Decimal trap

  How big is the big number?
  An article in a well-known weekly magazine urged everyone not to charge their mobile phones while driving. The article said that the electricity in the car comes from burning gasoline, this kind of power generation mode is too wasteful. How wasteful is it? Americans consume more than 200 million US dollars worth of oil every year because they charge their mobile phones in their cars!
  200 million dollars? Is this number big? There are almost 200 million people driving in the United States, which is equivalent to an extra $1 per person per year. And this one dollar can be used to charge the phone in the car-I don’t know how much trouble it will save, this may be the best dollar you’ve ever spent.
  So a good way to understand large numbers is to divide by a large base.
  It is not these large numbers that are more relevant to our daily lives, but the decimals.
  The risks are all decimals. The scientific way to describe risk is to give a probability, but it is difficult for us to visually understand the extremely small probability.
  For example, there are two types of childcare in the United States. One is run by the teacher’s own home and the tuition is relatively cheap; the other is a formal childcare center with many staff and complete facilities. Current data shows that the probability of children in family nurseries dying due to accidents is 7 times that of regular nurseries-then, if you pay special attention to safety issues, should you send your children to regular nurseries?
  Don’t just look at multiples for problems like this, but must look at the absolute value of the probability. The fact is that only a dozen children die in family nurseries in the United States each year; at the same time, the number of children of the same age who die in traffic accidents is 79 each year. So if the regular nursery is far away from home and the family nursery is close to home, even if the distance is only 20% away, if you only consider safety factors, you should send your child to the family nursery.
  Therefore, you can’t change your face as soon as you hear that there is a risk, you have to compare the various risks together.
  No matter how risky traffic is, we have to go to the streets. Instead of worrying about the dangers of various extremely small probability, it is better to focus on more important things.
  There is a loophole in the social security fund that the United States distributes to retirees. Some people have passed away, but their family members deliberately refused to report; or there may be a problem with the system, which caused his bank account to receive social security benefits. It is estimated that there are 31 million U.S. dollars in losses every year because of this loophole. So, should we quickly find a way to fix the loopholes? Someone made a calculation-this 31 million US dollars is equivalent to 0.004% of the total annual social security funds issued by the United States. In other words, the accuracy of the social security fund is as high as 99.996%, which is simply a perfect system! At this level, if you want to be more perfect, you often need to pay a high administrative cost-the cost is much higher than 31 million US dollars.
  Regardless of the order of magnitude, $31 million is a huge sum of money; at the order of magnitude, this loss is nothing. There are pros and cons to doing anything. In many cases, if you do a calculation, the pros and cons are easy to see, and there are often large-scale differences.
  Is an old thing worthless and not knowing when it will be used, is it worth keeping in a house worth ten million yuan in case of emergency? In order to increase the probability of children being admitted to key universities a little bit, is it worth the whole family to squeeze in a small school district room for more than ten years?
  In our daily judgment, we mainly use pattern recognition-if something is poisonous, the first reaction is not to eat; if something is dangerous, the first reaction is not to do it. But what is poisonous? How dangerous is it? The difference between 0.01% and 0.0001% is huge, but the psychological impact on us is the same.
  Therefore, being able to resolutely use this order of magnitude thinking regardless of psychological impact is a kind of “big man thinking.” Others look at 30 million dollars a lot, and he looks at 30 million dollars very little; others think that this fact is unbearable, and he doesn’t care about it at all. This kind of “adults have a large number” is not pretended, nor is it raised by “raising me with great righteousness”, but calculated.
  Having seen it, calculating it, and then being able to make a rational decision, this is called courage and knowledge.
小数陷阱

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