Suppose you have a large number of camels under slightly varying, very heavy loads of various things; about 40% of camels break their backs from overload.
You add extra straws to each camel's load, by accident. You observe a slight increase in the camel's probability of suffering the broken back - perhaps when you add 1000 grams of extra weight, the increase is from 40% to 41% . The common sense tells you to expect increase of 0.1% when you add 100 grams, and 0.001% when you add 1 gram - if you can plot a smooth curve of camel deaths versus weight, you would expect that you can approximate the curve with a line at small ranges - and you can expect that even if you add a single extra straw, there is a possibility that it would be the last for some unlucky camel.
Humans suffer from cancer, at a lifetime rate of approximately 40%; cancer is understood to be caused by a long, improbable sequence of mutations within a single cell's lineage. There is a very large number of mutations constantly occurring in the human body - vast majority of them not caused by external carcinogens.
Carcinogens, however, add a small number of extra mutations. Carcinogens are not expected to have safe doses - as the mutations are past the safe mutation rate - and the standards on the known carcinogens (including radiation) are thus extremely strict. No extra straws should be added to camels already at the risk.
The EPA standards for carcinogens - including radioactive contamination - are thus set to be as low as technically feasible. Strictness of the standard is not related to the danger, but to the ease of prevention. When those are exceeded, it is unacceptable, but is not a very big deal for you personally.
The EPA's standard for radioactive iodine in drinking water, in particular, is about 0.111 Bq/L . When this is exceeded by a big factor of 100, that is entirely unacceptable in the sense that the nuclear reactors have not performed as well as was deemed technically feasible - and that is entirely unacceptable because it can cause a few extra deaths in large population. But it is, in itself, not a reason to be afraid.
There is a second set of standards, set by relative threat to human life. Those are substantially more permissive. When food products exceed those standards, however, products have to be disposed of. Those standards are typically in the range of hundreds Bq/L. When those standards are exceeded, there is a sufficiently high risk to human life as to implement active measures to prevent consumption of contaminated food or drink.
Note: the camels are only an allegory. Of course the mechanics of back breaking and cancer are very different. However, both represent the situation where the normal is already unsafe and the extra risk is small.
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