. The result is a timid history without any sweep or penetration, just another record of ‘One damn thing after another’ like his earlier book on the Mediterranean “The Great Sea” which I did manage to finish — just.

One could be more forgiving if Abulafia hadn’t been so condescending towards Heyerdahl , referring to him as a “self publicist” unworthy of his fame in Norway. Thor Heyerdahl wasn’t a timid academic, he was brave man who risked his life to explore his own imaginative idea — which as it happens, — turns out to be substantially right.

Abulafia’s egregious failure illustrates the folly of attempting history without comprehending or even taking notice of Science. And the extravagant praise for his book from other historians, and the award of the Wolfson Prize, can only suggest that such incestuos myopia is widespread in British academe. How can we rely on them when they must be writing for each other, and not for us?

But there’s a more general point here. It’s much easier to spot what is wrong with an argument than to spot what is missing from it. For instance the Scottish National Party is aiming to take Scotland out of the UK, without recognising that Scotland, with its 6000 miles of remote coastline, is indefensible on its own, but secure as part of a united island. How foolish. We islanders all need to sit up and take notice of that!


February 22, 2021

The biggest fallacy in Education is that because you have a degree you are ‘Educated’; the second biggest that because you have not, you are not. I argue here that a bookworm may become more than 500 times more learned than a graduate .

Thinking of all kinds works through “The Association of Ideas” . Thus a new idea is valuable in proportion to the number of ideas in your head already, with which you can associate it, potentially leading to new insights. Thus the value of reading a new book is roughly proportional to the number you have read already. If you have read 100 say there are roughly 100 times 99 (divided by 2 to avoid double-counting) or roughly 5000 potential Associations to be made between them whereas if you have read 200 that number rises to 200 times 199 (divided by 2) or roughly 20,000. In general then the value of your knowledge lies in proportion to the number of Associations you can make, which rises with the Square of its size. This is a profound but unfamiliar truth, and the basis of my argument.

Now a typical university undergraduate will need to read something like 2 books/course, which comes to between 100 and 200 over an entire degree. A book-worm on the other hand, who reads 2 books every week, reads 2 times 52 times 50 or roughly 5000 books over the course of 50 years. Taking the above-mentioned Square into account that implies that the bookworm finishes up (5000/200) squared, or 625 times more learned than a graduate; which makes my point.

There are of course qualifications. If the bookworm reads only detective novels, or the undergraduate only critiques of Shakespeare plays, neither will become Learned. Some breadth is assumed, the more the better. I would guess most bookworms, because they have no imposed constrictions on their appetites, would be more widely read, generally, but not always , reinforcing the case.

Isn’t that surprising, and interesting? The most learned members of society are not university graduates, not even university professors (of which I am one), but possibly unqualified people who have always got their noses in a book.

What are we to make of all this? I would suggest:

One has no chance of becoming Learned unless one is a life-long bookworm, degree or not.

It must be a primary aim of both parents and educators to see that their charges become bookworms.

A great library in every suburb and school will be an indispensable measure of its Civilization.

All measures which curb or kill Natural Human Curiosity( the main driver of reading), such as bad teaching, or over-examining, must be curbed immediately before it causes life-long damage. What on Earth is the point of turning out qualified but unlearned graduates?

There will be plenty of critics of ‘unfocussed reading’, of mere ‘bookworming’, especially from the Academic professions. All I can say is that I haven’t come to my view lightly. Having made a twenty year study of how successful Science is done, I found it was Breadth that mattered, far more then ‘genius’, for which there was little evidence. Breakthroughs appeared to come mainly from those who could Associate ideas which previously appeared to have no connection. For instance the basis of the modern world is Electro-magnetic Radiation , a concept only born when Hans Christian Oersted (1820), reading about storms at sea, first realised that Electricity and Magnetism must be connected.. If you want to follow the argument you might read my book “Thinking for Ourselves” described elsewhere on this site (under ‘My books’ Category). Here is an excerpt from that book entitled ‘THE VALUE OF LEARNING:

So here’s to readers everywhere! Only you can become truly Learned , and capable of leading, or perhaps we should say ‘reading’, our way on up to new realms of thought…


November 6, 2020

Hidden Galaxies were Tom Morgan’s passion (and mine). We both fell under their spell when we were young and spent our lives, and other people’s too, searching for them. Were we mad, as many sensible astronomers thought, or were we lucky? After all, searching for a vast continent whose existence could only be inferred from coincidences and equations, seems close to insanity. But then Christopher Columbus had been driven to his own folly by finding tropical beans washed up on the wester shore of Ireland, and by scraps of manuscript written in Egypt but then left forgotten for a thousand years on a library shelf in the great dome of Byzantium — Agia Sofia.

The saga of of Morgan’s life-long obsession ( and mine) is the spine of my quartet of novels Written in the Stars, starting with Against the Fall of Night (AFN) and ending with Beyond the Western Stars (BWS), a sort of Sidereal Odyssey I won’t retell here. But what I can do for non-astronomers is add some scraps of the evidence, the tropical beans if you like and the pieces of parchment which kept Morgan and his comrades going when all the Odds looked to be against them.

The Wigwam diagram showing the Visibilty of any galaxy (upwards) plotted agains its dimness, plotted horizontally, dimmer to the right. It is the consequence of two plunging curves and so is very sharp and very thin, which surprised everybody. It is utterly unintuitive, yet entirely dominates our ability to see the extragalactic universe. It turns out that virtually all the galaxies we can measure lie right under the peak. That is either a miraculous coincidence or a warning that most galaxies are hidden out of sight.

Let’s begin with the calculation Morgan made back in 1975 in that caravan on the Teifi Estuary (AFN). Above we see it in the form of a graph. It shows the Visibility of a galaxy — that is to say how easy it will be to see, plotted upwards, against its dimness, plotted towards the right along the bottom. And what Morgan found, to general consternation and surprise, was an extremely sharp, narrow peak. The inference was that only galaxies of a very particular dimness (or ‘surface brightness’ in the jargon) would be visible to mankind. Those ones to the right (‘Icebergs’ Morgan called them) would be sunk too far below the night sky, whilst the ones to the left (‘Brilliants’) would be so small in apparent size as to be mistaken for background objects And here was the killer-coincidence: all the galaxies known to science at the time fitted exactly underneath Morgan’s peak. That is why the paper, with its implicit challenge, was published in the journal ‘Nature’ in 1976. What the diagram The ‘Wigwam diagram” as we came to call it, cannot convey is just how narrow the Wigwam really is. It is ten thousand times narrower than the total range over which the occasional galaxy has turned up by accident. Ten thousand times! Even Morgan sometimes couldn’t believe that. Apparently we are looking at the universe through a mere crack in the shutters. It was the Wigwam diagram which kept Morgan and his crew sailing on, through doldrum and tempest, for the next forty years.

Astronomy is beset by what are called “Selection Effects”. That is to say we build our picture of the cosmos selectively out of what we can observe down here, pretending that what we cannot observe, which might be much the greater portion, is not significant. What else could we do? Morgan’s wigwam was thus a rude shock, for it suggested, very directly, that Astronomy must be missing much of the extragalactic cosmos. What could be done about that? We had to try and devise alternative observing strategies which might enable us to see through one window, what could not be seen through another.


Using that approach Morgan and his colleagues decided to survey the sky in the radio band, and when they found a source, check what was there in the optical. The next figure shows some typical results, with a radio spectrum superposed on a negative image (easier to see) of the corresponding area of the visual sky..

Here are radio scans of the sky made with the Parkes Radio Telescope superposed on negatives of the optical sky behind. The receiver is tuned to the frequency of gaseous Hydrogen receding from the Earth at the velocities ( in Km/sec) shown at bottom. The two upper spectra corresponded to giant spiral galaxies, bottom left to a dwarfish Irregular galaxy, and bottom right to a dim galaxy barely visible above the sky. The area under each spectrum is a measure of the total amount of gas present while the width derives from the internal motions within the galaxy ,such as rotation. Much can be inferred from these measures. Copyright Monthly Notices of the Royal Astronomical Society.

Usually there is indeed a galaxy to be seen there. But of course the team were hoping to find cases where the optical counterparts were invisible — i.e. true ‘Hidden Galaxies’

A montage of galaxies found at Parkes and then observed in several colours with the Sloan Survey Telescope in New Mexico. The six bottom right are all colossal giants more massive than our Milky Way. Nevertheless, as you can see, some are very dim. This all ties in with the Wigwam diagram and indicates just how treacherous a purely optical survey of the Universe might be. Courtesy of Professor Julianne Dalcanton, University of Washington, Seattle

The figure above shows that, from time to time they came close. Each postage stamp in the montage shows the optical image corresponding to a radio signal found in a blind survey of the sky made with the Multibeam Receiver fitted to the Parkes Radio Telescope in Australia. As you can see some are almost invisible, lying in the very wings of the Wigwam diagram. It is important to emphasise that the Luminosity of a galaxy (which corresponds to the number of stars it contains — generally billions) and its surface-brightness (dimness) are entirely different concepts, the latter depending on how its Luminosity is spread out across the sky. Although the six galaxies bottom right are all luminous giants, some are nevertheless, extremely dim.

There is another trick though in astronomy for finding something invisible in Space: observe an object behind it and look for tell-tale gaps (‘spectral ghosts’) in its spectrum where specific atomic species in the invisible object have absorbed out the light coming from behind. That is what Frank Cotteridge and his like found, albeit by accident, when they observed the spectra of very distant Quasars — lots and lots of inexplicable absorption lines (‘spectral ghosts’). “What else could they be”, Morgan argued, “If not my Hidden Galaxies?” Thus the bitter battle over QSOALs or ‘Quasi Stellar Object Absorption Lines’ began (see especially “Crouching Giant“).

The spectra of Quasars showing the many absorption lines (spectral ghosts) etched into them. Measurements show they are caused by clouds of atoms like Hydrogen and Nitrogen lying in the foreground along the line of sight to the quasar. But what form could those clouds take? Morgan claims they are the numerous Hidden Galaxies you would expect. Opponents who don’t like that idea are forced to postulate that visible galaxies must have absolutely vast gaseous halos surrounding them. Controversy continues [see Whispering Sky and Crouching Giant in particular]. As you go down the montage one is looking at higher and higher redshift quasars. Out there, back in time, the absorbing clouds appear to have been crowded closer and closer together. The humps are features in the spectra of the Quasars themselves. Copyright The European Southern Observatory (

In 1987 the whole field was electrified by a paper written by Greg Bothun, Chris Impey and colleagues who were then based in California. Quite by accident, while observing dwarf galaxies in the nearby Virgo Cluster, they noticed that one wasn’t a dwarf, but the nucleus of a “Crouching Giant”, that is to say of an absolute monster of a spiral galaxy 25 times further away than the cluster but too dim to show much of itself above the sky. Here was unequivocal evidence that Hidden Galaxies of the most dramatic kind actually existed.

The Crouching Giant found by Greg Bothun, Chris Impey and co. by accident in 1987. The bright nucleus (this is a negative) was thought to be a dwarf galaxy in the nearby Virgo Cluster. But some very smart detective work revealed that it was instead the core of an absolutely colossal but dim giant spiral 25 times further away, whose spiral arms you can just pick out. It is no less than half a million light years across, ten times the extent of our own colossal Milky Way. Because of the accidental way it was found, finding others like it would be infernally difficult. Copyright Astronomical Journal 1987

That might have been that — except that nobody could find another such. The sceptics could, and did, write it off as a freak. If Hidden Galaxies were to become ‘significant’ they needed to make up a healthy fraction of the cosmic light and mass. In other words astronomers needed to find lots of Crouching Giants.

And how we all tried! But even when Jon Davies & co. did find one at Jodrell Bank (below) the opposition was fanatical.

Theoreticians who’d ‘proved’ that Hidden Galaxies couldn’t exist were furious; observers with even bigger telescopes than Jodrell were adamant that if they hadn’t found one then certainly we could not. And then there were the computer modellers who, at the drop of a hat, could prove or disprove anything, often without acknowledging the manifold frailties of their craft.

The putative Dark Galaxy VirgoHI-21 in the Virgo cluster. Left shows the radio contours superposed on a negative optical image. (Data obtained with the Westerbork Array in Holland) The giant spiral NGC4254 has obviously been disturbed by an encounter with a massive object which could only be Virgo HI-21, which is Dark, but note the bridge of gas between them. But the dynamical map (Right) shows it is spinning rapidly which can only mean that it is indeed massive. Massive, dark, spinning; what else could it be but a Dark galaxy? Copyright The Astrophysical Journal, 2007.

So although , after titanic refereeing battles, Virgo HI-21 did eventually get published in the prestigious Astrophysical Journal, most of the self appointed ‘experts’ stubbornly refused to acknowledge it as the first Dark Galaxy. But, in my opinion, if you read all the arguments carefully enough, it cannot be anything else.

In Big Science the problem is very often Lack of Breadth, rather than Lack of Depth. The clues are here and there but who has the breadth to spot them all, and assemble a coherent picture? Often we fail because no one individual in the field has the required breadth. And then there are the Systematic Errors that can bedevil any ambitious undertaking, errors held on to fanatically, especially by those who do not appreciate the frailty of The Scientific Method, and the need for caution in applying it (See my book Thinking for Ourselves) . This is highlighted in the following image based on observations we made with the Jansky Telescope in New Mexico, much the most powerful radio telescope on Earth at present. It reveals a huge cloud of hydrogen, the signature you would expect of a Dark Galaxy, but with a giant but optically visible galaxy to the South, receding away from us at the exactly the same speed as the Hydrogen. Previously the Parkes team, to which I then belonged, had mistakenly identified that as the source of the Hydrogen, and so overlooked what appears to be a true dark galaxy. Galaxies, Dark or Light, cluster so gregariously together that one needs a very powerful beast like the Jansky, to distinguish between them. None of us fully appreciated that, certainly not the Quasar observers with their spectral ghosts, who could always postulate, around visible galaxies, ‘gaseous haloes’ of unlimited size, to discount the invisible ones, which is what most of them choose to do.

What a Dark Galaxy ‘looks like’. Parkes 0039+03 was first discovered as a massive Hydrogen source out at 5,300 km/sec recession-velocity by Morgan and co. using the Parkes dish. They mistakenly associated it with the luminous optical galaxy (marked ‘cont’ here ) which happened to have an almost identical radial velocity, even though it is rather far away on the sky. But much later these more precise observations with the colossal Jansky array revealed that the Hydrogen and the bright galaxy are unassociated, as you can see. Even later a much deeper optical observations of the cloud made with the William Herschel 4.2 metre telescope in the Canary Islands revealed that it has tiny patches of light in it, but that is all. The strong clustering of galaxies together, both in space and in velocity, makes the search for Dark galaxies far harder than anyone had imagined. But if this isn’t a dark galaxy then what is? We found more like this out there.


Thus far I have spoken entirely of Icebergs, hidden below the sky on the right hand (dim) side of the Wigam; what about the ‘Brilliants’ on the other? They would be even harder to find so Morgan and co almost forgot them altogether. Apart from anything else, being compact, they would be largely shrouded in their own smoke, disguising their true brilliance, appear like ordinary galaxies, but far far in the background, and therefore of no particular interest.

It was only after WFC-3 was operating on Hubble (2009) that Morgan began to worry about the extremely high redshift galaxies dotted all over the background in deep Hubble images (see below). If the universe were really expanding they oughtn’t to have been there — dimmed out of visibility by the so called ‘Tolman Effect’. And they turned out to be very small physically, much smaller than galaxies of the same luminosity situated close by to us in Space. Then the penny dropped with a clang for Morgan. Here were his Brilliants but at very high redshift, dimmed just enough by expansion to place them in the Visibility Wigwam where they became possible for us to see. The implications though were startling: Space must be inhabited by vast numbers of Brilliants , just as it probably was by Icebergs. And together all their extra radiation would have sufficed to re-ionise the Universe — otherwise a major problem for Cosmology. So it all fitted together: Hidden Galaxies, Expansion, Brilliants, the Wigwam diagram, Reionisation…….if Morgan was right. If…….. This was the theory which obsessed him towards the end of Beyond the Western Stars.

The Hubble Ultra Deep Field, the deepest image ever taken. In an expanding universe distant galaxies ought to be dimmed to the point of invisibility by straightforward physical effects. Yet here they are, dotted all over the place. Either the universe isn’t expanding or these are normally invisible Brilliants, shifted into the Wigwam by redshift so as to be visible. Courtesy ESA/NASA

Who was right, and who was wrong can only be decided by posterity . But in my story of Hidden Galaxies I have tried to convey, above all, just how engrossing it all was: the tournament of ideas, the clashes of personality and ambition, the conflicts of evidence, the camaraderie, the bravery and the cowardice, the wild misunderstandings and the hazards of fortune……. They make science such an exciting career; though not one for the faint-hearted.

PS. I have actually left out the biggest reason for mystery here, because it has a post of its own entitled HOW DARK IS THE NIGHT?

Professionals who would like to see a fairly up-to-date review of this subject can look at my opening address to the International Astronomical Union symposium No.355 held at the IAC in Tenerife in 2019 entitled “The Realm of the Low Surface Brightness Universe” (Procs. edited by David Valls- Gabaud to appear soon in CUP) at:


September 29, 2020

Why not learn to think like Einstein? He attributed his success entirely to common sense. But what is Common Sense Thinking (CST) ? They don’t tell us in class because scholars don’t know how it works; it’s buried too deep inside us. So the author, who is a Space astronomer, has spent a lifetime unearthing it. Common Sense turns out to have nothing whatever to do with IQ, or with passing exams; it has to do with Curiosity, with the deliberate gathering of evidence, with a willingness to change one’s mind, and with the patience to wait until the Odds look decisive. But these common sense thinking skills are the very skills of the detective as well as the scientist; we can all learn them if we want to, whatever our educational attainments.

 To think efficiently for ourselves we require the right information and the right tools. At last the Internet is bringing an increasing flood of the kind of information we need to make crucial decisions for ourselves, and not have to rely any longer on expensive and often unreliable experts. But do we have the right mental tools? We do and we don’t. We do because Nature has embedded deep within us the sophisticated mental mechanisms  needed to survive in the perilous Stone-age out of which we evolved. We don’t, in the sense that we don’t know how those tools work, and so we cannot adapt them for best use in a modern world full of culture and technology. The author has unearthed those ingenious and previously unrecognised tools which Nature evolved  for dealing with conflicting evidence, for discounting bad clues, and for weighing up all the pros and cons.

The aim of this book is to open nature’s tool-bag and demonstrate her mental tools working one by one. The reader will end up equipped with an indispensable boy-scout’s penknife for the thinking mind.

         The book is aimed at two kinds of readers: those who feel they are educated – and those who feel they are not. The educated ones will discover that they have not learned Common Sense Thinking at school or university, and badly need to – while the uneducated ones will find that dropping out of education is no handicap if they now decide that they do want to think seriously and well. Anyone aged 14 or over could master it.

The approach is to work through numerous stories and examples, some serious, some light-hearted, all hopefully interesting and relevant. The book is really a series of detective stories in which we learn to work out rough odds on the various suspects (ideas) being guilty.

There are plenty of exercises for those who want to practice, with worked answers available free on the Internet.

Topics covered include:

  1. Different kinds of Thinking
  2. How scientists think and decide
  3. How to weight clues
  4. How to reckon the Odds
  5. Woolly thinking
  6. The Elephants in the room (Systematic Errors)
  7. Animal Intelligence
  8. Numbers and Errors in Thinking
  9. Why we don’t need Statistics any more.
  10. Common mistakes in Thinking and Deciding
  11. The extraordinary history of Thinking
  12. What is Science, and what is not?
  13. The meteoric ascent of mankind. What on Earth happened?

There are 16 chapters. Two hours devoted to each should equip the reader with the tools needed to go about tackling the hardest mental problems in life.

The complete Table of contents can be seen here:

The paperback book came out on Amazon early in 2020, has 600+ pages, is about 190 kw. in length and is priced at £14.50 with roughly equivalent prices in foreign markets. You can see much more by using the ‘Look Inside’ feature on Amazon. The Exercises, with answers, are on the web and elsewhere in this blog at


Corrections as of June 2020 can be found at: