"And, while it is extraordinarily unlikely, all of those million-odd unstable cesium nuclei could spontaneously decay all at once."

Just to note--this is a physicist's "unlikely", which is subtly different from the layman's "unlikely". It's entirely possible that a glass of lukewarm water would spontaneously transform into a set of ice cubes floating in hot water, but it's profoundly unlikely in the same sense.

I wish to describe the situation I as understand it and this point in the series. I am a laymen: I am not a scientist nor am I a doctor but I do have some science training and some medical training. The the extent to which I am wise I am a better person for my disparate training but to the extend to which I am arrogant, my little training in these fields makes me dangerous. I will admit to being quite arrogant.

I've been fallowing this discussion, Mr. Aaron and also the comments. It is something which interests me in an academic sense but I am still more scared of all of the chemical poisons around me then the radioactive poisons. I suspect that more cancers are caused by chemical byproducts of industrialization then by radioactive ones but I have been reminded of my ignorance on the issue of radioactivity and approach the problems of it differently because of your efforts. I thank you for them.

I don't think that this particular post questions the linear low dose model but questions the amount of dose one receives. This is dependent on the definition of dose, of course. What you describe here, I believe is a link between exposure and dose. For my own discussion I will take exposure to be in the vicinity of radioactive products or the internalization of radioactive products and a dose to be the absorption of a radioactive decay product by the body.

Given the discussion of yourself and others, I suspect that dose fallows a logistical harm profile: given that the body has absorbed a certain amount of decay products, initially the body can cope with it, then the coping mechanisms break down and the higher the dose the more it negatively effects things, then when there starts to be a risk of death, the risk approaches a flat-line of guaranteed death. At any point the model could be locally approximated by a straight line but in a logistical model and where the high dose is measured, the high dose linear approximation extrapolated downwards to low doses will undoubtedly underestimate harm at a given dose and overestimate a safe threshold. For low doses, however, the model appears to increase exponentially.

From this post, it seams to me that the expected dose received is linear to the amount of exposure but the maximum reasonably expected dose, for small doses, is logarithmic to the amount of exposure (I would think, it should be x+I*sqrt(x) where x is the amount of exposure (in curries) and I is the measure of what is reasonable and has units of root curie and this would hold for the entire range). In either model the expected dose monotonically increases with exposure and the chance of getting N doses also monotonically increases with exposure.

In either case, if both models hold, then the exponential behavior of low dose harm would dominate in determining risk of harm from exposure. It should also be noted that the way exposure happens is important. The route (in the same vicinity of a cloud of gas vs. digestion of an amount of the substance, for example), the chemical properties of the substance, and the byproducts of the substance all matter. It seams that a danger calculation needs to be made for each different isotope and route to have an accurate model but overall a combination should be used to get from exposure to harm which would look mostly logistic for all cases.

One other this to point out, for everyone dosed more then expected for a given exposure there is also likely someone dosed less then expected for a given exposure. For safety purposes, one should use a reasonably high (or reasonable safe) exposure to dose model, but use a linear exposure to dose model for calculating damage expectations once damage has occurred.

"The dose increases, of course, because the average number of disintegrations has gone up – but the likelihood of extreme events goes down. The net effect of these two conflicting trends is a slow increase in the frequency of dangerous, large-dose events with increasing (but small) levels of radioactive contamination in the environment."

Intuitively, I see how the increase in magnitude of large-dose events increases slowly with an increase in concentration at low levels, but it's less obvious how you reach the conclusion that the frequency of large-dose events increases slowly as well.

Actually, the one interpretation I've seen that begins to make sense of the evidence says the underlying reality does not involve chance. Which means the answer to your previous question is, "You killed my brother. Prepare to die."

But the math still has a hole if we assume that all 'worlds' contain conscious observers. So the world where all the cesium decays at once might act like a brief reflection that never comes alive. Ask me again when we figure out what "observer" means.

hf

My wife just spent half an hour last weekend talking to Inego Montoya's wife by happenstance when in NY, and she told Mrs. Inego that we often use his famous words in our family, which as a bunch of goofballs we do, and she told my wife that they do in their family too. Just thought you might like to know that bit of trivia even though it doesn't involve a cab driver.

As for the science, I've read it several times and am not close to following it all, but I get some of it. All I know for sure is that I could find an expert with good credentials to agree or disagree very impressively with aaron either way if the money was right. I don't think this is so different from how real science works, but I'm not thomas kuhn.

All the different units drive me crazy. Centimeters to inches is too much for me. Aaron is really good at making this stuff comprehensible given that I can get roughly close to almost being able to following along without devoting days and days and days to it. Good job Aaron! The physics for dummies crowd applauds you.

I

Many professional disciplines use a strange lingo then wonder why the layman in the public does not read it.

I read all of that, and God bless you Mister Datesman, for learning and knowing all that stuff. But now my brain hurts.

Dredd, comments like those are why we can't have nice things.

nice blog, will come back later :-)