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One of the mathematical principles of hysteresis effect
(This article is the experience of learning Wu Jun's "Mathematics Common Sense 50", and the pictures come from the course. )

Study hard, but feel no effect; Hard work, but no promotion; If you want to improve your interpersonal relationship, you can't seem to see any change ... but this doesn't mean that your efforts are wrong, just because of the lag effect, you need to persist in your efforts.

Why do these things have a lag effect? One of the reasons is "accumulation" (such as accumulation of knowledge, accumulation of feelings, accumulation of others' comments on you, etc. ) there is a lag effect in mathematical principles.

The black line in the figure below represents the acceleration (you can imagine it as the degree of effort, which is a constant in the figure), the red line represents the generated speed (you can imagine it as the ability to improve due to hard work), and the blue line represents the distance traveled (you can imagine it as the achievement or performance after the ability is improved).

As can be seen from the figure, the increase of speed lags behind the acceleration, and it takes some time to increase to a certain extent, while the distance lags behind the speed and even the acceleration. This is the reason why you work hard, but you don't appreciate it: it takes a while for your ability to improve because of your efforts to appear, and it takes longer for your performance to improve because of your ability.

Mathematically speaking, these three quantities are: speed is the integral of acceleration and distance is the integral of speed. Any value of integral will have hysteresis effect, and integral is an accumulation and a summation. Therefore, when you encounter something that needs to be accumulated in the future, you might as well be more patient, don't give up halfway and wait for good results.

Of course, the reverse is also true. Slack is hard to consume the fruits accumulated by your efforts, but if you continue to slack off, the bad consequences you can't see at first will gradually appear until you can't recover them, or you can reverse them again at a higher cost than before (more expensive than the first effort, because this time you are not starting from scratch, you must first try to reverse the bad consequences caused by slack off).