Syllogism: A tool of logic?

syllogism/sil-uh-jiz-uh m/noun(technical) a way of arguing in which two statements are used to prove that a third statement is true

I first came across the idea while reading Freakonomics. Renowned author Steven Levitt in his international bestseller Freakonomics uses syllogism to explain the decreased crime rates in the US in the 90s.

Syllogism struck a chord with me.

Why do coconuts have water in them?

At the beach drinking coconut water, my sister asks

"Do you know why coconuts have water in them?"

"Coconut trees grow in the deserts. They need to conserve water."

"No. The coconut is designed to float in water and traverse many miles in the sea to germinate on another coast. Either way, they don't grow in deserts."

"No? Coconut trees grow where there is a lot of sand. Deserts have a lot of sand. Therefore coconut tree grows in deserts."

I hastened to explain.

This kind of argument is used in Mathematics as well.

"If line p is parallel to line q and line q to line r, then we can say that line p is parallel to line r"

The Ram-Chagol Argument

Here, my father quips

"This is what they call Ram-Chagol [Mountain Goat] argument."

"Ram Chagol has beard."

"Rabindranath Tagore had beard."

"Therefore Rabindranath Tagore is a Ram Chagol."

Whether Rabindranath Tagore was a Ram Chagol or not (no offence intended), I will leave it to the reader to ruminate, digest and decide.

Tribute to Michael Jackson

RIP Michael Jackson You'll be missed! x

What a shock RIP Michael Jackson - loss of a true legend!

He might not be here but his music is still alive! R.I.P Michael Jackson

RIP Michael Jackson. You have transcended generations, music fads and skeptics. You are a legend.

Thanks for the music and the moonwalk. bye, bye MJ. RIP.

I couldn't make head or tail of these tweets when I woke up in the morning to the news of  Michael Jackson's death. It didn't seem real.

News channels were blaring the news on the headlines. Millions have been mourning over his death.

Fans on the camera talked passionately of his moonwalk, glove, ow!, crotch grabbing, plastic surgeries & his dress sense. Reporters dubbed him as the Peter Pan - the boy who never grew up.

For someone like me who has grown up in a milieu where Bollywood numbers are what people live and die by, Michael Jackson was certainly an exception. My mother who detests 'non-Indian' songs & movies to the core informed me of his sad demise the first thing in the morning.

I wasn't surprised. Nor was I shocked. It was a strange feeling. Very difficult to describe.

I wasn't a big fan of Michael Jackson. Never heard many of his songs.

But that doesn't mean a thing.

People discouraged me to listen to his songs. He was a drug addict, a child molestor & an eccentric character. Only his break dance stood out.

Nevertheless, I got to listen to some of his popular number when in high school & I was clearly mesmerised. I made it a point to see some of his videos when I got the opportunity.

Whether I am a fan of Michael Jackson or not, I cannot deny the genius of Michael Jackson - his ability. He is someone who has stood out & mesmerised generations. And that is why I am paying him a tribute.

May his soul remain the boy he always wanted to be.

Bangalore Revisited

Bangalore is a picturesque lively city that represents the changing face of India. In the heart of Bangalore is Brigade Road, one of the most happening places in Bangalore. Somewhere along the Brigade Road is McDonald's.

It is 1 pm on 21st June 07. A bunch of 14 are munching away at chips and burgers to their heart's content.

It looks like a regular bunch of college students enjoying their meal. Little known to onlookers is that these 14 were once part of the 2004-2005 batch of X-C.

The same X-C which took the school by storm. The same X-C which terrified not just its peers but also its teachers.

X-C is having a get together.

Somewhere a mobile beeps. The owner informs all that Sherin ma'am is herself coming to meet them in half an hour. The same Sherin ma'am whose name was revered and respected with the same fervour which is reserved for (temple priests?)(political leaders?)(celebrities?)

An hour later, Sherin ma'am arrives. Time hasn't changed her. She is still the Sherni - the Tigress.

Half an hour later, Sherin ma'am is serving Khas juice to a bunch of 4 who in their wildest imagination would never have imagined being present within a kilometer of the epicentre - i.e. Sherin ma'am's living room.

An hour later, she is escorting the 4 to the bus stop, again a first.

Now alone and in the bus, I wonder if it was a dream. As I am immersed deep in thought, images of the past keep haunting me.

On 20th, Arun had come to pick me up at the station. On seeing him, I had dropped my bag and hugged him in an embrace.

We had proceeded to our alma mater in the afternoon. Within half an hour, 5 of us were sitting at a tumble down bus stop talking of chalk fights, football matches and mass bunks.

And now I would be leaving Bangalore. Who knows when fate would bring us all together again when we can cherish the memories of the time we spent together?

Acknowledgements

Arun

For being the finest buddy I have ever had.

Without you, this couldn't have been possible.

HS, Vijay, G, Punit, Shalini, Shreyasi, Sangeeta, Swarna, Vindhya, Girija, Philomina, Harini

For turning up on 21st

Samuels & Suhas

For turning up on 20th

Anshul & Anand

For the last minute rendezvous

Sherin ma'am

You are the finest teacher I have ever had.

Purohit uncle, aunty, Kashika & Pratyush

For being my host, local guardians and much more.

Thank you all so much.

@HMT Watch Factory	@Garuda Entrance
@McDonald's	@Brigade Road
@Garuda: Couple? Nah	@Garuda : Couple? You Decide
@Bus Stop: Arun and Mainak	@Garuda Entrance: X-C
Mainak, the Gourmet?	Or the Glutton?

For the benefit of the X-C junta, the photos are available as a combo pack

File 1: Download [5 MB]

File 2: Download [6 MB]

Suicide at IITKgp

Manoj Kumar, a first year student of Naval Architecture Department has committed suicide.

These incidents do not surprise me any longer. Many may consider it my (moral?) responsibility as a blogger to write about the latest incident in Kharagpur.

Just Another Incident

Three deaths in three months. Just another figure.

Kgp no longer astonishes me. I have started looking at such incidents with a passive indifference. As if it didn't matter.

Drug cases. Theft cases. Accidental deaths and now suicides.

There was a time when Kgp excited me. But that period is over. The honeymoon is over.

Death: An end in itself

Can anything but death justify suicide?

This must have been the same Manoj Kumar who had taken part in the candlelight vigil on 23rd March. The same Manoj Kumar who stood for life less than 3 months back. The same Manoj Kumar who like all Kgpians wanted a well equipped hospital.

IITians: Are they rational?

What makes IITians take such an extreme step? IITians, who are selected on their ability to reason - because of their rational mind.

A suicide is not a rational act - it cannot be.

Poor grades, personal problems? Did the suicide solve the problem? His suicide has made life difficult not only for his family but also for fellow Kgpians.

The flip side of the coin

I do not wish to sensationalise the issue.

This is the flip side of life at IIT.

Things won't always go right. Expectations may be high. Peers may be doing well. Things may go horribly wrong. Frustration and anger may build up.

But a human life is too precious to give away.

5 Reasons to Read Books

Vasanth Kamath - speed cuber, curious character and my wing mate is a voracious reader. His room is always littered with books. I ask him - 'How do you manage to buy so many books?' He answers - 'I don't buy them all. I always ask for books as my Birthday present.'

One year on, I have become a bibliophile in some sense. The more books I read, the more I fall in love with them.

For the cynic who feels that reading books is a futile exercise - that what one gets out of reading 1000 pages is just 10 pages, here are 5 reasons to start reading books.

1. Authors are intellectual beings

An author's intelligence is almost always above the average human being's intelligence.

Research has shown that an author has an IQ of at least 130.

Even if you don't buy that or you don't believe in IQ scores, consider this. How many authors do you know who live in your neighbourhood?

I suppose, very few if not none. They are above the average plane. Their ideas count.

2. Powerhouse of Ideas

The author has specific ideas about a certain topic. And the author is an intellectual creature. Surely, their ideas count.

Pick up any book and you will find it packed with ideas and opinions which may well shape your life.

3. Role Models

There will be characters in certain books that may strike a chord. They might start serving as role models.

We would start looking up to the characters for courage and inspiration.

4. Pass Time

There is no better way to spend your time gainfully than by reading books.

Without having to attend any kind of courses, one can learn a lot just by reading books.

One can be satisfied of having spent one's spare time in a fruitful manner.

5. Experts recommend it

I was also a cynic. But when Arjun Malhotra and Sramana Mitra (who visited the Kgp campus) also recommended reading a lot of books, I started reading more and more.

If you are still not convinced, ask any person who you think is successful.

One thing they all have in common - they are voracious readers.

Books I have Read (in the last 1 year)

The God of Small Things; The Google Story; The Alchemist; Surely You're Joking, Mr. Feynman!; The Day of the Jackal; To Kill a Mockingbird; Joker in the Pack; Outliers; Angels & Demons; The Da Vinci Code; Blink; Atlas Shrugged; The White Tiger; The Guide; The 3 Mistakes of My Life; The IITian

Which book are you into?

Role Models: My 5

Role models are our idols. They are the ones from whom we draw inspiration and courage.

I admire

Dr. Manmohan Singh

For leading the nation.

It is no mean task to lead a nation of 1 billion - more so in as diverse a nation as India.

I admire him - not because he is an economist. Not because he is a visionary. Not because he is a man of character.

But because he leads India.

Roger Federer

For being as emotional as he is.

Federer may be ranked No.2. Or he may be the greatest player that tennis has ever produced. But I look up to him, not because he is a champion player but because

he doesn't suppress his emotions.

Because he is emotional - like normal human beings should be.

But aren't.

Ayn Rand

For believing in herself.

I find it difficult to believe that more than half a dozen readers should be interested in reading my posts.

Consider the faith Ayn Rand had in herself that made her come up with not just her own philosophy but believe that people would read her 1000 page epics.

Bill Gates

For being so rich.

He has not just created an empire that is difficult to create in the modern world, he has managed to ward off any threats that he has faced. 

I don't admire Gates for his philanthropic achievements but simply because

he is so rich.

Aung San Suu Kyi

For being so courageous.

Most of us would have given up. But she hasn't.

And that is why I admire her.

What is your 5?

Welcome to Kgp

Results of various competitive exams have started trickling in and the fortunate few who would have been selected in IITJEE would have started weighing their options.

This video was first screened on the opening day of the Spring Fest 09 at Netaji Auditorium & gives a bird's eye view of Kgp campus. A must watch for any IIT aspirant/IITian.

Played the video?

Noticed the guy in orange T-shirt in the Badminton Court. Second from left.

That happens to be Mainak Jas.

Didn't notice? Try playing it again :)

Ambigram: Patel

Patel is the first hall that makes the (in)famous PAN loop in IITKgp.

P stands for Patel. A for Azad and N for Nehru. The ambigram for Nehru that I made is here.

The base font is - Agency FB. It has been modified to get the ambigram.

How is it? Do you have any modifications to suggest? Do let me know.

Mathematical PJs

The trouble with Mathematics is - we first learn the formulae and then the application.

The education system is such that we treat these two aspects - theory and application as separate entities when they should be going hand in hand.

For instance, when we learn complex numbers in our +2 course, its applications are not apparent till our electrical course in 1st year.

In such cases, one has to look for simpler applications.

1. Multiplication by iota

I can very well recall how our Mathematics teacher in class was well known for his PJs (poor jokes).

Some, though were quiet useful!

Once, while a student had turned to gossip with the fellow behind him, our Maths teacher quipped, "Ashish, please multiply yourself by iota squared."

[Whenever a complex number is multiplied by iota, it is rotated anticlockwise by 90^o. Hence, multiplying it by iota squared would rotate it by 180^o]

2. The Exponential Function

Unfortunately for Ashish, he had to bear the brunt of most of the PJs as he was quiet irregular to class.

Once, while Ashish was giving some lame excuse for remaining absent from class, our Maths teacher remarked, "You are like the exponential function. Whether you differentiate it or integrate it doesn't really matter. It never changes."

I am unable to recall many of his other PJs. If you know of any interesting Maths PJs, do let me know.

Related Posts

Scientific Guessing

Real Life Applications of Mathematics - Traffic Rules

Scientific Guessing

Mathematics is often considered an exact science.

2+2 is always 4. cos²x + sin²x is always 1.

However, this is not always the case. Mathematics also deals with probability - a deterministic science.

Why Guess?

Objective examinations are considered a test of analytical skills and a test of nerves.

Now, it also tests your knowledge of probability. (Didn't it always test that?)

Regardless of the syllabus, objective pattern exams will test how well you apply probability.

Surprised?

Consider this. JEE in 2008 had 132 questions. In these, I would reckon there were 20 questions where I had a doubt. I wasn't sure. It was 50-50.

Did I guess?

Of course, I did.

Guessing in JEE

The objective questions had a +4/-1 marking pattern (+4 if you get it right, -1 if you get it wrong).

I figured out - even if I got 4 questions right out of 20, I wouldn't be losing out. (4x4 - 16x1 = 0).

How much probable is that?

Probability of getting exactly no question right = ²⁰C₀(1/2)²⁰

Probability of getting exactly one question right = ²⁰C₁(1/2)²⁰

Probability of getting exactly two questions right = ²⁰C₂(1/2)²⁰
Probability of getting exactly three questions right = ²⁰C₃(1/2)²⁰

Probability of getting exactly three questions right = (1/2)²⁰ { ²⁰C₀ + ... + ²⁰C₃} = (1/2)²⁰ (1351) = 1.28 x 10^-3

Probability of getting at least 4 right = 1 - 1.28 x 10^-3 ≈ 1

Once I figured this out, my JEE paper was practically finished.

I guessed left-right and finished with a rank of 1594.

Double Check

Still cynical?

Feel that something somewhere is wrong.

Let us double check.

Probability of getting either none right or one right or... 20 right = (1/2)²⁰ { ²⁰C₀ + ... + ²⁰C₂₀}

How much is ²⁰C₀+²⁰C₁+...+²⁰C₁₉+²⁰C₂₀?

It is 2²⁰!

We then get the probability = 2²⁰ / 2²⁰ = 1

That is what we should be getting!

What if I had no idea and simply guessed?

Probability of getting exactly

none right would then become ²⁰C₀(3/4)²⁰

one right=²⁰C₁(3/4)¹⁹(1/4)¹

two right = ²⁰C₂(3/4)¹⁸(1/4)²

three right = ²⁰C₃(3/4)¹⁷(1/4)³

Probability of getting less than 3 right = (3/4)¹⁷ { ²⁰C₀(3/4)³ + ²⁰C₁(3/4)² (1/4)¹ + ²⁰C₂(3/4)¹ (1/4)² + ²⁰C₃(1/4)³ } = 0.225

Probability of getting at least 4 right now becomes 1 - 0.225 = 0.775

It isn't as safe to guess now, even though the probability is still in the candidate's favour.

AIEEE/BITSAT etc.

AIEEE has the +3/-1 marking scheme.

If you use the same method to calculate, you'll find that

the probability of scoring non-negative in case of 50-50 ≈ 1

when one has no idea = 0.61

BITSAT has bonus questions if you complete all the questions. Suppose you have 20 questions left out. Should you guess and go for the bonus questions?

You are now empowered to decide for yourselves!

Related Posts

Real Life Applications of Mathematics - Traffic Rules

Mathematical PJs