Inspired by Information is beautiful. The site is maintained by David McCandless, a London-based author, writer and designer. And he says,

I’m interested in how designed information can help us understand the world, cut through BS and reveal hidden connections, patterns and stories underneath. Or, failing that, it can just look cool!

Here is my week.

My week in numbers

I have also pulled up power point charts for some presentation. It is always interesting to see the graphs. But I guess, off late I started hating pie charts and bar charts. They are not more than mere spaghetti some times. There is a famous saying -

Information is beautiful, but it is often presented ugly.

Not with this guy for sure.

Few of the favorites -

• Big money spent on this, on that – a relative picture.
• If twitter was 100 people.

It is lot better then stick charts and pie graphs.

There are two things I read this week and thought weird. One is about ‘Urinal protocol’.

Urinal protocol vulnerability

For those who don’t know what it is, read here. The point is, in a public rest room, every male should take due effort to use the buffer urinal. There are un-written rules, protocols people follow in using urinals. The common one being, using the urinal which is at the maximum distance to the one occupied already. Then, the point of using, allocating these resources effectively comes in as a concern.

• Is it possible to know / determine, the optimum number of urinals? So that, you will built the optimum numbers so that they are used efficiently.
• Are there any bad numbers? good numbers? any study on it? Want to know for what number there will be maximum occupancy, and less occupancy.
• Any civil contractor who is building a public building / mall / college wants to know what is the appropriate number of urinals to built? I guess there is no study available. Now we have one.

It happens to be that, there is a detail study available on urinal protocol vulnerability. I have already mentioned about XKCD here.

Urinal protocol vulnerability - Courtsey - blag.xkcd.com

He goes further and generalises, for how many urinals, the protocols work good and for what numbers bad.  Here are the results.

The good numbers are given by equation results in . When you have urinals in these numbers, and if people follow the urinal protocol, you will atleast get 50% occupancy.

And bad numbers are given by, gives . These number of urinals have only 33% occupancy.

Hilbert’s Hotel

Hilbert’s hotel is a nice paradox on set theory. Read here for more on this. And a nice explanation here.  It is about an important concept in set theory. It is told often that infinity is not  different from cardinality. Although natural numbers are infinite, the cardinality of natural numbers is lesser to cardinality of real numbers. This is explained using notations.

The story goes like this. Assume of a hotel. A traveler enters the hotel, goes to the receptionist and asks for a room. The receptionist tells, they have aleph-null rooms and all of them are occupied. It doesn’t mean, he can’t get room to stay. The receptionist says, he can move the person staying in the first room to second room, second room person to third room and so on. Then he can occupy the first room. This is fine. This is true with aleph-null hotel.

The paradox goes on, if a bus full of travelers come asking for a room? Say, aleph-null number of traveler’s? Then Hilbert says, you can occupy them by shifting, the 1 room person can be asked to move to 2, move 2nd person to 4, move 3rd person to 6, move 4th person to 8, move 5th person to 10… and so on. Once this is done, you will have all odd numbered rooms empty. And the aleph-null bus travelers can occupy them.

The idea is really difficult to get through. But that’s how abstract concepts are placed in math.

And strangely, I have read two entirely different concepts, relating to occupancy. One is used in every day and another one not so easy to even think off. That’s the beauty of math.

Recently I read a book about Microsoft’s Operating systems – Windows.

This happened to be a good read if you have interests in product / software development. I have long cherished other operating systems, like Linux and other UNIX systems. Mainly for their ability to do things and robustness. Windows was never in picture. After I finished reading it, I had a complete new look towards Windows.

It is of like, poor chap, he has tried so many things. No wonder why he couldn’t be like Apple mac or Linux OS.

Few pointers from the book.

• Windows was never a product in Bill Gates mind. His main aim was on MS-DOS for the IBM machines. Windows was born mainly to keep DOS business.
• Windows 1.0 was developed mainly to compete with VisiCorp’s system. VisiCorp applications has a attractive GUI and needs different setup (no DOS!). Gates saw this a threat to his DOS business.
• Windows 1.0 was not tested at all. When ever they had a working build ready, they compiled, made as a package and shipped it. Customers did the testing after buying and submitted bugs to Microsoft which fixed them in the later patches.
• At the earlier state, Windows 1.0 was loaded on MS-DOS. And needs MS-DOS to run. Gates would goto vendors and tell them to write software / drivers files saying IBM machines will run DOS and tell IBM that there are applications developed for DOS by vendors and thus DOS is a must.
• When Bill Gates happened to see one of Apple’s early system, he complained Windows 1.0 is nowhere close to it. He urged the Windows development team to copy Apple’s window rendering manager (Ah!, note: copy) and make Windows look more like Apple.
• Windows 1.0 was never thought as a product which will be supported for long run. Gates thought to keep Windows 1.0 support for few more releases and then stop supporting / developing Windows. His main aim was killing VisiCorp’s and safe guarding DOS. That is done now. Gates tried selling Windows to IBM, but IBM rejected Windows as it was developing some thing similar and decided it would be waste to invest on Microsoft’s application. Gates decided to develop a new generation OS in collaboration with IBM. Later IBM would break this as it finds fault Microsoft’s Windows 3.0. IBM would go on and release OS/2 where as Microsoft would release the software as Windows NT.
• Windows 1.0 & 2.0 can’t run applications parallel. You need to close notepad to open calculator. This was corrected in Windows 3.0. The underlying MS-DOS was modified to make this happen. The term multi tasking came to party for Windows at a big time.
• Unlike Apple, or any other LINUX like OS, Microsoft has supported so many vendors and thus that many configurations. Apple manufactured it’s own hardware and because of that, there would never be issue. Windows has to support so many third party hardware requirements and thus was error prone.

We have always planned quite a lot of trips but never made it. Eager to set this trend wrong, we decided to make this trip a reality. The biggest blocker was getting a day leave. We planned three day trip instead of two day trip. This meant, we need to take leave on Monday.

Train Journey to Mysore

We started from Chennai central to Mysore. Our train was Cauvery express scheduled at 2130 hrs. We took local train from Velachery to Central. Saurabh supposed to take train from Thiruvanmiyur. We were greedy in reserving a seat next us, but have to give in once crowd started building up inside. We messaged him after getting into train. We said, we are at the last compartment from front or the first compartment from last. I messaged from Faisel’s mobile at every station. When train stopped at Thiruvanmiyur and started with a jerk, there was no sign of Saurabh. For a brief moment I thought Saurabh missed the train. Later he came from the inter-connection of the coaches and we learned that he boarded the adjacent coach. We reached Park town and then central in quick time. Anyone who watched us would have wondered where we are going, because we were carrying big, thick rain coats in our hand, and it was scorching in Chennai. Geetha argued, we should carry this as he belived it is raining heavily in Coorg. Later we realised what a waste carrying it apart from the lonely use of keeping it for your head support in train.

It’s dinner time. And we were fighting where to have it. I suggested Saravana Bavan, and told them it is renovated and have extra seating capacity now. But Faisel and Geetha objected and they thought Ratna Cafe is a better option. Too tired to fight, I gave in. We had dinner in Ratna cafe, only to realise it can seat only a handful and serves only dosa and idly. No complaints as we finished with curd rice. It was almost 9. We have to rush in to catch the Cauvery express. Saurabh was still hungry and he bought some bananas to eat in journey. Our berths are middle and upper and we sat in lower berth for some time and once checker finished verifying our tickets occupied our berths. Faisel slipped in sleep as he does always, faster and deeper. I always wondered his ability in catching up with sleep. Some where I read an average male takes 7 mins to fall asleep; it always took more than that for me to sleep. I tried reading book on Vivekanada’s speech later to realise that even I could slip into deep sleep faster.

Day One – Saturday Plan

Our train reached Mysore by 830 in the morning. We took the over head bridge to come out of the station. While coming out, there was another checking for the ticket. I showed him the ticket and my driver’s license, since it is a photo copy, the checker demanded for an original. I didn’t carry it, so Faisel had to show his. We have already booked for a cab for out Mysore to Coorg trip. The driver is supposed to wait out side the station. I received couple of calls to my mobile before that. So, I thought he should be waiting outside, if I couldn’t find him, I can always call him. I said to myself and walked out of the station. Even before I could start looking around, I saw a middle aged person in his early 30’s, dressed in white and white, holding a printout, which shouted “Welcome Mr. Guru from Chennai”. I was overwhelmed. We rushed to the cab, our next destination is a small hotel where we can have a quick bath and then start out trip. We were told to finish couple of places en-route to Coorg. All of us know that there were lot of things to do, we need to be fast. Faisel tried in his broken Kanada to try and tell to driver to go to some small hotel. Our first try was in vain, and then we found ‘Guru Hotel’, were they accepted to let us to have a room if we can finish before 1030. But still they demanded half day’s rent. With no option and time running out, we shed out the money and rushed into the third floor. Faisel was first to take bath, I carried a tee for him. It turned out to be a hit, as he beamed with tee and his new coolers all day through.

We decided to have a small breakfast. We let Faisel to tell driver that we would like to eat some thing light in road side hotel some where. Driver took us to a good hotel, it was full with people. We had to wait for our turn. Waiter never bothered us standing in the way. We realised after getting a table he never came for taking order. And when we ordered, our light breakfast became the heaviest we could have. We ordered for two items for four of us at the single go to the waiter, thinking the waiter won’t come again for taking orders. I am sure it caused him some confussion in orders. But we could order for second time. It was tasty and good. Bill came around 250. Geetha secured a two liter water bottle for the trip.

Tibetan Temple

The distance from Mysore to Coorg was 90 odd kilometers. We planned to visit few places en-route. Our first place was the Tibetan temple. It was a Tibetan settlement around 1960s. You could see the monks dressed in characteristic orange and bark brown shawl. The Tibets had built a beautiful temple here. With Tibetan style houses and temple, with colorful flags decorating the skylines, you will forget that you are in India. The main tourist attraction is the Golden temple. We entered the golden temple. It was maintained very well with scenic garden and sacred hums filling the air.

We could enter the main temple, where you could pray to three deities. We spent some time there. Then took walk in the hot marble. It was almost noon. And we could hear the sacred humming of priests in one of the smaller temple next to the golden temple. Saurabh tried for a picture with one of the monks. But, he didn’t succeed. We started from there as it was getting late.

Cauvery – Nishergadhama

Our next stop was Nishergadhama. It is a small bamboo island in Cauvery River. It is connected via a hanging steel bridge. The river has big fishes and monkeys in the riverside trees. Monkeys never bothered humans as they were roaming very near. We entered the island. Inside we found a rabbit farm. It is covered with bamboo trees all over. We ventured in. We took some photo snaps. And then there was a deer park. People were feeding them with greeneries and with cabbage. One can get very closer with deer. Next to this you have tree top house. These are perhaps used for monitoring purpose but couples use it to have some privacy.

We entered the water. It is low but force full. We could see few familiar faces. Few of them are from the Tibetan temple. Most of the tourists take the same plan, I said to myself. After coming out of the river, Saurabh and Geetha managed to have a photo with the monks. I clicked it. We started from there after that. It was past two.

Dubera – Elephant Camp

Our next stop was Dubera – elephant camp. Unlike other spots, none of us know much about this place. But, in turn, this place turned out to be a natural beauty. A sleep riverside with mango trees and rocks is a splendor sight for one. People are trying boating and few rafting. But we are hungry. We decided to have lunch first. We can find a small dhaba near by and ordered fried rice and noodles. There is nothing available other than that. We had it sitting outside the hotel, over looking the river. The food was not all that good, but we had no options but to eat. We could see, people playing in water and at the same time cattle crossing the river side by side.

After our late lunch, we decided to go for water rafting. The time was 3:30 and climate was splendid. Up in the sky, clouds are getting darker and filling up very quickly. I thought finally the long awaited, forecasted, foretold rain going to lash us. But, very much like all forecasts it didn’t. Rain stayed away. We took rafting. Our instructor told how to hold plastic rowing hands and we were given life jackets. We had a good time in water. The instructor took us very close into trees and made us to duct for the branches. This was the only fun as there was little water and we were trying still water rafting. We had another group of four members in the boat but it was Saurabh, Geetha and the instructor rowing most of the time. I got tried quick but kept it for some time. Faisel was handling camera so he never accounted in for. We had a chance to look at group of elephant washed at the river side by their mahouts. We returned back to river side. And it was almost 5. We decided to start to our cottage in Coorg. We were growing tired.

Stay in Coorg

Coorg is also known as ‘kodagu’ and people are known as ‘kodavas’. With the help of my brother-in-law, I have booked a cottage in Coorg. Maddikeri is the district capital of Coorg. And this place attracts many tourists. The cottage was close to “Raja’s view or Raja’s seat”. We reached the place around 6 in the evening. The cottage turned out to be a wonderful find. It is hidden in-midst of thick lush greenery at slopes of the Coorg. We settled the cab driver his dues and took into the comfort of cottage. There was a debate, and no one knew what are facilities available in the cottage, when we could find television, we were happy. And the place was a good comfort. The cottage is maintained by Sharath. And he told us if we need dinner we can get it from home next to cottage. He also told about the people who stayed next to our cottage.

It was 6:30. I went to the near by home to order dinner, there was an alseasion dog. It was barking madly at any one who could walk into their home. The dog was chained and caged. I managed to creep in and order dinner. An old lady in her forties was kind enough to listen to me. I thought of getting Faisel’s help, but very quick I realized, she doesn’t speak Kanada, and she speaks only Kodava lore. She said she will prepare meals, I wanted chappathis. Our conversation was fast turning from Kanada to Tamil to I-don’t-know-what; at last I was waving my hands and making signs. To my help, I got her grand son to speak English, and I could order extra chappathis. But with the curiosity of the new place, we decided to go for a walk into the city. We realised how the place can be covered in mist so quick. It started to drizzle; Sharath told us that it rained previous day. We expected rain, but the entire mountain cliff was covered with thick mist. It was a breath taking moment. We walked to Raja’s view. This is a place from where the Kodava king used to sit and see the entire plain. A small building and beautiful garden is built around this. We paid two rupees as entry fee. In evening, there will be music and light show, and there was a huge crowd to the dancing music fountain. We walked around them; carefully avoid the mob frenzy, which went up and down for some Kanada song. There was some gang from college on educational excursion. Eager to have the Raja’s view, we rushed to spot. The climate was cold, and I rubbed my hands to keep myself warm. We sat into the gallery overlooking the vast valley. We tried taking few snaps and realised that we don’t have enough light.

End of Day One

We got some bhel puri from road side shop near a railway line and grew thirsty, it was hot and spicy. We walked into city, thinking of buying few things. We purchased snacks, fruits and other things. Then there was a talk that we should try strong coke or Pepsi, but all we could afford was director’s special mineral water.

When we reached room it was almost eight. And we had plans to play cards. I carried three decks of card and most of the time we play cards in all our travel. Our favorite one is five cards and rummy. We had frequent power cuts in room and we had generator to help us. Our dinner was served at nine. We had rice and chappathis. Some gravy was served; it was all prepared local style. We tried watching some programme and play cards side by side. It was the frequent power cut which got us tensed. After having taken the trip in train and then in cab, we could feel the tiredness. We retired to bed.

Day Two – Sunday Plan

I had asked for cab for our Sunday plan. We had few places in our mind to visit. Geetha had a print out but, Faisel kept it some where and found it after some trouble. We all woke early and finished our breakfast. We were served with pooris this time. We stuffed some dry clothes and towels, as we thought we will get into water some where. The cab is supposed to come by nine in the morning but didn’t not turn up until 1030. We utilized this opportunity by taking few snaps around the home. Finally I got the horn sound and we could confirm it was of the cab we asked for.

We have decided to book bus for our return journey from Coorg to Mysore. We were not sure whether we will get a ticket the next day. Went to local bus stand to book our tickets, but by the time we went there, the counter staff had gone for break. We decided to book in afternoon, and I said, we would do that by two o’clock. Others never agreed that we could come back by two as it was almost 11. Our first stop is ‘Triveni’. We reached this place in less than hour’s time. Our driver was driving at steady speed. He was playing some tamil songs also and could understand tamil. I had a huge sigh, as Faisel’s Kanada skills are done away now.

Triveni – Junction of Three Rivers

We reached this place, Triveni is a sleepy small temple, which is built at the junction of three rivers, and these are tributaries of Cauveri, with lush green trees all around it. You could hear the sound of water flowing in river and then devotional songs praising the power of Mother Cauveri in air. Few people were bathing in the river too. There is hardly enough water in river. The water was clean and moving. The temple is dedicated to Lord Siva and Karthikeyan. The temples are built in Kerala style. We spent some time there and decided to move.

Tala Cauveri – Birthplace of Cauveri

We started to Tala Cauveri. This is the birthplace of river Cauveri. It is of another 30 mins from Triveni. We we reached Tala Cauveri, we could see another temple, built in Kerala style. There is a small pool of water and people are dipping their feet in it. None of us are interested in that. I could see shades of disappointment in all out faces, there is nothing left in that place until we saw, people trekking in steady numbers a hill. There is cement path and we decided to trek it. It turned out to be a wonderful experience. On top of the hill, a beautiful scene unfolded. One could had chance to literally touch the cloud. We ventured into another nearby hill top. Faisel and Geetha got a SMS message from Airtel, welcoming them to Airtel Kerala. I never thought we were so close to Kerala.

Abbey Falls

Abbey falls is famous water falls some eight kilometers from Madikeri. It was at a short distance from the city center. When we went there, it was written that it is one of the dangerous places to get into water as scores of people have lost their life here. When we return back it was almost 4 o clock in the evening and it started raining. We visited the Raja’s tomb. Then we returned to our cottage. It was tea time, I asked for tea and thinking it will take some time, decided to have a look at the near by places, walked into the near by bushes. But it started to pour in quick time. We rushed back to drink tea.

Sunday Night Inventions – Copyrighted to Faisel and Saurabh

Sunday night was supposed for watching the Aamir Khan’s Gajini movie and India’s T20 encounter with South Africa. Aamir Khan didn’t betray us, where as India team did that. The biggest good thing about T20 is, even losing is fast. So you lose the match and move to the next channel and catch up the movie in half hour’s time. That was, you don’t have much to lose.

Faisel and Saurabh, did invent few things all through the trip. First one being, strange theory in H20 – Water. Another one that night they came up with, Auto BG feature in Television.

We played cards till late in the night. Around two o clock, we retried to bed. Geetha and Faisel tried playing prank on me. But soon Faisel returned to privacy as he was kept busy over phone by special one.

Big Flops – T20 and Rain

There were few flops.

• India lost their Twenty20 match with South Africa. We followed this match on Sunday.
• It didn’t rain. Like a seasoned weather man, Geetha predicted it is going to rain hard and we would be in trouble. We carried rain coats, but it dint rain.
• Never had a chance to play in water. We visited so many rivers, but didn’t get chance to get into water.
• Frequent power cuts. Looks like this is usual. Be prepared.
• Food. It was fine for the first day, but food is some thing we thought bad.
• Monday blues. Even though we had time in Monday, there was nothing much for us to enjoy. We visited the fort but apart from that it was a boring day.

Return Journey

We have already booked tickets in KSRTC. We had our break fast late, so decided to skip lunch, we bought some snacks to compensate. The bus started by 1.30 in the noon. Our plan is to visit Mysore palace in the evening. We reached Mysore around 5 0 clock and decided to have some thing as we are hungry. By the time we finished some thing it was over 530 and rented an auto rickshaw to Mysore palace. We were told that entry to Mysore palace is closed by 530. We stood outside and watched the Faisel getting busy in his phone again. It took almost an hour to finish the call. Even after that we were left with so much time. Our train was scheduled to start at 820. We walked our way to the railway station.

In train, all of us are allocated with side berths. Worst, one of us have to move to a different compartment. It was decided, that I have to occupy the lone berth. Our train reached Chennai by 8 in the morning. It was Tuesday. All of us have to rush back to fast-paced city life. Three days of slow-paced, enjoyable Coorg days will always be fresh in memory.

Always one is curios to do the best job. With economy going southward, it is only normal for people to save their job. And if you are not doing good work, no matter what job you are in, you will be laid off. Having said all this, I am looking into some of the best jobs around, in this recession time and afterwards.

Top 10 jobs, 2009

A recent study listed the top ten jobs. They took several parameters to identify the ideal career. And here are those results.

Mathematics all the way – One, two and three

The top most job is that of a mathematician’s. Work is fairly safe and interesting. All you need to do is, to take couple of lectures. Guide few Ph. D scholars and publish papers if any. Unlike other branch of studies, mathematics doesn’t surprise often. Apart from people who are doing cut throat research, there is no need to keep learning much.

The second job is actuary, again connected to mathematics, doing calculations and arriving on figures. They are employed in insurance companies and spend most of time crunching the numbers.

The third place is job of statistician. Statistician’s do lot of consulting. There are important in arriving at policy decisions. They design and run campaigns.

Programmer

In a surprise fifth position you will find the software programmer. Even though the recession has caused damages to the software industry, there will still be some demand and growth for the programmer. Another study, rates computer programmer as the top most job. A CNN money study points out IT Generalist as the fifth best job. In another study, it is rated as the best job again.

Future Perfect

Going by the trends in IT, the future holds bright for the one who is ready to shed some extra effort into it. There is good opportunity for people who study accountancy and practice law. Customer service is another industry that is going to be a big hit. And there is always the evergreen classical studies, which have their own patch of greenery.

Having said the best, I need to mention about the worst ones too. The first among the worst is that of a lumber jack. Thank be to God, that we do some decent job.

Mozilla labs has come out with a new browser. With the help of Adaptive path, mozilla has plans to bring out the new browser – Aurora. As what they call as, the concept series of browsers aims at the following -

The Concept Series aims to provoke thought, facilitate discussion, and inspire future design directions for Firefox, the Mozilla project, and the Web as a whole.

So, the future browsers are going to facilitate greater interaction between people.

Aurora – Concept Browser, Part 1

Aurora (Part 1) from Adaptive Path on Vimeo.

New user interfaces

Browsers have come long way since the first browser – Nexus. From plain interfaces to ultra rich user interfaces facilitating higher user interactions. When every thing seems like prototyped, here comes the new concept browser. It has so many functions and options in it, perhaps opening and running it up might require some level of expertise. Lets see how it works out.

Sudoku is one of the interesting puzzles one might have played. Sudoku gained popularity in late 1990s. Sudoku is a not a complex game to understand. Sudoku doesn’t have confusing rules. It doesn’t need accessories to play. All you need is a pencil and perhaps an eraser. I have seen old age people getting more interested in solving it because of its simplicity. There are bunch of guys, who tried writing computer programs, so that, it solves the puzzle. What’s interesting is, even though there are strategies on how to play sudoku. No one had a proved method for solving sudoku.

Enter mathematics

People started looking for tools, steps or methods to solve sudoku. The reason being, sudoku is ridiculously easy but still posed rigidity from being conquered. Some times people get so much frustrated because there might be two or three numbers away from solving but still not able to finish it. Computer programs are no good. All they could do is trail and error.

Sudoku - Game of numbers

Enter mathematics, and things started to settle down. Sudoku is now solved mathematically. I was expecting this to happen. Because, sudoku to a certain extend can be played purely based on logic. For hard puzzles, others used another technique known as back tracking to solve it. But a mathematical method was lacking. Recently, this was supplied in an mathematical paper.

Pencil and paper algorithm

A professor of computer science, J. F. Crook from Winthrop university, US, has provided an algorithm, what he calls as, a pencil and paper algorithm for solving sudoku in an notice to AMS. The paper can be read from here. In that paper, J. F. Crook discussed how sudoku is played, rules and known strategies for solving it. Couple of definitions, examples and finally the algorithm to solve sudoku using pencil and paper. Here is that algorithm for you.

Algorithm: J. F. Crook’s pencil and paper algorithm.

1. Find all forced numbers in the puzzle.
   This is a straight forward step. Just take a look at the puzzle and fix the obvious choices in the cell.
2. Markup the puzzle.
   This is where you do the guessing. Start writing the possible numbers into a small set for every cell. This is known as ‘markup’.
3. Search iteratively for ‘preemptive set’.
   This is looking for set of numbers or a singleton set in order to finalise the number for the cell. You need to repeat this for cells, rows and columns. Arriving at this preemptive set and hidden preemptive set is the key in finding solution for a sudoku puzzle. I am not going to explain in detail as needs lengthy explanation, and explained in detail in the paper.
4. If  solution is reached, stop. Else, make a random choice and continue from step 3.
   There are chances, that you may not gracefully finish the puzzle without making a random choice. So make the necessary random choice to continue the game and solve it. Crook explained the need for making random choice by demonstrating that there are chances for a puzzle to have several possible solution.

Most of the mathematics is done in proving how preemptive sets are used to solve sudoku.

Critics

Mathematical proof for sudoku was expected for long time. Crook used combinatorial techniques in proving solution. The pencil and paper algorithm also needed a random input. Even though this is because of the non-uniqueness of sudoku solution, the algorithm looks in-complete. Even the best computer algorithms use random methods to solve sudoku. A definitive method for solving sudoku is still needed.

What Crook has shown is very important. When the news that sudoku is solved mathematically spread, people feared instead of rejoice. Papers reported that they don’t need a mathematical solution. At times, it is like some one telling the climax of a thriller. But, looking at the Crook’s pencil and paper algorithm, it is easy to do sudoku as one used to do previously rather then setting it up with mathematical methods. An comparison in the same paper states, it took 4 minutes for solving a sudoku puzzle normal way compared to 50 minutes using the pen and paper method. Perhaps with time and practice one might reduce the time taken from 50 minutes to 5 minutes. But you won’t be doing sudoku anymore.

At least in the foreseeable future, there won’t be a definitive algorithm, strategy or method to solve sudoku. You can still enjoy the happiness of finishing the puzzle on your own.

There are some important, good, hilarious math sites you need to follow.  Two of them are listed below.

xkcd.com

xkcd is one the best comic strip site based on math and drawn Randall Munroe. Randall, graduated as a physics student, writes most of the time about mathematics, romance, sarcasm and language.

He draws panel comics. And the figures in stick forms. Most of the strips have comments in the mouse over tool tips. There are some wonderful comic strips in his site. Few strips from there.

Numerical sexual positions defined

Well, chill down. Not all strips are not like that. And my best.

Angular momentum

phdcomics.com

PhD Comics is the next best comic on math. This I think will be the most famous and favourite for many. Ph D is explained as piled higher and deeper. Unlike xkcd, phd comics is continous and bit lengthy form. Most of the stories are based on happenings of student who is supposed to be submiting his desertation for degree. Few of the best strips below.

My favourite one.

Seminar bingo - An interesting game to kill boredom

This happens in every seminar I have listened to. Next is the latest one after the economy went down.

Decision chart

And finally, this one -

Paper review comments

I had some experience on that.

This time around, some thing interesting from the world of mathematics.

All of us dealt with functions of different types. We are introduced to functions when very early in school. Single varriable, multi varriable, simple and complex functions. And in college, functions declared, defined and studied. In this post, one such function, known as “one way function” is used widely in computer science.

Wonderful functions from math

Mathematics is full of functions. These functions are applied far and wide else where. Few are used many times where as few others are used little. And very often functions and equations are interchanged. The most celebrated of them all is -

Equations are used to depict the functions. You can state functions without the help of equation also. Computer science use lot of functions. And for variety of applications. It is beauty of math that you can design a function for almost anything.

Some times these functions can be designed based on algorithms. Or even abstract algorithms. All you need to know is the ingredients you need as an input for the function, and output it need to produce based on the input. Some time you just keep outputing constant value irrespective the input. This is known as constant function. So for any function, three things are important, first, the input it takes, second, the output it provides, third, the logic it uses to produce the output based on input.

One-way functions

One-way functions are the most interesting functions for their applicational purpose. These functions are used widely on computer programs to design cryptographic applications. Before we could get into that, the most important question is, what is one-way function?

One-way road sign

One-way functions are functions for which given an output it is computationaly infeasible to find out (or guess, if you are good at it!) what is in the input which produced the given output. This is the essense of the one-way functions. If we consider the following function as one-way function (which is strictly not). Now, there are few fundas one need to understand here.

or mathematically

First, the logic which is used to compute the output for a given input will be available to all. Which is the square of input (for our example). Secondly, with the output and logic, is it possible to compute the input. If you are given as 256. Can you find what the input could be? The catch is in the term “computationally infeasible“. We are not saying it cann’t be reversed at all, but with the available computing power it is impossible or it would take hundred of years to do so.

It is still an important problem for mathematicians and computer scientists to answer, do perfect one-way function exisist?

Random functions versus One-way functions

If you could remember, a basic necessity for a function is, for a given input, there can’t be two different outputs. Where as, pseudo random functions, which might be based on a key, if given an input, the value of output will be random. This random image will be dependent on the key. And there are pure random functions which are very difficult to predict the value if repeated. If I define the function to be rolling dice. And to be the output of it. Then this function is a pure random function. That is, we throw the dice first time and get four. Second time, if we repeat the same function, then there is no surity that you still get four. In other words, the function is not image preserving.

On the other hand, one-way functions are image preserving functions. For a given input, no matter what, how many times you repeat the experiment. You will get the same output. These functions but still behave like random functions. Because of this property, one-way functions find many application.

Applications

There are plenty of applications. Many important from cryptography and software, including my favourite hash functions. They are worth a seperate post. We shall discuss them later.

Let me not get into the bitter fight of what does slumdog millionaire portraits India to the world. Personally, I think it could have been better. But looking at the brighter side of it. Slumdog millionaire got nominated for ten oscars. It has created lot of curiosity and animosity.  As the Oscar day nears, I asked myself, What are the chances for Slumdog Millionaire to win Oscar? What are the odds in favour and against? We shall analyse it here.

Bare math

If you stick to bare mathematics, and do some number crunching to see what is the chance for slumdog millionaire to win oscars. You could see, it is just below one fourth, i.e., 23%. The movie got ten nominations out of total 43. This assumes the events are equally likely to happen. Like, drawing a ball from bag, un-baised. But, this is far from reality.

Weighted Average – Category Wise

Out of nine categories the movie nominated for, in best original music alone it got two nominations, in this categary alone the chances for Slumdog Millionaire to win Oscars is two out of three, i.e., 67%. Which compared to the other eight categories, one out of five. i.e., 20%, is higher. So, chances are there for A. R. Rahman to win oscar.

Going by the records so far

And if want to go by the records so far, Slumdog Millionaire had won seven BAFTA awards. It also won four Golden Globe awards. It has won critics award too. Rotten tomatoes has given a rating of 94%, which is by its standards – remarkable. All of these are good indicators. And again just indicators alone. Lets wait till this Oscar night and see who gets what. After all awards are not decided and given mathematically.