Site
I’ve been thinking to have a writing space for myself for a long time. Now the intuition for having a web writing space comes from two parts. The first part is the idea of writing things, and the second part is to have them posted on the web. If you think about it, these two parts can both be the accelerator and the obstacle of each other. For example, when you knew how to host a website at the first time, you may want to write a lot just to tell others that you have such ability. But then you realized that most web themes shared on the Internet serve commercial purposes instead of quiet writing, you become struggling and will soon forget this project, since your production is just too ugly to watch.
To overcome this problem, we have several strategies:
- Forget about the techniques and post your writings on Medium.
- Keep developing your website and post writing about how you developed it. This can push you through the process, and I think it is also an usual strategy used by a lot of YouTubers.
- Lucky enough to know some techniques and encounter a theme that you like, while you also know a few tricks to tweak it. Nice.
I hope we are all lucky at this point, so have a fortune cookie. You open it, and it comes with:
“Everyone holds his fortune in his own hands, like a sculptor the raw material he will fashion into a figure. But it’s the same with that type of artistic activity as with all others: We are merely born with the capability to do it. The Skill to mold the material into what we want must be learned and attentively cultivated.”
Johann Wolfgang von Goethe
Tangent Space
Suppose that $M$ is a $C^k$ differentiable manifold (with smoothness $k\ge1$) and that $x\in M$. Pick a coordinate chart $\varphi:U\rightarrow\mathbb{R}^n$, where $U$ is an open subset of $M$ containing $x$. Suppose further that two curves $\gamma_r, \gamma_2:(-1,1)\rightarrow M$ with $\gamma_1(0)=x=\gamma_2(0)$ are given such that both $\varphi\circ\gamma_1, \varphi\circ\gamma_2:(-1,1)\rightarrow\mathbb{R}^n$ are differentiable in the ordinary sense (we call these differentiable curves initialized at $s$).
Then $\gamma_1$ and $\gamma_2$ are said to be equivalent at 0 if and only if the derivatives of $\varphi\circ\gamma_1$ and $\varphi\circ\gamma_2$ at 0 coincide. This defines an equivalence relation on the set of all differentiable curves initialized at $x$, and equivalence classes of such curves are known as tangent vectors of $M$ at $x$. The equivalence class of any such curve $\gamma$ is denoted by $\gamma’(0)$. The tangent space of $M$ at $x$, denoted by $T_xM$, is then defined as the set of all tangent vectors at $x$; it does not depend on the choice of coordinate chart $\varphi:U\rightarrow\mathbb{R}^n$.
Viva La Vida
Live The Life
生命万岁
Me
Things I’m doing
- Work for Google Cloud
- Piano Playing
(Also try this one)
Cities I’ve lived for years
- New York
- Shanghai
- Sunnyvale
Cities I’ve lived for weeks
- Ithaca
- Cupertino
- Ann Arbor
- Boston
- Adelaide
- Indianapolis
This is the weather of the city where I am currently in. I hope this can make you may feel close to me. :)