My Way or the Highway

Why it’s hard to arrive at a decision when faced with 2 horrid choices…

The other day we were having a heated discussion. The heat was all theirs and I was merely fanning the flames. It wasn’t summer yet so heat stroke wasn’t the thing that we were worried about. But one of the members of our discussion squad almost did jump out of the window from T-11 to prove his point. It’s good that his rationale stopped him, because ethically I had no reason to stop him. Or did I? But then who defines what is right (or for that matter wrong)? Why should helping someone to their feet be an accepted social more? Why is killing other human beings wrong? Don’t try to melt my heart by emotionally blackmailing me from behind those curtains of tears. That’s not logic. So, then is there a period to logic? Are there thus entire arenas where logic can’t be applied? Too many questions? Okay. Let’s take a break and listen to Hurricane from Thirty Seconds To Mars. Jared Leto’s voice is booming through my head:

Tell me would you kill, to save your/a life;

Tell me would you kill to prove you are right…

A very famous related ethical dilemma is the trolley problem. A trolley is running on a track where 2 people are bound to the track through which the trolley is plying. You can access a switch which moves the trolley over to the other track. However, there is 1 person bound to the track on the other side. Just to be clear, the trolley doesn’t slow down when running over any person. Thus if there are 1, 2 or more people bound to tracks and the trolley runs over them, they all die. Do you make the intervention?

trolley+problem1

The dilemma in the given scenario is due to our inability to categorise crime. Is 1 death better than 2 deaths? Who gives us the authority to choose who to “allow” to live? In fact this situation is so common in certain modified scenarios, that it has gained a significant traction among pop culture films. The most striking one which stimulates my memory cells (if there is any such thing ie) is the movie Dark Knight. This Christopher Nolan magnum opus is replete with references to the trolley problem. And at one pivotal point, Batman is forced to choose between the woman he loves and the person he regards as the “white knight” of Gotham. But far more interesting is a quote from the Joker himself:

If, tomorrow, I tell the press that, like, a gang banger will get shot, or a truckload of soldiers will be blown up, nobody panics, because it’s all ‘part of the plan’. But when I say that one little old mayor will die, well then everyone loses their minds!

In fact, I think he gives us a way to resolve our problem. So, the way to look at the problem cannot be strictly utilitarian. Killing in any form is unjustified. (As to why so, we’ll come to that later. Let that be an axiom for now.) This axiom thus makes us incapable of being the judge, jury and executioner to a life or lives that matter (or don’t). In any event, it cannot be treated as a simple binary problem. So when faced with the given choice, ideally one should look for more information. The Joker through his quote makes a strong point. A mayor is more important than some random Tom, Dick or Harry. One guy on the other track might be more important to save than the other 2 or 5 or 100 lying on the doomed rails for that matter. The other 5 may be criminals. In fact the possibilities are endless. And thus our decision should be a function of the information available to us.

In a variation of the trolley problem, one is asked whether one would push a fat but “guilty and evil” person onto the trolley to deflect it to save the lives of others. This was more an attempt to see whether people differed in views if the closeness to the action directly leading to the death of a fellow being changed the statistical distribution of people wishing to participate.  Interestingly, people favoured killing the embonpoint of a guy. Because he was guilty. The point thus resolves the fact that the information we have available regarding the people we can save (or kill) should change decisions. (For the record, in a paper published by PhilPapers in 2013 by Chalmers et al., 68% prefer switching while 8% were opposed. 24% had other views or couldn’t answer. This was in regard to the original problem I discussed without any additional information provided. This goes to show democracy is not always useful especially with regard critical policy making, for example asking people to vote if Global Warming exists. Yes. Sigh! I am one of those people!)

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But what if you have no information available? In that case run as hard as you can and save the two people. People have built revolutions this way. Overthrown monarchies. Upsetted the balance of power. Subverted authority. Okay, that’s a bit too far, but I’m sure you’ve all heard it. It’s called: For the greater good. But what must be kept in mind is that 2 lives are not always worth more than 1. Not always.

Some of this might appear distasteful to those who think with their hearts and not minds, which is most people I know. If I have a war to win, I will sacrifice a few soldiers than gamble away my general(s). That’s why chess pieces are ranked based on their abilities on the 8×8 checkerboard. That’s why people are rated on the world they live in. That’s why they have different values attached to their lives. Yes, the life of business tycoon or country head is worth more than yours. Perhaps an utopian socialist world order might lead to a 100% utilitarian approach. But the world we live in is not utopian. And decisions taken should reflect that. It should not be simply based on your view of the world or what you desire the world to be. Or mine. Or anyone else’s for that matter. Because as George Orwell said:

All animals are equal, but some animals are more equal than others.

And that is how the world is. For better or worse, you decide.

The Story

A short story about a story.

This has been submitted to The Mays XXV for its annual publication. The Mays Anthology is a collection of short stories/poems published annually as a book.

“Where are we going ?”, I asked meekly.

“A woman has been shot in Gresham Place. It’ll make for a fantastic story, don’t you think?”, finished Amol without a hint of inflection in his voice.

“You mean murdered?”

“Let’s not jump to conclusions so quickly like the tabloids do. A woman’s been shot. I think that’s an important enough reason to write her story.”

I grabbed my coat and my neglected umbrella. I had learned enough not to trust the British sunshine.

Amol seemed cheery, which was odd. Maybe, this was because this was our first true commission that we had been together. We left behind the chattering keyboards of the aging studio which masqueraded as the headquarters of the Cambridge Post and headed into the desiccating petrichor.

It would be a ten-minute walk. I had not yet finished my cup of Earl Grey when the editor had apparently found us our first scoop since my hurried employment interview a week ago. Indolence was my passion. Investigative journalism was paying my rent though, so I figured a few sacrifices were in order.

“Why do you think this story is important?”, boomed Amol’s voice over the residual white noise of my own thoughts.

“Is it important?”, I asked rolling my ingenuous eyes. Does he think we’ve struck gold, I wondered, bemused. The story had already been mentioned briefly in today’s morning news. What more could our feature piece add?

“Well, no story is more important than the rest anyway. There are seven billion stories just floating out there for someone to write about. But you see, journalists are the ones who get to choose which ones should be read. In a way, we are responsible for the class divide. What do you think of that?”

“Well, you see Amol, I don’t think too well without my morning Earl Grey.”

“You better start thinking mate because we are approaching Gresham Place. I’ll need you arrange the leads we get to make the readers think that the woman in Gresham Place could have been any of them and relate to it. An untimely death due to any reason is ultimately a failure of the society around.”

There was a big police van guarding the entrance after the crime had already been committed. A couple of scribes accentuated the dereliction of the otherwise desolate street. As we headed to the main porch, a cop at the door mouthed “no journalists” as if we were filthy creatures. Amol didn’t seem to mind. But I figured this story would probably revolve around the perspectives of the people around Gresham Place. We wouldn’t even get a shot of the crime scene.

I was right about the weather though. A mild drizzle had decided to soak up our spirits a bit more. The story would have better prospects, I hoped.

We knocked on the first door opposite to the police vans. He asked us if were cops and then slammed the door on our faces. It was all very quick. I wouldn’t miss my lunch after all.

We did a couple of houses like this with varying degrees of gregariousness, but too much of an increase in actual information.

“I thought you said journalists are powerful people who decide which stories are written. And now we aren’t better than random salesmen”, I yawned.

“People need to sell their stories if they need to be heard anyway. Besides, I thought you weren’t listening”, said Amol as he eyed me suspiciously.

“I guess it would be harder for a dead person to sell her stories”, I quipped.

But as we headed towards 81 Gresham Place, I grabbed those inertial doubts and knocked confidently.

“Ma’am, we’re cops. We need to ask you a few questions.”

“But didn’t you do that already?”

“We’re with the MI6”, I whispered with an air of secret urgency trying not to appear like a rooster. This was, of course, complicated with a half snort from Amol, but the septuagenarian didn’t seem to notice. We had been invited for tea. Earl Grey was not going to be missed after all.

“You need to lie, to hear the Truth”, l breathed into Amol’s ears.

“Or someone else’s version of truth anyway”, he smirked.

The lavender curtains betrothed to the yellowing wall paper shyly revealed the developing disturbances outside as an additional police van and a TV truck had seemed to have joined the bevy of growing onlookers. The Chesterfield surrounding the television set seemed to closeted to a different reality. Presently our host poured out a hot pot of tea as the Renaissance Napoleon peered at me from the left gallery.

She regaled us with her perspective on Mrs. Emily Hamilton. The lady in our story had at last been provided a name and a marital status. My editor would be proud. She had been a delightful soul, but after being subjected to intermittent domestic abuse, she had become a lot paler. She had had a miscarriage and only last month had obtained a restraining order against her husband.

Husband, possible suspect scribbled Amol on his notepad.

“How do you know she was cheerful?”, I asked innocently.

“She threw these lavish parties, didn’t she? All the top names in Cambridge and London would turn up in their fancy chauffeured cars.”

“And what about the neighbours?”

“She never invited them. Maybe, she never got along with them. Maybe they were too cold to her. I don’t really know.”

“Maybe she was a classist?”, I asked helpfully.

“I don’t think so. She invited me, didn’t she?”

I found the barrage of rhetorical questions irritating but hard to deflect.

“And she had a few of her close friends from school and other places. They were hardly what you would call ‘aristocratic’. And suddenly all those parties stopped six months ago. And I saw less and less of her.”

I continued sipping those delicately brewed Darjeeling tea leaves considering which of these details could be made juicy enough for the next day’s front page.

“So you see I was surprised when she invited me over to her place for another party yesterday night”

My throat seared as the warm flavour burned through.

Amol seemed to have recovered faster and gently enquired it further. I was still grappling with the pain and this sudden incongruity.

She continued, disregarding that the temperature in the room had fallen by at last a couple of degrees.

“I was surprised, obviously. But more curious actually. So I said yes, of course.

There had been four other people at this small party. The city council chairman: Mr. Raziq Khan, the lead hairdresser from Cicero’s on Mill Road, Mr. Emily Hamilton and an another woman who I had not seen before.”

“Her husband was there yesterday? Didn’t he have a restraining order?”, Amol asked, incredulous.

“Yes. Didn’t I just say so?”, she snapped.

“She had obviously invited him over. Why else would he be there? But I couldn’t see her for a long time. Eventually, I had to rest my old self and left early without bidding her goodbye. The prosecco was exquisite though.”

“I’ll return the tea cups to the kitchen if you fine gentlemen are done.”

While she bobbed to the larder, Amol flipped on the remote. Channel VI had somehow managed to get a feed of the crime scene.

The woman lay asleep with her right hand folded and her fingers coiled in the middle of the heavily pixelated room. In fact, it would be hard to tell she wasn’t merely sleeping save for the seared strands doing their best to hide the gaping hole on the right of the cerebrum.

A Colt 2000 was left beside the body. It was registered to a certain Mr. Hamilton.

Post-mortem had concluded that the time of death was around 10-11pm. This, however, seemed to be conflicted with an eye witness who seemed to have seen something like Mrs. Hamilton leaving her residence at around half past ten.

Police had named the husband as primary suspect for the murder of Mrs. Hamilton who was still at large. Everyone seemed to have a suitable alibi post 11 pm. Except for Mr. Hamilton, whose presence had been confirmed at his hotel last night at a half past midnight but there was no account of what he did in the four hours prior to that.

“Case closed, isn’t it? Channel VI seems to have done a pretty good job.”, I gestured to Amol who was trying to reduce some of those knotted creases from his forehead.

“But, that’s not possible”, whispered the old woman so close to my ears that I almost jumped.

“I forgot to say this to those cops. Actually, it was more because I didn’t want to get involved in this mess. But I went back last night to the Hamilton’s. You see, I had forgotten my scarf. It’s a pretty dainty one, that scarf. And before I even knocked, Mrs. Hamilton opened the door and handed it to me. She appeared a bit pale, but nothing unusual. This was around midnight. See, that’s why I never believe in this modern science stuff that your generation keeps coming up with.”

Maybe ghosts exist and that’s what you’ll become, I muttered to myself.

“You’ll tell those cops, won’t you. You are working on the case as well, right?”

“Oh yes. Absolutely”, I lied.

“You were not lying throughout were you”, she added recoiling a bit from my fake smile.

“Oh no. We Zoroastrians don’t lie on Wednesdays”, Amol interjected placidly.

“Is that even a religion. And isn’t it Thursday?”

“Rest assured ma’am, Zoroastrianism is a religion. And the Zoroastrian weeks are always six days ahead.”

“Or one day behind”, she added sternly. “Good day gentlemen!”

As we headed out, I almost lunged at Amol. Zoroastrianism? Wasn’t that the worst possible fib?

But the case still remained to be solved.

“The case is solved”, Amol said cheerily almost as soon as we were outside the earshot of 81 Gresham Place.

“So do you believe in ghosts now? Clearly, the post mortem can’t be wrong!”

“Oh no. She is a filthy liar. Why do you think I cooked up that bit about Zoroastrianism? But the husband is not the murderer.”

“So-”

“Wait, first tell me, why do you think people tell stories?”, Amol asked.

That was the first time he had asked me for my opinion.

“Mostly because you wish to experience certain things but can’t. So you invent these fantastic characters who may be perfect or flawed and then send them out on journeys. But importantly it allows the storyteller to share some of those emotions, not all of which could be articulated and not all of which could be spoken aloud.”

“That’s well spoken. But isn’t it all a lie. Which is why another name for story is fiction. And guess what is also a synonym for a lie? You see that old woman knew from the start that we were some journalists or some curious onlookers who had no business asking her those questions. Or maybe you just look like a pretty bad agent!”

I could think of several objections but held them back.

“As Conan Doyle once wrote, when you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

“So you mean the old woman was involved in Mrs. Hamilton’s murder”, I quipped wide-eyed.

“Hardly. She was never invited to any of Mrs. Hamilton’s parties. If you notice, she struggled to describe the lavishness and pomp of a house she had never visited and instead regaled us with small talk about gossip you could find by watching Channel VI all day. There was no mention of a fifth person at the party both in the news and the police report. No, she made that all up.”

I felt an emptiness thrusting down my stomach.

“So, how?”, I barely whimpered.

“It’s simple really. The old woman was able to do one great thing. She shook my belief in the rigor of post-mortem. The police report indicated that they are almost certain from witness accounts that Mr. Hamilton had not invited his husband over and his presence must have distressed her greatly. Besides, everyone seems to have a reasonable alibi save the poor Mr. Hamilton, who is missing since yesterday.”

“Go on”, I breathed.

“You see her body was found in the middle of a room and there seemed to be no sign of struggle. This means that her husband or any unknown person could not have barged in. She would obviously not let them in beyond the door. This leaves us with only known people. And all of them seem to have strong alibis. Thus, it was Mrs. Emily Hamilton herself who pulled the trigger. A standard case of suicide. I have a feeling that this was probably due to exacerbation of her mental health after seeing her husband.”

“But why are you so sure? After all, Mr. Hamilton’s whereabouts couldn’t be traced for an incriminating amount of time!”

“Not really. You see the fingers of Mrs. Hamilton were curled exactly in a way one would hold the revolver. It’s clear that when she fell, the Colt dropped out of her hand and that’s the position in which she achieved rigor mortis. And, after looking at the images Channel VI presented, you’ll notice that her hair was seared near the wound. This only happens if you place the gun close your head. A murderer usually shoots from an arm’s length or farther.

But the biggest puzzle was the conflict between the eye witness account and the post mortem timing. And I’ll need to thank our old lady for clearing that puzzle. Post-mortem timings are often affected by physical activity. It reveals a much earlier time of death if the person has been involved in a fight prior to her death. In this case, a lack of physical injuries rules that out. It looks like she went out on a late night jogging session and then came back and shot herself. And Mr. Hamilton seems to be confirmed to be seen at the hotel post-midnight.”

“This should become obvious a couple of days later when the comprehensive autopsy report comes out”.

“It’s going on print tomorrow”, I gleamed.

What could be the motive though, I thought. Weren’t we violating the cardinal principle of solving a case by avoiding that?

“If you are thinking about the reason, she took her own life, you need to only look at the people around. None of them had anything to say about her. And the one person that did, lied. What does that tell you about society today? Maybe your feature could focus on that?”, added Amol with a tone of clairvoyance.

My feature piece grabbed a lot of attention the next day while Amol became a fleeting star. The other seven billion lives continued as if nothing had happened to wait to read the next big story that popped up on the front page.

The Semicolon

Start. Pause. Repeat.

This is an impromptu post. I had not thought about writing this blog post in advance. I would not be terribly disappointed if somehow a power failure robbed me (and you the reader!) of reading the end product of what this post is going to end up to be. Unlike most fascinating news stories breaking headlines, this article will not provide exciting gossip fodder. This post has yet to find its main subject and so will, for now, meander in the sample space of possibilities. Without choosing a headlining topic and thus a route towards a suitable conclusion, all possibilities remain open. Yet, without choosing, none are. That is the beauty of choice.

You enter a carnival where there are a plethora of rides and attractions all enticing you to create wonderful memories for keeping. Old people above a certain age are of course restricted from entering most rides. As are most toddlers before they reach a certain legal age. Specially-abled persons have also myriad restrictions placed on them vis a vis rides. Further, you only have fixed amount to choose the rides which you can enjoy and you are to budget accordingly. Some people have more money than you. Some have less. Some can’t wait to manage a ride. Some can’t wait to control the whole carnival. Some can’t wait to serve food from the food stalls, while some are impatient to guard the rides from miscreants. Someone someday sabotages a ride to make a political statement. Someone makes those rides. Someone proposes a model for how rides could work better.

Image result for carnival

Of course some days there are strikes. Somedays the weather is better. But at the end, you are groomed to accept the system. To accept that there are rides and some people run it while others ride it. You could be the person working for the people running the carnival or rise to create your own ride. The people who create the rides are usually hailed as visionaries. There is also somewhat of a system in place which grooms people so that they are sufficiently trained to manage the rides.

Then, there are people who think about life outside the carnival. This couldn’t possibly the only carnival? How did we enter this place? What happens when we leave? No one has managed to return after leaving the carnival and several fables have been sent down oscillating across both extremes. The world outside then Carnival is a horrid place. The world outside is the place where angels flap their wings and smile at you. Of course, nobody knows anything and people are more worried about making the rides run well and on time than bothering about who set the gates in the first place.

That is not to say that the carnival is empty. Doesn’t it show the heights of human creativity? Such spectacular rides! Such colour and gusto! Such music to accompany the tempo with which the horses rise and fall while circling in the waltzer. Wasn’t Ferris such a visionary to have created the eponymous Ferris wheel? Aren’t humans amazing to build the machinery to create new and keep the existing rides running? Of course, there is the occasional mishap. Some people continue to be unable to afford the rides, while others make a profit at their expense. But a single individual can’t do anything about that. So we give vent to our feelings in some of the eateries where we meet our peers and the Carnival goes on for eternity. Of course, you come in at a specific time and leave after a few months, never to return. It’s what you do during those months that determines how the Carnival remembers you.

This article, this blog is my pause. My semicolon. Not a period, because the sentence must go on. At least for now. Residing on a corner of a pixel of a pale blue dot of a yet unexplored universe, all I can do ramble on incoherently about the deeper meanings of life in a language: English which is not even my first tongue. Part of me wants to rise to this and spend the rest of my days trying to uncover this mystery to the best of my ability. Read more about it and live on it. Part of me disagrees and wants me to join the Carnival to create the next ride and hail me as the next superstar. Part of me thinks that I’ve done enough and should join the management helping to run the rides before exiting the Carnival like the millions before me, have and will continue to…

I have so many roads open. So many possibilities. So many, that it scares me. What if I choose wrong? Someone whispers that this unpredictability coupled with the limitedness of time is what makes each moment and decision so valuable. But I am at crossroads. As Reality splashes on my face, I’m yet grasping at the strings which apparently ascribe value to existence. Most people have been running a race too long to figure out why they are running and for what prize. I have had my share of this race, but if I run again, it won’t be for a race.

I’ll leave this sentence incomplete though. Someday, I hope to come back to this particular article and end with a fitting conclusion. This might remain unfulfilled of course, but all the same, I’m willing to …

(Space Left below)

 Image result for semicolon

The F-Word

IMDb apparently has introduced an F-rating for films.

This article is part of a commentary that has been published in Varsity, the University of Cambridge newsletter. The original can be viewed here.

The next time you scroll down looking for IMDb ratings, you might be surprised to see some of these movies embossed with an F sign. No, the IMDb is sadly not becoming more hip by slyly introducing expletives as part of its ratings. Instead, this dryly lets us know whether the film has been written, directed or stars a prominent female character. So exciting! Imagine seeing an F sign and immediately knowing you have to watch it for no other reason that it features women in a prominent role. I’m already excited!

The fact remains that there are still movies created in 2017 that fail the Bechdel test. It’s a simple criterion, introduced by Bechdel in the 1980s, to see if a film had at least two female characters who spoke to each other on a topic other than ‘men’. It’s incredible that films could fail such a bare minimum threshold. But can we fault films for following their choice of a cast? For example, most superhero flicks follow the Smurfette principle where there is only one prominent female character. The fact that this eponym is derived from The Smurfs points out to us that animations aren’t immune to this bias as well. So, IMDb supposedly would bring more awareness to this issue by introducing the new letter. Or as I like to say it: The F word.

But would you like your movies to be marked like your groceries, organic or GMO, F or no F? And isn’t this a slippery slope? Where will we draw the line? LGBT, minorities and other under-represented categories should be given an equal voice as well, shouldn’t they? One could probably write a pile of supervision essays addressing why the LGBT community are probably more under-represented than women in movies. In fact, let me introduce the Guha-Bechdel test! (Yes, I just did that.)

Any movie that has at least two female/LGBT/ethnic minority characters who speak to each other on a topic that is central to the advancement to the plot passes this test.

While the idea is certainly bold, this should not be the sole measure of diversity. Movies cater to audiences and the producers assume that most people who legally end up viewing their artistic product are straight white males. This is an issue that needs to be resolved by varying the demographics more than increasing awareness. For my part, I wouldn’t necessarily sacrifice artistic quality over an F sign in viewing a movie. But there remains the enticing possibility that it would eventually end up irking some of the bigoted folks to the point of watching F-rated movies and then bragging about it! I would like to end with a few lines as given in an interview by feminist director Holly Tarquini to The Guardian:

“I hope that the F rating will become redundant as the stories we see on screen reflect our culture, and that 50 per cent of the stories we see [will be] told by and about women.”

Till then, F is the word

Killing time and people softly…

What would happen if you put a person in a microwave?

As a way of whiling my Sunday morning, I decided to ‘solve’ this unique question on Quora. The question was: What would happen if you put a person in a microwave? Yes, Quora has its dark side, and I’m loving it! Below is the answer.

Firstly it’s a terrible logistical and ethical problem. Considering that we have pushed these aside, we need to start by assuming that the person is a large sphere of some radius a! (Yep, physicists love to approximate spheres!)

Some standard mathematical approximations (Skip to the last paragraph if only interested in the final result):

We need to find the temperature on the surface as a function of time. The human is initially at temperature T_0

Now after a few seconds, the temperature boundary conditions are:

T(0,0)=T_1

T(a,0)=T_0

This is because a microwave heats mainly from the inside. Unlike an oven, the microwave will first heat up the centre and this heat then diffuses throughout the rest of body. (You might have probably noticed that while heating something in the microwave. Even if the outside is at room temperature, the insides are piping!) Now both T_0 and T_1 are functions of time.

T_1, the temperature at the centre directly depends on the configurations of the microwave, while T_0 will depend on the thermal diffusion rate from the centre to the surface.

Calculating T_1 is dodgy and depends on accounting for heat loss by evaporation rates of water and then extrapolating. However, for our timescales, we can consider T_1 to be more or less constant.

Now, the thermal diffusion equation for a sphere in steady state gives us: (T being the temperature)

\nabla^2 T=0

This should give us a general solution of the form:

T=A+B/r

with r as the radial coordinate.

Thus, inspired by the steady state solution, we can write:

T(r,t)=T_0+B(r,t)/r

Thus B(r,t) can be written as r(T-T_0)

This gives us:

\frac {dB}{dt}=D \frac{\partial^2 B} {\partial r^2}

where D= \frac{\kappa}{C}

I’m composed of quite a decent proportion of laziness (about 80\%) so am skipping a few steps which mean that I would not need to type out several lines of equations in \LaTeX. It should suffice to say that here I am merely converting the thermal diffusion equation to the standard 1-D case which is easier to solve.

This gives us B(0,t)=B(a,t)=0, the 2 boundary conditions. Also  B(r,0)=r(T_1-T_0), since T=T_1 at t=0. (ie the temperature at the centre due to microwave)

And feeding back these equations back to our diffusion equation, we obtain a solution of the kind given below. The general solution will involve expanding these terms with some coefficients.

B_n=\sin (n\pi r/a) e^{-D(n\pi/a)^2 t}

B(r,t)=\Sigma_{n=1}^{\infty} A_n \sin (n\pi r/a) e^{-D(n\pi/a)^2 t}

Similarly, we can obtain the coefficients A_n. Actually it involves wrting out the expansion with A_n for t=0 and using the orthogonality condition. A_n comes to \frac {2a}{n\pi}(T_1-T_0)(-1)^{(n+1)}

Combining both A_n and B_n, we finally obtain for the surface of the human body, temperature as:

T(a,t)=T_0+\frac {2a}{\pi}(T_1-T_0)\Sigma_{n=1}^{\infty} \frac{(-1)^{(n+1)}}{n}\sin (n\pi) e^{-D(n\pi/a)^2 t}

So, now let’s plug in some values.T_0, the average body temperature is 37^{\circ}C.

D, the thermal diffusivity is given by the ratio of conductivity to specific heat capacity. (It’s actually the Heat Capacity per unit volume for pedants. But since humans are mostly water, weight and volume cancel out.) Guiltily browsing figures for human thermal conductivity and heat capacities, I jotted down some figures. Again, plugging in those values, we get D=0.543/3470=1.6\times 10^{-4}.

I estimated the average chest width, a to be 1 m from available figures.

Now putting them back:

T(1,t)= T_0+ 0.63(T_1-T_0)\Sigma_{n=1}^{\infty} \frac{(-1)^{(n+1)}}{n}\sin (n\pi ) e^{-1.6\times 10^{-4}(n\pi)^2 t}

Conclusion:

The exponential term is extremely small. The second term only starts to matter heavily when t \approx 10^3 seconds or about 17 minutes or greater, which means that it takes at least 1/4th of an hour for the temperature at the skin to reflect significant changes. Thus, under approximations made, it should take more than 17 minutes to completely cook a human alive for temperatures sufficiently greater than 37^{\circ}C independent of configurations of the microwave.

Thus we see that the time rate to fry the human is mainly dependent on T_1 and thus the rate at which the microwave heats the centre of the human. Although other effects like surface currents due to the varying electric and magnetic field apart from an intense burning at the centre might not be a pleasant experience as well have not been considered, these could play important roles as well in the heating. Else, he would slowly be evaporated from inside out as his body is drained and heated at the same time. The human body is about 80\% water and what will be left of him in the microwave will probably be a mess best left for the morgue!

Caveat:

I would need to add if this wasn’t apparent already is that this is an order of magnitude estimate. Microwaves don’t really heat from the centre outwards, but it should give a reasonable enough estimate all the same. A better way to look at the problem including any further mathematical considerations that may be considered are welcome from anyone who has chanced upon this crazy article!

The Sailboat

 

Periwinkle brushed away the horizon from skies and oceans;

People wouldn’t be same.

Jonquil kissed Ecru with passion as the final sun bathed them in righteous flames

Without passing judgment.

Tenebrous cloaks billowed as it outlined the sail beneath which it hid;

The refuge the weak need to seek is.

The wind would, after all, direct the journey as the currents took the keel;

Because the powerful decided or despite.

 

 

Alarm bells gonged in protest;

            Winds could not be painted but its effects could brew a tempest.

Sailors hauled the broken shrouds;

            Clouds distempered the darkening sky as their spirits began to douse.

The boat, over and again, leaped;

            The captain whispered his last prayers and took the crew in a final embrace

But like Hope, it couldn’t be too loud;

            Is it in my capacity to alter course or is it all a charade until the final round?

Ruins

 

An empty canister strolled across crying for tea,

The kettle choked with soot lay smothered in somnolence,

The knight in his shining armour valiantly

Put up his final fight from the fading tapestries.

The sun refused to fracture through the intricate cobwebs,

Beetles declined to be satiated by the chesterfield,

The flickering lightbulb was yet unsure about

Whether to live to see yet another day or flip dead.

The mahogany danced with the sputtering flames,

The table lamp bent over the open diary

Waiting to resuscitate the heiligenschein,

The inkpot, carefully polished, forever anticipated the pen.

A handsome face peered back into the Hollows,

Past the raptures, the despairs and beyond.

A drop crawled down her bridge, smudging the eyes.

Her wail shattered the Peace as War beckoned.

 

The brow tightened, fingers curled in prolepsis,

As Misgivings hugged him in close embrace.

Compunctions fought Purpose and lost,

A greater cause would need the ultimate catharsis.

The lectern was steadied as banners fluttered,

The humdrum grew to a dissonant approval.

While subversive overtones

attained mellifluence, a frail figure emerged.

As the enfeebled man took his dais, left arm raised,

Silence plagued the swarm with its cadence.

“You may lose your friends but never your foes

The World is not your comrade.

Your lives will never matter; they tell you every day

Die for the Cause to paint an echo to remain.”

The lead agreed as it nestled in his head.

The fingers had curled through with little delay.

 

Sunlight filtered through the misguided casements,

As stanchions guarded the chesterfield against disuse,

The blanched knight in fading armour

Secured, now wore the glass veil as an ornament.

The roof and floors had been re-laid and painted,

The lighting was now a reliable monotone,

The humdrum grew without the overtones

As the swarm made their way to the frame.

The haggard face peered back to the future he helped create

With perhaps a lingering air of melancholy

His eyes still flecked with emotion and passion though

As ‘Freedom and Liberty’ were no longer dead.

For as long Man lives, He will find a Greater Deed

And men will die for It as to Fight is to Live,

But as I left what was now a museum, I mused,

It was History, not Liberty that He had achieved.

A Publication

Relation Between Taylor and Fourier Series

This article has since been edited because the sarcasm and humor with which it was initially written might have been misconstrued. 

The link leads to a relation between Fourier and Taylor series published at National Academy of Sciences Letters (Springer). I think it’s a decent enough result for a sophomore physics undergraduate to come up with. 🙂 Happy reading!

Relation Between Taylor and Fourier Series

The Road Not Taken

How Robert Frost’s seemingly innocuous lines resonanted with me one fine January evening…

It’s chilly outside, but the British rain has helped push the mercury up by a few degrees. Silence is complete apart from being punctuated by the regular rat a tat of my keyboard. The festive lights outside are flickering seemingly in disquiet about if and when to shut off completely. There are constant reminders from last day offer hoardings seeking to capitalise on the hurt bourgeois ego of the occasional passers-by. (I happened to fall prey to one of these today. But it did make me happy for a fleeting moment and I figure I’ll be able to live with this decision after all.) My parents leave tomorrow and I’ll be on my own after my third pilgrimage to London in as many weeks from the morning of 6th. Hiraeth. A Welsh word with no direct synonym. But sentiment needs to be deferred for now.

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Writing this whole thing out kind of puts an indelible finality to the whole thing. As if I’m prepared to face 2017 with my sword and armour and all. But the truth is that I’m merely procrastinating. I, like most ordinary mortals (oh, yes), am scared of what the future holds.

We can’t choose where we come from, but we can choose where we go from there

Years are neither good nor bad. They are what we make of them. There are quite a few interesting consequences which might go on to define my life scheduled along the first half of the year. But, it would be unwise to treat them as a make or break. Maybe we are defined by a sum total of all past events up to our present. But as Heisenberg’s Uncertainty principle states: the present cannot determine the future in terms of absolutes. And ‘tbh’ (Internet lingo), I’m not too satisfied with the way my present has shaped out. (Not too dissatisfied either, but at a risk of sounding too presumptuous, I decline to spend the rest of my days printing currency, buying food and lodging and expend my precious resources searching for a mate to procreate with.) So, I’ve made up my mind: this is the year where I decide to choose the maverick path.

Maverick, btw(continuing usage of said internet lingo), is an eponym. An eponym is when a proper noun becomes regularised and is used as a common noun. Maverick, himself, interestingly has his origin in a far humbler foreground. He was apparently a rancher (and a few other colourful things: but we’ll leave that out for Wikipedia) in Texas in the mid 19th century who didn’t brand his cattle. So out of sync was his action relative to the times, that any person who thinks differently is today branded as a maverick. Note, how the use of the word brand has evolved as well. But we’ll postpone etymology to another session.

No, I won’t wear a chicken costume and dance as if I’m cuckoo. (Although granted: loosely that might fit the definitions of maverick behaviour as well). But I won’t wait for the zeitgeist to define me anymore.

There was one related line in the Chamber of Secrets which appealed to me and still does.

So Harry was asking how or if he differed from Voldemort, the perennial villain of the series, as both of them shared the same abilities and qualities. And Dumbledore made an apt observation:

It is our choices, Harry, that show what we truly are, far more than our abilities.

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And I’ve been thinking over this lately, and not because of a sudden predilection towards magic or fantasy. I’ve always found it difficult to make choices as I tend to analyse perhaps a bit more than average. How do you know if something will work out unless you’ve taken the journey along that road? And what if, having taken that journey, some traveler comes and informs you that the grass was greener along the other path? It so happens that one can’t do much about it.

Most people want a comfortable home, a nice loving family and earn about enough to lead their lives without worrying about basic necessities at least unless the Circle of Life catches up and they are busy trying to make their next generation try and achieve a similar goal. And I try to see the point in that. I’m not the first person to question this drab of an existence, nor will I be the last. But while I’m at it, let’s see if I can contribute something to this issue.

Cosmologists say the universe is about 13.8 billion years old. (It may be older because my freshly minted knowledge of cosmology makes me want to seriously question the concept of Inflation.) The earth has been around for 4-5 billion years. Homo sapiens arrived at their current form about 200,000 years ago.(Let’s not quibble whether Neanderthals or Homo erectus were humans). The leaps in advancement since then have been amazing if not spellbinding. But we still enjoy on average about 75 years of oxygen and all other perks which come with one’s position on the social order at birth and possible incremental advancements over the last 200 millennia.

If you look at it, every organism evolves to maximise the longevity the species as a whole. When the individuals themselves become so advanced so as to want to advance their own longevity maybe even at the cost of the species as a whole, maybe we do have a problem. Humans have progressed well beyond this threshold in my opinion.

Or perhaps we don’t need to have an opinion.

42

That is the answer to the Ultimate question of Life, the Universe and Everything. Douglas Adams adds though, that nobody knows what the question is. And sadly (or perhaps happily enough?) that is the state of affairs.

We know that we are alive. We do not know why.

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Not that I necessarily agree with this particular Douglas Adams quote, but tbh, he looked pretty badass and imposing in this graphic, so I thought that this would fit in perfectly.

Oh yes. If you haven’t realised it by now: life is about making adjustments and accommodating changing realities to fit yours. That’s the key reason behind this post and the final picture. If you don’t find an appropriate quote and a picture, just use the next best one and fit a disclaimer over there. Evolution (over 200,000 years) also helps you out in these scenarios.

Cambridge Baby!

My uneventful first 2 weeks at Cambridge

So, it’s been like two whole weeks in a whole new country and I have so much to write about, literally! Firstly, of course, I must apologise to my ardent fans and faithful stalkers who always turn up to read my freshly typed out posts for such an inordinate delay between blog posts. I hear some of them were eating out their livers in anticipation. Some of them even deactivated their facebook profiles as protest! Nevertheless, I’ve picked up my quill again (or the keyboard perhaps?), so you can heave a sigh of relief! No more organ eating. Phew!

So let’s begin at the very beginning! The day was shiny with the sun up and glowing and then I stepped out of my flight. It has been raining since. If someone tells you that British weather is bad, don’t believe him. It’s not bad:it’s a marriage of horrible and what the f***? I’ve already caught a sneeze and am sustaining myself on paracetamol. One morning, you might feel like: “Wow! The weather’s so awesome! Let’s hold a party for such a rare event as being able to see the sun”. And then,the British clouds would be all like: “Haha, let’s drown his party, just for fun!”. Some of my English friends helpfully informed me that it’s even worse in the north near Scotland, where it apparently rains throughout the year. Haha. Nice joke. I honestly don’t see how that is possible considering the fact that rains in Cambridge twice a day seven days a week!

Actually, the journey was pretty cool (no, it wasn’t) as well, so let’s not skip that. Alone in a flight for 13.5 hours might be a romantic experience for most authors I read. But when reality splashes on your face, you realise that there is nothing so awesome about it at all. Yes, the flight was a Dreamliner with a stopover at Doha. I was offered on flight wine for the first time, walked into immigration myself, caught a bus from Heathrow to Cambridge all alone. But the end of the 20-hour ordeal, I just wanted a bed to sleep for the next 20 days. (No, that’s not what I’ve been doing since my arrival at Cambridge! Sigh!)

Culture shocks is what most people write about. So I’ll touch upon it as well without being much of an iconoclast. For a change, roads are clean. Cars don’t blare their horns at all. People are in general more polite and more obedient to the rules which exist. There is hardly any pollution. Cap that with some amazing Jacobean era architecture which Cambridge boasts and you get a splendid living standard (without mentioning of course, how extraordinarily expensive the UK is even with the post-Brexit exchange rate to maintain that living standard). But all this is drab compared to the shock which I faced in my room.

So, I live in a college house with 2 other guys and girls. Now, unlike our rooms in India, none of the rooms have fans. Instead, they have radiators with a central heating which breaks down every other day. The kitchen ovens are electric with no gas supply! (BTW, food is so expensive around here, I have been forced to learn rudimentary cooking to save my fast dwindling supply of Sterling). But the greatest shock I faced was in their toilets! These Europeans are extremely weird. They use toilet paper with no tap around the commode at all! Absolutely horrifying experience on my first day. For the uninitiated Westerner reading this, we Indians use water (jets or other sources) to clean *that* area after the smelly deed has been done. I couldn’t tolerate this initially. But now, I take a shower after the call I answer to mother Nature. It’s kind of a compromise, but at least I feel more comfortable! Phew!

I guess I left out quite a lot of stuff already because I’ve been on quite a few excursions with some *pals*, been to a few ‘bops’ and gotten really drunk. But that’s the usual stuff and I’ll come back to it later if I am depressed enough to talk about it. But I’ll come to the main point: education standard. Is it difficult? How hard is it?

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BTW, here is where I literally study: Centre of Mathematical Sciences

Well, it’s terribly hard. And even more so because they tend to squish their course into 8 week modules. Imagine learning a whole lot of General Relativity, Cosmology, Quantum Field Theory in under 8 weeks. Don’t try. It’s unimaginable. I seriously feel the course needs a relook. The lecturers barely teach than race to complete the course. The studying of course is left to poor souls like us: ostensibly called study groups,but I do that mainly by myself. Part III Maths is perhaps the hardest course possible and most of my classmates arrive at Cambridge with a 4 year undergrad degree, job experience or masters under their belt and intending to slay the course as “another revision”, while I’m perhaps dealing with these modules for the first time after my 3 year undergrad degree. So, yeah. That’s what I’ve been mainly trying to do over the last couple of weeks. Getting myself at par with the “other extraordinary people Cambridge admitted alongside me”! (Sly smile)

But, you’ll be glad to learn that I’ve made some significant progress. However, I cannot assure you people that I’ll continue a steady flow posts, I guess. :/

 

 

 

Adopted

Are you adopted? 😉

What if I tell you that you are adopted? Don’t look behind you. There’s nobody reading this apart from you at least right now. Of course, you might scoff. But it remains that you can never be sure unless you are crazy enough to do a DNA test. You have to believe your parents (at least that is who they claim to be!) Gulp. Unless of course if you are amazing enough to remember your birth (trust me: you’re not) you are at binds. This is basically what is called: Appeal to Authority.

So, when you are a kid, if some dickhead cousin tells you that the earth is flat and that a monster will eat you up if you throw away food or that your face will freeze into gargoyle while making faces: you believe that dumbass. Eventually, the school will take over and teach you the accepted truths: 1+2=3, Grammar, Biology, Chemistry, Physics, History, Geography and why those weird topics have such complicated names in the first place. (Of course, the second part depends on which school you studied in.) Anyway, you get the moot idea.

So, when I was a kid, I used to have these doubts crop up. Now our school was a sublime institution located bang in the centre of Kolkata and over 150 years old to boot. When school got over, our class teacher used to arrange us 50 uncontrollable toddlers in a line. Now obviously this was an impossible problem. But our teachers coaxed us to grab each other’s bags. So we built a mock train with our class teacher forming the engine. We were all coaches eagerly holding the strap of the bag of the one in front of us. Now obviously this wasn’t a simple task. The train would at times teeter from side to side, zig zag and then there would be this over enthusiastic soul who had somehow managed to sneak a watch at WWF (yes, at that time it was WWF, not WWE) and decided to orchestrate a similar pull on the bag in front of him. This usually resulted in the train getting torn in 2 with a lot of coaches colliding and fall on each other. But nevertheless, the engine was a delightful soul who would take the rowdy coach a reestablish order. Much like how America establishes world peace in the Middle East. Enough for about 5 minutes. But the next day there would be a duel and camps established (of course behind the teacher’s roving eyes). Anyway, when we went to the Parent’s Shelter: basically an overhyped shed where parents wouldn’t wait anyway, we were dispatched to our parents. I returned by carpool. But some rich folks had all dressed up mothers receiving their kids. Now, my mother while fabulously beautiful and all had never worn anything but a saree or a salwar. But these females wore shirts and jeans and called themselves mothers. So, I proposed a theory to a ring of passionately eager friends. The theory was that these mothers looked too young. Moreover, they did not have a tummy like most mothers with kids had had. So, there was no way a baby could have come out of that stomach. These kids were therefore adopted!

Now, one of these kids with a mother as described above was a regular bully. So, one day we called him and told him the reason why we felt that he might have been adopted. He became all pale and depressed for quite a few days after that. And I was genuinely airing my concerns btw lest I am accused of anything else.

Interestingly though I feel that these are exactly the principles on which modern science unravels. A few correct observations are made. But the deductions from these are confidently passed on as a correct explanation. And these are then fed to everyone. If the theory persists for sufficiently long, it transcends appeal because of appeal to authority. Now, not every theory is wrong or correct, but I believe we shackle ourselves waay (the extra a was intended) too much by believing everything that is told.

Questioning Authority may be the first step. But the last step is finding the answers, by yourself. There cannot be a greater satisfaction than that.

Even if you choose to believe your parents that you are not adopted that is!