Null Hypothesis, Astrology and Cargo Sciences

Recently, I came across this particular article in ToI.  After reading the article, I chanced upon the comments section.  I was quite surprised to see that most of the readers have accused Dr. Venkatraman Ramakrishnan of being an idiot, moron, a terrorist, not respecting Indian culture and quite a few have gone berserk with demands to withdraw Nobel Prize.  A couple of comments show surprise by the fact that he doesn’t believe in astrology inspite of being a Nobel Laureate in Signs.    Fine, I made up the last line. 😛

Anyway the main question is how do you test for the credibility of something like astrology, existence of God and other abstract things which is militantly supported by more than a billion people?  It may be true that astrology lacks scientific evidence but there maybe, just maybe an iota of truth in it.  Maybe it is not yet good enough to be called Science.  What if the astrological “principles” are sort of pointing in the correct direction but we are not able to grasp or make a breakthrough?  The problem is that if a person dare says a word against astrology, the entire populace of India seems to find trolling an enjoyable idea.  It is difficult to argue with people who weave stories about how astrology predicted one particular event in the life of one particular person.  This is where the beautiful concept of Null Hypothesis can make the difference.

The main idea of the Null Hypothesis is that you assume a certain stance unless proven otherwise.  Or to put in more compact terms, the default position.   To demonstrate the idea of Null Hypothesis, let me take an example of a random coin toss experiment.  I assume that the default position is that the coin is unbiased, that is, there is as much chance of getting heads as there is of getting tails.  So, I toss the coin 10 times.  Now the expected number of heads that I should get is 5, assuming independent trials.  But what if I get 7 heads and 3 tails?  Can I declare “confidently” that the coin is biased?  Not really.  What if I toss the coin 100 times and I get 70 heads?  Just maybe.  What if I toss the coin 1000 times and I get heads 700 times?  Now it is more apparent that the coin is biased, but is it biased (0.65,0.35) or (0.70, 0.30)?  I do not know that yet.  I need to conduct more experiments.  Of course this is just the property of Law of Large Numbers.  The question is how many trials do I require before being say “95% confident” that the coin is biased?  There is a bit of mathematics involved in it, which I will not go into the details of.   So let me assume that in I need 70 trials out of 100 to turn up heads to declare that with 95% confidence the coin is biased.  This is termed as “Rejecting the Null Hypothesis with 95% confidence”.

Now that the tutorial on Null hypothesis is over, let’s see what can be done regarding astrology.  The main problem with astrology is that there are so many contentions regarding the rules that it becomes difficult to have a comprehensive test.  So, a manual regarding the rules of astrology needs to be prepared such that there are no evident contradictions.  If the argument is that astrology is too vast a subject to be put down into a manual, let them take a small part of it, say zodiac sign and one dominant characteristic of the person belonging to that sign.  Now we need to prove that “most” of the times the Zodiac signs and the trait in question are predictable.  So, it becomes a binary random variable akin to the coin toss experiment – heads if the person has the same traits as the one predicted by the Zodiac sign, tails otherwise.  One obvious problem is what the Null hypothesis should be.  If my thesis is that the theory of zodiac sign is truly random, we take (0.5,0.5) as the null hypothesis.  If I believe that it predicts the behaviour 60% of the times, my null hypothesis would be (0.6,0.4).

Either way, it should be an interesting experiment.  I wonder about the technical feasibility of such a project.  Well, if not the entire nation, maybe at a smaller scale inside the insti campus.

Any views? 🙂

Advertisements

The Running Chronicles – I

And yet another year dawns upon me bringing with it the queries of life, the questions about those nauseating highs and dung-filled lows, the tyranny of seldom-kept resolutions and the unwelcome associated guilt that hits you hard when they are broken bringing the entire exercise to naught.  Anyway, coming to the point I have had a habit of making resolutions, a miniscule of them attainable, most being as a meme would suggest,

The common part about all these resolutions is that I have succeeded in keeping none of them.  This year I have come to the conclusion that I need to become healthy, a resolution bordering on the “IMPOSSIBRU”.

After being unable to wake up in the morning for two days on the trot, I am almost on the verge of giving up. Anyway, Adhok after paining me enough has made me register for the 10k Auroville run on February 12th. Right now, I can jog a maximum of 1.1 kms at a stretch before I run out of breath. From my hostel till Elec Department. Tomorrow, my training schedule states I have to run 4kms. Sigh. Keeping my fingers crossed. The main purpose of recording this here is so that I can shame myself into running if I ever stop again.

PS: After much contemplation, I have decided that I should increase my blogging frequency, given that I hardly have anything to do this semester.   Around 5 posts per month is my current aim.  Let’s see how things pan out.

Update: Finally. Jogged 4kms. Or rather jogged for 3.3kms and walked 0.7kms. From hostel till Velachery gate continuously. Walked from there till BT-department-turning. Jogged again till the hostel. I am quite sure that I will have sore legs today. Day after tomorrow, I am supposed to run 5.2kms. OMAIGAWD.

The Tipping Point – Part 2

In the first of what I would now term a series of posts, I forayed into the basal reasons of why freshers lose enthusiasm when they come to IIT Madras. My thesis was that the primary reason for the poor performance was not LAN as was assumed by the senate but it was largely to do with the position of fans in the Classroom Complex(CRC).

It did lead to quite a response in a couple of social networking sites, healthy discussions in Google Plus with a professor and a more trite, bordering on savage discussion on the Colloqium Page in Facebook which unsurprisingly took a turn towards questioning the parentage of some of the moderators. I observed a couple of days back that it was the most viewed post in my blog and realized that the administration has actually taken steps to install an air-conditioner in CRC. So, I will be bold enough to claim that _MY_ blog made the administration to take notice of the plight of the students and do the needful.  So with this momentum behind me and the associated self-pluming which comes with maintaining a successful blog, I will now selflessly, with all my expertise, delve into what I think is the second major reason freshers are the way they are and hopefully something will be done about it.

To go further into this analysis, I first ought to apprise you of two kinds of torture. One, the humane way. Pull out a tooth, piss on a stove kind of torture. It is over before you know it. The second, the route taken by those bereft of either civilization or civility. Like a HS department English exam where you write furiously in no more than 5000 words what Wordsworth thought the difference between white and yellow daffodils were. Or Analog Circuits Exam where you stare at the question paper for three hours hoping that by divine intervention you can make sense of the question. The slow, painful, repetitive, time-has-come-to-a-stop kind of torture.

Belonging to the subset of the second kind of torture is the one laid down sometime in 1960s, when hostels were being built. Every morning, thousands of kids are loath to open their eyes afraid that they have to face this cruel, brutal and unrelenting beast, a beast more savage than grumkins and goblins, just the image of which would turn men into weeping crybabies. This structure built by a man long-lost in living memory and cursed by all and sundry ever since, is akin to the great sphinx of yore. It challenges you to a battle which ought to be won before it lets you pass to your destination. It is not an easy task to defeat this beast. Every day, many fall prey to it and surrender, only to face it again the next day. It is not the difficulty in traversing it that gives it the power but the constancy, the knowledge that it is there everyday unfailingly, a grim reminder of the eternal struggle to be faced before you can enter the hallowed portals of your department. I introduce to you, gentle reader, with a hint of trepidation, the monster – the upward slope from Gurunath to Cauvery hostel.

This two-hundred-metre-long monster continues to be the bane of all freshers who foolishly, being in the green of their youth try to tackle the monster armed with nothing but a newly procured creaking cycles sold by BSA at a discount(only to IITians, mind it). After a couple of months, the comfortable bed under the mild breeze of a fan becomes more seducing than the classes on the other end of the battle, and all the enthusiasm present withers down like leaves on the onset of winter. This, ladies and gentlemen, is the biggest tragedy plaguing the institute now.

Hopefully, the administration will take suitable measures to level the ground and destroy this monster. I will keep my fingers crossed. Till then, the institute bus will be my saviour.

OOMAAAIGAWD!! I AM IN FINAL YEAR!! (Part Two)

A few days back, I was walking back with Umashankar… For the uninitiated, we have been classmates since 8th standard, with a common interest in mathematics and disdain towards Sanskrit, Biology and those girls(and Twister) who used to top in all the innumerable monthly tests, drawing us together. Anyway, I was walking back with Umashankar from lab to the hostel, after the mandatory midnight “konjum-strong-coffee” at Tifanys and invariably the topic of school came up.

It is interesting to note that there exists a finite set of “incidents” which have happened at school and everytime we meet, we laugh our asses off, remembering them. Everytime it is the same set of incidents. Narrated in the same style. Still it somehow seems to be funny. Always. I can recite these incidents while sleeping or dangling from a helicopter or facing a gun or all the three simultaneously and still laugh like a maniac. Let me recount one of them. We had to submit a “letter to father” in Kannada as a homework assignment. You know those fake letters in a format which no one uses. Respected-Father-How-are-you?-I-am-doing-well-How-is-mother?-Convey-my-regards-blah-blah-blah. Mundane, uninteresting stuff. My school used to start at 11:30 AM. So, I used to leave my house at 9:30 and reach school by 9:45. One of the muggu junta would turn up around 10. I, shamelessly copied the homework till the classes started. Considering that 90% of the class were copying the notes which other 10% wrote, it was a very efficient process and by the time class started everyone was done with the homework. Perfectly co-operative game. But, these things had its own drawbacks. On this particular occassion, I took the book and copied down the letter-to-father “makki-ka-makki” style. Lots of people copied from the same book. We all go smiling to the class and submit it. Next day, the teacher storms into the class seething with anger and asks, “How many kids has this…this Garudadwajan fathered? Apparently 40 out of you, 50 idiots.”

Oh, the way we laughed. I am surprised the roof didn’t fall on us that day. I miss it. I wonder how many of these incidents, I can take away from my past five years here. Quite a few, I think. An addition to these finite set of “incidents” happened two days ago. 🙂

OOMAAAIGAWD!! I AM IN FINAL YEAR!! (Part One)

“The end is nigh.”

“This is the end. My only friend.”

Damn it!! Strike that out. Tear the sheet.

Burn it. Out!! Out, you foul, filthy, defiling stench of clichés.

I started writing this article thinking that I will write spectacularly and drown the reader in that sweet feeling of nostalgia without being cloying or nauseating, but the final product turned out to be a massive junk of clichés. Damn, even saying cliché is such a cliché.

Let me tell you, gentle reader the reason behind writing this article. It is almost mandatory for every final year chap with a functioning blog to write a post describing his time in the institute. I am no different. Like every other final year guy, I tend to picture myself as a wise grand old man handing out “wisdom” to juniors. In the first draft of this article, I delved deep into the waters of nostalgia and as I found out later much to my disappointment, they are not unchartered waters. Nostalgia is a sin every man has been committing since the birth of time(or is it the time of birth?). Hence, any new articles on nostalgia can be expressed as a linear combination of writings on nostalgia of the entire human population since the beginning of time.

So, to do justice to my engineering education, which I am afraid I may forget too soon, I have mathematically modeled Nostalgia:

{\bar{{\eta}}_{i}(t)=\int_{\tau=0}^{t}\sum_{j=1 j\neq i}^{N}{A}_{ij}\bar{{\eta}}_{j}(\tau){\delta }_{ij}d\tau + \bar{\epsilon}_{i}}

where,

  • \bar{{\eta}}_{i} represents the Nostalgia vector of a person i. 
  • It spans the Writing Space, {\Omega}^{f(\bar{{\eta}}_{i})} where f(\bar{{\eta}}_{i}) is a function which gives the number of elements in the vector \bar{{\eta}}_{i} .
  • It should be noted that the \bar{{\eta}}_{i} has been integrated over time to give the vector at the present time t, for nostalgia is a sin man has been committing since the birth of time.  😛
  • An assumption that I make is that while writing an article on nostalgia, the content will depend only on other articles which induce nostalgia.   I am neglecting other possible influences like Characteristic Writing Equation and other quirks out of it for the sake of simplicity.
  • The total population of the world is N.  Assuming that a person i has had finite time to go over articles written by the total world population, we would like to define a {\delta}_{ij}, which takes the value 1, if the person i has read the article written by j, 0 otherwise.  I call it Nostalgia-Delta function.
  • A person i is influenced to different extent by different people.  . This dynamics is captured by the matrix {A}_{ij}.  I do a summation over the entire population and integrate over time to get the nostalgia vector for person i.
  • The term \bar{{\epsilon}}_{i} signifies the error.  If I neglect model errors, I can assume that this term quantifies the originality of the article.

You may be wondering why I am writing this….this…for lack of a better word… mathematics taken from a mad hatter’s hat.   To satiate your curiosity, I would like to state my objective function.  I wanted this post to be different from those millions of other nostalgia-inducing-boring-inane-silly-stupid-posts on the web.  So my objective would be to:

max({\parallel \bar{{\epsilon}}_{i} \parallel}_{F})

where,

{\parallel A \parallel}_{F} denotes the Frobenius norm.

I hope I achieved my objective.  🙂

You didn’t read the equations, did you? What do you want me to say? You want to read that stinking cliched article, don’t you? Meh :-/ Fine. It will come.  Soon enough.

If there exists Gods, the most powerful ought to be the God of clichés.

PS:  Don’t call an ambulance and admit me to the hospital for being a cuckoo.  I just wanted to test this script called LaTeX2WP to convert documents from LaTeX to WordPress style.  It works fine.  🙂