To be or not to be(Hindu)?

On Aamir Khan's latest movie PK being apparently offensive to Hindus, various lesser Hindu outfits have claimed that their outrage is not regarding the fact that Bollywood keeps ripping off posters from obscure Portuguese singers, but because Mr. Khan is a Muslim and he made fun of cows.

But by Shri Shri Hanumanji and Maa Kali, that is a contradiction by Lord Rama's line of reasoning. Hence, apasanskritik(or whatever).

1. Mr. Khan is a Muslim.
2. Mr. Khan's film is offensive because he's Muslim(I.e. Not Hindu).
Taking the contrapositive of 2., we get-
2'. Mr. Khan's film would not be offensive were he not Muslim.

A. Mr. Khan is an Indian. (For Ganesha's sake! He teaches you about being a good Indian on a frickin' Star Plus show)
B. All Indians are Hindus.
A. and B. imply
C. Mr. Khan is Hindu.

Now C. taken with 2' give us a contradiction.
So either PK is just offensive, irrespective of the religious identity of its lead actor OR Muslims are not Indians.

Also, a happy and sanskari New Year to you all!
Remember, no partying or sex outside marriage, or Lord Indra will strike you down with fire and brimstone.

Hyperreaction

Much of the outrage regarding the 'Taxi Sexual Assault' in New Delhi last week is centered around a belief that a proper background check on the driver wasn't done, one that would have revealed his past crimes as a sex offender.

What the media and the other Batmen and Robins tend to forget is that the concerned individual was acquitted of previous charges. In other words, the court of law found him to be innocent after assessing the evidence and questioning the witnesses, and there's no reason why he shouldn't have been employed as a taxi driver.

Allegations are simply not enough to deny a man or woman employment, or indeed, enough to boycott them socially or culturally. That's not to say that whoever so is let off by the courts is indeed innocent, but that more often than not, there exists reasonable doubt to question their guilt. Even so, mistakes do happen. These mistakes can go either way; guilty men may walk free, while the innocent may be in prison. Does your doubt regarding the efficacy of the judicial system translate into a belief that someone who has been condemned to a life in prison was perhaps wrongfully convicted?

And if we are turning into a society that presumes guilt before a proper examination of witnesses and evidence, our idea of justice is truly twisted beyond belief and it is rather fortunate that our judicial system does not have a provision for a jury. Else, we'd be condemning people to prison, or even the gallows, merely on the basis of suspicion and not actual evidence. 

Of Existence and Brains

Cogito, ergo sum!

Many of us are familiar with René Descartes' statement 'Cogito ergo sum' which is translated to 'I think, therefore I am'. Many of us take this as 'proof' of our existence, but it's not nearly that simple. First, we'll take a look at how he arrived at this.

Descartes arrived at this by systematically doubting everything that could be doubted and he could doubt no more. He realised that what he could not doubt was his own existence because to doubt his own existence, he would necessarily have to exist. Since he had set out with the building philosophy from the ground up, he took this as an axiom and said 'Je pense donce je suis'(Which is quoted verbatim from the Discourse on the Method), which is what I had quoted earlier in Latin and English.

Unfortunately, this statement is not logical inference of the existence of the self. Some of you must have already guessed the basic problem with this statement: The word 'I'.

Take the sentence, 'I think therefore I am'; I exist because I can think(and therefore doubt my own existence). But we are already presupposing the existence of 'I', making a statement about 'I' and then reaffirming that 'I' exists and that is a triviality. To think at all, one must exist in the first place!(Following Kierkegaard, Nietzsche and Russell)

Master of logical consistency

Now, one can actually go further and deny the existence of the self, but is it possible to deny thoughts? I'm not sure it is because even if you are a part of a larger consciousness, your thoughts being just images of that of something bigger and beyond comprehension, the thoughts still exist in some form. If we weaken the statement to 'Thoughts exist', the objection doesn't stand.

However, it is undeniable that there seems to be some truth to what Descartes says and his argument has definite intuitive appeal; it does feel right. So how do we go about justifying it?

The first step would be to stop treating 'I am' as a logical consequence of 'I think', but as a product of a process. The irrefutability of my own existence is a product of the process of my questioning it.

How? Let me say, 'I do not exist'. There's nothing logically wrong with the sentence, but there is something wrong with me stating it. For me to state this sentence, I would necessarily have to exist. If I try convincing you of the fact that I do not exist, by doing so, I am contradicting myself. This is an example of what Jaakko Hintikka calls an existentially inconsistent sentence. When you say 'I do not exist', you are not treating 'I' as an arbitrary quantity, but you are referring to yourself. When you make any self-referential statement, you necessarily acknowledge your own existence.

Who said old Finnish Logicians don't look cool? Jaakko Hintikka disproves!

But say all that exists are your thoughts and everything else is an illusion, what then? Isn't that a dead end too? Probably the simplest way to refute this is to rely on a principle that was championed by Bertrand Russell called Occam's Razor. This basically states that if there are two competing hypotheses, the one making less suppositions is the better hypotheses. It turns out that accepting reality as we perceive it requires far less suppositions than if we were to interpret these as illusions(Refer to Bertrand Russell's Problems of Philosophy).

But there's another approach to this problem and I'll explain it next:

"Your mind makes it real"

Let's modernise the setting, let's assume the I'm a brain in a vat which is being fed all sorts of information that corresponds to my senses by a computer. It definitely helps if you've seen The Matrix.(We're following Hilary Putnam's arguments).

Yes you are.

But first, let's consider a few things; If say, an alien from a different planetary system comes to Earth, sees our flora and draws a tree; without much objection, we can say that the picture does indeed refer to a tree. Now, say the alien has never been to Earth and draws a rather accurate picture of a tree quite randomly; can one say that the picture refers to an object or concept that it has never experienced before? According to Putnam, the answer is no.

This is what is termed as causal constraint and the principle is illustrated as follows:
'A term refers to an object only if there is an appropriate causal connection between that term and the object'

Now suppose a brain-a-vat(BIV for short) talks of 'trees'(note that the BIV cannot see a tree in your sense, and even when it talks of trees, it seems to speak because it's a brain in a vat -_- ), by causal constraint, it cannot be referring to a tree as we know it(and trees may not even exist), so what does it mean by the tree token? Putnam says that this can be one of three things:

1. 'Trees in the image' i.e. the experiences of the brain.
2. Neural impulses that stimulate the brain causing it to have experiences similar to those of a normal human while it sees trees.
3. The computer programme that is responsible for the stimuli and experiences.

   

   Trapped in a vat? Who you gonna call? Hilary Putnam!

Before Putnam, if the BIV had stated 'Here is a tree', it would have been taken that the BIV's token statement was false since we would have assumed that the BIV's token of a tree was referring to real trees. However, if we are to assign truth values to the BIV's statement on the basis of Putnam's assignments of possibilities, it would come out to be true. This is because its sentences express beliefs that are true internally in the brain's world. If you know no external reality, then what you experience is true inside your 'illusion'. 
Now, we are prepared to examine Putnam's arguments. Let us denote distinguish statements of the BIV from that of ours by suffixing the BIV's language with a '*'. 

1. Either I am a BIV(speaking vat-language) or I am not a BIV(speaking human language)
2. If I am a BIV(speaking vat-language),  then my utterances of ‘I am a BIV’ are true iff I am a brain* in a vat*.
3. If I am a BIV (speaking vat-English), then I am not a brain* in a vat*.
4. If I am a BIV (speaking vat-English), then my utterances of ‘I am a BIV’ are false. [inferred from 2. and 3.]
5. If I am a non-BIV (speaking English), then my utterances of ‘I am a BIV’ are true iff I am a BIV.
6. If I am a non-BIV (speaking English), then my utterances of ‘I am a BIV’ are false. [trivially, from 5.]
7. My utterances of ‘I am a BIV’ are false. [from 1., 4. and 6.]
8. My utterances of 'I am not a BIV' are true. [contrapositive of 7.]
9. My utterances of 'I am not a BIV' are true iff I am not a BIV
10. Hence, I am not a BIV

And as promised, I deduced that under certain assumptions, it is impossible to be a BIV. 

Contrary to what it might seem at first sight, this is actually one of the strongest critiques of metaphysical realism. According to the Stanford Encyclopaedia of Philosophy:

To metaphysical realism, the world is as it is independently of how humans take it to be. The objects the world contains, together with their properties and the relations they enter into, fix the world's nature and these objects exist independently of our ability to discover they do. Unless this is so, metaphysical realists argue, none of our beliefs about our world could be objectively true since true beliefs tell us how things are and beliefs are objective when true or false independently of what anyone might think.

If one were to subscribe to the position of metaphysical realism, he would be forced to admit the plausibility of a 'grand illusion' like the Brain-in-the-Vat thought experiment. However, Putnam showed that such a position is nonsensical even if we take the premises to be true.

Of course, there exist multiple counter-arguments and defenses of metaphysical realism. What is interesting to note is that Hilary Putnam himself was once a proponent of metaphysical realism. When he had published his critiques of metaphysical realism(the BIV experiment and the Model-Theoretic argument, which relies heavily on mathematical logic), he had changed his position to what he calls, Internal Realism. This internal realism resembles the metaphysics of Immanuel Kant on quite a few counts and has been termed as 'idealism in the guise of realism' by many. But it is beyond the scope of this essay to examine any of these.

References:

1. Key Philosophical Writings- René Descartes- Wordsworth Editions
2. Problems of Philosophy- Bertrand Russell- Oxford University Press
3. Cogito, ergo sum: Inference or Performance?- Jaakko Hintikka- Philosophical Review 71-1962
4. Reason, History, Truth- Hilary Putnam- Cambridge University Press
5. Stanford Encyclopedia of Philosophy- plato.stanford.edu

Of Hairy Balls, Fixed Points and Coffee

The title of this post must be inducing a giggle or two from the readers, and yes, you read that right; I will be discussing the 'Hairy Ball Theorem' in this post.

So what is the Hairy Ball Theorem? Formally, it states that an even-dimensional sphere does not possess any continuously differentiable field of unit tangent vectors.

In simpler terms, it basically states that you cannot comb a hairy ball flat without creating a cowlick(a point at which the derivative does not exist, a.k.a. a singularity). No! Not the kind of hairy ball you were thinking of, more like this:

.....or this:

.......and in case you were wondering, this is a cowlick:

Hang on! The coconut is not a ball!

No need to fret, this is topology and we can deform a sphere into a coconut-shape without making cuts or gluing stuff to it. Formally, we say that the coconut-shape is homeomorphic to a 2 dimensional sphere.

Wait a sec! Weren't we talking about 3D spheres just now?

Nope, what we normally call a sphere is mathematically called a 2-sphere for matters of convenience. The 1-sphere is the circle and the 0-sphere is a point. A 3-sphere would basically be a 4 dimensional object.

So coming back to our discussion, if you think about it for a while, you can convince yourself that it is impossible to comb a hairy ball flat.

But why just talk of even dimensional spheres? That's because this fails for the odd-dimensional case, if you need to convince yourself of this, draw a circle and start drawing tangents in an anti-clockwise(or clockwise) direction. You should be able to see that if it were a 'hairy circle', one might easily comb these hairs down in a clockwise or anti-clockwise direction without creating a cowlick. 

However, in mathematics, conviction isn't enough; there might very well be a way to comb a hairy ball flat which we haven't been able to imagine just yet. And moreover, although we have established that a hairy circle can be combed flat, we still haven't established this is true for higher odd dimensional spheres.

But before I go into a formal proof of the theorem, let me talk about its significance and history.

The hairy-ball theorem is actually the consequence of a very important in theorem in topology, first discovered by Henri Poincaré, called the Poincaré-Hopf theorem. This theorem relates the 'index' of a vector field(an analytic concept) to the Euler characteristic of a closed surface(a topological invariant), thereby bringing in a relation in between 2 fields of mathematics which were thought to be unrelated.

Henri Poincaré

However, the Hairy Ball Theorem was proved in generality by the Dutch Mathematician, and father of the Intuitionist School of Mathematics, Luitzen Egbertus Jan Brouwer.

It came about as he was trying to find a proof of what is now known as Brouwer's Fixed Point theorem. The story goes that as he was stirring sugar into a cup of coffee. As he was stirring, he noticed that there always seemed to be a point on the surface which wasn't moving. He concluded that at any given instant, there was always a point which wasn't in motion, even though this point could change in different instances.

What Brouwer's Fixed Point Theorem states is that every continuous mapping from an n-dimensional disk to itself contains a fixed point i.e. a point that remains invariant under the map. 

This theorem can be deduced from the Hairy Ball Theorem, and I will come to this in my final section.

L.E.J. Brouwer, proving Alfréd Rényi's statement, ''A mathematician is a machine for turning coffee into theorems''

The importance of the fixed point theorem(and its analogues) cannot be underestimated.... It has applications everywhere from mathematics, physics and logic; to economics and biology! Indeed, the Brouwer fixed point theorem was central to the proof of existence of general equilibrium in market economies, for which  Kenneth Arrow and Gérard Debreu received the Nobel Prize in Economics in 1983. It was also used in the original proof of the Nash Equilibria, for which John Forbes Nash Jr. also won the Nobel Prize in Economics.

Kenneth Arrow

G. Debreu 

An interesting physical application of the Hairy Ball theorem is that of wind patterns on planets. Now, since the atmosphere is always in motion due to the planet's rotation, this creates a vector field. By the Hairy Ball Theorem, there must be a position where there is no motion of the atmosphere and this corresponds to the eye of a cyclone or an anti-cyclone. Of course, this effect isn't always observable due to the fact that our atmosphere has layers, but even so, in every layer, there must be a point where no atmospheric motion takes place.

Jupiter with its massive Great Red Spot, a massive anti-cyclonic system

Brouwer's original proof relied on methods from algebraic topology, and that would be beyond the scope of this article. 

Luckily for us, a rather elementary proof of the Hairy Ball Theorem was discovered by John Willard Milnor(the 2011 Abel Prize winner, also a Fields Medalist and Wolf Prize Winner). This proof relies on little else but some basic calculus and analysis.

John Milnor, probably the most important topologist in the latter half of the 20th century

The proof will closely follow that of Milnor, we will first prove the Hairy Ball Theorem and then, using another statement of it, which will be used to prove Brouwer's Fixed Point Theorem.

And now for the proof:

A sphere \(S^{n-1}\) is the set of all vectors in

\(\mathbb{R}^n\) ,\(\alpha=(a_1, a_2,.....a_n)\) such that \(\|\alpha\|=1\)

A vector \(\beta(\alpha)\) in \(\mathbb{R}^n\) is tangent to \(S^{n-1}\) at \(\alpha\) if the inner product(i.e. the 'dot' product), \(\alpha\cdot\beta(\alpha)=0\)

If \(n-1\) is odd, the dot product in between \(\alpha\) and \(\beta(\alpha)\) will be null if \(\beta(\alpha)\) is chosen such that \(\beta(\alpha)=(a_2, -a_1,......, a_n, -a_{n-1})\), thus defining a differentiable vector field of tangent vectors on \(S^{n-1}\).

Now, we will break up the proof into two lemmas:

\(A\) is a compact region in \(\mathbb{R}^n\) and \(x:\to x+t\beta(\alpha)\) is a continuously differentiable vector field defined throughout the neighbourhood of \(A\), \(t\) is any real number.

Our 1st Lemma will be to prove that if \(t\) is sufficiently small, our function is a one-to-one function of \(A\) onto its image and its volume can be expressed as a polynomial function of \(t\)

Proof: \(\beta\) is continuously differentiable over the compact domain, by the mean value theorem, there exists a constant, \(c\) such that \(|\beta(x)-\beta(y)|\leq c|x-y|\)

We choose, \(|t|\leq c^{-1}\), then \(f\) is one-to-one because if \(f(x)=f(y)\), then \(x-y=t(\beta(x)-\beta(y))\) and the inequality \(\|x-y\|\leq |t|c\|x-y\|\) implies \(x=y\)

We write the matrix of the first derivatives of \(f\) as \(I+\frac{\partial\beta_i}{\partial x_j}\) where \(I\) is the identity matrix.

The determinant is a polynomial of \(t\) of the form \(1+tm_1(x)+....+t^nm_n(x)\), the coefficients are continuous functions of \(x\). For a sufficiently small \(|t|\), the determinant is strictly positive. 
The volume of the image region can be calculated by integrating over \(A\) and we see that it is a polynomial function of \(t\)

Now, if the sphere has a continuously differentiable field \(\alpha:\to \alpha+t\beta(\alpha)\) of unit tangent vectors, for any real number \(t\) this function has a length given by \(\sqrt{1+t^2}\)

Our 2nd Lemma will need to prove that if \(t\) is sufficiently small, the function maps the unit sphere in  \(\mathbb{R}^n\) onto the sphere of radius  \(\sqrt{1+t^2}\)
Proof: We assume that \(n>2\) since we've already settled the case for \(S^1\). If \(t\) is sufficiently small, the matrix of 1st derivatives of \(f\) is non-singular throughout the compact region \(A\). By the Inverse Function Theorem, \(f\) maps open sets in the interior of \(A\) to open sets. Hence, the image of the unit sphere is a relatively open subset of the sphere of radius  \(\sqrt{1+t^2}\). But since the image is compact, it is closed and since the image is both closed and open, it must be the entire sphere of radius  \(\sqrt{1+t^2}\).

With these two lemmas in hand, we can now prove the Hairy Ball Theorem.

As region \(A\), we take the space in between the two concentric spheres which is defined by the inequalities \(p\leq \|x\|\leq q\). We extend the vector field \(\beta\) throughout this region by setting \(\beta(r\alpha)=r\beta(\alpha)\) for \(p\leq r\leq q\), it follows that the mapping \(f(x)= x+t\beta(x)\) is defined throughout the region and maps the sphere of radius \(r\) onto the sphere of radius  \(r\sqrt{1+t^2}\) , given \(t\) is sufficiently small. Hence, it maps \(A\) onto the region in between the spheres of radius  \(p\sqrt{1+t^2}\) and  \(q\sqrt{1+t^2}\).

Now, we see that \(vol\ f(A)\)\(=\) \((\sqrt{1+t^2})^n\)\(vol\)\((A)\)

Now whenever \(n\) is odd, this expression is not a polynomial, which is a contradiction with Lemma 1.

Hence, we've proved the Hairy Ball Theorem.

Now another form of this theorem which follows as a corollary is that an even dimensional sphere does not admit any continuous field of non-zero tangent vectors.

I will not go through the pains of proving this, as TeXing is hard work. :P
But I will prove Brouwer's fixed point theorem using this corollary:
Brouwer's Fixed Point Theorem: Every continuous mapping \(f\) from a disk \(D^n\) to itself possesses at least one fixed point.

Proof: We prove by contradiction. If \(f(x)\neq x\) for all \(x\) in \(D^n\), then the formula \(\beta(x)=x-f(x)\) defines a non-zero vector field \(\beta\) on \(D^n\) which points outward everywhere on the boundary, i.e. \(\alpha\cdot\beta(\alpha)>0\) for every \(\alpha\) in \(S^{n-1}\)

If we set \(\gamma(x)=x-y(1-x\cdot x)/(1-x\cdot y)\), where \(y=f(x)\neq x\)

\(\gamma\) defines a non-zero vector field on \(D^n\) which points directly outward on the boundary i.e. \(\gamma(\alpha)=\alpha\) for all \(\alpha\) in \(S^{n-1}\)

\(\gamma(x)=x\) when \(x\cdot x=1\) and since the denominator never vanishes, the expression depends continuously on \(x\). When \(x\) and \(y\) are linearly independent, \(\gamma(x)\neq 0\) and when they are linearly dependent, \((x\cdot x)y\)=\((x\cdot y\)x\) implies \(\gamma(x)=(x-y)/(1-x\cdot y)\neq 0\)

Now, we will appeal to our geometric intuition for the sake of simplicity:
We take the our new vector field \(\gamma(\alpha)\) to the Southern Hemisphere of our unit sphere \(S^n\) in \(\mathbb{R}^{n+1}\). We identify \(\mathbb{R}^n\) with the hyperplane passing through the equator, \(x_{n+1}=0\) , we use stereographic projection from the North Pole to map every point \(x\) of \(D^n\), to a point \(s(x)=\alpha\) of the southern hemisphere \(a_{n+1}<0 .="" br="" nbsp="">

Applying the derivative of the mapping s at x to \(\gamma(x)\), we get a corresponding tangent vector \(\theta(\alpha)\) to \(S^n\) at the image point \(s(x)=u\) . We obtain a non-zero tangent vector field \(\theta\) in this manner, and not surprisingly, it is oriented towards the North Pole. This is because at every point of the equator \(\alpha=s(\alpha)\), \(\gamma(\alpha)=\alpha\) points outwards.


Again using stereographic projection, from the South Pole, the vector field \(-\gamma(x)\) corresponds to a vector field on the northern hemisphere that is also directed towards the North Pole. 
Now, if we join these two vector fields together, we see that the resultant vector field is directed towards the North Pole. If \(n\) is even, by the Hairy-Ball Theorem, this is impossible and hence we have a contradiction.

The visualisation of a stereographic projection; adapted from Milnor's original

Hence, our assumption that \(f(x)\neq x\) for all \(x\) in \(D^n\) is false. Or in other words, there must exist a fixed point.

We've proved it for the cases where \(n\) is, but even in the case that \(n\) is odd, this follows from our proof. In this case, \(D^n\subset D^{n+1}\). Hence any map from \(D^n\) to itself is also a map from \(D^{n+1}\) to itself and if such a map does not have a fixed point, it violates the fixed point theorem that we have established, as \(n+1\) is even. And hence this theorem applies to odd \(n\) as well.

References:

The proof of the Hairy-Ball Theorem and Brouwer's Fixed Point Theorem has been adapted from the following paper:

• [JM1] Milnor, John-Analytic proofs of "hairy ball theorem" and Brouwer fixed-point theorem-The American Mathematical Monthly- Vol. 85, No. 7 (Aug. - Sep., 1978), pp. 521-524

For a discussion of the Poincaré-Hopf theorem and an introduction to differential topology, see:

• [JM2] Milnor, John- Topology from the Differentiable Viewpoint- Princeton University Press

For the definitions and theorems from analysis, such as the meanings of open set, closed set, compactness and the inverse function theorem:

• [WR] Rudin, Walter- Principles of Mathematical Analysis- McGraw-Hill
• [TA] Apostol, Tom- Mathematical Analysis- Narosa

For general topology and some algebraic topology:

• [MAA]- Armstrong, M.A.- Basic Topology- Springer-Verlag 
• [KJ] - Jänich, Klaus- Topology- Springer-Verlag
• [JRM]- Munkres, James- Topology- Prentice Hall

LaTex Test

\[ x = \frac{-b \pm \sqrt{b^2 - 4 a c}}{2 a} \]\( x = \frac{-b \pm \sqrt{b^2 - 4 a c}}{2 a} \) \( x = \frac{-b \pm \sqrt{b^2 - 4 a c}}{2 a} \)

Art and Criticism

One of my conversations with a person I shall refer to as SM went like this:
Me: Have you read Kafka? (By the way, Kafka is one of my favourite authors)
SM: Yeah..... The Trial, The Castle, Amerika, Metamorphosis........everything
Me(Wondering whether he's actually read ALL of Kafka's works): I loved 'The Trial' and 'The Castle', but I didn't find 'Amerika' nearly as good.... Not quite as exceptional...(Note: I hadn't condemned it as 'bad', just ordinary)
SM: Wait! How can you criticise anything by Kafka? There are some people whom you can't criticise no matter what, you can't criticise Rabindranath Tagore, you can't criticise Shakespeare, you can't criticise Kafka.....
Me: So I can't criticise Kafka or Tagore? So basically I have to abstain from criticising Kafka, even if I dislike his writing? In other words, I'm not even allowed to have an opinion on his writing....
SM: No one can understand Kafka's works, and even 200 years down the line people won't understand Kafka...... To me if you can't understand something, you can't criticise it....If you criticise it, that's hypocrisy and I cannot tolerate hypocrisy....
Me(At this point, quite annoyed and wondering whether he really has read Kafka): Not all of Kafka's works are that difficult to understand for an average reader who doesn't go digging for meanings in every phrase.... Aside from the fact that his novels are unfinished, I don't think there's any major difficulty in 'understanding' the books..... And there's absolutely no difficulty with 'The Metamorphosis', which is also complete.... Moreover, if we aren't allowed to criticise, what good is critical reviewing ?
SM(Ignoring the first part of my reply): The point of critical reviewing is not to criticise or analyse a book, it is to find our own inner weakness blah blah.........(All this 'profound' blabber was soon cut short by the arrival of another person......)

The most significant point is that according to the speaker, there are some writers, directors etc. whose works can neither be criticised, nor compared; any attempt to do so is morally wrong.

Firstly, no one who wishes to read Kafka should be discouraged by the above conversation...... In my opinion, Kafka is not really difficult to understand, it's just that the incomplete nature of his works make it a bit unsuitable for casual reading...... By the way, if you like 'The Trial' and 'The Castle', I'd suggest reading Albert Camus' 'The Stranger' next.

Since I've gotten that out of my way, I'll get to the main point: Is it morally wrong to pass critical judgement on artists who are considered to be 'great'?

A few days after this conversation, Girish Karnad called Rabindranath Tagore a 'second-rate playwright', drawing flak from multiple quarters. Again, I do not intend on defending his position, but the fact that he is allowed to have his opinion without being ridiculed for it.

I don't believe in this principle at all..... Art is created as much for the enjoyment of audiences as it is for the artist himself/herself. There are some who completely disregard the audience while creating the art, but no one can claim that the audience 'doesn't matter'. If the artist only did it for his/her own personal satisfaction, why would he/she have bothered to release it publicly? This is especially true in the case of literature.

Literature is created with the primary purpose of being read, which inevitably means that it will be judged. Even Kafka, who hadn't published most of his work, had written with the intention of being read. I think that in itself is enough reason to read the works of any author and make a judgement for yourself.

Moreover, who dictates whether or not these writers are too great to be judged? Is it the writers themselves or the readers? The answer is quite obvious..... There have been some readers who did judge these authors for themselves and declared them to be great. To not say that it is morally wrong to criticise these authors actually means that it is morally wrong to criticise the judgement of certain individuals who proclaimed these men/women as great. Why should my own judgement be blindly dictated by that of certain critics? People should be free to judge art for themselves and not just because someone said so..... Importantly, the reason why Shakespeare, Tagore, Kafka etc. are considered great, is because people throughout the years have judged their works to be so..... Artists whose works are not appreciated by generations, are often forgotten by history. The judgement of an audience is critical in determining whether or not an artist is remembered or forgotten...... J.S. Bach was nearly not as appreciated as a composer in his lifetime, as he is in his death; Keats and Kafka never achieved much fame in their lifetimes.... The same was with Edgar Allan Poe, Emily Dickinson and Vincent Van Gogh. The greatest judge is the audience and while their works did not appeal to people in their lifetimes, they appealed to people after their deaths.

And what of the 'untouchability' of great writers, musicians, directors etc.? I do not believe in this either.... If you do not like a book, a piece of music or a film, you are entitled to say 'I do not like it', without having fear of being condemned as a person with bad taste and not worthy of being an 'intellectual', even if the writer is Shakespeare, the composer is Beethoven and the director is Satyajit Ray. It is not a given that the greatness of a writer prevents his/her work from being exempted from criticism..... When we read a book, watch a movie or listen to a piece of music, we judge that piece of work by itself..... The artist will be judged by the entirety of his/her work. Even if you have read 20 books by the same author, and liked all 20, there's no guarantee that the 21st will be to your taste. In fact, when someone has written as extensively as Shakespeare or Tagore, it is almost a given that some of his/her work will be sub-par. Not every of Beethoven's Piano Sonatas is in the same league as 'Appasionata', and in fact, a few are quite average. That doesn't mean that Beethoven becomes any less of a composer...... As pertaining to the discussion that triggered this essay, it is common opinion that 'Amerika' is not nearly as great as 'The Trial', 'The Metamorphosis', 'The Castle' and many of his short stories like 'In the Penal Colony', 'A Hunger Artist' and 'The Judgement'..... In fact, in my defense, I might add that Kafka abandoned writing 'Amerika' before all others. In my opinion, there is a body of work by other authors writing in German which are better than 'Amerika'..... Hermann Hesse's 'Siddhartha' and 'Steppenwolf', Thomas Mann's 'The Magic Mountain', 'Doktor Faustus' and his short stories; and Gunter Grass' 'The Tin Drum'..... As for writers in other languages, I can name James Joyce's 'Ulysses' and 'A Portrait of the Artist as a Young Man', F. Scott Fitzgerald's 'A Great Gatsby', George Orwell's '1984' and 'Animal Farm' and more.... The list goes on and on...... Yes, 'Amerika' in my opinion is outshone by all these works, as it is by Kafka's other works..... So, is it a moral sin to judge the book? Does it amount to hypocrisy? I think not.....

Our judgement is dictated by our individual tastes; as far as taste is concerned, I do not think there is any right or wrong; it's quite personal. What we call 'good taste' is that which is predetermined as good by critics and society in general. In my opinion, it should be inculcated through experience of both the good and the bad, than blindly following what is deemed to be good. It is also for ourselves to judge whether or not a particular writer is good or bad. As long as one stops short of making ridiculous statements(which again needs to be defined), he or she should be allowed to voice his/her opinion.

I for one, am not particularly fond of Tagore's prose and I find Sarat Chandra Chattopadhyay, Bibhutibhusan Bandyopadhyay and Manik Bandyopadhyay's short stories to be better than his..... I cannot claim to have read all of their works, but from the little I have, I am tempted to make the comparison. So is this bad taste /bad judgement? As a reader, am I not 'qualified' to make that comparison? I think I am.... If I've read the books, I am as qualified as anyone to comment on whether I liked it or not, or whether I find it good or bad.

What I find off-putting is the attitude of literary critics(and pseudo-literary-critics) towards the common reader in the way of we not being 'qualified' to have anything intelligent to say on literature in their presence...... While it's true that we haven't dug up every single word for hidden meaning, allegories etc. I do not see how that makes our opinion any less important than theirs.... Like I said before, it is ultimately the general public which will decide whether an artist is great or not..... The reason Mozart and Beethoven are great is not because some critics said so, but because their music is appreciated by all, even today. And in any case, I do not think writers write for people to dissect their works, they write for people to enjoy their works...

Vladimir Nabokov said that good readers don't read books, and particularly literary masterpieces, "for the academic purpose of indulging in generalizations". Similarly,  Stephen Joyce(grandson of James Joyce), said that his grandfather's works could be enjoyed by anyone without picking up guides and intricate explanations. He even added that had his grandfather seen people doing that, he would have died laughing.

While I'm still on the topic, I'd also like to discuss 'What is good taste?'..... Like I said before, I am an opponent of militant imposition of taste. However, there are some things that characterise taste... For one, not many will make 'ridiculous' statements like 'Jimmy Page is a better composer than Mozart', or 'Chetan Bhagat is a better writer than Charles Dickens', even though they might like Led Zeppelin a 100 times more than Mozart's Piano Concertos, or 'Five point Someone' a 1000 times more than 'David Copperfield'....... These are some things that we consider 'commonsense' and almost everyone(including myself) would laugh if they were to make such a statement...... On the other hand, one can have a raging debate regarding who writes better prose; Tagore or Sarat Chandra? No one will laugh at you if you say Mozart is better than Beethoven and if you mention that you like P.B. Shelley more than T.S. Eliot, you will have as many supporters as opponents........ That directors like Federico Fellini, Akira Kurosawa, Satyajit Ray, Ingmar Bergman, Jean Renoir etc. are a cut above most directors active today is undisputed, but does that stop people from enjoying 'trash' more than 'Eight-and-a-Half'? Not really..... In other words, our society has a pre-determined image of what is good and what is bad. People whose tastes lean towards what society calls 'good' are deemed to have good taste. It is seen that with gradual exposure to all forms and all sorts of art, people generally start leaning towards 'good art'..... For example, in my childhood, I watched and even enjoyed certain books and movies which I would balk at if asked to read and watch again. By the age of 17, I can decide for myself what is good and what is bad..... But this realisation cannot and should not be forced on anyone, it is for them to find out for themselves, one can can guide others towards good literature, music and films, but one cannot force them to like it.

In conclusion, it is my opinion that people be allowed to freely criticise artists(in the broadest of senses), and be allowed to develop 'taste' for themselves.

Writer's Block

It appears that I'm facing a severe case of writer's block; both mathematical and non-mathematical. There's a lot I feel like writing and sharing, but every time I sit and try to put something down, it just doesn't materialise!

So in an attempt to get over it, I have posted about the issue!

In other news, this blog is staying where it is. The wordpress blog will only contain my mathematical posts(if I ever get to writing them), and this one will be for everything else.

Moreover, I realised that I have posted about nothing of any interest for the past few months...... Maybe this blog is dying :P