The problem of scale in understanding the world around us
One morning early this week, I heard a news program which was interviewing candidates running for the Third Congressional district across the river in Washington. Three of the candidates, asked about their opinions of 'cap and trade' proposals, led their responses by vehemently denying that there was any "scientific consensus" about human causes for global climate change. They were of quite different opinions in their responses to the specific question, but I was struck by their strong assertions and lack of any specific data to support the position.
It reminded me of a problem I'd been struggling over some days earlier. The oil industry and government have asserted that slightly less than five million barrels of oil have flowed from the BP well in the Gulf of Mexico. What I was trying to imagine was how much that was in relation to the volume of water in the Gulf itself. Putting the BP Spill into perspective. is an interesting analysis of a different part of that issue.
Five million barrels seemed to me to be a lot, and undeniably it had bad impacts on the coastlines where it washed up, but I could not get a real sense of whether this was 'a drop in the bucket' or whether it was a bigger deal just in terms of volume. I understood a barrel to be a nominal but not real 42 gallon container and not the 55 gallon drums which we see in industrial sites everywhere. An American gallon is apparently a nominal .134 of a cubic foot. So I'm calculating a barrel as about 5.63 cubic feet. Which makes the BP spill about 28 million cubic feet? Round figures. So how big would that be? A different way of looking at it would be this. A swimming pool that was fifty feet long by fifty feet wide and uniformly twelve feet deep would hold slightly less than 225,000 gallons. So our oil spill would fill about twenty two and a half such pools. While those are darn big pools, that doesn't rank as very much volume compared to the whole Gulf of Mexico. If you put four of the pools together to form one that was 100 x 100, and then stacked the entire twenty two plus up that way, you'd have a pool about seventy feet deep and 100 x 100 feet in size. Looked at that way, it's tempting to say "heck, that's not such a big deal."
And, in fact, I think that's where the problem of scale comes into play. It may not seem like a big deal in terms of the plain volume to volume comparison. But it's hard to know impact simply from volume. If you had a one gallon jug of water, how much cyanide could you put into it before it was poisonous? I suspect not much.
My Dad, ever using his scientific mind, was always pushing himself and us to try to look at things with new eyes because he believed that new points of view could bring new insights. One of his favorites had to to with the atmosphere. He taught meteorology and was fascinated by things happening in the sky.
He would point out that Mt. Everest is about 9000 meters high. A regular US mile is about 1600 meters in length. Although Everest has been climbed without oxygen assistance, typically climbers use some oxygen above 5500 meters . So imagine if a friend told you to set out on a shopping trip, but noted that you would be wise to have an oxygen mask for assistance when you got to the 3.5 mile mark, and you would definitely want to have oxygen when you reached the 5.6 mile mark because you'd risk serious medical conditions without it. Were that the case, I couldn't even go from my house to Downtown Portland without oxygen! Take the example, then, and turn the road on its side. The layer above us is only breathable for less than six miles. That's a very very thin layer, not measured against the height of a human but measured against the consumption of six billion plus humans. Looked at another way, the diameter of the earth is nominally 8000 miles at the Equator. If you had a model of the earth scaled down so that the globe was one mile in diameter, the atmosphere could be represented as a layer about five feet thin.
Having a sense of scale. Makes a lot of difference. While we can look up at the infinite sky and the stars, it's a very thin layer that keeps us alive. And as with the question of toxicity and water, it's hard for the average person to make sense of the data, particularly when there are big numbers involved. Going back to my original observation about the political candidates, Recent studies strongly suggest that facts don't change people's minds which is a scary thing in itself. Logicians note that people have a tendency to commit the confirmation fallacy, selecting evidence which affirms their belief. (The Black Swan is a thought-provoking book which discusses this and similar issues affecting our thinking and decisionmaking. I think that many people, faced with numbing and almost incomprehensible facts, tend to select positions which are more comfortable over those that are not. And the scale of everything we see and weigh and research and examine is a big part of how that takes place in the mind. Reducing our measurements to levels we can intellectually handle, we risk becoming like the blind men measuring the elephant, unable or unwilling to see that we're in the midst of a universe and interactions of immense complexity. Simplification is dangerous.
It reminded me of a problem I'd been struggling over some days earlier. The oil industry and government have asserted that slightly less than five million barrels of oil have flowed from the BP well in the Gulf of Mexico. What I was trying to imagine was how much that was in relation to the volume of water in the Gulf itself. Putting the BP Spill into perspective. is an interesting analysis of a different part of that issue.
Five million barrels seemed to me to be a lot, and undeniably it had bad impacts on the coastlines where it washed up, but I could not get a real sense of whether this was 'a drop in the bucket' or whether it was a bigger deal just in terms of volume. I understood a barrel to be a nominal but not real 42 gallon container and not the 55 gallon drums which we see in industrial sites everywhere. An American gallon is apparently a nominal .134 of a cubic foot. So I'm calculating a barrel as about 5.63 cubic feet. Which makes the BP spill about 28 million cubic feet? Round figures. So how big would that be? A different way of looking at it would be this. A swimming pool that was fifty feet long by fifty feet wide and uniformly twelve feet deep would hold slightly less than 225,000 gallons. So our oil spill would fill about twenty two and a half such pools. While those are darn big pools, that doesn't rank as very much volume compared to the whole Gulf of Mexico. If you put four of the pools together to form one that was 100 x 100, and then stacked the entire twenty two plus up that way, you'd have a pool about seventy feet deep and 100 x 100 feet in size. Looked at that way, it's tempting to say "heck, that's not such a big deal."
And, in fact, I think that's where the problem of scale comes into play. It may not seem like a big deal in terms of the plain volume to volume comparison. But it's hard to know impact simply from volume. If you had a one gallon jug of water, how much cyanide could you put into it before it was poisonous? I suspect not much.
My Dad, ever using his scientific mind, was always pushing himself and us to try to look at things with new eyes because he believed that new points of view could bring new insights. One of his favorites had to to with the atmosphere. He taught meteorology and was fascinated by things happening in the sky.
He would point out that Mt. Everest is about 9000 meters high. A regular US mile is about 1600 meters in length. Although Everest has been climbed without oxygen assistance, typically climbers use some oxygen above 5500 meters . So imagine if a friend told you to set out on a shopping trip, but noted that you would be wise to have an oxygen mask for assistance when you got to the 3.5 mile mark, and you would definitely want to have oxygen when you reached the 5.6 mile mark because you'd risk serious medical conditions without it. Were that the case, I couldn't even go from my house to Downtown Portland without oxygen! Take the example, then, and turn the road on its side. The layer above us is only breathable for less than six miles. That's a very very thin layer, not measured against the height of a human but measured against the consumption of six billion plus humans. Looked at another way, the diameter of the earth is nominally 8000 miles at the Equator. If you had a model of the earth scaled down so that the globe was one mile in diameter, the atmosphere could be represented as a layer about five feet thin.
Having a sense of scale. Makes a lot of difference. While we can look up at the infinite sky and the stars, it's a very thin layer that keeps us alive. And as with the question of toxicity and water, it's hard for the average person to make sense of the data, particularly when there are big numbers involved. Going back to my original observation about the political candidates, Recent studies strongly suggest that facts don't change people's minds which is a scary thing in itself. Logicians note that people have a tendency to commit the confirmation fallacy, selecting evidence which affirms their belief. (The Black Swan is a thought-provoking book which discusses this and similar issues affecting our thinking and decisionmaking. I think that many people, faced with numbing and almost incomprehensible facts, tend to select positions which are more comfortable over those that are not. And the scale of everything we see and weigh and research and examine is a big part of how that takes place in the mind. Reducing our measurements to levels we can intellectually handle, we risk becoming like the blind men measuring the elephant, unable or unwilling to see that we're in the midst of a universe and interactions of immense complexity. Simplification is dangerous.
Comments
It should be someone's job to improve the way data/stats/numbers are communicated in the news, cos right now there don't seem to be many useful standards in place.
Basically, someone needs to raise the standards for the verbal communication of quantitative info, just like Edward Tufte did for data graphics.