I call myself a wonder of science and technology, and now I will try to prove Murphy's law mathematically.
Background: Murphy's Law 1949 originated in America. At that time, an aviation engineer named eddie murphy participated in the manned rocket test of the US Air Force. One of the experiments needs to install a set of *** 16 sensors on the experimental equipment, and then pressurize it. As long as the sensor does not give an alarm, it can continue to pressurize. But the experimental equipment has been deformed under great pressure, and the pointer of the sensor has not moved at all! After inspection, it was found that the three colleagues who were in charge of assembly had all the 16 sensors installed backwards. Depressed Murphy inadvertently played a joke on one of his colleagues: "If something is likely to go wrong, let him do it, and it will definitely go wrong." At the subsequent press conference, Murphy's boss stapp quoted this sentence and dubbed it "Murphy's Law". Since then, Murphy's Law has spread rapidly around the world, and produced many interesting inferences, including China's version of "No matter what you are afraid of". Some people even exaggerate Murphy's Law, Parkinson's Law and Peter's Principle as the three major discoveries of western culture in the 20th century.
At present, the main content of Murphy's law is these four sentences:
First, nothing is as simple as it seems;
Second, everything will take longer than you expected;
Third, things that can go wrong will always go wrong;
Fourth, if you are worried about something happening, it is more likely to happen.
At this point, the problem has been explained. You can look at my Sao operation to prove it.
First of all, the first, second and third sentences above contain the words "any", "all" and "all", which is a typical full-name judgment in logic and a nightmare for science and engineering men. Let's put it aside first. The fourth sentence "more likely" seems to prove slightly less difficult. Let me start with the fourth sentence. "If you are worried that something will happen, then it is more likely to happen." Let me translate it into the following mathematical logic language:
Assume that all the events discussed are random events;
Let A be the probability of a random event with a bad ending (a situation that people are worried about); B is the probability that a random event will have a good result (people are not in a hurry), (a+b < =1);
So the task now is actually to prove that A is greater than B (that is, A is more likely).
In order to prove that A is greater than B, I now define two concepts, the simplest event C and the complex event D. The simplest event C is an event that only contains an independent process (only one step) and two possible outcomes (that is, two sample points). For example, throwing coins involves only one step: throwing; There are only two possible outcomes: positive and negative. There are only two basic events in the sample space, S = {(positive), (negative)}; ? Therefore, coin toss is the simplest event. C. Similarly, there is only one independent step to guess the outcome of the World Cup finals: betting on France or Croatia can be completed with only one bet; There are only two possible outcomes: France wins or Croatia wins. So this also belongs to C. Another example is chasing the goddess. There are too many independent steps (such as meeting/introducing, knowing, communicating, eating, giving gifts, etc.). ), not in one step; Moreover, there may be more than two kinds of results, at least there are many kinds, chasing women successfully, chasing women failing, and cherishing, crying for women or even having no chance to start. So it is not the simplest event c, but a complex event d (including two or more steps, or/and two or more possible outcomes). For the above two possible coin toss results, it is considered that the probability of heads and tails is the same, both being 0.5. Guess the final win or lose, this probability is unknown. The probability of chasing the goddess is even more unknown.
1. Look at the real daily events we encounter in our lives, such as daily walking, living, sitting and lying, studying and working, pretending to struggle and so on. It is easy to know that most of the daily events are not the simplest events C, but complex events D; Because most everyday events have more than one step and more than two results. It is difficult to find an event that satisfies both conditions (only one step, only two outcomes). I will directly use this common sense as the premise of proof, so I won't say much.
2. Now I assume that the complex event D contains m steps and n results (m, n is an integer greater than 2). For example, finding an object includes at least m steps: meeting/introducing, knowing, communicating, eating, giving gifts, quarreling and being jealous, proposing marriage, planning and wedding. Finally, there are ***n possibilities, feeling, being dumped, being dumped, dying, once, being friends when we meet, getting back together, cherishing when we do it, Ma Rong, getting married and growing old together.
3. After the daily complex event D goes through m processes, among the n possible results, let's examine the situation of good results and bad results. It is easy to know that the possibility of a good result is far less than that of a bad result. For example, there are only a few "good" results in finding a partner, or even only one. For some people, marriage is the only good ending. Then according to the multiplication principle of step-by-step events in middle school mathematics and the addition principle of classified events, the probability of a good ending is obviously much lower than that of a bad ending. Because, if we must finally achieve the only good result, we must do it right in m steps and not wrong in one step. Finally, the only correct option among n results can be realized. In this way, the correct path is close to 1, which means you have to avoid all the pits perfectly. There are many, many kinds of roads, and you may go wrong. Let each of the m steps have the option r 1, R2, R3...RM in turn (r 1, R2...RM is a positive integer). According to the principle of multiplication, the total path of * * * is x = r 1. R2...R3...RM is obviously much larger than 65438. Even if there is no equal possibility between X paths, it can be safely judged that the probability of a bad ending is far greater than that of a good ending.
4. From the above 1 and 2, we can know that the real events that human beings face daily are rarely the simplest events C, and most of them are complex events D. Even the simplest events C have a good ending probability of only 0.5. As can be seen from the above 3, the probability of daily real complex event D having a good ending is far less than that of having a bad ending.
5. From 4, we can know that the probability of real random events facing human beings in daily life developing into possible bad endings is far greater than the probability of good endings. As for whether we can succeed in doing something, it is generally not that God randomly favors things on our side, but that we have successfully ruled out all the bad possibilities and avoided all the pits perfectly. Building a building needs the careful cooperation of countless technicians and workers, destroying a building needs countless days and nights, and destroying a building only needs a bomb in less than one second, that is, the function of any one of m important steps (such as calculating bearing capacity, steel strength, building stress, seismic performance, fire resistance, fatigue coefficient, etc.). If it is not realized, the building will be destroyed (such as explosion destroying the load-bearing function).
6. So far, it has been proved that the probability of bad ending of daily events is far greater than that of good ending, which is the fourth sentence of Murphy's Law. If you worry about something bad, it is more likely to happen. From this, we can prove the third sentence loosely, because mistakes are also worrying things, so the probability of making mistakes is greater than the probability of not making mistakes (of course, it is impossible to prove the full-name judgment sentence strictly). Similarly, the first sentence and the second sentence can also prove that the fear of taking too long and that things are not that simple is also one of the bad endings that people are most worried about.
7. Above, Murphy's Law has been proved.
Summary: The core idea of Murphy's Law is that if a thing may have a good ending or a bad ending, then the bad ending is more likely and the development of the world is pessimistic. My proof process is approximately simulated by the mathematical model of classical probability. Its basic idea is: the group cognition of human beings to a good ending determines that a "good ending" is only a few or even the only optimal solutions, and most real daily events are divided into many steps, and there are many possibilities for the ending. Therefore, in order to finally achieve the only good ending, every step must be made right for every choice, and any wrong step will lead to a bad ending. Therefore, according to the classical probability, the possibility of a bad ending is greater than the possibility of a good ending.