principle 1: fight against intuition and calculate what you can.
there is an arithmetic problem: suppose the earth is a regular sphere, and a circle along the equator is the diameter of the earth (with a radius of 64 meters). There is a wire, the length of which is 1 meter longer than the circumference of the earth. If a concentric circle is formed around the equator with this wire, a gap will be formed between the wire and the surface of the earth. Can a mouse with a diameter of 16 mm pass through this gap?
The earth is so big, and the circumference along the equator is so long, but the circumference is increased by 1 meter, forming a gap, which can be ignored intuitively, and there is almost no gap, and then the answer is drawn-this 16 mm mouse will definitely not get through.
however, after calculation, it is known that the height of this gap is h = 1/2 π = .1591 ≈ .16m = 16mm.
after calculation, the result is contrary to our intuition.
Therefore, in many cases, you can't judge by intuition, otherwise you will make mistakes.
Nowadays, behavioral economics, psychology, etc. all reveal psychological fallacies, and the counterintuitive way is to calculate according to scientific knowledge and avoid taking it for granted.
principle 2: look for conditions and increase the probability.
When Sherlock Holmes investigates a difficult case, he constantly discovers new clues and evidence, thus revising the original judgment, gradually discovering the truth and bringing the real crime to justice.
principle 3: believe in system and be long-term.
As we all know, gambling is not a good thing. People who gamble for a long time will eventually lose to "casinos", such as lottery tickets. The probability of winning is simply too low, but many people are studying "cheats and skills". That is because these people really don't understand probability. In the long run, gamblers will lose because the probability tends to the casino, otherwise the casino would have closed down.
There is a famous saying in the field of basketball: In training, the ball thrown with the correct posture is more valuable than the ball thrown with the wrong posture. If you rely on "ignorance" to play basketball, you can't win the game. After all, basketball is more skill than luck. Unlike football, it often "surprises".
the same is true for our study. Although many times, it seems that "reading is better than not reading", in the long run, people who read more are more likely to achieve something.
As the saying goes, "One good turn deserves another, and another bad turn deserves another." It's the power of the system and the power of time.