Posts Tagged ‘philosophy’


November 4, 2021

Despite three decades of effort and tens of millions of dollars spent on accelerators and their like, it looks as if Particle Physics is coming to a sad end. No new particles beyond those such as the Higgs Boson proposed 50 years ago, and in particular none of those Supersymmetric particles which theorists had hoped would explain that greatest of all scientific mysteries — Dark Matter. Of course there will now be cries for more money and even larger machines, after all the Large Hadron Collider at CERN in Geneva is a mere 27 kilometres in circumference. But wait! Perhaps there is something far more interesting and fundamental at work: Perhaps Particle theorists have misled themselves, and everybody else , through neglecting a philosophical principle at least a thousand years old called ‘Ockham’s Razor’ (OR), named after a mediaeval monk called Friar Ockham.

At the heart of the Scientific Method is the business of Hypothesis Testing, which is where OR comes in. It states “Always prefer the simplest hypothesis first” and that, I suggest, is where Particle Theorists went so horribly wrong. Their “Standard Model” — as they call it, is fiendishly complex — what with its Quarks, Gluons, ‘Asymptotic Freedom’ and so on and so on. How do we measure complexity in Science? By the number of ‘Free Parameters’ (FPs) needed to describe a theory. One way you can think of them is to say they are arbitrary numbers brought into a theory to force it to fit the experimental data. A ‘good theory’ doesn’t need many FPs because it fits the experimental world naturally(for instance Newton’s very successful Theory of Gravitation has only 2 FP s) The so called Standard Model of Particle Physics needs no less than 18 FP s which has always suggested that it is an ugly and unnatural construct. It should be no surprise then to find now that it actually looks to be wrong.

So why did theorists construct such an ugly model in the first place, mostly back in the 1960’s and 70’s? Probably because they didn’t understand just how fundamental OR is. And there’s some excuse for them — because the Philosophers of Science, the self-appointed arbiters of the Scientific Method, didn’t understand OR themselves. Even Einstein, who relied on it extensively, waffled about some plastic ‘God’.

As I see it Hypothesis Testing works like this. You have some data-points, with error bars of course, and you have your hypothesis which generates a smooth curve which you must try to fit through those points. If there are lot of points the Odds on your hypothetical curve fitting them all by chance must be small. So if it does so fit then the Odds are that the hypothesis is probably right. If it doesn’t fit then you can always complexify your hypothesis ,so twisting your hypothetical curve until it does fit. But you can see that’s not a very convincing way to proceed, because eventually you are always going to force a fit. In that case the Odds in favour of it being actually right vanish. And that, I would suggest is what happened to Particle Theory, starting half a century a century ago.

There’s nothing fundamentally wrong with modifying a theory to fit the facts, after all that’s how science progresses. But you have to be very frugal in doing so. Only introduce a new concept (FP) into your theory if it fits at the very least two more data points than its simpler predecessor. And that’s hard to do, but it won’t degrade the Odds on it being right. But if it only fits one more data point the Odds will generally degrade dramatically. And that’s what Particle Physicists were tempted to do; making names for themselves at the expense of undermining the Odds on their so called ‘Standard Model’ theory. And that’s why almost nobody believes in their theory anymore. It’s as if they’d undermined their currency by printing too many notes. It works for a while — then collapses!

I am not a Particle Physicist, thank God, I am an Astrophysicist. And what worries me is that those same Particle theorists have dragged their own dodgy practices into our subject, with predictably unhealthy consequences. Take “Dark Energy”, an entirely artificial concept dragged into Cosmology by a particle theorist called Ed Turner from the Fermi Lab (and the University of Chicago). Now astronomers are raising hundreds of millions of dollars to chase this fantasy around the cosmos when there’s no justification for doing so, none at all. It was a thoughtless quick-fix extra Free Parameter to fit the apparent acceleration of Cosmic Expansion inferred from Supernova measurements in 1998. Had its introduction explained TWO or more discrepancies between theory and observation we might have welcomed it in. But it didn’t. So it should never have been introduced in the first place. Never!

PS Actually the situation is far worse than I am implying because the bloody particle theorists who have undermined their own subject actually introduced two more unnecessary FPs into Cosmology before Dark Energy: ‘Inflation’ to cure Isotropy and nothing else, and ‘Dark Matter’ to fix the Cosmic chemical abundances. We need to throw them out too.

So where do we go from here? Cosmology should chuck out Dark Energy, Inflation and Dark Matter and start again without them. As for Particle Physics I suspect that they may have to go back 50 years and try to reconstruct a more parsimonious theory of particle interactions than the ‘Standard Model based on quarks and gluons. In his wonderful book ‘Constructing Quarks’ Andrew Pickering (Univ. Chicago Press 1981) suggested that that theory was a social construct anyway, the product of trendy acclamation, rather than sober assessment.

More generally all of us need to understand the process of Hypothesis Testing on which the modern world of ideas is entirely built. Because if that isn’t sound ,God help us all.

For much more on Ockham’s Razor see our post “Fuzzy Thinking and Ockham’s Razor’ under the ‘Thinking’ category here on our blog. For a detailed explanation of Ockham’s Razor and why it works go to the url:

But if you want to go into the whole business of Common Sense Thinking (CST) , of which Hypothesis Testing is only a part, try my book “Thinking for Ourselves” publ Amazon (2020) which is described in the ‘My Books ‘ Category on this site.



August 21, 2021


This post is so titled because it stands for “THINKING FOR OURSELVES-ADDITIONS” where “Thinking for Ourselves” refers to my book with that title originally published in 2020 and updated in 2021 (For details see elsewhere under ‘My Books’ Category or under Tags on ‘Thinking’.) But from now on I want the book to become live, so that it can be continually updated here on line. Here you will find Exercises with Answers, corrections, images, calculations, supporting data, more detailed and improved arguments, readers comments with my responses to what is intended to become what I call ‘A LIVING BOOK’.See at the bottom of this Post how to make such Comments.

All the additions are shown below, mostly under a Chapter number and page number in the paperback book, version 2021.



at the following url:


         I finished the book 3 years ago with the surprising but triumphal discovery of Categorical Inference – which connects the whole scheme for Common Sense Thinking so naturally and necessarily with Animal Thinking and Evolution. And IF it’s right it could change the world.

         At that point I sometimes get struck with what  I believe they call ‘Imposter Syndrome’– how could little me have unearthed a powerful scheme entirely missed by giants such as Francis Bacon, Isaac Newton and Albert Einstein? It doesn’t seem likely does it?

         But then I look at some of its manifest achievements such as:

  • Explaining Humankind’s dramatic leap in mental capability around 1000 BC.
  • Its unique mechanism for balancing conflicting evidence, as illustrated with its success with Hidden Galaxies.
  • A first transparent and convincing explanation for Ockham’s Razor.
  • Its powerful mechanism (PAW) for dealing with Systematic Errors, which have kept us back so many times  for so long.
  • It’s perfect dovetailing into Animal Thinking and Darwinian Evolution.
  • The multiple new insights which spring from it – see this blog and my other book “History of the Brits’ [HOB ch.5]. For instance  it comes up with the keys to human Progress, what I call ‘The Seven Pillars of Wisdom’ .

So then I am reassured. But, but……Why little me again? All I can say to myself, and to potential readers is :

 “It was bloody minded doggedness more than anything else. I started out with the modest ambition to find out what I believed was already known  –  the Scientific Method, only to find to my surprise that it was not, but that it probably had something to do with Common Sense, but that hadn’t been defined either. So I asked myself a different question: ‘How could animals think?’ and thereafter progress became relatively rapid  because now I could entirely  ignore Philosophy, Mathematics and Religion.

So I didn’t have to be a genius, which I definitely am not. And one doesn’t have to be a genius to make a great discovery. Look at Darwin – he spent the first  30 years  of his idle life slaughtering wild creatures for fun. Basically he was an illiterate lout – but he stumbled upon the greatest scientific discovery of all because he happened to be in the right place at the right time – the Galapagos Islands  in 1838. But he was only there because his exasperated father had sent him out there as a punishment, saying “You wouldn’t even make a decent rat-catcher.” Indeed there’s little evidence of ‘genius’ in science more generally [ See Chapter 3 of TFO to see how great discoveries have been made in history] – so even if I’m not a genius , TFO  could still be right.”


As of 21/8/21 there are only 2 because I have just made two dozen corrections to the original paperback edition.They are

P 302: replace ‘Sherman’ with ‘Pershing’.

P 456, line 7: replace 13 with 23.

But the most important of those for purchasers of the older editions are at:


CHAPTER 1 (‘Can we learn to think better?’) p 15

CHAPTER 2 (‘Different kinds of Thinking’) p25

CHAPTER 3 (‘How do Scientists Think?) p46

CHAPTER 4 (‘Natural Thinking and Bayes’ Rule’) p95

There are several Posts on the fascinating subject of ‘Galaxies’ , including ‘Hidden Galaxies’, in the ‘Astronomy’ Category here, with many images.

CHAPTER 5 (‘The Detective’s Equation’) p132

CHAPTER 6 (‘Numbers and Thinking’) p154

CHAPTER 7 (‘Woolly Thinking and Ockham’s Razor’) p170

There are several posts here on ‘Big Bang Cosmology’ — which I use as a case study in dodgy thinking, under the ‘Astronomy’ Category’.

CHAPTER 8 (‘Common Sense’) p198

CHAPTER 9 (‘Error Analysis’) p236

CHAPTER 10 (‘Systematic Errors, The Elephants in the Room’) p268

CHAPTER 11 (‘Statistics – or Terror Analysis’) p294

Statisticians turned themselves from humble clerks into a dogmatic priesthood based on several misunderstandings, on their part. They need to be put firmly back on their stools. Having spent 30 years trying to teach Statistics at university, I gradually came to realise that the profession has got itself hopelessly lost in the No-man’s land between Induction and Deduction. Look what confusing advice they have given to the government over the Covid pandemic, They’re not scientists, they’re mostly priests, who hide behind higher mathematics when they are challenged. See Post “Statistics: exposed at last” under ‘Thinking’ Category.

CHAPTER 12 (‘Persuasion’) p342 t

CHAPTER 13 (‘Poor Thinking’) p357

CHAPTER 14 (‘The Extraordinary History of Thinking’) p407

CHAPTER 15 (‘The Peculiarities of Science’) p451

In Sect (15:12) ‘What about Mathematics’ I only gave some modest examples because I didn’t want to frighten off non-mathematical readers but on this site its maybe worth drawing attention to some more spectacular examples. For instance on pp 471-472 I then failed to recognise the full and dramatic implications of mathematics when applied to immigration: basically because immigrants arrive every year, while children arrive only a couple of times or so in a female’s life, immigration is no less than 160 times more significant than natural birthrate when it comes to population increase! Thus immigration into the UK at present is equivalent to 3 British mothers out of 4 having an extra child! If you don’t believe me, and I found it very difficult to believe it myself, you should consult the url:

Then the modern world, including radio, broadcasting, television, Relativity, satellites, mobile phones, the internet…. were all implicit in a set of equations derived by two Brits in the 19th century, James Clerk Maxwell and Oliver Heaviside. You don’t have to understand the equations in detail but one can certainly admire a human artefact millions of times more momentous than either The Rosetta Stone or Tutenkamun’s Tomb. See:

CHAPTER 16 (‘Consequences and the Ascent of Mankind’) p476

On p486 there is a very brief discussion of Time. If you want to see a deeper discussion of a profound topic see the Post “WHAT IS TIME?” under the Category ‘Thinking’. Those who want to look deeper into TIME can look at the Post ‘MAXWELL’S EQUATIONS’ (under ‘Thinking’ Category )which explains why Relativity has changed our view that Time is absolute; it’s not, according to physicists. Even so Time is still a great mystery; there seem to be several different kinds of time. all mistakenly labelled with the same four lettered word.



APPENDICES pp 547 to 604

INDEX p612


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!


June 25, 2021

Common Sense Thinking needs some tool to discriminate between Truth and Falsehood, or more generally between sound hypotheses and unsound ones. ‘Hypothesis Testing’ ,as it is called, lives at the very heart of Science, Philosophy and Common Sense. As we now know it works by examining the various consequences C1 ,C2, …generated by that hypothesis to see whether they can be observed in practice. If they can be observed that improves our Odds O(H) on the hypothesis being true, if they cannot that reduces our Odds on it. But if the hypothesis generates no consequences we cannot test it , and so can say nothing about it one way or the other. That’s “Bayes’ Rule” which goes back at least as far as 1763 and probably much much further.

Take the hypothesis “God exists”. What consequences does it have? Once upon a time it was argued that the design of the natural world was so miraculous, perfect and improbable that it could only have been conceived by an Intelligent Creator. For instance how else to explain the spectacular plumage of the Rainbow Lorikeet ? [Click on the urls below to see their magnificence]

This was the very convincing “Argument by Design”, almost impossible to counter at the time. But in 1858 along came Darwin and Wallace who independently came up with the alternative hypothesis of “Evolution by Natural Selection”. As the Bishop of Worcester’s wife said of it: ” Dear me; let us hope it is not true. But if it is true , we must hope it doesn’t become widely known.”

The general point is that Inconsequential Hypotheses are hardly worth considering because there is no way of assessing their veracity, whereas Consequential Hypotheses are open to verification, at least in terms of their probability(Odds). Thus Evolution has subsequently been detected in, for instance, bacteria under stress , while I am not aware of any consequence for the existence of God which could be tested .

That’s not to say one can’t go on believing in a god — it’s just that the most consequential evidence on his/her hypothetical existence has an alternative, and partially verified explanation, even if it cannot be absolutely categorical.

Then there’s another important philosophical principle that can be brought to bear:Ockham’s Razor — “Always prefer the simpler hypothesis, because its more likely to be right’ [see my Post ‘Fuzzy Thinking & Common Sense’] .The problem with the God hypothesis is that there are so many inconsistent versions of it (4,000 known religions including 20 with a world-wide spread, according to Wikipedia).

Clever people have wasted a lot of their lives worrying about Inconsequential hypotheses — for instance the existence of Free Will [see Post. ‘Free Will and Common Sense] , or in the case of Mathematicians whether their subject was invented of discovered. It doesn’t matter. It’s Inconsequential.


May 21, 2021

The hoary old hypothesis that ‘There is no such thing as Free Will’ has fired up public debate yet again thanks to a recent article by Oliver Burkeman in The Guardian. And once again, to judge from the many letters and comments it has aroused, the result is inconclusion, if not total confusion.

But there’s no necessity for that if you appeal to The Scientific Method. At its very heart lies a technique for Hypothesis Testing called ‘Bayes’ Rule’. What it offers to do is alter one’s Odds on any hypothesis H by appealing to any evidence E consequent on that hypothesis. But if there is no such consequent evidence, as there appears not to be in the Free Will case, Bayes’ Rule is helpless, and any debate about the matter is therefore fruitless. The mediaeval scholars who didn’t understand that wasted their lives discussing such arcane matters as ‘How many angels could dance on a pinhead.’ Why don’t so many modern scholars realise that Inconsequential Hypotheses are undecidable and so a waste of their time, and everybody else’s?

I would suggest it is because Western Philosophy is rooted in a quest for Certainty. On the one hand the Ancient Greeks thought that Certain truths could be arrived at solely by Deductive, even mathematical, Logic. On the other hand, Abrahamic religions held that Man, who sat on the right hand of the only true God, could find Certainty in Holy Scripture. The idea that Certainty was unavailable, except in trivial circumstances, as we recognise now, and that gambling Odds would have to do instead, was anathema to both schools.

The sad result is that the Education Establishment, even today, largely ignores Bayes’ Rule, and thus Common Sense Thinking in general, because of its abhorrent roots in gambling. It’s not so surprising though when you recall that Oxford and Cambridge for instance were set up by papal bulls in the thirteenth century to train priests. Gambling was certainly not on their curricula. Nor did they even teach Science until forced to do so by the Government late in the 19th century.

Thus the Free Will debate brings to light an extraordinary situation. The academic world largely ignores Common Sense Thinking because it lies outside a 2,500 year old tradition rooted in unsound philosophy and Abrahamic theology. Science has only progressed by ignoring both.

Equally though it highlights a quite extraordinary opportunity. We could now teach Common Sense Thinking , with its key principles: Bayes’ Rule, The Detective’s Equation, Ockham’s Razor, the Principle of Animal Wisdom and Provisionality to everyone over the age of 13. It will probably lead to advances far greater than did either Industrialisation or Electricity. And importantly, it would teach us Tolerance, because provisional (i.e measured) thinking and Tolerance for alternative ideas, are opposite sides of the very same coin.

Anyone interested in these matters might like to read Thinking For Ourselves, a 20 year study of The Scientific Method and Common Sense Thinking, discussed here under the My Books Category. And look under the Thinking Category for many other allied Posts.


February 20, 2021

Every organism evolves to survive, but Evolution is an extremely slow process. That means that if we can think before we act (a distinct survival advantage) then so could our animal forbears. And modern studies of animal behaviour confirm that their mental sophistication is far higher than zoologists of any earlier generation could suppose1.

Life out in the wild can be extremely dangerous, so survivors (especially if they come from a potentially long-lived species, as we do) cannot afford to make unwise decisions. Caution must be their watchword.

We have elsewhere argued2 that decisions are reached using the Detective’s Equation (DE):

Revised Odds on H = Old Odds on H × (Weight of Clue 1)

× (Weight of Clue 2) ×………… and so on, for as many clues as you have.

in which the Weights are just numbers we attach to each clue as it bears on the particular Hypothesis H (e.g. ‘It is safe to try and catch that snake’) that we are trying to evaluate.

The great value of the DE is that it is multiplicative, so high Odds can be reached from only a few clues. But what if one of those clues, or our evaluation of it, is wrong? For instance that the tasty looking snake is not harmless but venomous. Such misapprehensions occur all the time, so we must have some mechanism for discounting them. An obvious possibility is insisting on the equivalent of at least three heavily weighted clues in favour before deciding. Why 3? Because one rotten plus one good could lead to fatal consequences, whereas with 3 strong clues one could hope that at least two would generally be sound.

But at what Odds would one feel it safe to decide? I would suggest at combined Odds of something better than 50 to 1 (for or against). Now the smallest whole number, which multiplied together 3 times, comes to more than 50 is 4 because 4 × 4 × 4 = 64 . That suggests (no more) that the highest Weight we should put upon any single clue is 4. And if two weak clues are equivalent to one strong that suggests weak clues should be given a Weight of 2 because 2 × 2 =4.

To the sophisticated statistician all this may seem very crude, but the truth is, in the real world we cannot put precise Weights on many vital clues, for instance on our assessments of say honesty or guilt or venomousness.

So we have a very crude suggestive scheme for making judgements using the DE, in which the ONLY permitted Weights are:


‘Strongly in favour’ = 4

‘Weakly in favour’ = 2

‘Neutral’ = 1

‘Weakly Against’ = ½

‘Strongly Against’ = ¼

which is, so far, only suggestive. The only real justification for this scheme , (which I call the ‘Principle of Animal Wisdom’ or PAW) will be its performance in practice.

At this point we need to step back and recall that, so far as we know, animals don’t count. So isn’t all this numerising pointless when we are looking back to animal decision-making as our exemplar? Not really, because 4’s and 2’s only stand in for Categories of Clue, “Strongly for”, “Weakly For”, “Weakly against”(1/2) and so on. Nor do we need that ‘50- to-1’, because all we were demanding was ‘At least the equivalent of 3 strong clues (net) before deciding, one way or the other. In other words, to reach wise decisions, we don’t need , nor do animals, to use any numbers at all, we can simply use CATEGORICAL INFERENCE instead (which is described in another Post3). But as we humans are familiar with simple numbers and simple Odds we might as well stick to 4’s, 2’s, ½’ s and so on.

It’s very difficult (as it was originally for me) for modern Scientists and Statisticians to imagine that anything as crude as PAW could play any useful role in modern thinking. However the more one uses it in practice, and thinks about its implications, the more convincing, and indeed profound, the PAW comes to seem.

History shows that progress in Science has often been completely halted by unsound conceptions, or ‘Systematic Errors’ as we label them. For instance:

The Earth is Flat

The heavens revolve around the Earth

The body is controlled by 4 Humours

The world is far too young for Evolution

Continents can’t move.

Child-bed fever is a natural part of birth.

Radio waves cannot possible girdle the globe.

Nothing can live in the Deep

Atoms are immutable

…..and so on.

Had we, instead of ceding them prime authority, given them low (i.e. PAW) Weights we might have progressed much faster.

Then again, carefully consider the definition of a Weight in Probability terms, which we have elsewhere4:

Weight of Clue = (Probability of Clue IF H is true) divided by ( Probability of Clue if some hypothesis other than H is responsible for it).

In an OPEN world, as opposed to a card game [CLOSED], this last Probability can never be zero because there are so many ‘other thans, indeed an infinite number. It follows that no Weight should ever be set very high; i.e. the PAW

We can see that very high, or very low Weights can almost never be justified because they require an assumption about “ all those hypotheses, apart from H, which could give rise to E”. But in an OPEN world, as opposed to a card game, those other hypotheses could be virtually infinite in number. Thus the profession of Statistics , with its 4-figure precise tables, has fooled itself into the belief that it is dealing with a real open world, when all it is doing is playing card-games (which are CLOSED).

But it’s only when one employs the PAW to deal with complex issues like Big Bang Cosmology that its true value shines out. Some of our conceptions about the Universe are probably wrong – but we don’t know which ones (Expansion?). But if we combine enough clues together, the unsound ones, because of PAW, won’t be able to twist the whole picture and obscure the truth. For instance I used to believe that the Big Bang picture, although it looked implausible, couldn’t be ruled out. But after I stumbled upon the PAW (2015) and applied it to the Big Bang, the Odds came out very firmly (128 to 1 ) against. That illustrates, somewhat surprisingly, that the PAW, even with its weak Weights, can actually be more decisive than the alternatives.(See our Post ‘BIG BANG COSMOLOGY IS WRONG’ under the ‘Astronomy’ Category, or click on the url below)

Science is of course only one application of a survival mechanism which is tens, probably hundreds of millions of years old. But humans, who are so easily persuaded by Culture, that is to say by ideas planted in their heads by others, need to understand and employ PAW even more assiduously today to preserve themselves from monsters employing modern media. Here is a short list of such CULTURAL MYTHS:

  1. You shouldn’t mind sacrificing your life because you will be rewarded in paradise.
  2. God is naturally on our side.
  3. There is a Hell awaiting, but if you pay us we will see you are spared the tortures of…..
  4. We ………s have a Divine Right to rule.
  5. The (other side) are evil and must be crushed.
  6. They’re savages; they don’t feel pain like we do.
  7. Education is good for you and for everyone.
  8. Our little father the Czar/ Stalin/ Mao….. will look after us.
  9. Newspaper proprietors have the best interests of their readers at heart.
  10. If you work hard you’ll get more stuff and that will make you happier.
  11. Our religion is the right one. Those others are blasphemers and heretics.
  12. All things bright and beautiful,….the Good God made them all.
  13. They’re only aborigines /gypsies ….If you gave them land they wouldn’t know what to do with it.
  14. Doctors/Lawyers/Professors/Managers …. can’t do their jobs properly unless they have much bigger houses and cars than you and I.
  15. Women are too emotional to drive vehicles.
  16. You can rely on the Government news channels.
  17. Anyone who criticises our Great Leader is a traitor.
  18. It’s our land; God gave it to us.
  19. Education is good for you.
  20. They’ve got Weapons of Mass Destruction.
  21. Education is good for you.

Oppressive regimes, knowing our susceptibility to propaganda, employ myth-makers to exploit us, impoverish us, and even kill us fighting their wars. That’s what priests, newspapers, propaganda ministries and PR firms are for. Thus the Pharaohs had priests who spread the lie that they were Gods who controlled the Sun and The Moon. Thus the Romans authorised the Christian Church to control Europe for over a thousand years. Thus Hitler whipped up the Germans into a thirst for revenge. Thus Big Business funds Think-tanks, News channels, and lobbying groups. And so on.

There is another way of looking at the matter. If one can set an arbitrarily high Weight on some particular Clue you can use it to ‘Win’ any argument. Thus it is ideal for Priests and Tyrants. But the PAW democratises Thinking. It makes all the different Clues and arguments which go towards reaching a Conclusion, almost, but not quite equal.

There is no such thing as Certainty in the real (OPEN) world. We all of us, whether we are seagulls or Professors of Computer Science, must navigate our way through life as best we can using the Balance of Probabilities. And to do so successfully the PAW is absolutely fundamental. Anyone who tells you otherwise is a Priest. And I cannot think of a worse charge.

If you really want to see how all this Animal Wisdom works out in practice click on;


1“Are we smart enough to realise how smart animals are”? Frans de Waal, 2016; Granta Books.

2 See Post here ‘HOW COMMON SENSE WORKS’ under ‘Thinking’ category or ref. 4 below, Chapter 5.

3 See my post ‘CATEGORICAL INFERENCE’ under Thinking Category

4 See Chapter 4 in my book Thinking for Ourselves (Amazon 2020) .It’s described elsewhere on this site under the My books Category


November 26, 2020



As far as I can see Common Sense Thinking (CST henceforth) works like this: we all get ideas, they constantly bubble unasked to the surface of the mind; the real challenge is to decide which ones are sound [‘Hypothesis Testing’ it is called]. To determine that we look for evidence (clues) bearing on our idea or hypothesis H and place each clue in one of only 5 categories (This is the ‘Principle of Animal Wisdom’, or PAW for short):

TABLE (5:1) The Weights of Clues bearing on Idea H





Strongly in favour of H



Weakly in favour of H



Neutral towards H



Weakly against H (underlined)



Strongly against H (underlined)



We then combine (symbol ★ ) the Weights in obvious ways thus:

w★w = s

w★w = n

s★s = ss

s★w = w and so on.

And we finally decide to act on H only when the combined evidence reaches either sss [decide for H] or sss [decide against H]. This is a precautionary measure which saves us from making premature, possibly fatal decisions based on only two strong clues, one of which might be unsound.


A detective is having to decide whether to charge X with a crime [her hypothesis is ‘X is guilty’. Her thinking, based on the available evidence, might look like this:



Her Weight

Accumulated Weight














Witness A




Witness B




Witness C




Witness D







Charges X


My scheme is nothing more than the systematic Association of an Idea H with different clues, combined with a simple precautionary mechanism for avoiding overhasty decisions. I suspect such CATEGORICAL INFERENCE (CI for short) is our main survival mechanism with roots that go back a billion years. You won’t find it in text-books on Inference or Logic; they appeal instead to notions such as Probability Theory, Bayes’ Theorem and Parsimony. The problem is that their authors disagree violently among themselves – so something must be seriously wrong. That’s why scientists ignore them and go on using Common Sense CI to progress.

Notice three important features of this scheme:

1) The more evidence the better. With a sufficiently long string of clues, even when they conflict, we can eventually reach a decision [sss or sss ] about H, one way or the other, provided (a major proviso) a record has been kept of the incoming clues, together with their Weights. For instance I was eventually able to bring my own tangled research project to a triumphant conclusion but only after using writing to compound 25 separate clues, some in stark conflict with the rest. This means the scheme can be used, but only by the literate, to handle highly complex tasks such as voyaging to the Moon.

2) The process is open-ended; there is always room to add new evidence to the tally whenever it is found. Thus it is Provisional in nature, and even after a decision to act has been taken there must be room for a change of mind – in other words to Adapt.

3) Rather than remember these unfamiliar symbols it turns out to be much easier to use betting Odds and replace “combine” (★) by the multiplication sign ×, ‘n’ by the number 1, s by 4, w by 2, underlined-w by ½, and underlined-s by ¼ . Then a decision in favour takes place when the Odds are 64 to 1 on or better, and against at Odds of 64 to 1 against or worse. In future that is what we do. But remember it is still Categorical Inference, no more and no less, a process innumerate animals could have used to survive in the wild. We have just changed the symbols

NB. This extract was taken from Chapter 5 of my book “History of the Brits” where it is later used to tackle some very thorny issues such as ‘Is America Britain’s friend or enemy?’, or ‘Would the Scots have been better off Independent’ and ‘Is mass immigration good or bad for Britain?’.


November 24, 2020

Fuzzy thinking is far worse than fallacious thinking for whereas the latter may be spotted, or overturned by new evidence, the fuzzy variety may linger for millenia, causing endless harm, as we shall see.

There is a remedy against fuzzy thinking called “Ockham’s Razor (OR)” named after a mediaeval monk, though its roots stretch back into the classical world where it was labelled ‘lex parsimoniae‘ or ‘The Law of Parsimony’.

Ockham’s Razor states: “ALWAYS PREFER SIMPLE HYPOTHESES OVER COMPLEX ONES” which is easy enough to write down but damnably hard to justify. For instance both Newton and Einstein utterly relied upon it but both gave unsound reasons for doing so. Newton averred: “….for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.” while Einstein waffled about God. He said, with regard to his Law of Gravitation “God would not have passed up the opportunity to make nature this simple.” [As it happens she had.]


1) Heliocentrism (A Sun-centred planetary system) was first advocated in modern times by Copernicus(1543) in De Revolutionibus. He didn’t have any new observations to justify his claim (the telescope wasn’t invented for another 30 years) but it was evidently much simpler than the traditional Earth -centred scheme, which needed twice as many arbitrary parameters to square it with the facts. [Confirmation only came in 1609 when Galileo with his spyglass spotted that Venus exhibited changing crescent- phases as it orbited the Sun.]

2) Newton recognised that the theory of Gravitation he proposed to explain the dynamics of the Solar System was ridiculous. He wrote: “That Gravity should be innate, inherent and essential to Matter so that one body should act upon another at a distance through a Vacuum, without the Mediation of anything else, by and which through their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe that no Man who in philosophical matters has a competent Faculty of thinking can ever fall into it.” Nevertheless that one simple law explained so many things about the heavens and about he Earth that it was quickly and universally accepted…. because it was so parsimonious.

3) In his Origin of Species (1859) Darwin acknowledged that there were so many difficulties with his hypothesis of Evolution that he wrote in his conclusions: “That many and grave objections may be raised against the theory of descent with modification through natural selection, I do not deny. And I endeavour to give them full force.” And he did. Nevertheless many readers came to accept it rather than ascribing every peculiarity of Nature as due to a special intercession by God. Again because it was so much more parsimonious. And in the fullness of time ( a century) the various objections to Natural Selection melted away as Radioactivity and Continental Drift came to light.

4) It was Henri Poincare’ (1904) who first realised that the grave difficulties which then faced Physics could be resolved by accepting the Lorenz Transformations and modifying Newton’s Laws of Motion to agree with them. This is called ‘The Theory of Special Relativity’. However Einstein got the credit for it a year later by making a single outrageous assumption: “The speed of light is constant for all observers”, which was much less satisfactory from a philosophical point of view– but oh so much simpler algebraically. As in Newton’s case one outrageous assumption explained and predicted a thousand surprising observations: parsimony again.

5) And Parsimony isn’t just about science. Not at all. Take for example Military Intelligence. R.V.Jones who was head of Air Ministry Intelligence during the SWW, and who was responsible for the threats to the UK of Nazi bombing, radar, the V1 and the V2 missiles , later wrote a very fascinating book about his experiences ‘Most Secret War‘. In his summary at the end he calls Ockham’s Razor : “The Cardinal Principle of Military Intelligence.”


1) The Four Elements was an idea promulgated by Aristotle around 300 BC in which all substances were supposed to be composed of a mixture of Earth, Water, Air and Fire. By adjusting this hypothetical mixture, and a deal of plausible sophistry, the old thinkers could explain everything – and therefore nothing. So long as it was widely believed, serious chemistry was unnecessary and therefore unpursued. This monster was a many headed gorgon bristling with free parameters. Whenever something didn’t fit you ascribed further properties (parameters) to your 4 imaginary elements and lo everything could be made to fit once again. Thus it couldn’t be overturned; because it was too fuzzy.

What we  would call Chemistry was ruled for over 2000 years by Aristotle’s hypothesis. Almost no material evidence supported his scheme but it appealed to religions such as Christianity and Islam looking for a comforting order to life. It wasn’t overturned so much as left behind by crisis, the firewood crisis which struck Britain in the 18th century after it had cut down most of its forests to build houses and ships. A new source of power had to be found and the mining of coal led to a desperate search for new materials and new contrivances such as pumps to stop the mines flooding. Experiments were necessary, and from experiments came evidence that made no sense within Aristotle’s fuzzy scheme. For instance burned in air some substances became heavier not lighter. And careful balance measurements initiated by Joseph Black in Glasgow University (1750, the English universities didn’t teach science then!) showed that substances combined in precise ratios to form compounds. Out of such observations the notions of atoms and molecules grew. These in turn gave rise to materials of great strength like steel, and to new compounds of great value such as artificial dyes. Crisis, experiment, discovery, understanding, wealth: The infinitely flexible, therefore unprogressive chemistry of Aristotle was simply left behind as unprofitable.

(B) The Four Humours was another fuzzy Greek hypothesis which held up progress for 2 millenia. Modelled on the Four Elements it imagined that health was determined by a balance of four liquids: choler, melancholer, phlegm and blood. Physicians who were learned in such jiggery-pokery dosed us, leeched us and charged us, shortening our lives as they impoverished our purses. Again the hypothesis was immune to criticism because it was infinitely adaptable. In place of bones it had an infinitude of free paramaters –  and what was more could earn good money. Again it couldn’t be displaced by evidence, being infinitely flexible. It was gradually superseded by more useful notions about physiology such as the germ theory of disease, a direct result of the invention of the microscope. But Greek Medicine held up real medicine for twenty centuries

(C) The ‘Argument by Design’ opined that all things wise and wonderful, all creatures great and small, were instances of The Creator’s wonderful powers of invention. After all no other cause could be imagined for the intricacies of Nature’s architecture, from the perfect spiral of a sea shell to the extravagance of a Rainbow Lorikeet’s plumage. Science at the ancient universities, even to the end of the nineteenth century, was solely aimed at uncovering such wonderful manifestations of the Almighty. Since nothing was outside His powers everything could be explained. There was no possibility of bringing Him down, since nothing was beyond Him, even burying fossils of inexplicable design merely to challenge our faith in Him. This ‘Argument by Design’ could have been rejected by nothing else but Parsimony, by the discovery of an alternative theory which was simpler, far simpler than a Great Designer in the Sky. And so it eventually was (see Darwin above) The trouble with Him was that he had an infinite number of free parameters (fudge factors).


To my mind the greatest obstacle to progress in Western Society was Christianity. Forced upon the Roman Empire by Constantine on his deathbed (337 AD) in return for ‘absolution’ for his sins (he’d murdered his wife and son) it brought Thinking to an abrupt end for over a thousand years for, as Saint Augustine its early theologian wrote (~400 AD) : “There is another form of temptation, even more fraught with danger. This is the disease of curiosity ……It is this which drives us to try and discover the secrets of nature, those secrets which are beyond our understanding, which can avail us nothing and which man should not wish to learn.” Shortly afterwards Christians burned down the Great Library in Alexandria and executed its head by torture.

With no good evidence for its core belief in Jesus Christ as the Son of God Christianity (and other Abrahamic religions) at least offered a very desirable and necessary explanation for “the wonders of Nature” [see ‘The Argument by Design’ above]. But when Darwin and Parsimony had punctured that, thoughtful Christians, like the Bishop of Worcester’s wife, knew that Christianity’s days were numbered. As she put it : “Dear me, let us hope it is not true. But if it is true, let us hope it does not become widely known.”


Why should anyone accept Ockham’s Razor? That’s the central point. All the explanations I have examined are either unconvincing, or go off into stratospheric mathematics — which is the same thing. The problem is that anything as fundamental as Ockham’s Razor has to be grounded on a clear understanding of Common Sense — which was lacking. Put it another way: any claim to understand Common Sense Thinking must lead to a crystal clear explanation for OR. But don’t expect it to be simple or obvious — otherwise it would have popped out of the woodwork long since.

The secret, as always, turned out to be The Detective’s Equation (DE). Whenever you are trying to understand Hypothesis Testing, which is surely the aim, the DE can be used to calculate the Odds for or against the hypothesis under test, whenever the evidence and the assumptions are changed. So you can play around and find out what adds to one’s certainties and what subtracts, and out of such calculations Ockham’s Razor gradually emerged from the shadows. The best reason to believe any hypothesis is that it fits the existing evidence better than it has any right to do by chance. A simple hypothesis has little chance of fitting more complex data unless it is actually right, whereas a complex hypothesis deliberately contrived to fit it is hardly convincing. Much the best way to understand how things work is to look at a specific example, and we shall go through one in detail below while there is a whole chapter in my book Thinking for Ourselves about OR and its multifarious implications.

Because most scientists still don’t understand CST they don’t realize just how counterproductive it is to complexify their pet theories to fit new but inconvenient facts. Thus Big Bang Cosmology has been so seriously challenged by modern observations that cosmologists have been forced to fuzzify it with strange new parameters like Dark Energy, without realising that in doing so they’ve entirely undermined its credibility.


Once a hypothesis conflicts with the facts it cannot be left unmodified. But fixing it by introducing arbitrary modifications one by one to remove the separate discrepancies won’t work either because each such mod. will weaken the odds on the hypothesis overall. Only if one can find a mod. which offers to clear up several discrepancies at once should it be seriously considered. Of course that will be much harder — but nevertheless that is the challenge.

Applied to Big Bang Cosmology (BBC), Inflation (to fix isotropy), Cold Dark Matter (to fix galaxy-formation) and Dark Energy (to fix acceleration) shouldn’t be considered seriously because none was ambitious enough to fix more than one serious discrepancy. It was, and is, much healthier to admit that as it stands BBC is seriously at variance with the facts (observations). Some of it might be right ( e.g. expansion) and it is certainly hard to think of a plausible alternative. But it is much healthier for now to admit that BBC has failed. Trying to keep it alive, (Like Ancient Greek medicine) is the kind of fuzzy thinking which can hold up progress for generations, millennia perhaps. BBC has failed — we’ve got to start again.

Looking at the wider picture beyond Cosmology, we can see just how fundamental Ockham’s Razor must be to clear thinking of all kinds, from Astronomy to Military Intelligence. What was lacking was a transparent explanation of just how and why it works, but now the Detective’s Equation (i.e. Common Sense) has supplied that.

Ockham’s Razor must surely be one of the cornerstones of all serious systems of thought, including Common Sense .

My detailed explanation of why Ockham’s Razor works is given at:

The best reference on the history and influence of Ockham’s Razor that I know of is Chapter 8 of Hugh Gauch Jr.’s volume “Scientific Method in Practice” CUP 2003. He goes so far as to say. “…. the scientific enterprise has never produced and never will produce a single conclusion without invoking parsimony. It is absolutely essential and pervasive.”

A readable but sceptical account of Big Bang Cosmology is In Search of the True Universe, by Martin Harwit, CUP 2013

P.S. Is there a quick way to check whether some hypothesis is unhealthily fuzzy? I believe there is: find out how many Free Parameters it has. BBC has 18. But so does The Standard Model of Particle Physics. That makes one wonder. That seems to be stuck in a cul-de-sac too: no exciting developments since the 1970’s . Umm. Do Quarks really exist? No one has actually captured one.[Constructing Quarks, by Andrew Pickering, Univ. Chicago Pr. 1984, makes for provocative reading].


October 23, 2020

Common Sense is our chief survival mechanism. It has seen us through a billion years of Evolution. Without it any organism would quickly go under. Watch any wild animal, even birds in your garden. They are constantly having to weigh the Odds of Opportunity versus Risk — and when they get it wrong they die.

Making decisions wisely will dictate the course of our lives: how we make a living, who to marry, where to live, how to raise our kids…… But how do we decide? Almost entirely by using Common Sense. But how does it work? They certainly don’t teach us at school or university. You might say: “But they don’t need to, we inherit Common Sense with our genes”. True enough, but today we live in such a changed world from our hairy ancestors that to apply Common Sense Thinking (CST) to it we need to understand exactly how it works. That means we have to learn concepts such as Bayes’ Gambling Rule, Categorical Inference and the Principle of Animal Wisdom (PAW)….., as anyone over the age of 14 could.

There is no room here to explain how CST works but if we look at some few of its manifold implications that might encourage readers to dig deeper:

(1) Philosophers don’t understand serious thinking — they never have. For instance the Ancient Greeks thought it was based on Deduction which, as one can demonstrate, it cannot be.

(2) If CST is an inherited survival mechanism, and we share 98 percent of our genes with chimpanzees, how come we can launch telescopes into Space while they are still struggling to crack nuts in the jungle?

(3) It turns out that, because of an invention made about three thousand years ago near Byblos in Asia Minor, humans have multiplied their capacity to use Common Sense a million-fold .

(4) If that is so, does that mean that some other animals might be, genetically speaking, just as smart as us? Very probably yes. For instance Sulphur Crested Cockatoos have solved the Population Control Problem, which seems to be alas, entirely beyond us.

(5) All serious thinking turns out to be provisional. One’s conclusions can always be overturned by new evidence. Thus Certainty is unattainable in the real world! This has profound moral, philosophical and historical consequences. All civilisation and progress must rest on provisionality, and thus tolerance.

(6) It is possible to demonstrate, using CST, that even small amounts of dishonesty can fatally handicap any agent involved in a competitive situation, be it an individual in society, a firm in business, or a nation at war. ‘Nice guys come in last’ is complete nonsense. In the long run ‘Honest chaps will come in first’.

(7) The secret of Science’s success is not just Logic, Mathematics, Experiment or superior evidence; it is CST.

(8) Not all subjects are amenable to the scientific approach enabled by CST. For instance Economics and Psychology can never become sciences and are mostly hocus-pocus capable, like witch-doctory, of inflicting considerable harm. For instance the case for Free Trade, beloved of Economists, is , as one can show using CST, arrant nonsense. Indeed half-baked economics is the cause of much misery, including mass employment.

Those who would like to get to the bottom of Common Sense Thinking could read my paperback ‘Thinking For Ourselves’ [Amazon, 2020, 605pp, £14:50. There are exercises with answers on this site as well as stuff about the book in the ‘my books’ category] .Meanwhile there is more about the History of Thinking which you can download from:


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: