# Math Camp

## Corner Reflector

Uses of the Corner Reflector

## Solar System

Exploring the solar system

## Goffman, John

Poisoned Power, Forward

$$R \times h \times \frac{N}{300~\mbox { person-rems}} \times {\rm 1~death} = D$$
where

$R$ is the number of rems per hour,
$h$ the number of hours exposed
$N$ Number of persons exposed
$D$ number of deaths which will occur later.

## From the BEIR VII

Analysis of Hiroshima survivors shows (Figure ES-1) that when the estimate dose was 2 Sv the Estimated Relative Risk of dying by cancer was 1. This means that this dosage resulted in twice as many cancer deaths as in the rest of the Japanese populate.  The data assumed that exposure was at age 30 and counted deaths up to age 60.

In order to relate these statistics to the formula given by Goffman we assume that 22% (22 000 out of 100 000) of the population dies from cancer. An ERR of 1 would imply 44% would die from cancer (not including leukaemia). Thus the 300 person-rem number in the first equation would be different from this analysis.

Let $\rho$ be the “person-rems/death” figure which was equal to 300 person-rems in the first equation. In order to determine the value of $\rho$ one can solve the equation as follows:

$$R \times h \frac{100000}{\rho} = 22000$$

$$\rho = R \times h \frac{100000}{22000} = \frac{ 2{\rm~Sv}}{0.22}= 9~ \mbox{person-Sv} = 900~ \mbox{person-rem}$$

There are a number of reasons this may be an over estimate of the dose required for 1 death:

1. The age restriction is 30 to 60. Younger people are much more sensitive to radiation and people who died from cancer after 60 are not counted.
2. Leukaemia cases are not counted.
3. The dosage estimates are determined by comparison with bomb  tests in the US and not by direct measurement at the site (of course). There is some discussion whether these are correct

## Gunderson, Arnie

http://www.fairewinds.org/cancer-risk-young-children-near-fukushima-daiichi-underestimated/

“That is what BEIR says, it is called the L.N.T., Linear No Threshold approach. Now what that means in BEIR is this: if somebody is exposed to 100 rem, that is one sievert, the chances of getting cancer are 1 in 10.”…

Notice that this is 6.7 times less sensitivity than Goffman’s estimation because the estimation is for getting cancer not dying from cancer.

“Now in Japan, the Japanese government is allowing people to go back into these radiation zones, when the radiation exposure is 2 rem. What that means is that they are willing to say that your chances of getting cancer are 1 in 500 if you go back into these areas that are presently off limits, and the exposure levels are 2 rem or 20 milisieverts in a year.”

(2 rem) x (500 persons)/$\rho$ x 2s deaths/cancer = 1 death

$\rho$ = 2000 person- rems = 20 person-Sv

Note that this is talking about “getting cancer” not dying from cancer. There’s a factor of 2 between getting and dying. 2 rem per year for 50 years is 100 rem.

“So if you go into the BIER Report and you look at Table 12-D, you will see that young women have a 5 times that number chance of getting cancer than the population as a whole. So young girls in the Fukushima Prefecture are going to get 5 times the exposure they would get from 2 rem. That means that about one in 100 young girls is going to get cancer as a result of the exposure in Fukushima Prefecture. And that is for every year they are in that radiation zone. If you are in there for 5 years, it is 5 out of 100 young girls will get cancer.”

This implies for young girls $\rho$ = 2000/5 = 400 person-rem

## Discussion

These estimates are not complete in agreement, but are of the same order of magnitude. They do agree in that the model to use is the linear, no-threshold dose-response model. In other words, any exposure to radiation increases the cancer risk and there is no absolutely “safe” dose.  The moral from this is that any increase in radiation exposure must be justified. The assertion that additional radiation exposure is safe because it is small or comparable to background radiation, medical x-rays, cosmic-rays from airplane trips is not relevant. All of these sources are unfortunately harmful.

In terms of epidemiology the exposure of thousands or millions of residents to an additional dose of radiation is certainly going to cause an increased number of cancers and  cancer deaths.  On the other hand, the increase in probabilitly of dying from cancer for any individual person could be considered small and, given informed consent, might be judged by the patient to be a worthwhile risk.

Exposing a large population could occur when a nuclear power plant is operating and is not performing to spec. Mass screenings such as mammography would also increase the incidence of cancer when applied to a large number of patients. For example, a typical mammogram exposure is 0.4 mSv (http://www.radiologyinfo.org/en/safety/?pg=sfty_xray)

Number of cancer deaths when mammogramming 1 million women would be in the best case given the above numbers would be

(0.4 mSv) x (1 Sv/1000 mSv) x( 1 000 000 persons/20 person-Sv) = 20 deaths

If the mammography is repeated every 2 years for 20 years then one should multiply by 10, or perhaps less due to the aging of the subjects.

Likewise, there would be 40 extra cases of cancer in the million women by these numbers. In fact, since breast tissue seems to be more sensitive to radiation and women are also more sensitive, one could estimate up to perhaps 100 cases of cancer without exceeding reasonable limits of uncertaintty. This may be a risk that’s worth taking since early detection of cancer saves lives. The number I have heard is that the routine mamographic screening of  about 150 women  can save one life due to early detection. In the one million women examined by mammography, nearly 7 000 lives could be saved due to early treatment compared to the 20 extra cancer deaths. (from this article http://www.nlm.nih.gov/medlineplus/podcast/transcript022414.html one can calculate that in the cited study 7 deaths/1000 screenings or 143  subjects being examined routinely. The error on this estimate is large– about ± 20 out of 500 in each sample so the difference would have an error of ±30 at a 68% confidence interval.)

# iPad stand from an egg carton

Telus Optik recently dropped RT from the channels included in their basic package.  So I am relegated to watching on an iPad to hear the other side of the Ukrainian situation. Unfortunately, we don’t have a convenient stand or one of those Magic Cases that allow it to sit upright so  it can be viewed from a relaxed position.

XS Cargo had advertised an iPad stand for $\$1.98$but when I got there all they had left were stands and cases ranging from$\$9.98$ to $\$14.98\$.

Disappointed, I decided that one could easily make a stand from a stiff piece of cardboard or plastic. A little rummaging  turned up an 18-egg cardboard egg carton that supports the iPad upright at an angle. If one puts the iPad in landscape orientation and inserts it into the front row of egg indentations and leans it back against the inter-egg pillars. It is stable,. However, for added stability and security I folded back the flap and stapled it in place. The top of the carton folded down to touch the top of the iPad and that seemed to enhance the sound output.

Below are pictures of the assembly.

Hefty staples could be used to secure the flap, but I used slide clips, a Japanese version of Bulldog Clips without handles.