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Utility companies, to support their claims of nuclear reactor safety, present artificial risk estimates — such as no more than one core meltdown per 30,000 years of reactor operation — that are based on faulty assumptions, guessing, and unvalidated theoretical models. Our most solid source of information on reactor risk is the historical record. According to the International Atomic Energy Commission (2013), as of 2012 a total of 581 civilian reactors had logged 15,247 years in operation. There have also been three major reactor accidents: Fukushima, Chernobyl, and Three-Mile Island (counting the three reactor accidents at Fukushima as a single event). This yields an estimated rate of 3/15247 or 0.000197 such accidents per reactor-year. That number may seem small, but, as we shall see, it actually indicates extreme danger.
The number calculated above is an empirical rate based on a limited sample. What we really seek is the true or long-run average population risk rate. (Similarly, we might flip a coin three times and observe heads each time, making the empirical proportion of heads 1.0, but the true rate is 0.50.) Standard statistical methods can be used to appropriately adjust a sample estimate.
Because the numerator of our fraction, 3/15247, is a count, one can use the Poisson distribution to compute a confidence interval to identify the range of likely population risk rates around the historical risk rate. Such intervals vary in width according to how conservative we wish to be. A non-conservative approach would simply accept 0.000197 as the population rate. A minimally conservative estimate would be the value for which the chances of underestimating true risk are only 20%. Moderately and strongly conservative estimates make the chances of underestimation of true risk 10% and 5%, respectively.
Using a well known method (Garwood 1936; Soper 2015), we obtain variously conservative estimates of the population risk of a major reactor accident per reactor-year as shown in Table 1 (Column 2).
Table 1. Risk of Reactor Meltdown Disaster for a Single Site and Total Risk in US Over 25 Years
|Level of Conservativeness||
Total Risk (25 Yrs, 1 Site)
Total Risk (25 Yrs, All Sites)
Total Risk (40 Yrs, All Sites)
Example. For an observed count of 3, the 90th percentile estimate of the expected long-range average count is 6.68. Dividing this by 15247 gives 0.000438, the moderately conservative estimate of risk of a major meltdown per reactor-year.
While the risks per reactor-year may look small, the problem is that we have to consider the Total Risk in operating a reactor over time, and, on a national scale, many reactors over time. Total Risk is the probability of at least one major event happening in a certain length of time. For a single reactor, this is given by the formula:
Total Risk (%) = 100 × (1 – (1 – Risk))Years
where Years is the window of time. So, for example, the Total Risk of at least one major meltdown accident at a given reactor (say, Diablo Canyon) over 25 years ranges from a minimum, nonconservative estimate of 0.49% (about one chance in 200), to more appropriately conservative estimates of about 1% to 1.25% (or one chance in 100 or 80, respectively). These values are alarmingly high. (Ask yourself: would you eat a jellybean from a jar of 100 knowing that one contains cyanide?)
The danger becomes even more apparent when we consider Total Risk nationwide. Here the formula becomes:
Total Risk (%) = 100 × (1 – (1 – Risk))Reactors × Years
Assuming that 100 reactors operate in the United States for an average of 25 years each, the conservatively estimated Total Risk of at least one meltdown accident ranges from about 60% to 72%. (Over 40 years, even the nonconservative estimate is above 50%.) These estimates are consistent with other recent analyses (e.g., Ghys 2011; Smythe 2011; Lelieveld et al. 2012; Ha-Duong & Journé 2014).
One can easily imagine a utility company looking at these results and countering: “You can’t go by past events. The industry learns from mistakes. Reactors today are better designed and safer than those at Chernobyl and Three-Mile Island.” However it is unlikely that today’s American reactors are better designed than those at Fukushima. Further, more complex designs supply new opportunities for malfunction. And human error is always a danger.
In short, if we base risk estimates on the historical record — our best, most objective, and perhaps only reliable source of data — it is more likely than not that a serious accident will occur at one or more US reactors within the next 25 years. The unacceptability of this risk becomes even more salient when we consider that we are all neighbors. An accident that happens anywhere in the country is not “the other guy’s problem.” We’re all in this together.
Garwood, F. Fiducial limits for the Poisson distribution. Biometrika 28.3/4 (1936): 437–442.
Ghys E (2011). Accident nucléaire: une certitude statistique, un article de Libé, Images des Mathématiques, CNRS. Published online 2011-06-05. http://images.math.cnrs.fr/Accident-nucleaire-unecertitude.html. Accessed 20 June 2012
Ha-Duong, Minh; Journé, Venance. Calculating nuclear accident probabilities from empirical frequencies. Environment Systems and Decisions 34.2 (2014): 249–258. http://link.springer.com/article/10.1007/s10669-014-9499-0#page-1
International Atomic Energy Agency (IAEA). ‘Nuclear Power Reactors in the World.’ Vienna, 2013. http://www-pub.iaea.org/MTCD/Publications/PDF/rds2-33_web.pdf
Lelieveld, Jos; Kunkel, Daniel; Lawrence, Mark G. Global risk of radioactive fallout after major nuclear reactor accidents. Atmospheric Chemistry and Physics 12.9 (2012): 4245–4258. http://www.atmos-chem-phys.net/12/4245/2012/acp-12-4245-2012.pdf
Soper, D.S. Poisson Confidence Interval Calculator [Software]. 2015. Available from http://www.danielsoper.com/statcalc
Smythe D. An objective nuclear accident magnitude scale for quantification of severe and catastrophic events. Physics Today (‘Points of View’). December 12, 2011. http://www.davidsmythe.org/professional/pdf/NAMS%20Points%20of%20View.pdf
John S. Uebersax PhD • www.john-uebersax.com • 31 March 2015 (rev. 19 April 2015)
23 March 2015
Dear Representative Capps:
I am disappointed that you voted ‘yea’ last Friday on the House resolution calling on President Obama to provide military assistance to the Ukraine:
- It is widely reported, plausible, and probably true that the US, via the CIA, helped instigate the crisis in the first place, actively seeking to separate the Ukraine from the Russian orbit.
- It is further common knowledge that Germany, for its economic gain, is also responsible for instigating the crisis.
- The text of the resolution is fallacious. It implies that whereas a “prosperous Ukraine” is “in the national interest of the United States” that we have some right — if not indeed a moral obligation — to supply military assistance to the Ukraine. Such reasoning is worthy of Machiavelli: it assumes without question that we have a right to make war merely for the sake of promoting our national interest — rather than, as our Founders wished, only to protect our national *security* interests. It is also fallacious to assert that our unquestioned goal should be to help other countries be prosperous — as though material wealth were the purpose of human existence, and that higher values (like peace and friendship) are not our true goals.
- It overlooks the potentially reasonable position that the Ukraine itself is ethnically divided, with the eastern Ukraine being more culturally Russian, and therefore having a valid wish to remain within the Russian sphere.
- We have had enough war, and enough of shipping arms around the world!
- When will the Congress recognize that it is not only possible, but better to cultivate peace rather than to pursue war?
San Luis Obispo
I had a long chat with an NRC statistician to discuss their methods for estimating the probability of a reactor accident. He confirmed what I already knew: no existing statistical methods can accurately predict such events. Rather, their theoretical mathematical models only indicate which parameters, out of hundreds, have the most influence on net risk (sensitivity analysis); but the models do not supply accurate net estimates for the risk of a critical reactor incident.
Bottom line: nobody really knows the probability of a meltdown or major radiation release at Diablo Canyon.
Historical evidence (number of actual reactor failures) might suggest a probability somewhere between 1/100 and 1/500 during its term of operation.
Two revealing quotes:
Kaiser 2012, Empirical Risk Analysis of Severe Reactor Accidents.
time to the next accident among the world’s 441 reactors … is estimated to 11 years.
Raju 2014, Estimating the Risk of Nuclear Accidents
The existing record of accidents … [and] their probability distribution is sufficient to rule out the validity of the industry’s analyses at a very high confidence level.”
A database (Excel spreadsheet format) on all US reactors is here: http://www.globalnucleardata.org/
The other day I noticed an interesting and often-overlooked detail of Plato’s Republic. The entire conversation which it records took place in the midst of an all-night festival dedicated to Bendis, the Thracian Artemis, a goddess associated with the Moon and the sister of Apollo.
Imagine, if you will, the goings on. Socrates, the protagonist of the Republic, walks 10 miles from Athens to the port of Piraeus, where the newly established festival in honor of Bendis takes place. First there are opening ceremonies and rituals, then a procession. At night there is a mysterious horse race where riders carry torches. Finally, the crowds disperse to enjoy a night-long festival, the details of which we know little.
Between the afternoon and evening festivities, Socrates runs into some acquaintances, who invite him to their nearby house for conversation. There they carry on into the late hours or morning in conversing about the nature of Justice. Meanwhile, all around them, the religious festival to Bendis is taking place. Surely this must have created a unique ambient energy that charged and inspired the conversation. (Anyone who has experienced such an all-night festival will understand this, and those who have not can easily imagine it.)
My musing (no pun intended) on all this produced something like a personal epiphany: I suddenly realized how, while Plato is so often considered the ‘son of Apollo,’ that is, a philosopher of the intellectual or solar aspect of the psyche, he is also a philosopher of the lunar, feminine element — and arguably no less so.
Indeed, it is testimony to the vice-grip that rationalism has had on philosophy during the last 150 years that Plato’s strong feminine aspect is not readily apparent. In earlier centuries this was not always so. The ‘other’ Plato — the mystic, the philosopher of love and Beauty, of poetry and music — was known and celebrated. Thus we have the vast European esoteric tradition which owes so much to Plato, the love philosophy of the pivotal Renaissance Platonist, Marsilio Ficino, and the Platonic/Neoplatonic great chain of being central to Medieval art and culture.
Academic philosophers for the last century-and-a-half have explored every nuance of Plato’s rationalism. Indeed, this has reached the point where the productions are too often sterile exercises in vanity and mere scholasticism. To ignore Plato’s lunar side and his love mysticism, is to remove the heart and soul of his philosophy — indeed to deny the very meaning of his word philosophia, love of Wisdom.
The place to begin, of course, is with Plato’s Symposium, Plato’s great work on love. An indication of the extent of modern neglect of this dialogue is that the last book on the topic that even tried to be definitive was written in 1963 (Thomas Gould, Platonic Love, Oxford). Meanwhile dozens, if not hundreds of books have appeared since then treating of Plato’s more rationalistic dialogues, exploring in excessive detail every part and nuance of them.
We are indeed living in a hyper-rationalistic age. A good term to describe this is orthocentrism — the oxymoronic nature of which describes precisely the issue: a rationalistic bias which removes us from our center, assuring disharmony, conflict, incompleteness, and, in the end, untruth.
Of course, it may be objected that the opposite error can occur — to be too mystical, to intuitive, not rational enough. Let us not forever operate at the level of excess, reaction, and counter-reaction. We must have both: rationalism and mysticism, Apollo and Artemis.
But we must not imagine that Plato, the wisest of the Greeks, was oblivious to this. Let us gain a new understanding of Plato as a holy (whole, holistic) philosopher.
How better to conclude than with verse? Here is a beautiful specimen of Platonic cosmic love poetry by the Florentine, Girolamo Benivieni (1453—1542; J. B. Fletcher, transl.)
In Primal Good flows to the world of sense;
When it had birth; and whence;
How moves the heavens, refines the soul, gives laws
To all; in men’s hearts taking residence,
With what arms keen and ready in resource,
It is the gracious force
Which mortal minds from earth to heaven draws;
How it may light, warm, burn; and what the cause
One love may earthward bend, one heavenward bear,
A third sustain midway ‘twixt earth and heaven …