QUANTIFYING UNCERTAINTY IN AN UNCERTAIN WORLD


In November, 1958, three boy scouts died on Mt. Wrightston, a 2900 meter peak (9453 feet) that rises 1200 meters from the valley floor.  Mt. Wrightston is my favorite hike in southern Arizona.  I have camped on Baldy Saddle (2600 meters) 5 different times, in snow and hot weather, and I have been to the top another dozen times.  On Baldy Saddle, one has simultaneous views below to the western desert, where Green Valley and I-19 are located, and to the eastern valley, where Sonoita and Sierra Vista are visible.  I’ve been on the summit at sunset, alone, with s spectacular 360 degree view and swifts soaring above me.

The scouts died because they hiked in a warm day, and a sudden cold front hit them, with a heavy early season snowfall.  They died from falling and hypothermia.  Today, this would not likely happen.  Weather predictions would have warned against a heavy snowfall, and the warm weather (“the warm before the storm”) would not have changed a winter storm watch, which today would have been posted.  This scenario is playing out in New England as I write.

Weather models showed that a storm would hit New England on the second weekend in February.  On Thursday night, New England was clear.  But every weather model and weather forecaster predicted that two storms, at the time about 1600 km from each other and from New England, would strike New England the next day.  This is exactly what happened.  This is science helping give people time to get emergency supplies and be prepared.  We aren’t praying our way out of this storm:  it is coming, we know where it will be, and we will have a good idea of how much snow will fall.  There will be some differences from what is forecasted, but the major event will take place, and it is science that is used to make this forecast.  I stress science, because members of the House Science Committee included Todd Akin, of “a woman’s body blocking pregnancy from illegitimate rape” fame, and Paul Broun, who, still present, doesn’t believe in climate change, the Big Bang Theory, and evolution.  He does believe in the pit of hell, for which I have no evidence; I have plenty of evidence supporting the other three concepts.  Broun and others would love to defund NOAA and the NWS, hoping, presumably that their states (Missouri and Georgia) would not be devastated by either tornadoes or hurricanes.  Given their location and climatology, this is not likely to occur.

Indeed, this is crazy thinking, and I can’t put it any other way.  We can predict with high confidence major tornado outbreaks and hurricane landfalls and strength.  To stop funding these organizations is akin to being the Taliban in this country, and I know exactly what I am saying.  Both of these men, in fact, are more restrictive on abortion than is the Taliban, and that is also a fact.  But back to science.

When I practiced neurology, I used to anti-coagulate patients with posterior circulation strokes, because at the time, this was felt to be the appropriate treatment.  It became evident that the consequences of anticoagulation were worse than any potential benefits, and I had to stop the practice.  That is science acting.  I did what I thought was best, and when it did not work, I changed what I did.  Many doctors, when faced with evidence that surgery for asymptomatic carotid artery stenois was more risky than no surgery, still operated.  I took a great deal of heat for my beliefs, but I changed my practice.

A while back, I got into a Facebook argument with someone who did not believe that manmade climate change was occurring.  He asked me to make my case without using models.  Why?  Perhaps it was because this individual was a realtor, and we all know what happened to the housing market, when mathematical models failed to include the possibility that prices might actually decline.  The fact that one is a realtor and not a scientist does not a priori make his arguments specious, but his quoting a magazine that was not scientific and had significant right-wing biases in unrelated articles hurt his case.

The Facebook argument occurred for a short while, before I quit, out of respect for the individual’s “wall” on which I was posting.  I let my “opponent” have the last word.  What he used as “proof” was an 8 year trend line, without regression diagnostics, that showed the Earth was cooling.

Let’s discuss trend lines briefly.  They are regression analyses of scatter plots, data points tracked on two axes.  For a regression analysis to be accurate, one has to assume the residuals, the difference between a data point and the line generated, are normally distributed (have a Gaussian distribution or a bell curve) with equal variance.  Regression requires this.  In addition, there are several other diagnostics one should use, looking at outliers and other aspects of the data.  Nowhere in the article that the person quoted was any of this mentioned.

Why would I not use models?  Statisticians use models all the time; most scientists do.  We model the weather using a variety of weather models.  I find some to be very good; the predicted rain and strong cooling that Tucson has as I write was a significant likelihood to me about a week ago.  I could see the jet stream predictions, and when they held up day after day, I became more confident.

We model the Earth’s climate the same way.  The fact that models may be wrong does not make them a bad idea.  The fact that models differ does not negate the whole concept of modeling.  Models may use different initial conditions and handle variables differently.  They change over time, as new data become available.  What we believe in science changes with time as we get more data.  But climate change models are all trending in the same direction; the biggest area of disagreement is that they appear to be underpredicting what is going to happen.

The classic issue of weather modeling occurs with hurricanes, where there are “spaghetti” models–several–each indicating a slightly different track.  Next hurricane season, follow these tracks from the beginning through the end of the hurricane.  Notice how the uncertainty gradually decreases; indeed, the uncertainty in forecasts is far less than it was 25 years ago.  There is not a weatherman discussing these models who does not allude to uncertainty and multiple possibilities.  The fact that there is uncertainty doesn’t mean the models are worthless and that we know little.  The world is uncertain, including the high temperature tomorrow, although we can quantify the uncertainty very well.

Let me quantify uncertainty a little better, using a common example.  If you throw two dice, there are 11 different sums they may show.  To some people, each sum has the same probability.  Anything can happen.  But if I were betting, I would put my money on the sum being 7, and if I were allowed three different sums, I would choose 6, 7, and 8.  These are far more probable then the others: a sum of 2 has a 1/36  probability; a sum of 7 has a 1/6 probability; 6,7,or 8 has a 4/9 probability.  Roll dice 100 times, and you won’t get these exact numbers, but you will be very close to them.  Roll them 1000 times, and you will be very, very close, but probably not exact.

I believe low probability events are poorly understood by many.  The probability of winning Power Ball is about 1 in 110 million.  If we have 220 million players, we would expect 2 winners.  We might, however, have 0,1,2,3,4,5,6,7 or 8 winners.  But 98% of the time there will be 5 or fewer winners, and there is a 1 in 7 chance that nobody will win.  An individual’s chance of winning, however, YOUR chance, is equivalent to picking a random minute I choose between today and the signing of the Declaration of Independence.  Small wonder some call gambling a tax on those who do not understand math or probability.

In Carl Sagan’s book , The Demon-Haunted World, Science as a Candle in the Darkness, he alludes to one problem that really bothers many religious people about science:  science is often right.  We can pray our kids don’t get polio, or we can vaccinate them.  Vaccination has practically eliminated polio in this country–for now.  I am concerned what will happen when a very large cohort of unvaccinated children here are exposed to the virus, which they will be.  Religion and science really aren’t at odds, but when either is misused, it causes a lot of problems.

I am going to Uganda in November, because on the 3rd, in the late afternoon, there will be a 22 second total solar eclipse.  I didn’t pray for this eclipse, I didn’t read it in any religious work, and I’m not wishing and hoping for it, except for clear skies in which to see it, because we cannot yet predict local weather months in advance.  Climatologically, there is a decent probability, but on the given day, it is quite likely I may not see the eclipse, even though it will take place.

I am alive today because scientists found cures for Group A Streptcoccus, which infected me many times, and I got neither rheumatic fever nor acute glomerulonephritis.  From science came the concept of putting a pin in a femoral neck fracture, so when I broke my hip, an orthopedist could put me back together.  So I could walk.  And run.

And hopefully see a total solar eclipse in Uganda.

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