There Is No Escape With The Gaussians

This afternoon, after Dr Roland Caballar delivered a lecture to the Theory Group of Dr Eric Galapon, something was observed after sometime - there is no escape with the Gaussians. In quantum mechanics, most of the topics to be dealt with involve such kind of function. That is why if someone wants to practice research in quantum mechanics, particularly in quantum measurements, he should be able to master dealing with such functions.

Actually, I first heard of this Gaussian functions, or should I say Gaussian distributions, in my high school statistics. This function seems to be something easy to deal with because of its trend. Someone may be familiar with this Gaussian function by seeing a kind of a graph that is "mountain-shaped." It starts with low values asymptotic to the x-axis, goes up at some point until it reaches a peak in the middle, and declines ones more to values asymptotic to the x-axis.

However, one may ask why Gaussians are the ones worth more attention in quantum mechanics. Why not the Bessel functions or the other ones? Now, this may put on some interest to a curious researcher because he may always try. And who knows? He may also get something more interesting out of dealing with those functions other than the Gaussians.

These dealing with the Gaussians does apply not only in quantum mechanics. Actually, the complex system scale-free principle is also obeyed. This scale-free principle is the one that states "the rich gets richer." Gaussian functions are easy to evaluate that's why more researchers tend to deal with it than the others. However, this does not mean that there is no one left to be interested with the other functions but those interested with the others are much lesser in quantity.

Now, this Gaussian thingy also applies in life when one things seems to be easy to achieve or is very popular. If that's the case of something, everyone wants it. But, there are some things in life other than the ones easy to achieve or the ones popular. Some do try to go with those things and tell that they find something more worth enjoying with them.

Gauss Theorem of Social Status

"The surface integral of a vector is equal to the volume integral of its divergence."

Seems to hard to understand, isn't it? Actually, this is a concept in mathematical physics known as Gauss' Theorem. In more complicated terms, it is a relation of the surface integral of a vector to its divergence integrated in terms of the volume. Well, a person who knows some elementary calculus may understand this further.

At one side of equality, the vector is integrated in terms of the area. In simpler terms, it is integrated twice. However, at the other side, it is already integrated with respect to volume (or integrated thrice). But, when this theorem was derived, in order to preserve the equality with respect to the area, a divergence appeared on the side of the triple integral. And as this talk gets more complicated, does this relate to our lives?

Well, in layman's view, it does not. This only applies to the matters of the intellectuals in the physical sciences. But looking deeper, we see that it relates. Let us say that we ourselves represent the vector being integrated. From time to time, we admit that we can never stop ourselves from being integrated. But, when this integration is forced in the wrong way, the function becomes degraded. And so, trying to make one's self look superior in comparison to others just degrades his or her personality or appearance.

From this day on, this theorem just tells us to be ourselves and stay humble. And so we call this the Gauss Theorem of social status.

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By the way, congratulations to Dr. Christopher Monterola for his excellent air time. Sir, I might not have been able to here your air time last night. But as I have heard, you had a good time with Tado and the gang in discussing love and consistency in terms of gravity and relativity. The whole physics community wishes you to keep inspiring more students not only to like but also to stay in this course. Again, congratulations!

Holy Week and Easter Physics

Belief or non-belief – these are the two things that wait for an idea in the world of physics. Someone else’s idea will lead into only one of these. For example, a theory may be either proved or disproved only soon. Upon proving it, it will be entertained with queries that seem to disprove it. But in the end, the theory (and so as the other theories that follow it) is accepted because their proponent/s sacrificed a lot to prove it.

The same thing also happens in life. There exists a certain duality in the life after death – paradise or inferno. Ones destination on either of the two is judged through purity or sinfulness. If one is sinful then he ends up to the sea of fire and sulfur, where there is endless screaming and gnashing of teeth. So, this just means that everyone goes to hell in the end.

However, as said in the writings, the sinful is forgiven just because someone has made a sacrifice, and that is Jesus the Christ. And so, everyone knows that a lot of temptations may hinder us from heavenly life. But in the end, just like a system acted upon by sorts of dissipative forces, it will all be well because one pushes the struggle to make it through with an addition of our Savior’s great sacrifice.

These things can be seen through different stories. It seems that the system may not go well because there is an existing dissipative force. It seems that life gets harder from time to time because of what is going on. But, it takes just an inch to move on and it takes some faith on His great sacrifice to reach a destination.

A blessed Holy Week and Happy Easter, everyone!

Elastic Limit

Stress and strain. These terms might be defined in physics as the ratio of force per unit area and the ratio of the change in a dimension over the original. The ratio of stress and strain is called the elastic modulus, which further determines the capacity of the material to be deformed.

As said by Dr Christopher Monterola in his lecture today, things same as the different forms of stress and strain also apply in our lives. When pressure comes into one's life and if all of it were concentrated in just one part of a person, he is more prone to being deformed by the challenges of life. He may even not survive that pressure and just break down.

Through those challenges in life, our elastic limits are being tested. Different persons, just like different things, have different elastic limits. There are those who are as tough as iron. However, sometimes, these things just don't matter. The more important thing, despite our elastic limit, is our ability to balance all the pressures.

After all, you will see that a thing with a very weak elastic limit might even overcome the strongest one.

The Feb 14 Equation

Happy Valentine's Day, everyone. At the same time, Kung Hei Fat Choi especially to my Fil-Chinese friends.

Now, what are the relations of the observation of these?

First of all, learn from the wave functions. At first, we would see that aside from its dependence on the dimensions, it is also dependent on time. However, squaring a wave function would require a complex conjugate of it, which is time-symmetric. When multiplied, the natural exponents would cancel out, letting the square of it be time-dependent no more. Same things happen in life. Some people do try to fulfill everything for nothing after all, that is why they realize that their pace is either so slow or so fast. But, try being inspired even for once and you'll realize that time is so perfect.

Second, learn from the lesson of integration in mathematical physics. Functions are integrated from time to time. But, there are some functions (i. e. Bessel functions) that when integrated using the common methods, would result to no asymptotic expansions. But, try using other methods and see that there really is an asymptotic expansion (this was actually investigated by my adviser in his paper). Same thing goes in life that we all need to grow and change. If we just go with the flow, we would amount to nothing. But try exploring new ways in life and see that there is yet more things in waiting. It also goes with our own emotional lives that it sometimes, we see less when we don't care so much about something or someone. But, try to put on more care and concern and we'll see that there is much sense that we will owe for that thing or person.

And lastly, I would want to form a new equation out of the two postulates of life mentioned above: Inspiration + Love + Growth + Change = Perfection. Happy Valentine's Day and Kung Hei Fat Choi once again, everyone.

Integrating Life

Mathematically, there are many instances in physics wherein we cannot find the answers. However, there really exists an answer for that certain instance. Just like what my adviser, Dr Eric Alvarez Galapon, showed in his discussion during our research meeting this afternoon.

As he showed, there are problems that one could not solve using the ordinary methods of mathematics. Specifically, this pertains to integration. However, using some methods of mathematical physics with some relation to quantum physics, these problems actually have an answer.

The same thing exists in our lives. There are so many thing that we assume to end up with nothing. A good example would be the research in theoretical physics. Many people assume that theorists are doing some things worth wasting time. They would even say "what the heck would these nerds get from studying those laws?" However, they never realize that the theoretical approach is responsible for what they are and what they have. Without the theorists, there would be no theories and laws in physics. And if life were to be that way, what a kind of world we have! No internet, no computer, and even no life after all.

All in all, the discussion has a morale. Things seem to end up with nothing at the first look. However, continue to pursue what you believe is true. Even if you don't see anything that makes sense right now, after sleepless nights of perseverance, you'll soon see an answer.

After all, you'll see that you have been integrating life.

Quantum and Relativistic

As we all see, every system in physics has its own behavior. There are systems whose components are very large and there are those which are molecular. There are those that behave with low energy and there are those that are in high energy states. And if you want to escape the laws of the classical physics, then let yourself be small enough to fit into holes and fast enough to reach one point of space to another. By that, you are quantum and relativistic.

Actually, these are just my reflections as my life gets faster and faster at the same time. There is nothing to regret because I enjoy everything. After all, I am the one who wanted to put my life in a very fast pace.

I know I need to take my life one step at a time. But as I grow older, the thing that should be considered the most is today. After that, it is tomorrow. And those are mere reasons why I behave like this. Once I have the chance, I seize it once and for all. If I am doing something, I want to do it as if it is a grand performance. If I am very serious, I look at things as if one small component of it is very crucial for the whole. And if I am happy, I smile as big and laugh as hard as I can.

I want to be quantum and relativistic in this life. You'll soon know the reason why I'm so in a hurry of fulfilling everything.