An interesting text about luck, luck and logic.
Misconception: In order to understand how to succeed, it is necessary to study the success stories.
Truth: If the failure is negligible, then the difference between success and failure is not visible.
The text description.
Once in New York, in an apartment a few blocks from the center of Harlem, gathered a group of scientists and was the equation that could equally well how to kill, and save hundreds of thousands of lives.
People walking along the same street, and did not suspect that the four floors above are hard at work, which could tip the balance of World War II, while the secret agents of the United States, the soldiers of arithmetic, have entered into a statistical battle. By opening their umbrellas and lighting a cigarette, people might not know also that in an apartment overlooking the "Morningside Heights» [Morningside Heights] one of the soldiers has saved effortlessly US forces from one incredibly stupid mistake. Incidentally, such an error does each of you every day.
For the opportunity to work with these masters of mathematics moved their families here, some even came from the other side of the ocean. While they were unpacking their things in their hometown theater poster for "Citizen Kane" has replaced the poster "Casablanca" and the newspapers in which they wrapped up their plates and photo frames, still were full of articles devoted to the events of Pearl Harbor. Many of them abandoned their positions in universities. Other abandoned such work to be able to completely surrender his thoughts in teams working on the armed forces, and not sprayed on any other obligations except evening zachekinitsya home in the kitchen and throw a food for the brain. All of them left their work and rushed to the military service to help defeat Hitler, but not guns and muscle, and integrals and exhibitors.
These people - all as one, potential Nobel laureates - have been collected on the orders of the White House in the so-called "Group of statistical research." ICG was opened at Columbia University and worked mainly statistical analysis. Philadelphia computing unit consisting exclusively of women mathematicians, six days a week poring over the University of Pennsylvania ballistic tables. At Harvard, Princeton, Brown and other universities also work in groups with other specializations, there have been 11, each headed by a trend established by the government to defeat the Axis. Together, they were called the military department of mathematics.
Well, actually, they were not called so menacing and seductive. In fact, they had the name of poskuchnee: Committee of applied mathematics, but they worked as if it was the military department of mathematics.
Department, uh, okay, okay, the Committee was established, because the United States needed help. A huge wave of new technology has swept daily life and the miracles that were collected before huge crowds at the World Fair, and now no one is surprised. The numbers and variables involved are now in a much more complex scenarios that can not be solved so easily with the help of maps and binoculars. Armed Forces realize that they face a problem that did not get up any more in front of one soldier. For things such as missiles, radar posts and carriers, we have not even come up with the best ways to manage. The most advanced computing devices at that time were a clumsy experiments of telephone exchanges or electronic tubes. Calculator was like the ugly fruit of love old-fashioned typewriter and antediluvian cash register. To solve the problems of the modern art of war, you would have needed a powerful computer and the most powerful computers of the time to work on coffee and sandwiches.
Here's how it happened: somewhere deep in the mechanisms of the terrible machines of war commander encountered any problems. He sent a report of its Chief Committee, which redirects the job to the group that, in his opinion, would deal with it the best way possible. Researchers from this group went to Washington and met with senior military leaders and their advisers, and explained to them the vision of this problem. It's kind of like a call to tech support, only you call geniuses of computer technology, which later invented a new way of understanding the world through the lens of mathematics, and this method was found by them in an attempt to win the global battle for control of the entire planet.
For example, the Navy really wanted to know the best path of torpedoes against a large enemy ships. All they could do - is to give a series of shot in a hurry, blurry black-and-white photographs of turning Japanese warships. The Committee gave these pictures to the processing to the central computer (you know, at that time the central computer was made of flesh and blood), which was looking for the optimal solution. Military Mathematics issued a decision almost immediately, as you have seen the problem description. As they explained to the Navy, Lord Kelvin invented the calculations even in 1887. Here's a look at the shape of these waves, they disagree as blossoming fern. The distances between the waves carry all the necessary information, everything is clear as day. It is necessary to calculate the distance between crests, and you get the value of the speed with which the ship is moving. Lord Kelvin has not provided, of course, what to do in case of turning the Japanese vessels, but that's okay, they said. And mathematician wrote in their notebooks, and to draw on the boards, as long as they have not studied the issue thoroughly and found no solutions. Then they measured the parameters of the waves from these ships and to make sure their calculations are correct. In the arsenal of the Navy, a new skill: the ability to launch torpedoes on target turns on the ship on the basis of only one form of waves of the ship.
Devotion Mathematical soldiers increased at the same time as the war grew bloodier, and they knew that from the settlement, which they filled with secret board and protected pieces of paper, depended on who will return home to his family, and someone - no. Leading minds of all disciplines willingly joined the battle, and although modern textbooks devote a couple of paragraphs only work decryptors and creators of the atomic bomb, in fact, there were many groups of scientists, the history of which will never make headlines, because the outcome of their work was the equation used for military operations. One such story was nearly forgotten forever. This is a story about an outstanding statistics on behalf of Abraham Wald, who saved uncountable number of lives by preventing a group of generals from doing normal human error, error that each of you makes every day.
Colleagues described Wald as a gentle and kind man, a genius, has no equal in his area of expertise. One of his colleagues said that Wald "made a decisive change in the method and purpose" of the social sciences. Wald was born in Hungary in 1902 on a piece of land that later became owned by Romania. The son of a Jewish baker, Wald spent his childhood studying the equation, and finally made his way through the academic thorns and became a graduate of the University of Vienna, where his teacher and mentor was Carl Menger himself, a famous mathematician. He was one of those students who make suggestions for improving the book on which the study and followed to their suggestions were incorporated into the new editions. His mentor Wald acquainted with the problems over which puzzled the experts of this field of science, for example, stochastic differential equations and intermediate between the ternary relationships in a metric space. Not only that, Wald returned puzzles solved within a month or something like that, so he still politely asked him to send him more of the same. As he studied the science of probability and statistics, his name became famous mathematicians of the United States, and eventually he flew to the United States in 1938, reluctantly, because of the growing threat of the Nazis. His entire family, except one brother later died in the concentration camp Auschwitz.
Shortly after Wald moved to the United States, he joined the Committee of Applied Mathematics and started working with the team at Columbia University in the same apartment with a view of Harlem. His team tried to discover the laws and apply statistical methods to the problems and situations that were too large and bulky for the warlords to deal with them yourself. They converted the geometry of air combat in the graphs and charts, the success rate was calculated bombsight and different tactics. The longer the war lasted, the more attention has been focused on the key issue of the war to keep the planes in the sky.
During World War II bomber crew chance to survive in a military operation were the same as a coin toss and throw tails. For a moment, imagine yourself any member of the crew of a bomber in the war: you spend hours to fly over a country in which everyone wants to kill you, hang out in the middle of the sky, you can see from anywhere, you are vulnerable from all directions, above and below, you fly flows antiaircraft fire to knock you out. "The Living Corpse" - that is as described by historian Kevin Wilson [Kevin Wilson] all the pilots of the Second World War. They were willing to die as a chance to survive the bombardment were such as to run a football field infested by angry wasps, and did not get a single bite. Once, perhaps, it turns out, but if you run back and forth all the time, no luck is not enough to protect you. Any benefit that could come up with mathematics, the tiniest, could yield a huge difference from day to day operation of the operation.
Senior management has resorted to the same pattern as in the case of torpedoes: to provide all information known to them by the Committee and this issue has been put before Wald and his team. How, I asked Aviation ground forces as much as possible to increase the percentage of returning bombers. Military engineers explained that Allied bombers could do with more armor, but the ground crew could not sheathe planes as tanks, they are not just soared. Then the commanders were asked to identify the best place to add armor only there. Wald was then prevented serious mistake that almost made the armed forces, the victim of "mistakes survivors" - errors of perception, which would have completely changed the course of history, if left undetected and uncorrected. See if you notice it.
Military examined bombers who managed to return from the enemy territory. They pointed out all the places in which aircraft were damaged most. Examining one plane after another, they noticed that, in general, most of the bullet holes were along the wings, near the arrow tail gunnery installation and center bottom. Excellent. Wings. Housing. Tail. Given this information, where would you put dopbronyu? Of course, the team decided to add a reservation there, where we saw the most damage - which was the biggest holes from bullets. But Wald said that it would be absolutely wrong. Installation of additional armor in these places do not improve their chances.
Do you understand why it is a stupid idea? The mistake Wald noticed immediately is that the bullet holes showed a strong space bomber. They showed, can be reached so that this plane will remain sufficiently whole to return home. In the end, it's just a bullet holes and all. It does not need more armor, just enough, and the standard, but a place where there is no trace of the bullet does not hurt to protect better. Wald said, "Look for a place where the surviving bombers are not damaged. These are the most vulnerable places. They came back only because there were no ».
So, Wald took into account the error of survivors and began to computing what level of damage can withstand every part of the aircraft to the total destruction of the aircraft: engine, flaps, pilot, stabilizers and so forth., And then use the heap complex equations he showed the commander of the probability with which the average Bomber will be damaged in these areas during normal military operation depending on the strength of resistance. These calculations are used to this day.
The military was all available information, at stake was the fate of the country, but still commanders could not notice the error in his logic. So many aircraft would be in vain reinforced armor, if not for the intervention of one person.
Now in front of you must be wondering. If the chief of the armed forces of the United States of America made such a simple and stupid mistake in dealing with such an important issue because of the mistakes of survivors, as you think, does the error surviving on a set-by-ozhestvo daily decisions that you take? As you know, the answer is yes. Always.
Roughly speaking, the error of survivors - a tendency to focus on survivors rather than killed, depending on the situation. This means focus on living instead of the dead, to winners instead of losers, successes instead of failures. In the case of Wald military pay attention only to the aircraft returned to base, and almost made a terrible mistake, because it does not take into account the aircraft remaining on the battlefield.
So much easier. If, after some process has "survived", that means "nevyzhivshie", which is usually destroyed, forgotten or removed out of sight. Once the failure is invisible, you are, of course, much staring at the successful outcome. Not only that, you do not even notice the missing part may be important, because often you do not notice that something is missing.
Every time you divide the world into winners and losers, and the losers luckies, living and dead, you should keep in mind that paying much attention to one side, you ignore the second. If you decide to open a restaurant in the city, based on the fact that there are a lot of profitable restaurants, you ignored that you see only the survivors who have become successful restaurants, surviving in the competition. Perhaps 90% of all public schools in your city went bankrupt in the first year. But you do not know, because for you they do not exist. As Nassim Taleb wrote in his book "The Black Swan", "the cemetery closed restaurants very quiet." Of course, survive the best and most successful, so those restaurants that have survived in this brutal environment, look and are very successful. You look at them every day and think that this is evidence of the ease and profitability of the restaurant business, but actually in front of you a secret sign from above, and it is written: Run away.
Error survivors makes you reach for the nutrition gurus, the directors of companies and famous sports stars. It is very hard to avoid this irresistible desire to understand success and pieces, like a magpie, to drag out all the most brilliant in their nest. You look at the lighter side of success in the search for clues as you live better, how to cope with the forces that oppose you. Everyone loves public speaking people that are rare examples of how they overcame adversity and survived despite everything. The only pity is, you rarely carry forth from these inspiring speeches recommendations on what not to do and what to avoid. Because the authors of these speeches are usually stupid do not know.
Such information is lost along with the people who were not able to win the circumstances have not been put on the cover. Such people are no calls to act on the presentation of diplomas and inaugurations. Actors who moved from Louisiana to Los Angeles and returned home empty-handed after two years, do not sit next to James Lipton and watching his Oscar-winning film, while students eagerly swallow every word, as a source of holy wisdom.
In short, the advice given only survivors. According to psychologist Daniel Kahneman in his book "Think fast and slow", "if stupid decision led to success, then it is remembered as a genius." All the actions of companies like "Microsoft" or "Google" or "Apple" that we see - it's like the bullet holes on the wings of airplanes. Nobody remembers about those who fell into enemy ground, getting too serious damage. Kahneman says that before you start to repeat the history of well-known company, is to return to the days when the company was in its infancy, and ask ourselves whether the consequences of decisions predictable. If not, it is likely that you now it seems coherent strategy, in fact, is a collection of chaotic action.