Marrying a Draupadi Constant.

If you have a deep understanding of e, this piece is certainly not for you.  However, if you want to go ahead and read it, please do contribute a few of your harshest and most painful words to the poverty-stricken comment box. 

To establish an understanding of something, we need to define it and we also need to know what should not define it. However I shall employ a different strategy.

Reach out for your phone and look for an online definition of e. This is what you will find:

“The number e is an important mathematical constant that is the base of the natural logarithm. It is approximately equal to 2.71828.”

I used the copy-paste functionality because typing that out would be quite a shameful exercise I would rather avoid indulging myself in.

Wikipedia is not wrong. The definition above is true but this is why a lot of math haters exist. There must be a better way of learning what e really stands for.

We could start by drawing a few circles.

Steps to follow:

Note:  If below 14 years of age you may skip steps 2 and 3

  1. Take out a sharp pencil and compass.
  2. Go out and buy a pencil, sharpener and a compass.
  3. Stop sulking and carry out step 2.
  4. Draw circles of radius 1cm, 2cm, 3cm and so on.
  5. You may draw 1mm, 2mm, 3mm or 1 micron, 2 microns and so on, if you have invented superfine rulers and possess amazing microscopic vision.
  6. Baptise the first circle as the mother of all circles.
  7. If you mentally did step 6 without hesitating, ask yourself why you did it and then continue reading.

The smallest circle is the mother who gives birth to all the other circles in your drawing. It is like calling number 1 the mother of all positive integers.  You can scale down to 1 from 10, 15 or even 347.

The constant, pi, is common to all circles and it would be utter stupidity if we have to give it a puny and meaningless but true definition of 3.14. Instead think of pie as something that represents an idea that all circles, as well as all other shapes derived from circles, share. If you use Mahabharatha to explain this concept, Draupadi would be pi and the Pandavas would stand for all possible circles.

(For readers unfamiliar with Mahabharatha, Draupadi is the wife of five brothers and has been used as a symbol to represent someone common to all five.  One of the readers pointed out that Kunti, their mother, might have been a better symbol to use because the Pandavas could have existed without Draupadi but not without Kunti.  It might seem like a reasonable argument. However, on closer examination of the epic, you realize that Draupadi was born to marry the five Pandavas.  They existed because she did. I would be glad to hear out a differing opinion).

Now for the less dramatic definition of pi;

Pi is the ratio between the circumference and the diameter of any god forsaken circle in this universe. Try to find the truth in the above statement with your own circles.

You could alternatively adopt an eccentric route of taking a stick and pulling it to the ends of the earth from a central point.  Make as many circles as you can but pi will stubbornly sit in your equation without flinching.

A million dollars from my pocket to anyone who can draw a circle that is not married to pi.

Likewise, e is a Draupadi constant.

It can be thought of as a common base rate to describe ALL continually growing/decaying processes that we encounter in our daily lives.

One example lies in banking.

Banks sanction loans with a fixed interest rate that increases continually.

Steps involved in loaning 1 rupee to buy coffee toffee:

Interest rate: 50%

There figures represent the loan along with accumulated interest rounded off to two decimal places because beyond that, the figures are “insignificant”.

 

  1. At 0 years:           1 rupee .
  2. After 1 year:        1.50 rupees
  3. After 2 years:     2.25 rupees
  4. After 3 years:     3.38 rupees
  5. After 4 years:     5.06 rupees
  6. After 5 years:     6.83 rupees

An elaborate explanation of the first three years:

  1. 50% of 1 rupee is 50 paise interest, therefore 1 rupee + 50 paise= 1.50 rupees.
  2. In the second year the bank charges you for your loan AND your interest which involves 50% of original 1 rupee loan and 50% of 50 paise interest.  This is added to the original 1.50 rupees of the first year (1.50 + 50% of 1 rupee loan + 50% of 50 paise interest i.e. 1.50 + 0.50 + 0.25 = 2.25.
  3. After the third year, it becomes 50% of each of the components comprising the second year added to 2.25.

The bank wants you to pay for not only the loan you sanction but also for the interest.

 

img_20160821_133514

 

To sum it up the bank never forgets, hence the phrase “paisa vasuli”. Your loan and even the interests of your interests that keep piling up, are charged with a fixed interest rate every single term.

Another instance of exponential growth is observed in case of bacterial cell division.

Non biological steps involved in bacterial growth:

  1. 1 cell divides or multiplies (I am not sure) into two.
  2. 2 cells become 4 cells (the original 2 cells + 100% of 2 cells)
  3. 4 cells become 8 cells (the original 4 cells + 100% of 4 cells) and so on.

I do not think (I might be wrong) that 8 cells of E. coli  sit and wait for 20 minutes before deciding they need to finally become 16. Probably if you could zoom in and observe the cells in each second comprising those 20 minutes you could possibly observe a slow increase from 8 to 16 involving fractions as well. Since we are talking about living cells we cannot even begin to imagine fractions of it, hence for convenience, we adopt to understanding it in a series of 2 raised to x.

Radioactive decay is another similar process. I leave it to the readers to ponder over it.

Now the question circles back to e which ties up all these processes in a sacred knot of marriage.

Can you connect the dots yourself and define e in your own way?

This time try not to reach out for your phone.

(Edit: One of the readers pointed out a flaw in the analogy which I graciously accepted to an extent after carefully reading it. I pinned the existence of the Pandavas on Draupadi. The same treatment with circles would imply they existed because of pi. Circles were there even before the concept of pi was known.  I wanted to convey the idea that you cannot draw a circle leaving out pi. It is an inherent property that has an impact on all calculations of circumference and areas for circles and shapes arising from circles. The analogy, if you read carefully, could go either way.    Thank you, Parth Raval, for your feedback).

.

A note to my 20 year old self

Foreword: Events described are inspired from real life incidents.   Any shocking resemblance to fantasy is purely coincidental.

A note from my seven year old self to my 20 year old self,

 I remember you learning the multiplication tables in 1st grade.  Mother, a math enthusiast, had imbued her love for counting and logical reasoning to you and sister.

 I can still recall, with a smile, your futile attempts at making 60 divisions of a circle to represent each minute with an incompetent ruler.  You would curse and cry because each time you tried hard to get them to be equally spaced but to no avail. Now you might laugh and think it was trivial but back then everything captivated you.

How was a clock made? That question was enough to make you ‘tick’.

Was it Magic?

Despite attempting to memorize tables you would constantly forget what 9 times 6 was.  It never seemed to make any sense to you back then.  Instead of blurting out the answer, you would recall watching a certain episode of Dexter’s laboratory while mother was teaching tables of 9. To make matters worse you had an overachieving sister who was brilliant with multiplication tables.  To add a feather to her cap, she had secured 2nd place in fast math tables competition.

The grimmer side of the picture ( black and white) carried your struggle to grasp why 9 times 6 was 54 to begin with.

Remember outside 2nd grade classroom we had a macadamia tree.  All of us would spend our free time cracking open the hard outer shells with stones larger than our fists before devouring the nuts. As a child you were fascinated by symmetry even though you had no idea there was a word like that.  You loved anything that was equally spaced.  You would fight for equality because it seemed like the embodiment of impartiality to you.  What has happened to you now?  In all ‘fairness’ I thought you would become a judge but here you are, wasting time in Grad school wondering whether you want to join the herd of misdirected PhD cattle moving towards “greener pastures” of advanced learning.

Good luck with that!

Getting back to memory lane:

You took it upon yourself to ensure that amongst our friends, everyone received an equal number of nuts. (You were nuts back then but anything is better than what you have become right now).

You started grouping the nuts, keeping 6 friends (including yourself) in mind.  Based on how many you could crack open, you would split the nuts.  After repeating this for days it soon hit you that you were dividing and multiplying. Making 6 groups of 9 nuts each involved using 54 nuts.  Both multiplication and division were happening simultaneously. Finally everything started making sense. 

Magic!

After grasping the tables you faced yet another difficulty.  How was 9 times 6 and 6 times 9 giving the same answer?  By using 54 nuts to begin with, you could get 9 groups of 6 nuts as well but it always left you shocked.   It was hard to wrap your head around this.  

You got your answer one afternoon on a bright sunny day. (To be honest it could have been in the morning because you do not have the best memory but in the spirit of good story telling I shall choose a bright sunny afternoon).

While sitting on your balcony, you fixed your gaze upon a small section of a brick wall that separated our estate from the neighboring one.

That section of the wall looked like this:

wall

With the power of imagination (which was at its peak thanks to Harry Potter and J. K. Rowling) you could overturn it by 90 degrees and instead of 4 columns with 8 bricks cemented one on top of the other, you got 8 columns with 4 bricks. Therefore the same segment of the wall was simultaneously  4 times 8 as well as 8 times 4. 

Magic.

Only a seven year old can think like that.

I hope you  understand how little you have progressed from there on. We had hopes for you till you were 12 after which we lost you.  This is an attempt at reviving your seven year old self.

Yours with great concern,

Signing anonymously out of pure shame.

Note: The extremely incompetent writer, whose work has no structure or flow, welcomes any form of criticism ranging from mild mockery to heart-wrenching insults.

A study on How to Effectively Build Sand Castles in air

Snippets might be missing; hinted by the lack of flow in the writer’s thoughts. Decoherence rules this material world.

27th July 2016

Let us throw all the complicated “bull-shit” out of the window. In fact I can provide you with a “jembe” (a Swahili word whose English equivalent I have willfully forgotten at the moment) to take it all out because we have built a lot of crap we have no flying idea about in our “important lives.”

I am officially conducting a naming ceremony for Science. It should be called  “A Study on How To Effectively Build Castles In The Air.” Here is why I think so:

  1. Physicists start with the famous line we all started with when we set out to pompously write our answers in exams; “let us assume”. I always found it pointless and unmotivating to continue after beginning on that note.  In school I was an idealist who fought vehemently against assuming but now I could not care any less. 
  2. Biologists study animal models to understand a human being! I have a lab rat and because I have found out this is how a certain X pathway functions, I will apply this “so called knowledge I have” to design a drug and help mankind in his endless endeavors to find a cure for diseases.
  3. Statisticians consider a hypothesis to be correct if it is statistically significant. They are the true culprits and should be charged with gross discrimination. They forget the minority and bully them in some corner with a star or a dot  forgetting to take them into account when interpreting data for the sake of convenience. Such lazy arses. I am one of them.

Before I set out to even try to understand what transcription is and how nerve cells conduct impulses I think I need to get the answer to a question I had back in school.

Why is the square root of 2, an irrational number? My teacher could never give me a satisfactory answer and as time flew by, I became more stupid. I forgot to ask questions and/or avoided thinking when they did crop up. It seemed easier to slip them all under the rug.

Anyone who knows me well enough admits I am a huge lover/hater of Math who foolishly took Biology because I fell for it passionately for a brief period of time. As a rule of life I harbour no regrets though. Life is like a drunkard’s walk. We make random choices and fall but we get up and walk again with the same stupor. We still reach where we need to. You will notice as you read this (good luck doing so) that my thoughts are scattered and I seem to have no flow in this piece. I refuse to structure and order it. “Let it flow”. Chaos and randomness is how this universe works anyway. Or so I am led to believe. I need to take this moment; pause, reflect and laugh. What would I know about the universe? A note to a few readers I have managed to hoodwink to read this piece of crap. Do not believe anything I say. I know absolutely nothing.

I am currently doing a Masters in Biology but I had to google what the difference was between a neuron, nerve fibre, nerve and a neuro-fibril.

I have always been an absurdist. I constantly questioned everything I “seemed to know” and arrived at the same conclusion. I knew absolutely nothing. With time this feeling has exponentially increased and at the moment an unknown measuring device has captured and recorded peak values of distress and stupidity waves oscillating in my brain’s electromagnetic field.

This leads me to the next question. What does this electromagnetic field in the brain do? It is claimed to be just there due to generation of electrical impulses and it seems to be just a bystander (like a by-product in a chemical reaction that is produced but has no role in the reaction). But what if it plays some significant role?

My turn to build a majestic castle.

The brain is a funny organ. Is it an organ? Can I call it an organ? I might be wrong.

Let me rephrase. The brain is a funny thing.

Let us take this moment (or a lifetime) to “think” about how exactly we think.

I look at titan showroom and my mind wavers to a memory of my father buying my first watch, followed by a string of unrelated thoughts. Titan showroom leads up to cricket somehow and before you know it I am thinking about dark chocolate ice cream and my mouth salivates because the brain decided (I decided or the brain decided? Is there a difference?) I need a reward. Selfish bastard.

What unifies all these thoughts into a single moment of your life? How does this funny thing manage to conduct such an AMAZING feat?

A lot of small pieces of information encoded in different regions of the brain and arising from different sensory regions congregate to form an idea, a notion or a clear concise thought (in my case, a fuzzy one) and to add to the complication, this idea/thought has to keep evolving every split of a split second.

When I watched “Finding Nemo” back in school, a lot of information such as the words, colours, textures and other random thoughts/memories/questions came together all at once, like  a hurricane descending upon you, and kept changing. How did all of that come together? They were fired electrically by separate nerves/neurons and they somehow fused together at their destination. How does an idea form? My roommate, Sneha, would probably exclaim, “what sorcery is this?” Note: I still have doubts about the difference between a nerve and a neuron and you are still reading this piece. You must be more foolish than I am. 

Some unknown measuring device is capturing a private thought in my brain (a note on this later in bold).

My private thought: I propose that this field created by electrical impulses could be a by-product but it also plays an important role in Unifying everything. It is the One that gives birth to an idea. It makes One see the “bigger picture”.

But I propose a lot of crap. I am an absurdist.

Note: The biggest flaw is the act of measuring. By interrupting the private “lives’ of whatever you are trying to observe you alter what it does. A mere act of observing and measuring changes the phenomenon (at least in quantum physics) as opposed to when you do not observe. But how would you know anything for that matter if you did not observe it in the first place?

If I have not yet disappointed you enough, here is the real kicker in the nuts. Question what you are reading right now. Your brain could also be defined as a sort of measuring device. The act of reading and trying to understand this piece might disrupt and alter these Holy Words and there might be a discrepancy between what you read and what you think you are reading. Imagine the Horror if that statement were true. It makes you question everything that you think you know over all these years of fine learning! Now you have to deal with  a severe case of the “Doubt Syndrome” like I do.

Let me get back to the question I had in school. Why is the square root of 2, an irrational number?

Let us believe it is a rational number. Some incredibly brilliant chap opposes its irrationality and proposes a hypothesis whereby he firmly believes it is rational. He needs to prove it.

In order to prove a hypothesis, you need to prove certain other facts. If they stand true the hypothesis is true. No one looks at the bright shining light from a torch directly. Everyone looks for the faint shimmer. If they spot it they conclude that the light is indeed from a torch even though no one saw the latter. It could have easily been from a blazing old fashioned bonfire.

Hypothesis: The square root of two is rational

Certain other facts: For a number to be rational it has to be expressed as a fraction, x/y where x and y are whole numbers written in the lowest terms. The lowest terms simply means that there is no common factor between x and y. I cannot divide it any further (I shall write another absurd article where I will talk about the “sense and sensibility” of division and proportions).

For instance 8/18 have a common factor of 2 but when you divide, you obtain 4/9 which is the same value expressed earlier, but now it is in its lowest terms.

In this scenario I used a subtle example that involves a big white flash of light without the flashlight in sight so as to not completely discredit the entire methodology adopted in research but I shall have my day! There will be a shimmer of light at the end of the tunnel!

The big white light with no torch in sight: For a number to be irrational x and y should certainly not be even. All even number have a common factor of two.

Statement: Square root of 2 = x/y

By squaring both sides you get 2 = x^2/y^2

The answer is blatantly staring at you but your funny thing refuses to see it.

x^2 can be expressed as 2*y^2.  It is therefore a multiple of 2 so it has to be an even number. I really hope your funny thing does not require me to state explicitly that the same applies to y^2.

The brilliant chap who thought square root of 2 is rational may not be wrong but he needs to prove he is right.

If you do not observe something, it does not mean that it ceases to exist or is untrue.

You might be obliterating the existence of something crucial.

A final word of advice to the Brilliant chap: Continue trying to prove that the square root of 2 is a rational number. I shall fund your absurd idea with my imaginary cash.

For the Love of Speed!

To follow the story-line click on the link below for the first part:

https://schrodingersdaisy.wordpress.com/2016/05/10/deception/

May 31st 2016

“Based on my calculations, we are moving at a speed of 14 km/hr.  We will arrive with enough time to spare,” I screamed optimistically against the sound of the motor threatening to drown my voice.

Flaw( I am sure there might be more) pointed out by a friend: Even the slowest motor boat in the choppiest of water moves upto 50km per hour as far as ‘Google’ knows. Thank you, Sudarson for your long critical remarks.

Uncle rolled up his long sleeves before turning his head sideways towards the banks of the river. I could see him smile. 

“Varvara, I have never expected such sloppy language from you.  What do you mean when you tell me that we are moving at a speed of 14 km/hr?  Explain yourself.” He kept his gaze fixed on the banks as he spoke. 

I looked at him, questioning my own conceptual understanding of speed.  There seemed to be no error in the statement I had made.  Was this one of uncle’s tricks? 

“Your calculations are based on speed with respect to still water but you have not considered the water current.  Depending on whether we are moving with the current or against it, the value of the speed varies. Remember motion is relative.  If there was a cyclist moving at a similar speed of 14 km/hr on the banks of the river in our direction, we would appear stationary to him and he would appear stationary to us even though both of us are moving.  In a likely event, wherein, the poor cyclist slows down due to exhaustion, his perception of motion will change.  We will no longer appear stationary to him. In describing any kind of motion we should always have a reference frame.”

“What is a reference frame?” I asked.

Uncle leaned forward and picked up a small pebble lying in the corner of the boat.  He picked it up and dropped it. 

“How would you describe the motion of the pebble in the air?”

“The stone traces a straight line,” I answered hesitantly with a hint of doubt.

“It traces a straight line(as long as the boat is not accelerating) but for a person sitting on those banks the pebble traces a curve.  By virtue of the observer’s lack of motion, he perceives the stone traversing a parabolic curve.  The above observations made are both true but it leads to another question.  Does the pebble trace a straight line or a curve ‘in reality?’ This is the reason describing motion ‘in space’ is not an easy task.  Space seems like an ambiguous term of which, I confess to have not the slightest fathomable idea.” He paused, escaping into a reverie of sorts.

I wish I knew what he was thinking. Only on very rare occasions was uncle rendered taciturn.

“Do you remember our visit to Greece?” he suddenly broke the silence; although the creepy sounds of the crickets did not exactly account for complete silence.

How could I forget Greece?  It was the first time I had boarded an aeroplane but my excitement was soon taken over by unexpected motion sickness, consequently ruining any prospects of what people would call a “happy journey”. I blame the nachos.

“You ate nachos on the flight and watched a movie.  Which one was it again?”

“Piter FM.  I must add, a great movie with an unexpected ending.  Masha’s cell phone slips from Maksim’s hands and falls into a river under the bridge when he tries to get her number.  How could they end it on such a note after building it up for two hours?” I pouted as the memories of the movie lingered around.

Uncle laughed before he declared it was my turn to row the boat.  He handed over the pair of oars to me before he dipped his hands in the ice-cold water.  The motor had stopped working and we had to use the emergency pair of oars on the boat.

“I will present to you two cases.  You are watching Piter FM while travelling to Greece, eating a plate of nachos. The window shutters are down.  This flight experiences no turbulence; an extreme case.  In the second scenario, you are at home doing the same.  Do you think you would you ‘feel’ different at home as compared to a uniformly moving aeroplane?  Would you be able to ‘feel’ the motion in the former case as opposed to the later?  Perhaps a child back on earth, flying a kite, would ‘feel’ the aeroplane in motion and dream of becoming a pilot someday.  According to the child, the aeroplane certainly does not appear still.  However according to the passengers in the scenario I described the entire surroundings move along with them, hence distorting the idea of speed.” He concluded before leaning towards his left side to indulge himself in one of his childish antics.

“In Arabic, there is a word for the amount of water that can be held in one’s hand. It is quite conceivable; the need for such a word among people who have traditionally lived in water scarce areas.  But I interpret the word differently.  Gufra signifies the little knowledge we have today with respect to the vast amount of unanswered questions left to explore. In other words, we are still trying to find a way to an oasis.”

He exhaled deeply before he let the water slip past his fingers. We spent the next minutes thinking in silence.  I kept going back and forth in my mind, struggling to conjure everything he said. Something did not make sense.

“According to what we have learnt so far, motion is relativistic and different with respect to the reference body used, hence the concept of relative velocity.  How then, can light have a constant speed? Is light an exception?” I asked.

“I will show you the answer in the laboratory.  At the moment I recommend basking in the warmth and splendour of this sunlit landscape.”  He almost recited in a dramatic tone.

“Can I ask you one more question? It is quite a silly one but it has been bothering me for quite a while.” I spoke softly, letting the crickets win in a ‘battle of the loudest.’

He nodded approvingly.

“When the Flash (DC Comics) runs so fast relative to other “earthlings” why does time slow down for him?”

“Although I have not read the comic books, the concept you are referring to is called time dilation.   I want you to learn about it yourself.  There is a young chap, I reckon a brilliantly foolish one, on the internet who has posted a wonderful article with a small thought experiment called the ‘Parable of His Holy Balls.’ You must read it.”  he said before he looked at his watch.

It was dusk.

The last gleam of light dancing on the water as day turned into darkness.

Kawaakari.

I think the boat remained motionless for a while, or we must have drifted along with the current. Either way the speed of the boat was the least of my concerns.

 

The next day, Uncle Pyotr sent Varvara the following link:

https://malenkybitpoogly.wordpress.com/2016/05/23/the-church-of-unrelentingly-impotent-reason/

Spin A Thought Topsy-Turvy

This is the fourth part in the series of Schrodingersdaisy. To follow the story-line click on the link below:

https://schrodingersdaisy.wordpress.com/2016/05/10/yugen/

October 19th 2013

“You and me against the world.” I read out as I closed the book.

“If I was writing that book, that line would have been different,” uncle claimed as he feasted on the Tiramisu. 

I looked at his coffee coloured teeth as he grinned in delight, failing to see why there was a need to change such a moving line. 

After a long pause, he kept the dessert aside, pulled up his chair and sat down.  I noticed his receding hair line as he placed his base-ball cap aside.

“How would you describe the physical state in which you are in at the moment?” he asked as he looked at me intently.

“I am sitting on a chair in your laboratory.” I answered, wondering how his question was relevant.

“Are you moving?” he continued.

“Uncle, why are you asking me absurd questions?” I asked in a puzzled tone.

“Varvara, answer my question first,” he seemed amused, as he reached for the tiramisu.

“I am not moving at all, unless you count swinging legs under your precious table,” I quietly laughed as he raised his eyebrows.

“In the grand scheme of things, you are moving.  The earth is rotating on its own axis at a speed almost twice the average speed of an aeroplane.  It is also revolving around the sun.  The entire solar system is revolving in the Milky Way and in a super cluster of galaxies. If I consider myself a speck in the solar system I will see the sun standing still.  However, if I move further away, I observe that the sun is revolving in reference to the Milky Way (but at rest in reference to the solar system). We are part of something bigger and more exciting.  The universe is expanding at a rate faster than the speed of light.  Think about how insignificant we should feel.  Can there ever be a “you and me” or “here and now” and “against this world”?” he asked.

milky way

I looked at him in disagreement.  I had just finished reading the most romantic book and uncle was morphing the idea of love for me.  Father always said uncle’s idea of romance was cosmic and unearthly.  I finally understood what that meant and why he never married.  He was already in love with the Unattainable. 

He looked at me, arms folded against his chest. He was challenging me about my own existence. Someone should remind uncle I was only thirteen years of age and my idea of love was a fifteen year old boy and not the universe.

“But don’t you feel that even the smallest component plays its part?  In our body, all chemical processes happen on a cellular, molecular, atomic and ultimately, on a quantum level.  If I am able to talk to you right now, it is the result of the forces existing between fundamental particles in my cells.  The human body might not be as grand as the universe but surely, you cannot undermine the significance of what might seem tiny?” I replied

“If that is what you believe, ask yourself whether it would matter to the “universe” if there was no life on earth?  Would it have any impact?  Why do you exist?  What purpose do you serve in this grand scheme of things?  Are you an evolutionary accident?” he asked

“Or are we created by God?”  I interrupted, waiting eagerly for his response.

At this point I must add, whenever a conversation with uncle shifted to God, he would squirm with immense discomfort. I never quite understood what uncle stood for.  Whenever I did ask him directly, he would reply vaguely and vaporize like a dementor into his room of doom.  Maybe Schrodinger’s cat got his tongue.  Nevertheless I remained resilient in my endeavor to search his soul between the shadows he cast.  

“I will continue this conversation some other day,”  I thought out loud as I watched him enter his room.  A room that could be anything I imagine it to be.

Note: The extremely incompetent writer welcomes any form of criticism to the views put forth in the above journal entry.

An old man’s tale.

 

15th July 2013

“Keep your eyes on my lantern.  As soon as you see the light, you will be enlightened.” He said with a glint of wickedness in his tone.

I laughed inwardly at his remark. I knew what I had to do.  Uncle and I had practised for days.  He kept emphasizing on how important it was to get the timing right.  All I had to do was open the shutter of my lantern as soon as I saw the light from his lantern.  Uncle would then note down the time lapse between the two events.  We would repeat the experiment (uncle preferred the word duel) switching our roles. This would go on until we achieved consistent values.

We waited for dusk before we set out to the country side.  For our duel to work successfully we had to avoid interference from other artificial sources of light. Uncle left no stone unturned in trying to recreate Galileo’s experiment of the 17th century. We looked like we had stepped out of a time machine; wearing long robes and holding lanterns.  Uncle insisted on walking instead of taking the bus and speaking in Latin, of which I knew not a word.   Suddenly I regretted asking the question. If only Ms.  Darya had answered it instead of brushing it aside with her usual taunts.

28th June 2013

“How could someone, living in the 17th century with no technology available to us today, calculate the speed of light?” I asked.

“You are too young to understand the answer, Varvara,” Ms. Darya replied.

Uncle would never dismiss my questions.  On the contrary he would get excited about all the different ways he could play around with the answer.  This time he outdid himself with the re-enactment. I remember the last time we did one of his re-enactments. It was a fun exercise.  A fact I dare not openly admit to him. Father said any form of praise would breed his insanity.

An excerpt from 13th May 2009

‘’I was hoping that I would give these books to my daughter one day.  But you are just like my daughter, Varvara. I want you to keep them,” uncle said as he kept a dusty box in front of me.

I looked inside to find seven books.  The mystical number 7. 

“Once you finish reading the entire Harry Potter series, I will answer your question of what light consists of.  You will see why I need you to read these books first.”

According to uncle, Galileo was one of a kind.  A man who thought outside the box.  Prominent scientists during his time believed light had infinite speed but Galileo wanted to test whether it was true.  He believed light had a finite speed. However his experiment failed to prove so; a piece of information I was not privy to until the end of the duel.

Back in the laboratory

“Then why did we do it?  What purpose does it serve to re-enact a failed experiment?” I asked dejectedly.

Uncle nodded his head and looked at me with a crooked smile, showing his prominent dimples.

“Simple ideas lead to great discoveries. Take the example of Armand Fizeau, a French scientist who learnt about Galileo’s failure.  It prompted him to devise an improved experiment that successfully found the velocity of light within ten percent level of accuracy.  Over the years, Fizeau’s experiment has been improvised in order to achieve greater precision and accuracy.” He continued.

“You might fail sometimes but never think your failures are insignificant in the face of your success. You will only be able to connect the dots looking backwards.  Only then will you appreciate the role failures played in moulding your character.”

Uncle reached out for a sheet of paper and pen.  I sat next to him, keeping my hands as far as I could from his table.

“Write down a basic speed equation for me.” uncle said handing over the pen and paper to me.

Speed = Distance/time …

He took the paper from my hand and started drawing an experimental set-up. 

speed of light 2

  1. A source of light; a candle. No fancy laser beams in the 17th century.
  2. A semi-reflective mirror tilted at an angle to allow only a fraction of the light to pass through.
  3. A toothed wheel rotating to either allow or block light to an almost perfectly reflective mirror placed 8.63kms (in Fizeau’s experiment) away from the toothed wheel.
  4. The ‘eye’ of the experiment to represent the observer.

 

Uncle disappeared to his room of doom, or as I called it, Schrodinger’s room only to reappear with a box full of coloured markers.  He took out a green marker and started colouring the eye.  He then took out the black marker and started drawing long dense eyelashes under the eye.  Father was right.  Uncle was insane. 

 “Now I want you to observe the toothed wheel.  Why do you think Fizeau used it?” he asked me.

 I nodded, clueless about what the answer could be.

 “The toothed wheel, as you can see, has gaps in between the teeth.  If you picture it rotating it will serve to “chop” up the light coming from the mirror into short pulses which are, in turn, reflected by the mirror 8.63 kilometers away. One of two things can happen to the light when it is reflected back to the toothed wheel. It can EITHER pass through a gap of the toothed wheel OR it can be blocked by a tooth.  Fizeau adjusted the angular speed of the wheel such that the incoming pulse was blocked by the tooth adjacent to the gap through which the pulse had passed through to begin with.” Uncle continued as he reached for his pen.

 “Now I will show you the math to make it clearer.  The unknown variable in this experiment is the speed of light, which we now know, is in fact a constant. We know the distance the light has to travel…”

 “I know!  On doubling 8.63 kilometers we get the distance the light travels since it had to make a roundabout trip in the measured time.”  I answered excitedly.

 He smiled before he continued.

 “Since you seem to have understood the experiment so well, answer this question. How did Fizeau measure time then?”

 “He must have used a pendulum.” I answered confidently.

 “Why do you think Galileo failed to find the speed of light?  Even Galileo had a pendulum,” He paused to let the question sink in.

 He looked at me acutely before arriving at an appropriate conclusion that I had no answer to his question.  I asked him to continue.

 “The time it takes for light to travel is not appreciably noticeable.  That is why Fizeau gained an advantage over Galileo when he decided to use a wheel.  Since angular velocity was known to him he could find the frequency.  Time and frequency are inversely related to each other.”

 f = 1/T (s) …

 “We have everything we need to plug into the speed equation. Do you have any other questions?”  He asked looking with great anticipation towards me.

 “What was the value of the angular velocity he chose in order to block the incoming light?” I asked.

 “Varvara, there are books and papers for that.  You cannot expect me to remember precise experimental values.  Ponder over what you learnt today and come back to me if you have any further questions.”  He said before he disappeared into Schrodinger’s room.  I dare not follow him.