Time and again we see the statistical fallacy pop up in regards of volcanoes, and then as a letter in the mail, the word “Overdue” is dropped in our mental mailboxes. But, fear not, there is a hero of sanity out there in the form of the greatest philosopher of all time to save us from such silliness.
Here I sincerely apologize for the headaches I am about to cause to you poor readers, so before going forward I suggest that you go and fetch a towel to put over your heads when it becomes to brainwhacking. Remember, Don’t Panic and you can always take a pan-galactic gargle-blaster at the end of reading this.
But let us instead start with something that everyone with a high school diploma can understand, the much loved and hailed Bell-curve.
The decreasing fit probability problem of the Bell-curve
Let us begin with that a Bell-curve is by nature finite and not analogue, there are no decimals in the probabilistics here. As soon as you go below 1 you get a probabilistic quantum foam of undeterminable chances.
In high-school statistics you just chop off those pesky undeterminables and leave them be. And most likely you will never get back to them unless you study advanced mathematics or fall in love with quantum physics.
There is no doubt that the Bell-curve is useful and that it can help us to determine a few things about our world. Problem is that the more detailed you try to be when using it, the less precise it will be.
In a Bell-curve based on a population of ten measured instances of when a volcano is most likely to erupt you will typically get a 70 percent probability for the 3 most likely events to occur. 70 percent sounds good doesn’t it? We pretty much nailed it! Nope…
Let us flip it around. We have a 30 percent probability that something completely different will happen compared to the 3 most probable outcomes. And it becomes even worse if we go for the single most probable outcome. The percentages here will be something like 30, 40 or 50 percent. If we now flip that we see that there is between 50 to 70 percent chance that something else will happen. Bummer.
In other words, it is more likely that a volcano will erupt prior, or after the “due date”. In reality it is even improbable that it would erupt on the “due date”. This also goes for behaviour; a volcano exists in a probability field of what it can do in eruption styles and sizes. It is all more or less fuzzy until after the eruption has occurred.
It is a human trait to do ever more complex models of our reality, and a population of 10 in a Bell-curve is to low to give any meaningful result. A population of 100 measurements are seen as a minimum value.
Here comes a funky thing. As you increase the population more things will start to crop up above the value of 1 further out on the Bell-curve. Or in other words, the Universe will start to throw us more and more odd-balls the more and longer we measure something.
This inevitably leads to the 3 most likely events to happen having a slightly lower percentage with a population of 100 than with a population of 10. That 70 percentage probability will drop down to typically the low 60s.
And as we get more data into our model spanning ever longer time, we will see that probability continue to drop. This is where statisticians start to bin probabilities into groups that are ever larger, five most likely outcomes, seven, nine and so on these bins grow. And lo and behold, the probability ratios start to soar, but in reality, we are stating less and less about the important thing. When will the volcano erupt. Or in other words, statistics has become almost pointless at this point.
Problem is that humans like to see things from our limited lifespan, and a volcano lives from anything to a thousand years up to millions of years.
Let us take an example, Grimsvötn. We do not know the exact age of the volcano, but we believe it to be between 100 000 to 250 000 years old. We have great record of it’s antics for the last 1000 years, and a fair one for the last 10000 years. The rest is just “out there”. So, we have data for just a small percentage of the time it has existed, and we for obvious reasons lack all the data that we need from the future to see how it will develop.
Still we try to wrangle useful statistics out of the 1000 or 10000 years of data we have, even if that is less than 10 percent of the lifespan of the volcano.
Volcanologists are well aware that any statistic bandying will never give an answer to when a volcano will erupt, at least in any useful manner.
Still the statistical fallacy rears its ugly head even among volcanologists. Quite often volcanologists say things like “if you want to know what a volcano will do, look at what it has done historically”.
Now, let us go and use Fuego as an example for this kind of fallacy. After hearing that from volcanologist X, volcano-lover Y will go to The Global Volcanology Page entry for Fuego and see that it has behaved quite well in recorded history producing VEI-1s to VEI-4s. Our volcano-lover will also find a reference to the ancestral Meseta volcano and the Esquintla-debris avalanche.
And here the fallacy turns into a full-blown Dragon. What has happened historically is not the same as all that has happened in the 250 000 years that the Meseta volcanic complex has existed. It has changed behaviour many times, and thrown some quite large black swans into the camp fire.
So, in other words, at best we can say that a particular bin of eruption sizes and styles are most likely, but out there are dragons lurking aplenty just waiting to happen, ranging from quite plausible up to almost impossible.
We often use the term black swan in here for those improbable things that lurk out in the fringes on any Bell-curve. And as we have just seen, there will be more and more of them lurking about as we get closer to a 1 to 1 parity with reality.
The name black swan comes from a very rare black swan that was born outside of Paris in the early seventies. And in one of these great jokes of the Universe it turned out that the gene that produces white swans are recessive, and that the gene that produces black swans is dominant. It also turned out that swans sexually prefer black swans to white swans. So, we now have an ever expanding amount of black swans, resulting in the white swan turning into a true black swan event in a few hundred years.
This kind of begs the question if it would be possible to predict how realistic a black swan event is, and if we can predict what type of black swan would be coming for us?
Grab your towel and let us venture into the field of quantum-probabilistics and then into the heartland of Douglas Adams.
First relax, I will not go into any great depth here. To do that I would have to transform to Feynman and write QED. Oh wait, he wrote that book, read it.
It is said that humanity only have proved two things, these are parts of mathematics and formal logics. The rest is just probable knowledge. Just remember that a scientific theory is thousands to million times more likely to be correct than a half-arsed theory. See for instance the Entire Scientific Community™ against the Flat Earth Society…
Two different scientific theories stand apart and are by now seen as so well proven that they are very close to be upgraded to being True. These are Einstein’s Specific and General Theories on Relativity. The second is the Feynman Interpretation of the Copenhagen Interpretation of the double-slit experiment, that is the foundation of Quantum Electro-Dynamics (read QED).
The foundation of the latter is quantum probabilistics. The mathematics here is quite exotic, and Feynman himself ventured out into the rarefied field of path-integrals to quantify certain aspects of quantum uncertainties. I will do my darnedest to keep it far simpler, so much so that our dear Albert will groan bemusedly, and hit me over the head for splitting the proverbial beer-atom.
Well, I might be a Yahoo, but I take this subject ever so Serious.
Remember that I said that the Bell-curve is finite since we can’t measure anything less or larger than 1? It is either a 1 or a 0 in the boxes of the Bell-curve. But, what about 0.42? Problem is that we can’t know anything about a probability below 1 (with the exception of 0 and -1).
Still it is between 1 and 0 that most of the interesting stuff in the Universe happens. In that box we find not only Yes or No, we also find Maybe, and all sorts of Black Swans. Due to the Heisenberg Uncertainty Principle we can never accurately know what is inside that box far out on the Bell-curve. We can just assume that it is containing something, unknown what.
And even if we know that there is a cat inside the box, we will not know if the cat is alive or not. The cat is literally alive and dead at the same time. Or we will know if it is dead or alive, but we can’t know if it is existing or not. We can never know both at the same time.
Heisenberg’s Uncertainty Principle and Schrödinger’s Cat may seem funny, but they are the fundamentals upon which our Universe rests. Personally, I believe that the reason for the existence of the Universe is to laugh it’s arse off at us as we try to understand it, and that if we ever truly understand it fully, it will change into something even more bizarre. “Some say that this has already happened.” (Douglas Adams)
What physicists do is to bin those boxes of uncertainties together into something that is called probability-fields that will through mathematical wrangling divulge what it is most likely to be. This of course gives off more black swans further lowering the significance of the most likely outcome of the Bell-curve.
So far nobody has bridged the gap between the quantum world and our mundane relativistic one. So, we do not know how these quantum uncertainties affect our life, we just know that they probably do.
Now it is time to go into the world of one Douglas Noel Adams.
The Douglas Adams Model of Quantum-Improbabilistics
In a true quantum fashion, we will never know if Adams became the greatest philosopher of all time through intent, or if he just bumbled across all the marvels he wrote about. We just know that he did. Another view might be that the Universe churned him out to prove it’s hilariousness. Be that as it may.
When I was 11 years old I read 3 books that forever changed my life. Those where Einstein’s ‘The Meaning of Relativity’, Richard Feynman’s ‘QED – The strange theory of light and matter’ and ‘The Hitchhiker’s Guide to the Galaxy’ by Douglas Adams.
The lesson I learned from the third book was that you can always look at the Universe from a completely different angle than the rest of humanity, and still be equally correct.
The book also talked about the Infinite Improbability Drive based on the theories of Finite Improbability and Infinite Improbability. Adams never further expounded on the subject, instead he just gave glaringly improbable examples of the effects of infinite improbability.
Back then nobody had done any work in the field of Improbabilistics, and to date there is only one major work done in the field, David J. Hand’s ‘The Improbability Principle’ (2014).
In short, Improbabilistics is the study of how improbable an event is, and what the characteristics is of improbability. It works explicitly with the part of statistics that is not covered, and can not be covered by probabilistics.
It takes over where quantum-probabilistics leave off. Instead of determining the strength of a probability field out in the far yonders of the non-finite Bell-curve, it instead is giving the means to calculate the properties and value of how improbable an event is. It also deals with emergant groupings of improbabilities.
One may say that it is the evil twin of probabilistics and quantum physics. It is the tool for studying the outer fringes of reality and beyond, and to be quite frank, it is a larger field than probabilistics.
In the world of volcanoes statistics will never tell us when a volcano will erupt, probabilistics may at best tell us what is most likely to occur, but only improbability can give us data on the next upcoming black swan, since we can calculate the improbability number for an upcoming event (but still not getting a date for it).
Since I love volcanoes and other potentially horrendous things that can happen I more and more found that Improbabilistics was a good way to understand the Universe. So, when there is no light I ventured forth with great fervour to create light.
At 16 I sat down and filled a blackboard with strange math, sat down exhausted, and then started to laugh. Unwittingly I had produced a mathematical law that is simpler to write in ordinary language than in mathematic symbols (or, I just suck at math). I call it the “Law of Miracles”.
An Improbable amount of Improbabilities will happen to you Improbably often.
This means that there are more unlikely things that will happen to you, than there are likely things. This does not mean that there will be colossal bad things all the time, it instead means that you should well and truly expect the unexpected, if not even the outright weird and outlandish.
Instead of being the theory of big colossal bad things, it is the theory of the ordinary every day miracle. If you look carefully you will start to see them happening everywhere. Just remember that they can be both good, bad, neutral, or just plain odd.
Whereas it is hard to calculate the value of the quantum probabilistic field strength of say 58, it is always easier (but requires more computational power) to calculate the Improbability number of 42.
One of the most blatant miracles in our lives is love, most people are not aware how improbable it really is that you will find your wife or husband, fall in love, and get married. It is a true miracle with a calculable improbability number. The one for me and me wife are 2276709 to 1.
I am not going to go any further into this, except than to say that thanks to Douglas Adams we now know that a volcano will almost certainly not erupt when it should, and when it does it will be at least subtly different than it was expected to happen, or even wildly different. In other words, statistics be arsed in a Douglas-field.
An example with volcanoes
Let us say that you live in the perfect of worlds. In it there is a volcanic system with 100 equidistant volcanoes, and that each of those volcanoes erupt on average once every 100 years. Down in history there has mainly been one eruption each year, but with some exceptions with years of several eruptions, and some years without eruptions. And you live in the middle of this marvel of volcanism.
As 2018 started you knew that there was a 61 percent chance that you would see a single eruption, and 17 percent for two eruptions, and 17 percent for no eruption. You can confidently expect to see fireworks, if not this year, so surely the next year.
Here we have covered the regular finite Bell-curve as described above.
Since you live in the best of worlds you are also immortal. So, as years go by you start to notice odd occurrences in the statistic pattern, ever longer time spans with no eruptions occurring, and changes to the eruptive statistics of many volcanoes. And even more frightening, you notice unexpected changes to the eruptions of some volcanoes.
You have now entered the land of quantum probabilistics. But, since this is the best of worlds you are fluent in the usage of Improbabilistics, so you apply the tools you learned millennia ago to the problem.
By now you discover the obvious thing. You are living in the middle of a very large caldera volcano, and those 100 volcanoes equidistant from you are flank vents, and the changes are caused by an increased pressure right below you. Right before the unexpected VEI-8 eruption occurs you utter the most frightening word known to man, a very quiet “Oops”, and all goes dark.