Saturday, June 26, 2010

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! :)




Thursday, June 24, 2010

Moving Threshold

Threshold.

I have been fortunate enough to be involved in the integrative field of Biomedical Engineering. And being in the center of the merging points of the purer faculties, I have heard several definitions of this word.

Let me first define the word, "threshold" as listed in most dictionaries: The point of a beginning.

Most people will nod their heads in agreement, but we as engineers or scientists or mathematicians know that threshold can mean something different to us. To an engineer, a threshold voltage is the value at which a chain reaction may begin. To a neuroscientist, it is the point above which an action potential will occur. To a doctor it is the physiological value necessary to diagnose a patient. To a mathematician, it is the point at which there is a 50% probability that a response will be elicited. To an artist, it is an entrance to something exciting. And to my mother, it is my age beyond which all decent men will have found a wife.

These definitions can fall under the roof of the dictionary definition, except maybe the mathematician one. It claims the point of a beginning only 50% of the time. Or my mother's definition-that one claims the END of freedom as we know it. But more or less, the dictionary definition says it well. The point of a beginning. A definite point.

Not really. The more you examine this value of a threshold, the more uncertain you find it. Threshold is really a range in practice. Make sure the error is less than 5%. Make sure your blood sugar stays between 100 and 126mg/dL. Make sure the voltage is between 1.45mV and 1.55mV. Make sure you're home between 1:30am and 2:00am(this is my curfew).

But a beginning is always well defined. My life began on January 24th 1987. I start work at 9am every morning. Featured soccer matches for FIFA air at 1:30pm CST. The record breaking Isner-Mahut tennis match began on June 22nd 2010 at 6:18pm (British Summer Time). Of course, the ends are foggy. Sometimes it takes days before we realize something is over.

So maybe threshold isn't just the point of a beginning, but it is a limit. It is like an asymptote, you approach it, but in order to reach the value, the function must change. In simple words, threshold is the end of one event and the beginning of another. When the threshold is crossed, the limit surpassed, there is a spike.

I have crossed this limit several times and stumbled over to fight with the spikes. And in order to cross these limits, I've had to move them first. Often we set limits for ourselves so we can keep our actions in check. But sometimes these are put forth by others, either to protect us or to restrict us. I am sorry, but neither of these conditions are acceptable to me. I've negotiated the value of thresholds in my life to expand my cage. When the tree can no longer bend, it must break and perhaps a new tree will grow there in its place. Safety might be a result of protection, but wisdom is the product of experience and I cannot keep myself from that. As for restriction, I value my freedom more than I value my life. I follow my own rules, make my own mistakes and develop my own theories.

Thresholds are the gates to an adventure. They are the end of boredom and the beginning of an organized turbulence. For a while, you can extend the tunnel and remain sheltered. But one day you break free. You discover your true potential. You rise above your threshold.

And your life begins, for real!