"The cat flips itself right side up, even though its angular momentum is zero. It does this by changing its shape. In terms of gauge theory, the shape space of the cat forms the base space of a principal SO(3)-bundle, and the statement "angular momentum equals zero" defines a connection on this bundle."
Richard Montgomery, 1993
Now, I guess everything makes sense to me in some sense. May be because it is a "falling cat problem" that let me feel the problem more "physical" in mathematical sense. I’m not a mathematicians (may be partially), but I do appreciate the beauty of mathematics to describe physical systems.
Anyway… 1 more historical aspect about maths – in fact, not really math, but math in daily life – have you ever thought of why 1 foot = 12 inches, 1 hour = 60 minutes, or 1 day = 24 hours? I meant, why the numbers like 12, 24 and 60 have been used in measurements?
I always think about such very common but wierd questions in our lives…
No clue about them, just feel magic~
p.s. 爱因斯坦等牛人就是这样疯掉了，因为地球上的一切都太神奇了！
嗯… 当哲学演变成科学… 科学演变成数学… 数学再演变回哲学的时候… 绕了一圈, 就连自己是活在梦中还是现实中都不清楚了 =)
哈哈, 真的疯了!
P/S: 还是可以在这些"空间"中选择性地自由跳跃… 没事, 我还是知道我什么"时间"处在哪一个"空间"的. 希望不会迷路 =)
还有忘了说… 如果猫猫也懂得数学的话, 估计她会被活生生地摔死的. 人家还开开心心地从树上滚下来呢!
怪不得人会摔死, 因为他们研究数学.
i am totally lost. but sometimes it is happy to find some beauty in math. i still remember in the topoloty class, i alway feel bored. but once, the teacher just proved sth, and i was so surprised about the way how he proved it. wow , it is amazing, math sometimes is beautiful.hahah
Trying to learn more about topology, but still a lot of work needs to be done. At least, anything regarding "invariance" is very important to my area of research. Some times it feels really amazing when having something great to be proven. I personally haven’t been able to do that yet – at least rigorously – I still hope that I’m getting there… haha, just hope =P
My first ever lemma – "slippery when wet". Please let me know if anyone can prove it rigorously =)