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Loves Me, Loves Me Not (Do the Math)

数学
爱的微分方程
This article is a ‎ ‎ for Opinionator by Steven Strogatz.
“In the spring,” wrote Tennyson, “a young man’s ‎ lightly ‎ to ‎ of love.” And so in keeping with the ‎ of the ‎, this week’s ‎ ‎ at love ‎ — mathematically. The analysis is offered ‎, but it does ‎ a serious point: that the laws of ‎ are written as ‎ equations. It also helps ‎ why, in the words of another ‎, “the ‎ of true love never did run ‎.”
To ‎ the approach, ‎ Romeo is in love with Juliet, but in our ‎ of the story, Juliet is a ‎ lover. The more Romeo loves her, the more she wants to run away and ‎. But when he takes the ‎ and backs off, she begins to find him ‎ ‎. He, on the other hand, tends to echo her: he warms up when she loves him and cools down when she ‎ him.
What happens to our ‎ lovers? How does their love ‎ over time? That’s where the math comes in. By writing equations that summarise how Romeo and Juliet respond to each other’s ‎ and then ‎ those equations with calculus, we can ‎ the ‎ of their ‎. The ‎ ‎ for this ‎ is, tragically, a never-ending ‎ of love and ‎. At ‎ they manage to achieve simultaneous love a quarter of the time.
The model can be made more realistic in ‎ ways. For ‎, Romeo might react to his own ‎ as ‎ as to Juliet’s. He might be the type of guy who is so worried about ‎ himself at her that he slows himself down as his love for her grows. Or he might be the other type, one who loves ‎ in love so much that he loves her all the more for it.
Add to those ‎ the two ways Romeo could react to Juliet’s affections — either ‎ or ‎ his own — and you see that there are four ‎ types, each corresponding to a different romantic ‎.
My students and those in Peter Christopher’s class at Worcester Polytechnic Institute have ‎ such descriptive names as Hermit and ‎ ‎ for the ‎ kind of Romeo who ‎ his own love and also ‎ Juliet’s. Whereas the ‎ of Romeo who gets ‎ by his own ‎ but ‎ off by Juliet’s has been called a Narcissistic Nerd, Better Latent Than Never, and a Flirting Fink. (Feel free to post your own suggested names for these two types and the other two possibilities.)
Although these examples are ‎, the equations that arise in them are of the ‎ kind known as differential equations. They ‎ the most ‎ ‎ ‎ has ‎ ‎ for making ‎ of the ‎ world. Sir Isaac Newton ‎ them to ‎ the ‎ ‎ of planetary motion. In so doing, he unified the heavens and the earth, showing that the same laws of motion ‎ to both.
In the 300 years since Newton, ‎ has come to ‎ that the laws of ‎ are always ‎ in the language of ‎ equations. This is true for the equations governing the ‎ of ‎, air and water; for the laws of ‎ and magnetism; ‎ for the ‎ and often ‎ ‎ realm where quantum mechanics ‎.
In all ‎, the business of theoretical ‎ ‎ finding the right differential equations and ‎ them. When Newton discovered this ‎ to the ‎ of the universe, he felt it was so precious that he published it only as an anagram in Latin. Loosely ‎, it reads: “It is useful to ‎ differential equations.”
The ‎ idea that love ‎ might progress in a ‎ way ‎ to me when I was in love for the first time, trying to ‎ my girlfriend’s ‎ behaviour. It was a summer romance at the end of my sophomore year in college. I was a lot like the first Romeo above, and she was ‎ more like the first Juliet. The ‎ of our ‎ was ‎ me crazy until I realised that we were both acting mechanically, ‎ ‎ ‎ of push and pull. But by the end of the summer my equations started to break down, and I was ‎ more ‎ than ‎. As it ‎ out, the ‎ was ‎. There was an important variable that I’d left out of the equations — her old boyfriend wanted her back.
In ‎ we call this a three-body problem. It’s ‎ ‎, ‎ in the astronomical context where it first arose. After Newton ‎ the differential equations for the two-body problem (thus explaining why the planets move in elliptical orbits around the sun), he ‎ his ‎ to the three-body problem for the sun, earth and moon. He couldn’t ‎ it, and neither could anyone else. It later ‎ out that the three-body problem ‎ the ‎ of chaos, ‎ its behaviour unpredictable in the ‎ run.
Newton knew nothing about chaotic dynamics, but he did tell his friend Edmund Halley that the three-body problem had “made his head ‎, and kept him ‎ so often, that he would think of it no more.”
I’m with you there, Sir Isaac.
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