Best 10 Jobs in and after recession times

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.

One Way Only…

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 -

The de Finetti Game

Probability can be divided into two major topics on broad sense, Subjective probability and Objective probability. Simply said, anything we can be quantified and acceptable without any doubts is objective probability. Like rolling a die, and the chances of getting a number 4 from it, assuming the die to be a fair die although. Or, like tossing a coin, probability of getting head from it. Every thing can be quantified and measured without problem. And the exact opposite is what makes subjective probability more interesting.

Things like – probability of rain on a given day, or probability of a particular stock to move up on a given day are all subjective probabilities. The sample space is not always finite.

Thus the question we would be interested in is –“How to measure the subjective probability?” Or put different, how will you objectively measure the subjective probability? The heart of this post is all about that only.

Bruno de Finetti

Bruno de Finetti, an Italian statistician has given a way to compute these. He has proposed a game to measure the subjective probability for few things. The game he defined lies in the middle ground of Probability and Psychology. There are many variations of the de Finetti game.

Say, your friend tells to you, coming out of exam hall, that he is getting a maximum score (a centum). How much is that certain now? To measure this, all one have to do is to ask few questions. Tell him that, in a bag, there are hundred balls. Out of which 98 are white and 2 are black. Given a chance, like, a thousand rupees bet, for either drawing a white ball from the bag or wait till exam results and on getting the score as 100. Assume that the answer of your friend as “draw the balls”. Now, increase the black ball count to 20 (80 White + 20 Black). And ask him to pick between drawing a ball from the bag or wait till the exam results.

If he chooses to wait for the exam result for the thousand rupee bet, increase the white ball count to 90 (90 White + 10 Black) and repeat the same test. If he wants to draw, then increase the black count to 15 (85 White + 15 Black) and repeat the experiment. End this game with a sufficient interval. Say, between 85 and 88. This means, that the subjective probability of your friend getting a centum is any where between 85 ~ 88.

The Rationale behind the game

Now, let us analyse the rationale behind the game. For the first time, when given a chance between 98:2 and “waiting till exam results”, you friend went for the draw. Meaning that, he thinks drawing the white ball is easier than getting a centum in exam. So, the subjective probability of his centum is lesser than 98% (or .98). This is the upper limit of his chances of getting centum. When you change the balls in the bag to 80:20 and ask him for a pick, he chooses to wait for the result. Meaning that, he thinks the probability of getting centum is more than choosing the ball, which was 80% (or .8). This serves the lower limit.

For the third time, when you repeat the same experiment, you are trying to find the finer details. Hope that I have explained the rationale of the de Finetti game.

Real World Experiences

I have tried these games with my friends. Most of the time, I have modified to suit my requirements. Like, say, last time, I have a bet with one my colleague over a test case. I told her, it won’t work as she thought. She resisted. Then I challenged her with an initial bet for Rs. 10 and told her that she can choose between checking the test case and proving it and get seven times the initial bet amount or she looses Rs. 30 if she checks and found what I said was actually happening. Simply put, she has the chance to check and win Rs. 70 if she wins or Rs.(-) 30, if she looses. You can even ask her choose the times she need. That way, you can come to some conclusion on her subjective probability

She doesn’t know that I was the person who coded it and exactly knows which way it would work. Now, the pitfall of this game, never challenge any one with for personal things like love, marriage and others. They seem to have sentimental attachments and can’t be assessed for subjective probability correctly.

Small life

You come across all kind of quotes very often. Most of them will be quotes, interesting, strange and if not bizarre. I came across one such quote. I don’t know whether you can call it as a quote. It is an equation.

“Small life + 1 = Very Small life”

That’s interesting. My favorite equation was of Reimann’s zeta function. I have it as my on-line avatar display picture.

Try understanding it! On the outset, it looks absurd and meaning less. But it has a meaning. Okay, let me not keep speculating it. “Small life” is the age of you. “+1″ is your birthday. So, Small life + 1 is your process of getting old, you are left with vey small life to live with.

This equation, remembered me of a kural (4th kural from 34th Chapter, see below). The entire chapter of that kural is given below

Thanks to IIT-Madras -Kural initiative. So, tell me now, isn’t that equation correct?

Abstract Confusions

I have changed the blog title to “Abstract Confusions”. I was looking for a suitable title for quite a long time. Previously the blog title was “Now I will have less distractions”. This the quote of great mathematician Euler. The blog title, ideally has to be of two words and not a dialogue or so, I was telling to myself. So, I started searching for a blog title.

I have decided that I will have a math jargon as the title. Searched a lot and couldn’t settle for one, that caused me lot of confusions (Ah, now you might have got the clue from where I got this name! ) I was equally impressed with so many blog titles from the blog-o-sphere. Among them, one stood out. It is “Abstract Nonsense“. Abstract nonsense is a technical term used in category theorem.

So finally I got – Abstract Confusions. I googled it as soon as I christened. There is no exact hit for the search. I searched for  this blog, and found it no-where. I was bit ambitious. I am waiting.