Lets say I'm telling a story about some hiker heading up into the mountains. I mention that when passing under a cliff a pebble came loose and landed on him. That might sting but it wouldn't occur to you to ask if he died. Lets say that instead I mention that a boulder had landed on him. Then you'd expect him to be quite dead.
That's the nice thing about these old English words that've been around a while and encode distinctions that make sense in our everyday lives. The difference between the pebble and the boulder is just a matter of degree but it's one where the quantitative difference is big enough to become qualitative. If we just had one word whoever I was telling the story to would have to ask questions and because we run into rocks so often I'd know when I'd have to use an adjective.
When you're talking about scientific things, though, you don't often have this choice of words. Energy is energy and you're expected to use a number if you want to say whether it's a lot or a little. Same with radiation. The radiation emitted by your cell phone is so subtle you'd never be able to perceive it but a large enough amount of that same type of radiation could cause incredible pain or even cook you alive.
So "radiation" as a word can be dangerously ambiguous even before considering how it's frequency effects things. "Ionizing radiation" is a completely different beast in terms of hazards even though we often use the shortcut "radiation" to refer to it too.
And the word "radiation" quickly brings us to the word "fallout." In the first hydrogen bomb test at Bikini Atoll the explosion was even large than scientists anticipated. Huge amounts of calcium from the coral of the atoll were sucked into the fireball. It was bombarded with neutrons and transmuted to elements that were ferociously radioactive. The bunker built for the observers was barely enough to save them from the radiation as particles of this radioactive material rained out of the sky. Far downwind, the crew of the Lucky Dragon fishing boat were also exposed. They were burned and sickened and one of them died.
The public soon learned that radioactive fallout was a deadly serious matter. Bombs that explode high in the air aren't so bad, the nitogen, and oxygen that make up most of the air can get whacked by neutrons and not turn into anything too unpleasant. But the ground is another matter and nukes detonated close to the ground to destroy command bunkers, missile silos, hardened aircraft hangers, or sub pens would send plumes of deadly fallout downwind.
There's a website, Nukemap, you can use to play around with if you feel like frightening yourself about nuclear wars. According to it a 5 megaton ground explosion in New York could, if the wind is blowing the wrong way, deposit about 1 Gray/hour's worth of fallout here in Boston. The single Gray from the first hour would be enough to give me radiation sickness but not kill me but unless I could get to shelter it would keep building up. I'm not quite sure how to figure the decay curve but without a shelter I'd either die in a day if I was lucky or die in a couple of weeks if I wasn't.
So fallout, in this context, is an immediately lethal threat. A deadly danger which people believed, entirely accurately, would probably kill you if you were exposed to it.
In this context it's very understandable that when people heard that the Three Mile Island nuclear plant had released radioactive fallout, they were just a tad concerned.
The problem is that we were using the same word, fallout, to refer to both the 10 gray doses that'll kill you dead quickly in a nuclear war and the .0008 gray doses you might get around Three Mile Island which would increase your lifetime odds of getting cancer by about 5 in a million assuming the most pessimistic model of radiation induced cancer. There's a unit people have put together called a micromort for thinking about very small chances of death. Assuming that all cancer is deadly the radiation was 5 micromorts which is about as dangerous as going scuba diving or driving 1000 miles by car. Not so small a risk that it doesn't deserve respect but small enough that it doesn't deserve fear.
Fukushima had similar levels of radiation released. Expose millions of people to a several micromort risk and you will get deaths at a population level but again, not at a level worth treating with fear rather than caution. Chernobyl, well, Chernobyl occupied a "stone" level between the "boulder" level of World War III's fallout and the "pebble" fallout of Three Mile Island.
I've talked like the effect of using one word for two very different situation has been all about making people too afraid of small amounts of fallout but that's not the only direction this confusion goes in. Growing up after the Cold War and MAD and only worrying about radiation from power plants I had this idea that fallout was something that would maybe give you cancer after a few years and that mostly people had fallout shelters during the Cold War as a matter of long term health rather than short term survival. I was very badly misled by my understanding of the term. I think that this is a problem for people of my generation that while we might be more afraid of radiation from reactor meltdowns than we should be we also treat the idea of fallout from a nuclear war with inappropriately low levels of terror. Terror is the appropriate response to the continued existence of the huge US and Russian nuclear arsenals and when we think about the dangers that may face humanity it's important to remember that the shadow of the mushroom cloud hasn't gone away.
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