Integral Infinity

Om 

Purnamadah Purnamidam

Purnat Purnamudachyate

Purnasya Purnamadaya

Purnameva Vashishyate

Om shanti shanti shanti! 

Om

That is infinite, this is infinite

From that infinite, this infinite comes.

From that infinite, this infinite removed or added,

Infinite remains infinite.

Om. Peace peace peace!

I start with this verse from Isha Upanishad, because it reads like a mathematical proof. When adding or subtracting from infinity, infinity remains infinite. I can't recall the first time I learned about the concept of infinity, but I can imagine how difficult it must have been to grasp its abstractness in context of something as defined as mathematics. In theory, if you add up every number from -∞ to +∞, you get 0. This is an unbounded sum, one which has an indefinite beginning and an indefinite end. And yet, its solution amounts to nothing. 

However, if you take this concept from the realm of mathematics and into that of philosophy, the equation changes. As is described in the verse above, the beginning and the end of time are on this spectrum between -∞ and +∞. Yet, this unbounded philosophical sum encompasses not just the existence of humanity, but that of our entire universe. It truly is, "through infinity and beyond!" And if you assume mathematics and philosophy to be on a continuum, then our universe should also amount to nothing.

 

So is it? Is the infinite breadth of our existence not even a mere speck? Or is this a more relative theory? Perhaps when compared with the truly infinite, as in God or Science or some other supreme force of nature, our being is truly miniscule. If this is true, then maybe it shouldn't matter what my legacy is. And assuming that my essence means something, is just a fancy way of expressing my vanity. 

On the flip side of infinite sum is infinite precision. Like the digits in pi. It is both irrational and necessary. Everything in this infinite universe may sum to nothing, but the details of this world are infinitely defined. This is why all constants are approximations. It is impossible to fathom these values, yet so easy to experience them. All of sudden, my existence which amounts to nothing in the infinite sum, is still infinitely defined. The forces that act upon me and the energy I release into this world is precisely defined. At a given moment, something happens because it was infinitely planned. The parameters of this infinite definition and this infinite precision are also infinite. 

I use this symbol of infinity to validate my existence every day. Sometimes, I stare at my infinity sign and use it to zap people's brains. Other times, I stare at it and wonder if this infinity sign can truly transform lives. But most of the time, it only serves as a reminder of the infinite knowledge I have yet to learn. And while this is overwhelming, for that moment I find a purpose for my miniscule self in the vastness of infinity.



Occasionally I also use infinity to define my indolence. My laziness is like the number 8. If it lays down, it becomes infinite!

Thought Pangaea

In order to reboot the economy, we need to learn from the game of Monopoly. Everyone starts with the same amount of money and as the game goes on, people can use their wit and luck to progress.

You might think this thought crossed my mind while reading a finance article or a book on Economics (or while playing Monopoly). However, this thought really entered my unusual brain while I was analyzing the power in the beta-band of my subject's EEG data. Let me you walk through my intricate and strange thought process.

1. EEG Analysis
2. Thinking about a conversation that distracted me during lunch
3. History of how China got its name
4. How these distractions can postpone my graduation (Thanks Yan!)
5. If the recession persists, will I have to move to China?
6. What is the solution to this problem?
8. Monopoly!

This bizarre process, which only took about 100msec, led me to another question. What is the significance of of our brain's digression? Wouldn't we be more efficient if we could compartmentalize our thoughts? Our productivity would increase; our emotions would be less obstructive and overall, we would be much happier. Then why are we evolutionary programmed to think within this mess?

Despite of what the textbooks illustrate, there are no defined boundaries for brain regions. Every brain is unique. In addition, the brain is an organ of both complex anatomy and even more labyrinthine function. Each crevice has its individual purpose and yet it blends in with the whole. Unlike computers, we cannot choose which programs to shut down and which ones to run. They are all running simultaneously without regard to the RAM available. Even past events are saved comprehensively. A distinct smell or an unusual color are capable of provoking the most profound memories.

While this enables us to appreciate the potential of the human brain, isn't it in some ways throwing us off-course? Do I really need to think about summers in India and consequently, sweet mangoes, whenever it rains? Must I let my mind wander among the memories of an old friend at the whiff of AXE? Is there a purpose to thinking about Monopoly while analyzing EEG data?

I view this phenomenon as a Pangaea of thoughts: one in which there are no boundaries to where your mind can wander.  Once upon a time, our world also used to be boundary-free. I am not going to dwell on the influence of plate tectonics on the development of culture and society. However, I will comment on the significance of digression.

"Perhaps imagination is only intelligence having fun." Scialabba is right. If Steve jobs did not let his imagination take over, we would not have the treasure that is Pixar. If Salinger had not digressed, my favorite book wouldn't have been The Catcher in the Rye. Chocolate chip cookies are a result of Wakefield's creative cooking. And the implantable cardiac pacemaker is a product of a wrong sized resistor that was inserted in a recording device by Greatbatch. To his surprise, the circuit began pulsing, just like the human heart.

Our brain's ability to digress is a symbol of freedom and a sign of potential. So, the next time I space out in lab, I will consider it a blessing. Who knows, while indulged in signal processing, I could come up with a way to achieve world peace!

Reciprocity Theorem

In electromagnetism, reciprocity states that if the current densities (sources) are exchanged, their respective fields can be switched too. In terms of electrostatics, if the voltage source in one branch of the circuit produces a current in the other, the same current will be produced in the first branch if the source is moved to the second. Reciprocity has applications in politics (Canadian free trade with the US) and photography as well. In simple English, source and destination are interchangeable.

This is a mighty, powerful theorem for it simplifies computation, eases understanding and supplements the modeling of many complex systems. But as usual, I wonder if this scientific concept can be translated into real life. Can we exchange sources and destinations without changing certain results?

When it comes to traveling, this is true. The distance from point a to point b is the same as the distance from point b to a. However, can we elevate this concept into something even less objective?

I just watched My sister's Keeper. I am not one to get sensitive during movies, but this one certainly captured my emotions. It's a story about a teenager, Kate, who suffers from cancer. Her younger sister, Anna, has been donating her marrow since birth. During an incredibly crucial moment, she refuses to allow her parents to make any more medical decisions on her behalf. When Kate was three, she was diagnosed with cancer. Since they could not find a marrow match for her, the parents had to conceive another child. This child was Anna. To me, this is a brilliant case of irony. There is ambiguity in who is the source and who is the destination. Is Anna the source since she has been donating her marrow to Kate her entire life? Or is Kate the source as her sickness is the very reason for Anna's existence? The truth is, no matter who the source is, the result is still that of sisterhood. Reciprocity exists.

It is difficult to justify reciprocal relationships in our subjective lives. However, we can analyze this concept for a single instant. At a particular time point and in a certain relationship, there must exist a source (someone who is giving) and a sink (someone who is receiving). At a later time point, the relationship may be reversed. One such example is that of parents and kids. Until a certain age, parents are the care-givers. However, at some point, it becomes the child's responsibility to care for the parents. I suppose reciprocity exists for romantic relationships in an oscillatory fashion.

However, today is a day to discuss the reciprocity between a prankster and his victim. If you are the prankster, make sure you devised an intelligent trick. If you are the victim, have a sense of humor and make sure you reverse your role next time ;). Either way, the result is to have fun.

Happy April Fool's Day!

ps: Add me on Draw something. It's the technological epitome of reciprocity. You can switch off between being the draw-er and the guess-er oh so frequently! ;)

Twenty Five

" The years teach much which the days never knew."-Ralph Waldo Emerson

In less than two weeks, the clock will strike twelve and on a cold Tuesday, I will complete my twenty-fifth revolution around the sun. I will officially become eligible to run for the House of representatives and will enter the world of lower car insurance and quarter-life crises.

I am pretty sure that in the past 25 years I have only learned one thing. Growing up is difficult. Most people who know me closely can attest to my childish qualities. I am overly stubborn and passionate. I am incredibly opinionated. And I like toys and chocolates. I break into dance moves randomly, laugh obnoxiously and obsess over frogs. When someone gives me the silent treatment, I pretend they are planning a surprise. When someone is mad at me, I appease them with knock-knock jokes. And when someone suffers from insomnia, I recommend a dose of Arthur!

But there's more. On my first day at Marquette, a professor mistakenly assumed that I was a high-school senior on my college visit. She consequently explained her imaging research with incredible simplicity. I recently got carded before watching a rated R movie. I am sporting the same hair-cut that I had weeks before I turned 21. And my current favorite pair of denim shorts is from 8th grade.

So how can I convince the world that despite my quirks and my looks, I truly am 25? How can I assure you all that I will certainly become older and wiser? The honest answer is that I can't. I may become older, but that definitely will not make me wiser. I will continue to indulge in my childish pleasures. I will send out random presents and get excited for Christmas lights. I will giggle like a giddy child as my birthday approaches. And I will ask you eight times to explain your joke before I finally get it.

My naivety is a boon though. Being gullible helps one believe in fairy-tales and happy endings. Don't get me wrong, I am a sucker for a good action movie, but fables impart an essential cheer along with faith. Children never stop believing. That is why Santa is so popular. That is why losing teeth is a great money-making scheme as a child. And that is why they take that fearless leap from the dense branches of an unusually high tree. I will soon be a 25 year old child. And I believe. So I will continue taking my leaps and turns, and jumping from tree to tree. Surely, sometimes I will fall. After which I will just stand up with a smile on my face and skip to the next sandbox.

I won a copy of Peter Pan in the 1st grade during a dance competition. Since then, I have held a special attachment to that story and perhaps that is where the desperation to hold on to childhood comes from. It is the best depiction of friendship and the wonders of childhood. Chicago is my Neverland and I am Peter Pan: the perfect amalgam of mischief, charm and adventure. Now, why would I ever trade that for growing up?

Ivy City

"The trouble with you Chicago people is that you think you are the best people down here, whereas you are merely the most numerous."-Mark Twain

No offense Twain, but I object. We are certainly not the numerous (we rank 59th based on population density in the USA) and we are most definitely the best. It's a challenge to be a Chicagoan. You may think of Chicago as the ivy league of cities. Only the best and the brightest belong here. And I can prove it.

It was 47 F in Chicago today. And most of us Chicagoans agreed that it was a beautiful day. It had just the right amount of wind and sun. The average high in December is usually around 35 F and so this exceptionally warm day was welcomed with open arms by us. Walking around on State St. with many others, I was reminded not just of how beautiful my city was, but also about the uniqueness of Chicagoans.

Many people have spoken in praise of this amazing city. And many more have defamed it. But there is more to this city than meets the eye. The city of Chicago has a way to creep into your soul. Being a Chicagoan is more than just loving the eccentricity of a city life and enjoying the plethora of food options. Perhaps one of the most important attributes of being from here is the ability to live truly and to live always.

What most people consider cold and gloomy, Chicagoans consider warm and sunny! We are the epitome of people who believe the glass is half full. And why shouldn't we? Our politics, weather, neighborhood and the overall infrastructure of the city and its culture begs one principle of us: Carpe Diem.

Two glass bottles were placed on a table with a pile of large rocks on one side and a pile of sand on the other. The task was simple; Put the sand and the rocks into the glass bottle. The first person examined the two piles and reached for the sand first. However, he failed as he tried to fit the large rocks on to the bed of sand. The second person reversed the order. He was easily able to fit the rocks into the empty bottle. He then poured the sand down that gracefully filled up the precipices between the staggered rocks. The rocks here represent the major priorities of life and the sand represents the simple amusements. This is Chicago, where we occasionally find a warm day trickle into the crevices of cold, dark reality, and we most certainly seize it.

We have the most corrupt of all politics, the harshest of weathers, and the most dangerous airport. Yet, we are happy. It's because we know what's important and have a way of making the best of everything. If life gives us snow, we make snowmen, if life gives us sun, we make people jealous at the beaches, and if life gives us Derrick Rose, we make MVPs. We are a city of people that open our luxurious lofts to strangers when Lake Shore Drive is blocked. We are a city of people that make Pizza more delicious than it's ever been in Italy. We are a city of people that combine the traditions of the world to make our own unique identity.

Yes, not everyone can live in Chicago. But a Chicagoan can live everywhere!

Eternal moment

Consider time as a complex element. Now re-consider it as a mathematically complex element (a+bi) with a real term and an imaginary term.

If you are like me, you are probably thinking, WTF?!! How can time be defined on the imaginary axis? Of all the parameters we investigate, time is the only parameter that should be both real and irreversible. However, a recent seminar (http://prezi.com/s-ezktsfry-w/wanted-nails-to-be-hit-with-numerical-ode-hammers/) I attended presented time as a particularly complex phenomenon.

Now switch modes from your objective, scientific mindset to perhaps a more subjective, artistic one. And re-evaluate the concept of time. Perhaps, think about the real component as time in which we live and imaginary term as time in which we think. It adds value to the mathematical point of view that begs one to think about time that way.

Needless to say, I wandered off on a tangent as I began thinking about how this concept falls into place in our lives. I immediately referred to my good friend, wikipedia (http://en.wikipedia.org/wiki/Time) and was amazed at the analysis of time in terms of biopsychology, time travel, big bang theory and core philosophy.

Ironically, by the time I returned to reality, the talk had reached conclusion. Time went by incredibly fast. The discrepancy between real time and imaginary time was finally apparent. I thought about the last 24 years. It seemed like they went by so fast. Then I thought about every time I had to present or perform a dance and each moment leading up to it seemed like eternity.

Even in our neuromotor control discussions, we are repeatedly faced with how we learn time-dependent tasks. Most of the studies have concluded that we in-fact don't learn in time-dependent coordinates, but instead in velocity, proprioceptive or visual coordinates. So, there is obviously an inconsistency of time in our perception, but it isn't obvious whether the real time is consistent either.

So what is consistent? What is real? This is clearly an open question and I am not sure anyone really has an answer, but we can definitely admit-- Time is a complex element!


"Time is making fools of us again." -J.K. Rowling

Kaleidoscopic Karma

Do, or do not. There is no 'try'!

Yoda's wisdom is unmatchable. Often, we fail to notice how many times in a day we shield our incompetence with the word 'try'. This word is our tribute to the saying, "it's the thought that counts." But is that true? Is the thought enough? For that matter, is 'try' enough?

As part of our moral science lessons, we were taught, "try try again, and one day you will succeed!" However, success is not a product of trying; Rather, it is a result of doing. I believe neither the thought, nor the try, are sufficient. They are a mockery of our true potential and just hinder our progress. We deliberately choose to live in the blurry middle instead of clarifying our true intent and moving to a side. We must do something or we must not. There should not be room to say, "I tried to do it and my thoughts were in the right spirit."

I think back to high-school physics. When learning about the concept of work( Work = Fx), our teacher emphasized that in order for work to be non-zero, there MUST be displacement. So, if there is infinite force, but no displacement, no work is done. Perhaps this definition translates into real life. 'Trying' is like applying infinite force with no displacement. The end result of both is zero. Nothing lost, but nothing accomplished either.

Karma, or action is emphasized in every major philosophy. Simply put, it's the law of cause and effect. However, not all karma leads to good results. Therefore, I'm advocating kaleidoscopic karma: Action that is rapidly changing. A kaleidoscope is an instrument built with a series of mirrors that reflect a constantly changing pattern. Our actions should resemble this. They should be directed in an effect to change something. If the change isn't reflected, the course of action must be altered.

The kaleidoscopic method was also employed by Faulkner in writing A Rose for Emily. His story follows a sequential path in which one object or action triggers the next scene. It's about time I focus on my kaleidoscopic karma. One action must lead to a better action. Eventually, this cascade of actions should help me achieve my end goal. At any point if I feel that the path is leading to nowhere, it is only wise to abandon and begin on a different path. But what if it's not the path, not my actions, but the goal that seems unattainable? To this I'll quote from Star Wars again.

Luke: I can't believe it.
Yoda: That is why you fail.

So, one must do and believe. That leads to success. But isn't belief a thought? While a thought might not be sufficient, it is a precursor to action. I will explore the concept of force again. Physics describes a static condition(velocity and displacement are both zero) and a dynamic condition(motion). Thought is like the force applied in the static phase. And the static phase must precede the dynamic phase. The dynamic phase resembles action during which work is being done. So, it's not really the thought that counts. It's the action, especially one that changes your thoughts and leads to better actions.

So I will (try to) commit to kaleidoscopic karma: Indulge in actions with a cause and discard the other ones. I will (try to) believe that my goal is attainable. I will (try to) follow Yoda.

May the force be with (me and) you!