The Dumbest Graph of all Time

It's the dose rate profile, stupid!

Figure 1. The dumbest graph of all time.

Practically every discussion of radiation harm models starts and finishes with some version of Figure 1. The debate rages as to what is the shape of the response (in this case, cancer incidence) to the dose. This graph is also the basis for LNT-cannot-be-disproven argument. The LNTer will say look at the left lower corner. There is so little difference in absolute terms between all the curves at the very low end, it is statistically impossible to separate them. LNT cannot be disproven. LNT is the simplest. Ergo, LNT.

Where is the time dimension?

This dumb graph encapsulates three major errors. The most glaring is made by the anti-LNTers. In focusing on the dose, all sides are implicitly accepting the premise that the only thing that counts is the cumulative dose. In reality, we do not receive the dose; we receive a dose rate through time. Dose rate profiles range from an extremely high dose rate over a very short time such as an X-ray, to a low dose rate over a lifetime, such as natural background.

Nature has equipped us with an amazing ability to repair radiation DNA damage. She had to do this to cope with the internal damage from our oxygen based metabolism. But repair or cell disposal takes time, up to a day. The one thing that our repair processes have a problem dealing with is two or more closely spaced double strand breaks (DSB). Such damage can lead to viable misrepairs. A tiny proportion of the resulting mutations can lead to cancer. If the dose rate is high enough, the inventory of currently unrepaired DSB's will build up, and the chance of two closely spaced DSB's rises rapidly.

When they focus on the dose, all sides in the debate are ignoring this all important process. But only the LNTer is being consistent. LNT is the only radiation harm model that posits that the only thing that counts is the dose. We can see this by dividing the dose rate profile into time chunks, Figure 2, based on the repair period. Only LNT says the harm associated with adding up each repair period harm separately is the same as the harm associated with the dose that is the sum of all the repair period doses. This property is called superposition. It's the definition of linearity. By focusing on the dose, the opponents of LNT have accepted LNT.

Figure 2. Example individual dose rate profile

All the response curves are nearly the same as the low end

The fact that Figure 1 ignores the all important time dimension would be enough to make it the dumbest graph of all time. But it cements its title by claiming that the differences between the curves at the low end are so insignificant as to be statistically indistinguishable. Nothing could be further from the truth.

The dose-response curve can be resurrected but only if it applies to the dose received within a single repair period, the hashed area in Figure 2. In this case, while the absolute difference at the low end may be tiny, what counts is the relative difference. To see the relative difference, we must use a log-log figure. Figure 3 compares LNT with SNT, a radiation harm model which claims low end cancer incidence goes as a bit more than the square of the repair period dose. To be conservative, SNT assumes the repair period is a day.

Figure 3. Loglog plot of Linear versus Sigmoid NT Excess Cancer Mortality

At a repair period dose of 25 mSv, the difference is a factor of 9. At 5 mSv, it is a factor of 60. At 0.1 mSv, the SNT curve is 6000 times lower and the models are diverging very rapidly.

This difference shows up most dramatically when we are dealing with release plumes spread over very large areas. Table 1 compares LNT and SNT for the Chernobyl release, using the Union of Concerned Scientists dose rate numbers. The UCS numbers are somewhat inflated; but, for present purposes, we can ignore that. Check out the last row. According to the UCS, 3 billion people outside Europe received 0.01 mSv. Per LNT, this will cause 3400 deaths. Per SNT, it will cause 0.0002 deaths. The difference is a factor of 17 million.

Table 1. UCS estimate of Chernobyl cancer statistical deaths excluding thyroid.

LNT cannot be disproven

The third reason why Figure 1 is the dumbest graph of all time is that it supports the LNTers' claim that LNT cannot be disproven, a claim that many people fall for including some anti-LNTers. This is like claiming that Newtonian mechanics cannot be disproven, because the difference between relativistic and non-relativistic motion of a apple falling from a tree cannot be detected. To test a theory, you must look for circumstances where it can be proven to be wrong. Einstein was great at coming up with good tests for his theories.

In the case of LNT, we do not have to look very far. We need only compare the response of people who have received a large dose in a single repair period, with people who have received a far larger cumulative dose spread over thousands of repair periods, Table 2. LNT says the cancer incidence for the second group should should be far larger than the first.

Table 2. Populations which have received large doses

Focus on the circled areas. In the top circle, we have the bomb survivors, who received their dose in a single repair period. In this group, we start to see a significant increase in cancer as soon as the total dose is much above 100 mSv. Call it 1% per 100 mSv, as LNT does. Now look at bottom group. Here we have people most of whom received 10,000 mSv or more; but that dose was received over a decade or more. According to LNT, just about all these people should have contracted radiation induced cancer. In face, we find no detectable increase in cancer in several thousand people. It's hard to be more wrong than that. Despite Figure 1, LNT is easily disproven.¹

Non-linear models such as SNT can replicate the increase in cancer when a sizable dose is received over a single repair period, and the lack of detectable harm when far, far larger doses are received more or less evenly over many repair periods.

There is no second.

In the original America's Cup race, as the American schooner was approaching the finish line, Queen Victoria asked one of the sailors onboard her yacht if the contestants were in sight. The sailor replied "Yes, your Majesty". The Queen asked who was first. "The America, your Majesty". The Queen asked who was second. "Your Majesty, there is no second". I submit that, when it comes to really dumb graphs, Figure 1 has no second.

1. There is also the fallacy of making LNT the null hypothesis. But we can't blame that on Figure 1.