Crush function

Disclaimer: Because my crushes generally follow a similar trend, this is both an open letter and an apology to all the amazing crushes I have disappointed. I am sorry I stalked you through high-school only to fall for your best friend. I am sorry I made you drive to Greek town at 2am for chilli cheese fries! I am sorry I made you dance on bar tables and then ditched you for someone else. I am sorry I laughed at you when your car fell into a ditch next to my apt. I am sorry that I threw your keys into the ditch a few months later. I am sorry I stopped responding to your messages even though we had a pretty good date. I am sorry I dragged you to a horrendous local band concert. I am sorry I gave you nicknames and snickered around with my friends. I am sorry I made fun of your hair.

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Dear crush, you are a sinc function.

I use this analogy mainly because I assume you will not understand it (unless you google it). Nor will anyone else who lives a life of sanity. If you do understand though, please share that with me so my attraction towards you can increase exponentially.

You seem to alternate between realms. Not in a multiple personalities sort of way, but more like melting ice-cream. You are in two states, simultaneously. This is precisely why you emulate this extraordinary function.

The normalized sinc function (time-domain) is the fourier transform of an ideal-low pass filter (LPF) (frequency domain). Your emotional attachment is like the LPF. Only casual emotions (the friendly wave, the random bumping into each other and the small talk) are allowed to filter through. The more intense emotions (I just had a fight with my mother and I need you to hug me) are cut-off. However, the definition of our relationship is like the sinc: relatively indefinite and with ringing side-effects. The narrower you set your cut-offs with the emotions, the wider the indefinition of our relationship becomes.

I wish you could choose a side and commit to it. If you choose to adhere to the time-domain, then be vague and ambiguous about everything. At least then I can label you as a flake and move on. However, if you choose to venture over to the frequency domain, then define everything-your emotions, our interactions, or the name of the dog we will never get.

I wish I could choose a side. The truth is that I don't REALLY know you. But I know me, and I definitely am a sinc function. I linger in a sea of confusion. My emotional attention span is about 2 weeks long. I too have a LPF for emotions. It is a delta function. As a result, none of my emotions ever make it through. And most things in my life remain indefinite.

Best,
YP

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!

Apoptotic blues

"It is a storm indeed,
but a storm of murk." - William Styron

My adviser sent me an article (http://nyti.ms/HK1jIQ) about an hour ago. It outlined the history of a field that I am very intimately involved in: depression. While I leave the scientific questions that were triggered, for the development of my dissertation, I will paint a picture here of the cascade of emotions and a train of philosophical questions(that are also structured in a scientific manner) that were provoked.

The basis of the article was that much of the brain is still a mystery. Although great minds are slowly uncovering the layers, we are finding underneath them a plethora of messy details that need to be sorted. Amidst this disarray, lies the phenomenon of depression. What struck me most about this article, was the connection between neuronal growth and the maintenance of a "happy" state. It implied that emotional well-being was buried in the connections between different brain regions.

So then it makes sense why some of your memories are permanent while others still are transient. To relive a memory means to strengthen the connections associated with it. If that memory is associated with an emotional high, you assume a joyful state. However, if that memory is associated with an emotional low, you descend into a sad or depressive state. This led to several questions.

What is the statistical mode of my memories? In other words, which of my memories do I re-live the most? If I assume my theory about strengthening connections is true, then an old childhood memory probably has been relived the most because it had the most chances to be retrieved. Maybe it is the time when I won my first dance competition at age 3. Or maybe the day I dressed up as a frog for my ice-skating show. Or perhaps the time when I got stabbed in the back with a pencil by my sister. Or it must be the incident from National Park in Dubai when I spelled "red" incorrectly. Yes, it must be the last one since I now spell my colors correctly.

In contrast, I could have only re-lived an event that happened yesterday a couple times because of the limits of time. However, is it not true that our recent past is more indicative of our current state than something from decades ago? I instantly feel a sense of pride and nostalgia when someone mentions Cornell or IIT. I can't help but blush when a song comes on and the lyrics include the name of my latest crush. And I am still experiencing a happy high from the chocolate binging I indulged in last night. Perhaps the element of temporal distance (how far is t-event from t-present) should be included with the weight of frequency.

However, this model fails to include another aspect of current state. The brain lives in 3 tenses: the past, the present AND the future. In order to accurately predict the present state, one must also account for future events. Our minds are constantly preparing for the future whether that future is a few hours away (thinking about your next meal) or a few days away (thinking about your upcoming deadline). Sometimes we look forward to these events and on other occasions we just want to get through them. Our attitude towards this future event further determines our current state. I can attest to this personally, because every year, I am in a constant state of joy from Dec 24- Feb 24th and on Jan 24th, my birthday, I experience an exceptional high. For this reason, I will re-label temporal distance and call it a temporal radius to add the effect of future.

For now these parameters will suffice in helping me determine my current state. In a mathematical sense:

C-present = sum(C-past) + sum(C-future)
C(memory) = {frequency*(-1)^n}/t-radius
---- n = 0 for positive memories and 1 for negative memories
---- t-radius = absolute value (t-event - t-present)

However, this leads me into a infinite sum since I have infinite memories. This is because the reality of my brain which includes my thoughts, imaginations, dreams and experiences is much more complex than the reality of my life which only includes facts. So I return to my initial observation: emotional state is an enigma. And to make a conclusion about your current state, all you can do, is ask yourself. How do I feel right now?

I feel like I am crawling through a nebulous tunnel in a dense jungle with no cracks for a ray of sunshine. And to this my old friend Mary said, "Burn a match!"


:)

Awesomely Normal

My parents just returned from a 10-day vacation to the West coast. Having forced them to take a day trip to the Grand Canyon, I was especially interested in their experience at my favorite spot. Needless to say, they loved it. However, what intrigued them most was not the marvel of nature, but that of man.

It was the skywalk at the West rim that made the most impact on them. The beauty and the elegance of this amazing experience were secondary. The core of my father's conversation was the intriguing engineering and construction of this wonder. He began with an instant glow in his eyes. The 5 hours of flight exhaustion instantly wore off. He included every intricate detail in his eloquent story and his amazement with each added fact was apparent. He compared it to the construction of the skywalk at the Sears tower (it's not Willis tower!) and admitted that the construction of the one at the Grand Canyon was both more difficult and superior.

I couldn't help but recognize the grandeur of engineers. An experience becomes doubly enjoyable when we indulge in the effort and the challenges that were involved with its being. But even so, I couldn't help but wonder why my dad found this skywalk special. He continued his story with examples of similar constructions. What made this particular one awesome for him was the fact that it was 70 feet from the edge and over 4000 feet above ground. The details associated with the creation of a frame structure and scaffolding would have demanded intense engineering and immense creativity.

However, all his examples seemed awesome to me. I thought the minar he built for a mosque in Dubai was awesome. As is my belief about the skywalk at the Sears tower. Yet he so quickly reduced those brilliant structures to the manifest of normalcy. Perhaps this is the difference between education and experience.

I find it awesome to listen to lectures about diffusion imaging. I find it awesome to learn about sensory integration. I find it awesome to discover the workings of electrical and magnetic stimulation. I find it awesome to link electromagnetic theories to the properties of the brain. But maybe, I find these awesome because my naive and immature mind is unable to discern between awesome and normal.

Often, I go into my adviser's office with a question I have been struggling with for weeks. I finally have an answer. It's brilliant. I just uncovered a milestone. So I walk in there, cheery, with big bright eyes and describe my finding. He replies with a solution far more efficient and sophisticated than the one I proposed. It takes him ten minutes to nullify what has taken me weeks. Alas, I implement it and it works like magic. Hence, my awesome has been reduced to normal.

Perhaps the journey of PhD is to attain that balance of education and experience to finally differentiate between that which is normal and that which is awesome. It is the awesome that gets published and cited and followed up. So, I may still be floating in this world of intrigue and curiosity. But it is those qualities that make for a true student and an honest researcher. If we knew all the answers and how to get them, why would we research?

I watched Proof this morning. It is a story about a mad mathematician and his devoted daughter (played by Gwyneth Paltrow). While taking care of her mentally ill father, his college drop-out daughter assists with his work in mathematics. During this period, she writes a 40-page proof that may be groundbreaking for the field. However, she hides this notebook until her father passes away. The irony is that she must now prove that she wrote the proof and not her genius father. Her only evidence is the use of modern methods that makes her proof more "hip" instead of "classic". The education of those techniques were the tools at her disposal when she didn't have experience.

The modern methods and contemporary science are our biggest weapons in advancing from normal to awesome. Sure experience is great, Dad, but it is modern education that makes it seemingly obvious that when you forget to carry your phone charger along, you don't have to freeze in the car to charge your phone. You can just unplug the USB cable and hook it up to your laptop in the warmth and comfort of your home. And while this bit may seem awesome to you, it's really just normal.

Thanks for the lesson! :)

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

Quantitative Romance

Matlab, to you this is an ode,
As you define the variables of my life.
Perhaps one day I can format a code,
And computation won't be a strife.

You are the heart of engineers,
The breath of mathematicians,
The ignorance of philosophers,
But truly a boon with pre-defined conditions.

With elegance you can model the hip,
Recreate the human eye,
Calculate the area of a feather tip,
Help me understand the value of pi.

I wander awestruck in your 800 line program,
With loops of if, for and do while.
Sometimes they cause a system jam,
But your uses are so versatile.

Numerical methods to approximate,
Matrices and arrays to store.
Functions to simplify and differentiate,
Integration is no longer a chore.

You may interpolate and Gaussian eliminate without any error,
But behind your tricks, I am the cognition.
So no surprise, this ode is slightly rarer,
It's not really for you, but for your magician! :)