Tuesday, September 23, 2008

Rambo mode of Linux kernel

Ok this is interesting......

Kernel enters *Rambo* mode in out_of_memory() :mm/oom_kill.c
and what does it stand for..well, kernel starts to "shoot down" processes hoping to increase amount of free memory in the system.

Friday, September 19, 2008

What does 'I' stand for?

No, I am not going to answer that question in this post.

The book I am a strange loop is a search for the answer. I just read 50 pages of it and came up with this thought...

In that book 'being alive' is described as having a set of complex reflexes. Then one of those relexes (one of the strongest) should be a reflex that generates the answer 'I am alive' whenever I ask myself 'Am I alive?'.

"I think, therefore I am"

Church numerals (numbers and arithmetic using lambda calculus)

Here's how one would define zero and increment function using lambda calculus
(define zero (lambda (f) (lambda (x) x)))

(define (add-1 n)
  (lambda (f) (lambda (x) (f ((n f) x)))))
- From SICP
Here zero is a function that takes a function (f) and returns a function which takes an argument (x) and applies f to x, zero times (or do not apply f to x).
The definition of add-1 can be easily understood by looking at the body of inner lambda expression. The body applies f to x (n+1) times, where n is the parameter.
So one would be
(define one (lambda (f) (lambda (x) (f x)))) ; We apply f one time to x
I'll leave the definition of one as an exercise.:-)

Tuesday, September 16, 2008

Bug fixing

Two ways to fix a bug

1. Change the implementation to match the spec.
2. Change the spec to match the implementation.

Monday, September 15, 2008

Some thoughts on mass

F = (Gm1m2)/r2, is the force of attraction between two bodies with masses m1 and m2 and r being the distance between them.

  1. So when two bodies are brought sufficiently close together (such that r becomes very small), the force of attraction will be very large. This force will pull them closer. So masses does have a tendency to combine.
  2. Two masses always attract each other. The universe is full of masses, but ever expanding why??
Law of gravitation

First drive after driving test

I drove all the way from mannuthi to palakkad (1 1/2 hour drive). The drive was OK, but I've got to get lot more practice.

Created a blogger template!!!

I created a blogger template with 2-column layout. You can watch a demo here.

Saturday, September 13, 2008

Implementing conditionals using lambda calculus

Lambda calculus is a way of modelling programming constructs by using only function definition and function application.
This shows you how to model if-then-else using lambda calculus
>>> true = lambda x, y: x
>>> false = lambda x, y: y
>>> ifelse = lambda x, y, z: x(y,z)
>>> ifelse(false, 1, 2)
>>> ifelse(true, 1, 2)
Well that was simple enough...Now for some explanation..We'll look at it top-down.
The chracters in this play are ifelse function, true function and false function [All characters are functions :-)]. The ifelse function takes three arguments and let's it's condition argument chose between 2nd (then-expression) and 3rd (else-expression) arguments. The true function always chooses true's first argument and false always chooses false's 2nd argument.
Note: - There is one catch though. Since python uses applicative order evaluation, this if else doesn't work exactly like the built-in ifelse construct. The following code will cause an out-of-memory exception.
>>> def p(): p()
>>> ifelse(false, p(), 1)

Factorials as summation

The factorial function is defined as
n! = 1, if n = 0
= n(n-1)!, if n > 0
It is recursively defined using products.
It can also be expressed as a recursive summation
Let's see what 3! looks like
3! is simply 3 groups of 2 groups of 1
(1 + 1) +
(1 + 1) +
(1 + 1)
similarly 4! is 4 groups of 3 groups of 2 groups of 1 (I.e. four copies of the above)
((1 + 1) +
(1 + 1) +
(1 + 1) ) +
((1 + 1) +
(1 + 1) +
(1 + 1) ) +
((1 + 1) +
(1 + 1) +
(1 + 1) ) +
((1 + 1) +
(1 + 1) +
(1 + 1) )
Now we can visualize why factorials "grow" like crazy..(10! may take up an entire book)
"Why bats, Master Wayne?"
"Bats frighten me. It's time my enemies shared my dread."
-From Batman Begins

Thursday, September 11, 2008

Stack permutation

I was trying to solve a stack permutation problem in taocp. The question asks us to find no: of permutations of n numbers from 1...n that can be generated using a stack. The no:s 1...n can be pushed into the stack in that order only. When an element is popped of the stack, it is appended to an output queue. Once all elements are in output queue, the order of elements in the queue is a permutation obtained using stack.

For ex:- To obtain 2,3,1 from 1,2,3 we follow the sequence of operations
push 1,push 2,pop 2,push 3,pop 3,pop 1
Not all permutations can be obtained using the stack (for ex: - 3,1,2).

Let the no: of permutations of 1...n be a(n) with a(0) = 1 (only empty permutation possible with no numbers).

We have to find a(n+1)

Suppose that nl no:s appear to left of "1" and nr no:s to right of "1" in a permutation. The process of obtaining a permutation for those nl numbers to the left of "1" can be considered as permuting 2...(nl+1) using a stack (The "1" at the bottom of the stack can be ignored). This no: will be the same as no: of permutations possible for 1...nl using a stack(Only the number of numbers matter).

Then no: of permutations possible for nl numbers to the left of "1" = a(nl).
Similarly no: of permutations possible for nr numbers to the right of "1" = a(nr).

For each of a(nl) permutations of numbers to the left, a(nr) permutations are possible for numbers to the right.
So a(nl)a(nr) permutations are possible for a particular position of "1" in the permutation.
Now nr = n - nl
So a(nl)a(nr) = a(nl)a(n-nl)

No: of elements to left of "1" can vary from 0...n.
So total number of permutations a(n+1) = sum(nl, 0, n) {a(nl)a(n-nl)} = a(0)a(n) + a(1)a(n-1) + .... + a(n)a(0)}

The term a(n) is simply the nth catalan number.

"Never believe in history, because history is created by those who win."

Driver's license

I got my driver's license today.....now I've got to learn to drive(properly)..

"I can only ride in 8's and drive in H's.."
- balu

PS: - This post should be dated 3-Sep-2008