or “Now where did I leave my glasses?”
An engineer, a mathematician and a physicist look out of a window of a train passing through the highlands of Scotland, and see a black sheep.
“Ah!”, says the engineer, “Look, they have sheep in Scotland!”.
The physicist looks at it and reflects “Well, we can say only there is at least one black sheep in Scotland”.
The mathematician looks at them both in surprise “That’s not right at all! All we can tell is that one side of one sheep in Scotland is black”
Ho. Ho.
This is one in a series of posts , about evidence and how it does or does not support a claim.
Such pedantry is over the top, but it serves to illustrate a simple point about what we can really infer from a piece of evidence, and its limitations.
It’s easy to decide what to believe when you have clear positive evidence in your hand: the photo of your girlfriend in bed with that sysadmin from finance is fairly firm (heh) evidence of her faithlessness.
It’s not so clear when there is no evidence for something, and interestingly there is more than one way in which we can not have evidence for something.
‘Bounding’ what we don’t know
Those who are old enough will know what it’s like: we lose our reading glasses, or the screwdriver, or pen or mug of tea we had in hand only a few minutes ago.
At this stage, if somebody rather stupidly asks “Well where did you leave them?” we would rightly and angrily reply “I don’t know, if I knew where they were, I wouldn’t have lost them”.
So we don’t know where they are, but we do know some places where they are not. They are not on Mars. And although we may not remember all the rooms we’ve been to since we last remember having them, we tend to remember unusual places; mine are not, for example, in the attic as I know I haven’t been there.
This gives us some limits, some ‘boundaries’, to the area of ignorance.
Reducing the area of ignorance
As we start to look we start to limit these boundaries further.
A quick walk around the usual rooms glancing at the surfaces for example is a good first stage search; it covers a lot of ground for a fairly likely result.
By discounting the places we’ve looked – and by starting with the most likely and easily surveyed places – we reduce the places the glasses could be.
“Knowing it is not” is not “Not Knowing”
Having thoroughly searched the mostly empty fridge, I know to a high degree of confidence that my glasses are not in there.
I have no evidence of that, and I have no proof that they are not (I may have forgotten to search the bowl of three week old leftover gravy) but my memories of looking are ‘evidence of no glasses in the fridge’ (‘evidence of lack’) rather than ‘no evidence of glasses in the fridge’ (‘lack of evidence’).
The latter though is still how you might reply to “Are they in the fridge?”, even though it doesn’t capture whether you’ve looked or not.
This causes problems when people want to know if there’s any danger in some treatment or chemical. To be told “There is no evidence of any harm” is useless; it doesn’t tell us if nobody’s checked, or if they’ve had a quick look and everything seems fine, or they’ve had a really very thorough search that would have turned up any significant harm and found nothing.
What we think we don’t know
So I continue with my exercise in limiting my ignorance, hoping one day to find my glasses so that I can carry on doing what I was doing… whatever that was… it will come to me in a moment… and sometimes we get a bit irrational. How many times, frustrated, have we looked in the same box, under the same small piece of paper that couldn’t possibly hide a pair of glasses?
Similarly our boundary reducing exercise is not ‘certain’; it may be I’ve looked somewhere but not seen them (after all, I’m not wearing my glasses). It may be I’ve looked in an area where they are hidden, and have declared and marked the whole area ‘glasses free’ when in fact it is not.
In more general terms, not finding doesn’t necessarily mean it’s not there: just because all the swans I’ve seen are white, does not mean there are no black swans.
This is where we reach the limits of our understanding of our limits of our ignorance. We rarely properly match the boundaries of what we think we don’t know with what we actually don’t know.
This gap is where my lost glasses still lurk when I give up and use an old pair: in the world of places I haven’t looked well enough, but can’t think of to look.
Theories of what might be
I was slightly too certain above about where my glasses are not, as aliens might have stolen them and taken them to the Mars.
And if we return to the railway carriage with the sheep-observing pedants, we might claim that “There are luminous pink sheep in Scotland with legs on one side shorter than the other. Scostmen hunt them down and turn them into haggis and bagpipes”.
We can make up any silly story we like (“Aliens live in clouds!” “Pixies ate my hamster!” “Magnets healed my cancer!” “Hair loss makes you sexy!”) and some may be accidentally true but it’s no more sensible to assume they are true without evidence than it is to believe in Garibaldi Mountain Shrews.
Not knowing something is no excuse to make up any old thing and then believe it to be true, any more than it is to believe that your glasses are in the kitchen, because you don’t know where they are, and they could be.
This is the ‘out’ for a lot of so-called ‘open minded’ views: “Just because you haven’t seen pixies, you must be close-minded to disbelieve them”.
Pixies might exist, this is true.
But when you consider all the things that might exist, such as invisible baby-eating multi-coloured pixie-swans that live with aliens in clouds, then you can see that believing in any random made up fantasy can be fun but it’s not very practical.
If someone tells you some far fetched story and says “well, you’ve got no evidence against it, so it could be true couldn’t it?” then the answer is “yes, and aliens are painting your ears”
“I don’t know”
A straightforward ‘we don’t know’ seems a bit of a cop out, and the mind abhors a vacuum, but this is no excuse to fill it with speculation and then infer ‘truths’ from them. (It’s fine to speculate and test: Perhaps the glasses are in the bathroom? I shall go and look)
Even if you’ve only ever seen white swans, you can’t be sure that all swans are white. You just might not have seen one that isn’t.
Yet lack of evidence is not evidence of lack; just because we haven’t seen something doesn’t mean it’s not there.
It’s alright to say we don’t know. It’s alright to say we think things are likely, or unlikely, but we’re not sure. And working out what we don’t know – or what exactly we’re not sure about – tells us a very valuable thing: what we still need to find out in order to know.
Background evidence
The above of course is a bit “simple”. It ignores all the background evidence we hold; there are very few sheep with black on one side and white on the other, so we can happily infer that a sheep is black from seeing the one side of it that is. This is material for another post…
