Third Thought

What’s in a name?

Initially I thought that this would be an appropriate title for my blog. However the perils of joining the blogging community 20 years after the Internet opened were laid out bare to me. Such names were common place and some person had even ventured to pen a book with a similar title. This, thus had to be relegated to be merely the title of my first post. In fact the more that time passes, the more difficult it becomes to choose a name or get your voice heard because of course there are now more candies in the candy jar or as Moore would have said, more transistors per IC.

There were quite a few other candidates jostling for a trial to be the legend of this blog as well. But who cares? Nobody will know them ever. And in a few days, not even my own self will recall what those other captions were. Their candidacy was much appreciated and time will helpfully obliviate them for good. Fortunately there can only be one legend which is credited. And that credit, ladies and gentlemen, goes to THE THIRTEENTH THOUGHT. Curtains rise. (Slow claps)

stage_curtains_1_t658

Let the play begin…

 

Total Number of Possible Words

The total number of words that can be composed in English…

This article has since been published in Varsity and can be seen here.

Let’s look at this for the most ubiquitous language: English. (Although, this should work for any Latin script language like French or German. The means and standard deviation will, however, be possibly different.)

Let us assume a Gaussian distribution for the number of words with respect to the no. of letters per word. Here is what a normal distribution looks like:

By simply eyeballing through passages (or Quora text) we can estimate that most probable word length is 5 letters.

Now, to estimate the standard deviation, we can notice that 66.67% of words are of lengths between 3–7 words. Thus $latex 1\sigma =2$ letters. This is a rough estimate based completely on eyeballing approximations.

Now to calculate the maximum possible words:

We know that the longest word in the English Language is pneumonoultramicroscopicsilicovolcanoconiosis. A 42 letter Leviathan which is a kind of lung disease due to inhaling ash particles (‘silicon’). This word is a good 18.5 standard deviations away from the mean! This means that the likelihood of finding a word this long is close to zero.

However, if we want a strict mathematical limit we have: (based on largest word length)

$latex 26×26(42 times)=26^{42}=2.6846064×10^{59}$

A 59 digit number! It could obviously go higher if using 100 or 150 letter words comes into vogue. (I hear that the Germans already do this!)

This doesn’t really appear ‘realistic’. So let’s see how we can arrive at that figure. First, we note, that since the right side of the Gaussian can extend asymmetrically much more than the left side which is bound by 1 letter words. (Zero and negative letter words don’t exist!). However, since the likelihood of words greater than 10 is very low, we can for current purposes ignore them. ( This is an approximation used to make my life easier to solve this. If you are interested, you could as well use MATLAB to plot a skewed Gaussian and let me know about the percentage error due to this. I’m reasonably confident it won’t be too significant.)

Therefore about 67% of words are:

$latex 26×5×26+26×5×26×5+26×26×5×26×5+26×26×5×26×5×26+26×26×5×26×5×26×5=69006080$

The above accounts for the frequency of vowels in all words of length 3–7 as well.

That is about 69 million. A 100% (total no.) of possible words would be about 103503945. Or around 100 million total words.

Dictionary Facts – Oxford English Dictionary says that they have around 414,800 ‘entries’ defined. These are the words that we most use on a day to day basis. The culturomics folks came up with these numbers in a paper in Science in 2011:

Using this technique, they estimated the number of words in the English lexicon as 544,000 in 1900, 597,000 in 1950, and 1,022,000 in 2000. Quantitative Analysis of Culture Using Millions of Digitized Books (they only looked at 4% of English-language books in Google’s corpus)

At Wordnik, we have knowledge of nearly 8 million wordlike strings. Many of these are lexicalized phrases, some are in-jokes, some are names or foreign-language terms.

That is still about 10% of total potential word strings which could be formed.

Order Tea or Tea Order

I put my taste buds to test to check if we can distinguish whether you put milk first in your tea.

Image result for tea act of 1773

With a slew of formals and May Balls being organised by societies to mark the end of the academic year, you couldn’t possibly be more nervous about being judged on tea etiquette. Gowns can be rented for a special day. A white (or black) bowtie could be borrowed from that dependable friend. But what if you strike up a conversation with a Cambridge don (with possibly an OBE to boot!) at one of these events and don’t know whether to add the tea or milk infusion first to the sparkling bone-china. There ends your reputation. This question is so sensitive that celebrated English tea connoisseur (and writer) George Orwell famously described himself as a tea-before-milk person. Here we try to assuage such fears by approaching this quintessential question from the perspective of a mathematician. Does it really matter whether you add tea or milk first and can your taste buds detect such an order?

8 cups of tea were to be presented to a subject with 4 of them having tea poured first.

The story goes that on a particularly unremarkable summer afternoon (probably not very different from today) in Cambridge in the 1920s, Caius alum, Ronald Fischer devised his eponymous test. 8 cups of tea were to be presented to a subject with 4 of them having tea poured first while the other 4 having milk first in various concentrations. The subject would be told in advance that she would be asked to taste eight cups and that there would be four of each kind.

There exists 8!/(4!4!)=70 distinct possible orderings of these cups. By telling the subject in advance that there are four cups of each type we guarantee that the answer will include four of each. Next, we compare whether the subject can detect any better than random chance which is 4 out of the 8 cases or exactly 50%. We can compute the probability of a sample of correct detections of tea or milk first using Fischer’s exact test or a hypergeometric test (not the binomial test, since the events are no longer independent).

This is compared with the so-called p-value to the null hypothesis. In this case, the null hypothesis is: The lady is not right any more than random chance would allow.

lol
The permutation table of possible cases.WIKICOMMONS: KIEFER WOLFOWITZ

In a hypothetical scenario, in which 8 cups were offered and the subject guessed correctly 6 times, the p-value is approximately 24% (17/70). In a purely randomised guessing environment, the subject would be expected to guess as well as she did 24% of the time. Usually, we consider a significance level of 0.05 (5%) as an informal rule to disprove the null hypothesis. Therefore, the above p-value of 24% is considered insignificant. On the other hand, a greater deviation from randomness (such as guessing all tea cups right or wrong) would be described as significant, and a significant deviation would have the function of rejecting the null hypothesis.

The null hypothesis is: The lady is not right any more than random chance would allow.

In an actual scenario, an algae researcher (phycologist) named Dr Muriel Bristol working in Hertfordshire took Fischer’s test and legendarily got all 8 cases correct. The p-value for this test result for Dr Bristol was 1/70, or 1.4%: a ‘significant value’, in terms of statistics. In doing so, she beat Sir Fisher’s stated odds, and he rejected his null hypothesis.

It is not possible to prove that she would never be wrong because if a sufficiently large number of cups of tea were offered, a single failure would disprove such a hypothesis. However, a test that she is never right can be disproven, within a certain margin of uncertainty, given the number of cups offered. And that is what we did here.

Finally, we pour a bit of chemistry for taste to the above resolution to explain why this taste change occurs at all. It appears that the degree of denaturation of proteins with heat is what causes the taste difference in pour order which we proved above could be distinguished by at least one person, at least some of the time

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.