This Model Caused A Nuclear Disaster

Key Takeaways

foreign a massive earthquake hit Japan up to this point it Remains the most powerful earthquake ever recorded in the country but that was just the beginning the earthquake triggered a tsunami with waves as high as 130 feet that's the height of a 12-story building and it all started going down from there here is a map of Japan and that right there is the fukuchima power plant now I found this picture from 2007 where you get a pretty good view of the plant well the waves caused by the tsunami hit the nuclear plant and damaged the emergency generators right when they most needed them they lost electric power leading to the most severe nuclear accident since Chernobyl in 1986 around 154 000 people had to be evacuated it was brutal now I'm not a historian but I wanted to show you this because this disaster could have been prevented Behind These devastating nuclear accident there was a model that failed so I started the research for this video with one specific idea in mind but while looking through some of the information that came after the accident I found something that I wanted to share with you this report right here has hundreds of pages and I did not print them all but I found buried inside what could have been one of the first mistakes the engineers made when designing the nuclear plant let's talk about probabilities the structural engineers who built the Fukushima plan knew they had to be ready for earthquakes and tsunamis it's Japan right the question was not whether a disaster would happen they knew there would be plenty of them the question was how bad it could actually get let's run through some ideas here let's say the probability of an earthquake and of a tsunami is 10 to the negative four I got these numbers from the report the question we need to answer is what would happen under the pressure of of the combined force of these two natural disasters more specifically do we even need to worry about this happening simultaneously that's what this formula can help us answer this equation represents the probability of our worst case scenario a tsunami and an earthquake occurring at the same time fortunately we know what this term means is 10 to the negative 4 but we don't know what this is this term is the conditional probability of a tsunami given that an earthquake occurs we need to find it to determine whether we need to worry about our worst case scenario there are two possibilities here if these two events are independent we can say that the probability of a tsunami given an earthquake is the same as the probability of a tsunami this means that an earthquake will not make a tsunami any more likely let's see what happens now if an earthquake and a tsunami are independent events this is how we will compute the probability of our worst case scenario we know these values the probability of an earthquake and the probability of a tsunami they are 10 to the negative four so if we substitute those into this equation we will get the final probability and look at that result 10 to the negative 8. this is so small that it will be almost impossible for an earthquake and a tsunami to occur as they did the report claims that this could have been one of the mistakes and the holy state was assuming that earthquakes and tsunamis are independent events it's actually very likely to see a tsunami after we see an earthquake of that magnitude shock waves that gave birth to a massive tsunami that started 35 minutes later assuming the conditional probability is one here's how we will compute the probability of our worst case scenario look at the result is substantially higher than 10 to the negative 8. that's one of the conclusions that's one of the conclusions of this report right here people responsible for the plant safety might have considered earthquakes and tsunamis as independent events so they didn't think the worst case scenario was actually possible unfortunately that was not the only mistake they made [Music] the Fukushima nuclear reactor was ready to withstand a magnitude 8.6 earthquake that's not bad except the earthquake of 2011 was a massive 9.1 but again we're talking about Japan here they get plenty of earthquakes so why were they underprepared for starters they had not seen an earthquake that big before okay so it sort of makes sense they were not necessarily expecting something like that to happen but come on we were scientists we cannot just assume something we haven't seen will never happen right we have to go deeper than that so let me show you this book here the signal and the noise why so many predictions fail but some don't written by Nate silver you've gotta check this book out Nate looked at the data and what he found was fascinating here it is let's start with the plot of the historical frequency of earthquakes around Japan the x-axis shows the magnitude and the y-axis chose the annual frequency of these earthquakes right off the bat it makes sense that smaller earthquakes happen very frequently while big ones rarely happen two interesting things in this plot here first notice how the data does not show any earthquakes larger than eight remember up to that point there was no indication of such a large earthquake ever happening there and second there is a kink here in the shark notice how it doesn't follow the same pattern the curve bends a little this is not surprising first there is not a lot of data about large earthquakes because they're less frequent and second there had been no earthquakes as large as a magnitude Aid in the region since 1964. all right decent data was available to the team who had to make a crucial decision how to prepare how to fortify the nuclear reactor to do that they needed to predict the frequency of these large earthquakes fortunately we've got the gardenberg rooster law which expresses the relationship between the magnitude and the frequency of earthquakes are in a very convoluted way this page explains that we should expect a straight line pattern in a region like Japan this is a straight line notice how this model ignores the kink in the data if you use this model the straight line to compute the frequency of an earthquake of magnitude 9 in that region you should expect that they will happen every 300 years or so it's a long time but it's not crazy so why didn't they use this information well maybe this has something to do with it this is what overfitting looks like this line here is called a characteristic fit and it follows the historical data notice how this model bends with the Kink right here the model assumes that there is a good reason for the Kink so it's not just an accident or lack of data so the model follows it not a big deal right well this model predicts an earthquake of magnitude 9 every 13 000 years if you ask me that is pretty much impossible compare that with the 300 years predicted by the first model the team in charge of all of these ignore the Gothenburg register law and instead overfit their predictive model to the data a hat now the law did not predict that an earthquake of that magnitude was going to happen that year of course not but it hinted at the possibility of an event like that happening within a reasonable time span two big mistakes dire consequences there is a lesson somewhere in there [Music]