Gauss and the Black Swan

Gauss and the Black Swan

• The Black Swan

  I have a nickname, the theorist of magic, which is probably also a joke about the nerds, because I am very stupid, I prefer to summarize a principle from a bunch of things. I am a good statistician, I like to find the average of things around me, grasp their magic essence, and ignore the trivial details, thinking that just by grasping the general trend of things, the magic principles in my head can be turned into reality in life, but reality teaches me that I am a stupid fool, and will even fool a skilled monkey.

  My father didn't read many books, but he was a recognized old fox who often won surprises in real life.

  This makes me a theorist, because I can ignore details in my eyes, like noise in the radio. My belief comes from the famous Gaussian distribution (see below), which tells us that it is not the individual details that dominate success or failure, but the overall attributes. It's like I might lose a girlfriend because of one date without a wallet, but I'll have to deal with a lot of women and have a lot of dates in my life, and if I'm good in general, there will always be one.

  But the father's words are in reality a trick.

  So I thought, what's wrong with this world that I've always been proud of, this world of beautiful Gaussian curves and harmonious Newton's laws?

  Before the appearance of the black swan, the swans in Swan Lake were all snow-white, and you can imagine the feeling of tens of millions of white swans flying over that blue lake, looking as far away as the snow in Kilimanjaro. So I thought white was the sign of the swans, and I predicted all swans were white with almost 100% probability. Until one day a pure black swans flew over the lake, as if from another world, but it broke my daydream.

  The world of classical physics is a world of averages, where details and exceptions can be stripped away. But once they enter the domain of biological dominance, they become kings.

  

Before we enter the filthy, chaotic biological world, let us mourn the death of the white swan, the ruler of Gauss's law.

• Gaussian distribution and the theorem of large numbers

  We often express the general state of things with averages, such as the Chinese man's height of 1.7, for statisticians, averages almost become a belief, and we have often forgotten the basic assumption behind this belief - the Gaussian distribution, that only in our statistical objects does the Gaussian distribution, the average can really represent the properties of things.

  Preliminary knowledge: The sum is equal to the mean. The calculation of the mean depends on adding up a lot of data and then dividing by the number of individuals in the data. The size of the sample deviation near the mean is represented by the standard deviation.

  

  Gauss tells us about the power of addition. For a random event, such as a jackpot in a casino, the outcome from one to six is of course completely unpredictable, but if you bet 10,000 times and add up the number of points you get each time, you get a number that can be predicted more and more accurately. This result can be described by something called a Gauss curve, which has two characteristic quantities, the mean and the standard deviation.

  

  The power of the law of large numbers lies in the fact that he made it possible for a world of certainty to arise on top of enormous uncertainty. It is as if the sun rises tomorrow and a spring flower will bloom, which we know will not happen, with a probability of almost zero. In fact, the Gaussian distribution and the law of large numbers are guarantees of the law of large numbers, because the sunrise is the result of the interaction of the countless atoms and molecules that make up the sun and the number of atoms and molecules that make up the sun.

  The normal distribution and the big number theorem are the roots of all certainty, since our visible world is the result of the continuous addition of countless uncertain microfactors.

  The revelation of the importance of detail: he tells us that when there are enough factors to decide events, the number of trials is large enough, every thing, the tiny details no longer matter, because they are averaged out in the sum of the huge sums.

  But don't get too excited too soon.

• The Trap Behind Gauss's Law

  A.细节因素要独立

  It seems a bit abstract, but the fact is that the elements that make up the plus-minus are not able to communicate in private, as if all the women you know were secretly linking up to say that you are good or bad, and then the person you are dating will no longer get the result determined by the ideal average. Because all women actually get the same idea as the person you started dating. What you get is just a magnified standard deviation, the randomness of your first date is allowed to be the result of a lifetime.

  B.时间平移不变形

  This is a bit of an oddity. The simple example is that if you were to throw the ball and the ball was changed into a ball with a point on each side, and the back was changed from time to time, then you would never get a stable average, and if you were still there doing Gaussian addition and hoping that you would eventually win a given amount of money, you would be a fool to be fooled.

  The number theorem is the basis for our understanding of the random world, and he tells us how certainty emerges from the basis of chance. But he is like Newton's first law and the ideal gas model, that smooth horizontal and non-interacting elementary particles do not exist as illusory in the real world of living things, although we do get some approximations at times.

• Black swan effect and rhythm distribution

  Gauss's curve and the law of large numbers govern the solemn theoretical physical world, where, with good study, one can rise day by day, and Cinderella must meet the prince.

  The nature of the black swan is that the individual has a decisive influence on the whole, and the details have a decisive influence on the whole. When a black swan appears in the water, the properties of the whole group of swans change, and when a pure white world swan turns gray. Here, of course, more special effects are seen.

  From the point of view of Gauss's law, the probability of the appearance of a black swan could have been ignored, because we had previously calculated a huge sample of diurnal swans, but the black swan still appeared, its appearance seemed an unintended coincidence, was it particularly unlucky for us?

  In the biological world, the dominant is the power law, which, like power, is related to rights and wealth (see Figure 6, Pareto distribution). The mathematical expression of the power distribution is unparalleled in its conciseness, with different power distributions reflected only in the difference in the Gaussian index. It differs from the Gaussian distribution in that events with small to negligible probabilities are not as rare in the Gaussian distribution.

  

  

  Why is the influence of the black swan so great? - Here the theory of variation in modern physics gives a shocking answer. I'm naming it with a specific example - an avalanche. An avalanche is the collapse of a large area of snow that would have been almost impossible to push to a mountain, and an avalanche fits the definition of a classic black swan event and normally hardly ever happens, once it happens. Why do we hear about avalanche accidents so often in reality?

  The critical state is a fragile state of equilibrium, where the force of holding the snow together is almost equal to the force of breaking it up, but only if the plane is slightly tilted. You throw a small stone on a huge snow slope, and the force of the stone is not absorbed by the local snow body but spreads throughout the snow body, like the last straw of a dead camel, causing the balance to collapse.

  The critical state makes the black swan a decisive force.

  

  At the heart of avalanche theory is the infinite amplification of the effect of detail in a critical state (positive feedback); a small, locally limited factor spreads throughout the body in a critical state. Theories of avalanches span fields such as earthquakes, stock market crashes, financial crises, and even the outbreak of social revolution.

  In an even-handed battle, any individual's small role can be magnified and alter the battlefield. For example, in a two-sided tug-of-war, a team member's mobile phone rings, causing him to panic, and the effect is to spread panic throughout the team, resulting in a game being ruined by the ringing of a mobile phone. The so-called loss of a nail, breaking of an iron, breaking of an iron, breaking of a war horse, breaking of a war horse, wounding of a knight, wounding of a knight, losing of a battle, losing of a battle, an empire.

  The nature of the flood of life is a special kind of transformation. So everything related to life, including the history of life and the history of our humanity and the life of each of us, happens in a critical state, that state full of avalanches, big and small, that unpredictable detail determines the state of the whole. Since you are alive tomorrow, the black swan will fly.

  NOTE: Biological evolution is the most primitive black swan effect, where the variation of organisms is already exceptional, and the variation that can survive is even more exceptional, and it is such exception rather than the mainstream (average) that dominates the evolution of organisms. Our world-ruling mammalian ancestors, who for billions of years hid in the shadow of the mainstream reptiles (dinosaurs), ate the remnants of their fallen life, until one day, the black swan came down and a plague ended the dominance of the reptiles...

  The black swan brings uncertainty deeply into our daily lives, and as a theorist, I feel that the world of perfect lines, parabolic lines, and Newton's laws is like an empty city. Its massive reinforced concrete, which still supports modern industry and even led us to discover the secrets of the black swan, does not allow us to understand ourselves.

• The Book of Revelation

  • Black Swan on the Front - Opportunities to be Treated:

  Living is a hard truth. Our culture encourages heroes, but history is written by survivors. Living well, with your heart open, your eyes open, your eyes open, your eyes open, you have more opportunities to wait for your black swan.

  • Negative Black Swan - Thailand is at risk:

  The characteristic of the black swan is that it is black, it hides in the darkness before it appears, and even if it is watching you from behind you, you can't know.

  • Risk management:

  Stop the damage. When a negative black swan falls, the only thing to do is to limit its impact locally and not trigger an avalanche.

  • Treatment of academics:

  Nevertheless, do not underestimate Gauss, because even the rational distribution can only be appreciated by understanding Gauss.

Translated from several dimensions of wealth