Let's look at this situation of the double well potential. Here I have the system in one of the wells. Okay, it is rattling around in the bottom of the well because there's always some noise in present in the system. And once in a while that the noise can be strong enough to kick the system from this left well to the right well. Okay, this is not a critical transition, this is called an equilibrium transition, and it always involves an energy barrier delta E, okay and it is noise driven, okay. And if you actually measure the rate of at which these kind of things happen, are there any chemistry majors here, no chemistry person. Well, I mean anyone have you taken say biology and a lot of Arrhenius law? Okay, Arrhenius law says that the, the frequency of this kind of change is proportional to exponential minus this energy barrier divided by the temperature, okay. So, any equilibrium transition is characterised by Arrhenius law. So, if you notice something changing frequently and you what you should do is immediately you should test it against a, a model of equilibrium transition. If there is an energy barrier for a given temperature then this is an equilibrium transition. Now, in this kind of picture, how would a critical transition look like? So critical transition looks like this. You start off with a symmetric well, and then you increase the tilt. So the, the, the wells become increasingly asymmetric. Eventually the, the energy well the less energy well disappears. And it is definitely not possible for the system to stay here anymore. So, it makes a very sudden transition over to the right well, okay? So, this kind of transition is actually happens when the energy barriers itself completely disappears. So therefore, if you measure the frequency, it doesn't depend on the energy barrier itself. And it is actually control parameter driven, okay? So obviously you know as you drive this know basically. As you tilt the energy well, you can actually have an equilibrium transition happening before you reach the tipping point. So, this is why sometimes it can be confusing talking, clarifying whether you are dealing with equilibrium transition or you're dealing with a critical transition so confusing. So there are ways to think about to become less confused. Now, he actually doesn't mention all the fantastic work that his student and him has done. But I because I tried to move further, I start to go into areas where you don't find many people doing things like this. So, in fact if you attend a conference on complex systems, and when that doesn't matter where the weather is held in the US, in Europe or in Asia. You find many people saying that complex systems in other critical transition regime shifts in complex systems. They cannot be predicted. Okay, now that is true if you're dealing with chaos. But a complex system is not chaotic. Okay, so at this very, very interesting window between regular behavior and chaotic behavior so, can a regime shift be predicted? It turns out that yes, it can be predicted, okay? So this is the value of Bitcoin, okay? This is the value of Bitcoin, I think versus the US dollar. You can see that there's this gigantic bubble growing in the Bitcoin exchange rate and then, of course, this day you know it crashed. Okay, so obviously if you dabble in bitcoins you don't want to be holding on to bitcoin past this highest point. Now here you want to convert US dollar, maybe you can buy it back afterwards. Okay, so this is Rob by the academy can be forecasted. One way to forecast would be if we know the equation of motion. If we know exactly what the equation of motion is, then we can tell how far away from the tipping point we can time our exit from the Bitcoin market. But of course that is asking for too much, we don't know the equation of motion for Bitcoin. Okay, so there are many people out there that try different kinds of methods. So if you come from economics background, you might have heard of the auto regressive models. So this is a model that looks somewhat like this. The variable time t plus one is proportional to the values of the variable at previous times, plus some noise term you fit. You fit the model to the data to extract all these parameters as well as the strength of the noise term and I say you can predict something, okay? And of course, you don't frequently succeed. But when you don't succeed in one, maybe you just add in some jump diffusion term in there. And then maybe, then you think that you succeeded. Or if you are coming from a electrical engineering or computer science background, you might actually try to fit the data to an artificial neural network. Now, how many of you follow AlphaGo. The Saga of AlphaGo versus Lee something that the world champion in goal so the world champions lost one game against DeepMind already. And deep mind is actually two neural net artificial neural networks is one that actually plays a game and they want another one that supervises the one that plays the game, okay. So this is the artificial neural network and these are the artificial neurons. And you can fit to any kind of data you like provided you provided the training set. If the training set you provide is good you can have relatively good predictions. If not then no good and of course, you have to do it the you have to go and pick some other data selection again. You're in a stock market, you might believe a lot in technical trading. Technical training is nothing much more than a straight lines and things like that. So if you see a W then is followed by a V, if you see a V is followed by some inverted w or something like that. And as of course, there's no basis behind this kind of thing. And all these methods, what I'm claiming is that they are no good for predicting regime shifts because they are not regime shift away. There are no regime shift in the equation here. No ignore regime shift the equation here, no regime shift equation here, no regime shift in equation here. And certainly no relationship here, while maybe here there's some regime shift. Now I've used technical trading to trade in the past. I've got but so, after that when I use technical trading again, I remember that I got burned. So unfortunately the model that the regime shift aware part is in my brain, not inside the technical trading model.
