Advice to a Beginning Graduate Student or What is Research? or The 4 R's of Graduate School: Reading, Rithmetic, Research, and Writing
a.Books are not scrolls. 书籍不像卷轴
Scrolls must be read like the Torah from one end to the other. Books are random access -- a great innovation over scrolls.
Make use of this innovation! Do NOT feel obliged to read a book from beginning to end.Permit yourself to open a book and start reading from anywhere.In the case of mathematics or physics or anything especially hard, try to find something anything that you can understand. 翻译:
b.Read what you can.
c.Consider writing what you read as you read it
a.You are all computer scientists.You know what FINITE AUTOMATA can do.You know what TURING MACHINES can do.For example, Finite Automata can add but not multiply.Turing Machines can compute any computable function.Turing machines are incredibly more powerful than Finite Automata.Yet the only difference between a FA and a TM is that the TM, unlike the FA, has paper and pencil.
Think about it.
It tells you something about the power of writing.
Without writing, you are reduced to a finite automaton.
With writing you have the extraordinary power of a Turing machine.
a.CLAUDE SHANNON once told me that as a kid, he remembered being stuck on a jigsaw puzzle.
His brother, who was passing by, said to him:
"You know: I could tell you something."
That's all his brother said.
Yet that was enough hint to help Claude solve the puzzle.
The great thing about this hint... is that you can always give it to yourself !!!
I advise you, when you're stuck on a hard problem,
to imagine a little birdie or an older version of yourself whispering
"... I could tell you something..."
b.The importance of PARADOX and CONTRADICTION.
When you can prove that a statement S is true,
and you can prove that the same statement S is false,
then you KNOW that that you're on to something:
Something is wrong somewhere.
Never underestimate the power of a contradiction.
It is one of our most potent sources of knowledge
c.Make a list for yourself of good ways to pursue a problem.
My own favorite is to try small examples.
d.Brains are muscles.They grow strong with exercise. And even if they're strong, they grow weak without it.