Hurricane Harvey is termed to be a 500-year event. The problems with labeling it as such is multi-fold.

First, it is confusing to call something a once-in-500 year event. People don’t live for 500 years. There are very few things that live for 500 years. It is essentially outside of the scale of human biology. To say that something is a once in 500 year event is the same as saying there are stars 100 lightyears away. We have no mental framework to understand how far 100 lightyear is, nor do we have any mental capacity to understand how long 500 year is in relation to our personal history. It is the time difference between now and when Columbus first set foot in America.  If we think about how much has happened since then, it is basically meaningless in everyday language. Thus it is confusing to call something a 1-in-500 year event.

Second, it is pragmatically unwise to call something a once-in-500 year event. There are quite a few articles mentioning and explaining that a 500 year storm does not mean that it is a storm that happens only once in 500 years. What it really mean is that this storm has a 1 in 500 chance (0.2%) of occurring each year. The practical problem with this wording of something to be a 500 year event is that it actively induces the Monte Carlo Fallacy. The Monte Carlo Fallacy is the belief that if you’ve flipped a fair coin and it came up heads 4 times in a row, it is more likely to even out and come out tails the next time. An event with a 0.2% chance of occurring each year has a 99.8% chance of not occurring. This actually means it has a 1 in 3 chance of occurring within as little as 200 years. The algebra is as follows. (1-0.002)^x = (1-0.33), solving for x. It also means ironically, that within a 500 year period, a one-in-500 year event only has a 63% chance of actually occurring at least once. (Taking 0.998⁵⁰⁰ would obtain the probability of such an event NOT occurring in 500 years, subtracting that number from 1 would obtain the probability of such an event happening at least once within 500 years.) So it is simply poor wording from a pragmatic point to label these events as 500 year events. Note, this is the main statistical explanation that most mainstream news article gives to why 500 year events are occurring more often.

As an aside, it might be interesting to see how a 100-year event would perform in a time span of 500 years. Mainly what I mean is the question: How likely is it for an event with a 1% yearly probability to NOT occur even once in 500 years. So here, we know that this event has a 99% chance of NOT occurring each year, raised to 500^th power would give us the odds of it not occurring once in 500 years. The answer is 0.0065, in other words, 0.65% of the time, a 1-in-100-year events may not happen at all over 500 years. Aside #2: the chance of a 100-year event masquerading as a 500-year event, (i.e. the probability of a 100-year event happening only once in 500 years) is about 3.3%. The math is as follows: 500 x 0.01 x 0.99⁴⁹⁹.

Lastly, and I believe the most important problem with such labels is that these “500-year storms” are not truly 500-year storms. One must realize that these labels are simply extrapolations from historical data, and historical data, especially historical data of tail events are always incomplete, simply because there hasn’t been that many 500-year periods in recorded history. If we remember the initial argument, 500 years on a time scale is about the time passed since Columbus’s discovery of America. Now if we consider the second argument above, the probability of a true 500-year event only has a 63% chance of occurring in 500 years. Thus it is impossible to accurately label something a 500-year event if there is not 500 years of data, and that even if there were 500 years of data since Columbus’s initial landing, we have shown that we still cannot be confident at all about the label. All of this brings me to my ultimate question. Can we confidently call Harvey a 500-year storm? I believe the answer is a definitive no. Thus it is no longer a mystery why Houston has supposedly had multiple “500-year floods” in recent years. Because these 500-year events are not really 500-year events! If a “500-yr event” occurs more frequently than roughly every 500 years, then it is far more likely, given the incompleteness of the data, that the probability was originally misjudged rather than there being any concrete underlying changes in the probability itself. The probability of a true 500-year event occurring even once within any 3 year frame is 1-0.998^3, or ~0.59%, and to have had multiple occurrences exponentially reduces that chance even further. In other words, striking a 1 in 500 event once in 3 trials is 0.59%, twice in 3 trials would be 0.0059² or 0.0035%, and the probability of what the Washington Post article attached below is suggesting, that this is the third time a 500-year event has occurred in three year, would be a puny 0.00002% (1 in 5million). The point venues like New York Times and Washington Post is trying to make is that this type of catastrophes could be due to the underlying climate changes from global warming that altered the probability of what was once a 500-year event. That could be true, but such claim would require much stronger evidence than simply showing that something purported to be a 500-year event is in all likelihood, to not be a 500-year event. The problem with using every catastrophe as a platform for climate change is that it is a false platform, and it misinforms the audience about climate change. I believe this recent backlash against science is deeply rooted the media’s overzealousness in plating to the public serving after serving of undercooked scientific studies. When the readers of such venues read one too many report of a scientific claims that later becomes falsified, it is the same feeling as eating one too many piece of undercooked chicken. The result is a visible disdain and distrust for science.   We as a society must respect science for what it is.  Science is the process of pursuing the truth, and not the truth itself. The more we toss “climate change” as a buzzword and a sound bite explanation for everything, the less receptive the general public are when it comes to true discussions in regards to climate change. NYT and WaPo must stop blaming climate change for everything, stop watering it down, and stop undermining the platform that true scientist spent years building.

To end, I will quote an idea from Nassim Taleb. He called it Wittgenstein’s Ruler. Its basic premise, which Taleb associates with the philosopher Ludwig Wittgenstein, is that since a ruler can be used to measure the length of the table, the corollary would immediately be that if given uncertainties in regards to the length of the ruler; the table can be used to measure the ruler. In this example, I have shown that a model can be used to estimate the probability of an event, the corollary being that the probability of the event can be used to assess the accuracy of the model.