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

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