Purity of Mathematics

My friend, Abhishek has put up a series of posts which describes various branches of Mathematics (Applied Mathematics, Pure Mathematics). Some of you may not be able to read them as they are in hindi.
Reading these I remembered a similar post on xkcd comparing purity of various field (branches)

I’ll agree with it but comic misses the Applied Mathematics, which i think will have application in the whole spectrum of various branches mentioned by comics. On the other side Pure mathematics is purely based on reason, ignoring its usability.

Mathematicians have always had differing opinions regarding the distinction between pure and applied mathematics. One of the most famous (but perhaps misunderstood) modern examples of this debate can be found in G.H. Hardy’s A Mathematician’s Apology.

Applied mathematics sought to express physical truth in a mathematical framework, whereas pure mathematics expressed truths that were independent of the physical world.

June 26, 2008 | Filed Under offbeat | 1 Comment

Yahoo search is improving

Earlier I wrote about Sometimes yahoo is better is better than google in providing search results when I was searching for Installing latex on hostmonster. And now with its open search platform SearchMonkey its trying to close in to Google. SearchMonkey allows you to create data services to built search apps that can enhance your search results.

Yahoo search gallery provides you many existing search enhancements that you can add after logging to yahoo. [Via labnol.org].Try various enhancement like LinkedIn Profile, IMDB results, StumbleUpon Reviews and other popular ones.

And you can also create your own search enhancement using step by step method using Presentation application (SearchMonkey Guide).

SearchMonkey API unables you to modify how particular links appears in search results. You can add images, related links and other html formatting but it does not unable you change position of a page in search result. I was unable to find feature which will enable us to filter sites which requires you to login or sites like ebay and amazon which may not be relevant to us by making their appearance farther in search results.

But still these enhancements provides you little summary of search results which is very useful like in case of movie reviews, people profile via linkedIn, stock information etc thus sometimes making opening the actual webpage unnecessary.

June 20, 2008 | Filed Under webdev | 2 Comments

Puzzle puzzle every where

Past few weeks have been puzzle/problem solving weeks, which includes 4 google treasure hunt problems. (Robot in a Maze, Puzzle 2 (getting lines from specific files in zip archive), Network routing table and last one:Prime numbers ). Solving these was fun.
puzzle
Two days back my friend shared this (Galton’s Paradox) on Google reader (My Google reader shared Items). Try explaining it not that difficult though.

But what drew my attention again? Yesterday I was watching 21 movie, Its based on real story of six MIT students cashed in millions in Vegas Casinos by counting cards. Here comes the puzzle, In a classroom scene Prof Micky asks one of the student (Jim, our hero)

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

I’m sure you will be left puzzled for a moment, when you hear the solution by Jim, at least I was. Its a tricky one, But you can get through it . So what choice would you have made, I’ll update the post with answer after few days.

Update:

This is famous puzzle known as Monty Hall Problem. Wikipedia has very good explanation for this.

Because there is no way for the player to know which of the two unopened doors is the winning door, most people assume that each door has an equal probability and conclude that switching does not matter. In fact, in the usual interpretation of the problem the player should switch—doing so doubles the probability of winning the car, from 1/3 to 2/3.

Also Read: Classic Computer Science Puzzles

Orio’s Riddle Completed
Twisty Puzzles

June 7, 2008 | Filed Under puzzle | 3 Comments

Google treasure hunt: last puzzle

Few days back google announced about last leg of google treasure hunt journey. This time they provided unix epoch time 1212448500, time when puzzle was supposed to get released.
You can use http://www.epochconverter.com/ to convert it to human readable format. This side also provides list of available methods to get epoch time, convert it to human readable format and vice-versa.

PHP date(output format, epoch); Output format example: ‘r’ = RFC 2822 date
Python import time first, then time.gmtime(epoch)
MySQL from_unixtime(epoch, optional output format)

So the puzzle was supposed to release at
Mon, 02 Jun 2008 23:15:00 GMT, for India: Tuesday, June 03, 2008 4:45:00 AM (middle of the night).

Forth Puzzle is available here. Its a bit tricky, but i wrote a c program to calculate the number using brute force method…and it worked.(Share how you did it or is there some shortcut which works without any programming). Problem is to find a prime number which in turn can be expressed as sum of of n consecutive prime numbers. Your answer should satisfy 4 such list of prime numbers of given length.

So its over for now and soon they are going to contest winners and rewards. Hope i could have been one . But I have submitted this puzzle after long delay.(Was sleeping when it was released)