06 September 2012

The Relativity of Wrong

Recent political comment brings me back to a point I'd written about before, under the label of Successive Approximation.  The better title, unsurprisingly, is Isaac Asimov's The Relativity of Wrong. 

I first became aware of Paul Ryan's lie when my wife asked me, having mentioned nothing about context, whether a runner could conceivably mis-remember his marathon of somewhat over 4 hours as having been somewhat under 3 hours.  As has been reported in many places, and some reporters having done some experiments, the answer is no.  It is completely implausible that someone, especially someone with only one marathon, could make that mistake as an honest mistake.  Confusing a little over 4 for a little under ... maybe.  You would likely have trained for some time under 4 and that number could have stayed with you longer than your disappointment in not making your goal. 

But confusing your over-4 hours, a perfectly respectable time to cover a marathon if nothing to brag about for an open class man, for sub-3 -- a time that entitles you to some bragging (as a friend worked to earn the right to) and is achievable only with some serious training and talent -- is not an accident.

The political side of this, well, not so very interesting.  Except for the fact, perhaps, that Ryan is supposed to be a leading light for Republican number-crunching.  Number types are even less likely to make a mistake like that.  At least as a mistake. 

More interesting, and perhaps useful, to the local purpose is to look some at how to assess the relativity of wrong.  The route I took in the successive approximation post was quantitative.  Some articles have taken something like that, observing that his claimed time was about 70% of his actual time, or, conversely, that he lied by about 30%.  That's actually much too generous to his lie.  The problem with that is that if he had claimed the world record time (a bit less than 2 hours faster than he ran, as opposed to the somewhat more than 1 hour of his actual lie), it would only be scored as 50% wrong.  You can't run faster than the world record, or you'd be the record holder, which even Ryan didn't claim.  So, the most he could have lied by is about 2 hours (iirc his actual time was 4:01, and the world record back then was about 2:07, so 114 minutes).  His actual lie is about 65 minutes (taking 2:50-something as 2:56) wrong, so 57%, more than half, of the span that he could possibly have lied by.  That could be refined some by comparison against, say, the race winner's time, or the Olympic qualifying time.  But you get the idea.  And the 57% is about double what the other approach shows.  Compare how wrong something is with how wrong it could be.

But some things, and this is where I'll especially invite comments, don't lend themselves to that kind of quantification.  For instance, I'm comfortable with saying that it is more wrong to say that the earth has no greenhouse effect than it is to say that CO2 is not a greenhouse gas.  But how can we assess this comparative wrongness with the error in saying that CO2 levels have not risen over the past 200 years?

So I'll invite description of approaches to assessing relative errors, preferably with examples.  Note, too, that it's best to have them be objective examples -- so which candidate is better kinds of things are not going to work.  Marathon times and the radiative properties of the earth's atmosphere aren't partisan matters.


William Connolley said...

If you're trying to measure wrong, in something like marathon times, or just general speed, then you need to account for the "difficulty of difference", which you'd have to scale by something, possibly proportion of people able to get that time, rather than a simple linear time difference. So claiming sub-3, which only, say, 5% of runners can achieve when you're really 4, which perhaps 30% can get, makes you some fn of 5% and 30%.

On a similar note, his mountaineering record appears open to question too: http://www.theatlantic.com/politics/archive/2012/09/paul-ryan-mountaineer/261904/

kyril said...

Well, I would generally apply the following test for relative wrongness:

If Proposition A is only true when Proposition B is true (i.e. B follows from A), and if both are false, then A is at least as wrong as B.

If A does not also follow from B, then A is more wrong than B, because in order to believe A, one must also believe B, but one can believe B without believing A, and obviously believing wrong claims A and B is more wrong than simply believing wrong claim B.

So clearly it's more wrong to say that the Earth has no greenhouse effect than it is to say that CO2 is not a greenhouse gas, because if the Earth has no greenhouse effect, then (given that CO2 exists on Earth) CO2 is not a greenhouse gas.

Now, the claim that CO2 is not a greenhouse gas is basically a claim about the spectral properties of CO2. It could be a broader claim - there's no such thing as a gas, greenhouse gases don't exist - but at its narrowest, it's a claim that carbon dioxide doesn't absorb and re-emit light at the wavelengths we think it does.

If that were the case, it would call into question all data points on the instrumental record that were measured with instruments that rely on the spectral properties of CO2. That would be enough to make the weak claim that "we don't have enough evidence to conclude that CO2 concentrations have risen in the last century."

So I would say fairly confidently that the claim "CO2 is not a greenhouse gas" is more wrong than the claim "we don't have evidence that concentrations have risen."

The stronger claim, "we have evidence that temperatures have not risen in the last century," is harder to analyze for relative wrongness because it contains a claim that's logically unrelated to the ones we're discussing.

Alastair said...

It seem s possible to me that an occasional marathon runner forgets that his respectable time was just over four hours and confuses it with just under three. But is that any different to scientists claiming that the Arctic sea ice will melt at most down to just over four million sq km when in fact it has collapsed to around three and a half?

Whose crime is worse? Aren't we entitled to an apology from the scientists?

Cheers, Alastair.

Kevin O'Neill said...

A decade ago I wrote this little blurb that speaks to the relativity of wrongness:

There is no crime in being ignorant. We are all ignorant on different subjects. I am ignorant on most things Canadian. I don't know how many provinces they have, couldn't name all of them, haven't a clue what the population of each is, etc., etc. You name it -- if it's Canadian -- I probably don't know it. It's nothing to be proud of, but neither is it something of which to be terribly ashamed.

But then, I'm American. They taught us mostly US history in school. If I were a Canadian and didn't know those facts about Canada, I'd have to be pretty stupid. And there are stupid Canadians just as there are stupid Americans and stupid people of every nationality, race, creed, or population grouping of your choice.

Ignorance and stupidity are generally identified by a lack of knowledge. Insanity is a little different. The insane know something is "true" despite overwhelming contrary evidence. It's one thing to be wrong, it's another thing to persist in being wrong when every fact is against you. Often these loonies have conversations inside their heads (delusions) that justify their beliefs. Just completely irrational.

Evil. Knowing right and doing wrong -- intentionally, with eyes wide open. Generally as a result of avarice or a lust for power -- or for the sheer joy of corrupting something good. Evil knows.

As I go through life I play a game. The rules are simple: Observe conservative right-wing zealots, and then identify them correctly as ignorant, stupid, insane or just plain evil. Each of them will fall into one of the four categories, but sometimes it can be difficult to decide which one.

Now this only has a four star grading scale, but it's a start :)

Anonymous said...

Memory's a funny thing, and more so than you guys undoubtedly having memories on the sharp side of normal may realize. Here are three examples of how weird it can be from my own experience. (I should add that everyone around me tells me my memory is bad.)

1 I had had a valuable half-inch socket set for many years. It was in a big red metal box. I didn't remember having used it since we moved into a new house and rented out the old house, but one day I needed it, and couldn't find it. I distinctly remembered having stored it between two boxes on a particular shelf in a particular cupboard in the garage, but it was no longer there. We had had a boarder in the new house who had since shifted out, and an electrician and a tiler had been doing work, and all could have had access to it. I kept going over who could have taken it and toying with going to the police, but had no proof or idea who was more likely than the other to be the thief. I felt angry but helpless for a long time. Months later, I went back to the attic of the old house, and there it was - I had never even taken it to the new house. Since then, I vaguely remember that it might have been my much smaller, cheaper, socket set in a blue metal box that I was thinking of when I thought the good one had been left in the garage.

2 My library told me I had not returned a book, but I remembered, again distinctly, having put it through the after-hours return slot a few days earlier. I was highly disillusioned with a library system that enabled books to get lost between the return slot and the shelves, and I argued with the librarians. I would have been comfortable with swearing in court that I had returned it. Then a few weeks later, I was cleaning out the car and found it under the driver's seat. I had had the intention of returning it, and had put it in the car, but must have confused my memory of putting another book through the slot. If, in fact, I had been in the situation of stating what I believed in court, anyone later on would have felt quite justified in accusing me of lying under oath.

3 This next is one where I know my memory's limitations, because it's always happening to me. If I buy something for $1.99, I always think of it at the time of being $2, because who cares about 1 cent, right? A while later, when I come to recall what it cost, I may have the figures 1, 2, and 99 all in my head to varying degrees. So, what did it cost? I probably have the vague feeling it was something 99, but was it 1.99, or 2.99? I no longer have a clue, yet percentage-wise they are wildly differing figures. At least with this sort of example, I'd never even consider swearing what the original figure was.

By the way, the first two examples make me wonder what percentage of uncorroborated witnesses' statements, sworn under oath in court, by completely honestly-motivated and upstanding citizens, can actually be relied on.