Heisenberg's Uncertainity Principle & Fourier Series ??

Hello folks,

Was really busy with loads of work....but in the mean time, I was working on PDE's...and Fourier Series....

Well had an itneresting conversation with my Prof. on some issues...like Gibbs Phenomenon, Efficiency of a Fourier Series, Heisenberg;s Uncertainity Principle...would post that soon...

Time to catch some sleep..

Let peace prevail in this world.

--

Sun.

Fun- filled Day - Proxy#8

Dear friends,

Today was fun-tastic...visited the Niagara, and for the first time in my life, shopped for around 4 hours, and then back to home, for coooking.......tomato rice, mouth-watering sambar and wonderfulll dosai's.......Add some Broccoli curry tot hat, and the day ended with browsing through the pictures taken during the day...

Catch you tomorrow...

Let peace prevail in this world...

--

Sun.

An excerpt from "The Lost Symbol"

Dear folks,

I had similar thoughts on this issue, and here they are presented ina  fantastic manner by Dan Brown.

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“As you know, this little grain of sand has mass. A very small mass, but mass nonetheless.”

Trish nodded. “And because this grain of sand has mass, it therefore exerts gravity. Again, too small to feel, but there.” “Right.”

“Now,” Katherine said, “if we take trillions of these sand grains and let them attract one another to form . . . say, the moon, then their combined gravity is enough to move entire oceans and drag the tides back and forth across our planet.”

Trish had no idea where this was headed, but she liked what she was hearing.

“So let’s take a hypothetical,” Katherine said, discarding the sand grain. “What if I told you that a thought . . . any tiny idea that forms inyour mind . . . actually has mass? What if I told you that a thought is an actual thing, a measurable entity, with a measurable mass? A minuscule mass, of course, but mass nonetheless. What are the implications?”

“Hypothetically speaking? Well, the obvious implications are . . . if a thought has mass, then a thought exerts gravity and can pull things toward it.”

Katherine smiled. “You’re good. Now take it a step further. What happens if many people start focusing on the same thought? All the occurrences of that same thought begin to merge into one, and the cumulative mass of this thought begins to grow. And therefore, its gravity grows.”

“Okay.”

“Meaning . . . if enough people begin thinking the same thing, then the gravitational force of that thought becomes tangible . . . and it exerts actual force.” Katherine winked. “And it can have a measurable effect in our physical world.”

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Extraordinary!! that was the word in my mind, after reading those lines..What a fantastic approach to explain the science behind human thoughts and ideas.....Lots more........

Pour in your ideas friends....See you again tomorrow.

Let peace prevail in this world.

--

Sun.

Ordo ab chao

Order out of Chaos...

Does it strike a bell??

The search for the ultimate truth. The answer for the primitive question...Determining the probability...How important are human thoughts? What effect do they have on nature?

and lot more questions......answered in this book by Dan Brown...."The Lost Symbol".. One of the best books I had ever read....629 pages, and I completed it in 12 hours, with an interval of 2 hours...

Science, Theology, Philosophy, and many other subjects are beautifully intertwined to produce this wonderful work. In particular, I felt excited when to read some paragraphs which represented similar  thoughts of mine. It was really a wonderful experience reading this book. It stimulated my thoughts.

I would definitely recommend this book and I am more than excited to share my experiences reading this book, which I would do in the next couple of days.

Got work to complete. See you tomorrow.

Let peace prevail in this world.

--

Sun

Coming up with some really really good stuff...soooon..

Hey folks,

I just wanted to tell you that I got engrossed reading 2 books now, and they are absolutely wonderful. giving insight into what I love the most....Analogies.......Some of the points are below...

2nd order Partial Differential Equations and Physics??

Ancient Scriptures and Modern Science.....Relation to "String Theory"

and much moree....The two books are:

Partial Differential Equations by Weinberger, a distinguished Professor of Mathematics, at University of Minnesota.

The Lost Symbol by Dan Brown....

Do check these books out...these are awesome......


Time to open those books again....


Let peace prevail in this world.

--

Sun.

Gunman at UB ???

Hello folks,

Today was quite different. A video footage from the surveillance camera showed a gunman entering the Lockwood library at UB North Campus. UB Public Safety immediately took hold of the situation by sending updates through e-mails and text messages. It was told that an anonoymous person carrying a shotgun was found in the University premises. The University reacted promptly and played safe all the way.

A thorough search was conducted by the police, and finally at 21:30, a mail was sent telling the situation is under control. Take a look at these

 http://www.foxnews.com/story/0,2933,586204,00.html

 http://www.buffalonews.com/home/story/958675.html

 http://videos.apnicommunity.com/Video,Item,233278483.html
 
By the way, over the past couple of months, I worked for 12 hours a week at that Library. Nothing much to type now. Feeling sleepy. Do post your feelings on this issue.
 
Let peace prevail in this world.
 
--
 
Sun.

Exam was okay - Proxy#7

Hello folks,

The exam was okay....it was a 50 min exam...with complex values to deal with...Did the best I could...Would update you guys, as soon as the results are out...:)

How was your day?? I was planning a trip during the spring break...lots to do...okay then...its bed-time..
Shall catch you guys tomorrow...

Let peace prevail in this world.

--

Sun.

--- All Set --- - Proxy#6

Hello folks,

Hope you had a great weekend. Well, mine was pretty good. Catching some sleep now. Just updating this space for today with these words. Shall come back to you with interesting stuff tomorrow.

Let peace prevail in this world.

--

Sun.

Curvilinear Coordinate Systems - Proxy#5

Good evening people,

How was your day?? As I said earlier, I was preparing for my exam scheduled on monday. Completed 30% of the portion, lot more left to be done. Wish me luck. See you tomorrow. Enjoy your Sunday

Let peace prevail in this world.

--

Sun

Changes to the Blog - Proxy#4

Hello folks,

How are you doing??

And here we are at the dawn of another weekend. An exam is scheduled on Monday, the 15th, and I would not be posting much till then. Enjoy your weekend.

By the way, I changed the template of this blog, added three quick reaction tabs at the bottom of the posts, so that you can give share your opinion on it. Also, I had attached a chat box, which would allow us to discuss thigns other than the blog stuff too.. Hope you would enjoy your visit to my blog.

Let peace prevail in this world.

--

Sun.

Astrology & Mathematics - 3

Hello friends,

Hope you all had a wonderful day. Let me continue from the last post in this section. I remember my words, and here I am to share that story in Hindu Mythology with you. Read below....

Once upon a time in Kailasa (The home of Lord Shiva), Brahma (The Creator), Vishnu (The Sustainer) & Shiva (The Destroyer), meet for an auspicious occasion, and while their time talking on various issues. A heavenly Astrologer who was  passingby that place, greeted the 3 Gods. The Gods, pleased with his obedience, invited him to share their talk. As the time passed on, Lord Shiva casually asked the Astrologer, about how good his prediction of future would be, for which the latter answered that, what he predicted is the future. This reply surprised Lord Shiva, and he ordered the Astrologer to prove himselves, by letting them know what Goddess Parvati (wife of Lord Shiva), is doing. 

The Astrologer made his calculations but was afraid to answer the question. However, not answering the question would only prove his words false, so he picked up his courage and with all due respect he told that Goddess Parvati was enjoying her bath. This infuriated Lord Shiva, and he immediately cursed the Astrologer, and also cursed Astrology that never would it be able predict future again. This changed the atmosphere, and the astrologer started to pacify the anger of Lord Shiva, telling that he was just following the order and never had any other intention. 

After things calmed down, Lord Shiva, modified his initial statement, telling that any prediction by Astrology would never be entirely true, and would always carry some ambiguity with it, and I guess you would definitely agree with that.

Thats it for today folks... Post your comments, and any suggestions to improve the content or look of this blog.

See you tomorrow....

Let peace prevail in this world.

--

Sun.

Integrals involving logarithmic and trigonometric functions - Proxy#3

Helloooooo people,

Phewwwwwwww.....

It is a damn goooooood day. I was working on the integrals involving logx and trigonometric functions, which took quite a time to evaluate. It was riding on a 1350cc bike @ top speed, during the ngiht in a horrendous storm. It did whet my appetite for much more Mathematics. I would definitely reccomend it during leisure time. Fun-filled, with lot of enjoyment. All I can do is just sleeeeeeeeeeeeeeeeep. We shall talk about the rest-of-the-world stuff tomorrow.

Let peace prevail in this world

--

Sun.

Astrology & Mathematics - 2

Good evening,

Let me continue from yesterday. Both the times, I had to make similar type of calculations.

In the first case, it was more abstract, like the birth chart was drawn, based on the data obtained from the Almanac, and predictions were made based on standard procedures.

In the second case, it was completely Geometry. It is believed that the geometrical configuration of the solar system during our birth, influences our traits and characterstics. The geographical location, planets' time period of revolution, the angle from the birth star, and many other such geometrical constructions were made to interpret the information about that particular planetary configuration  --> Mathematics, all the way...

The latter reminds me which reminds me of the Coloumb's Law of Attraction/Repulsion, which states that two bodies at a particular distance experience a force of attraction or repulsion depending on their relative position, and the Coloumb's constant depends on c, the speed of light in vaccuum, and the permittivity. This is one of the fundamental laws in Electrostatics, and helped me to strengthen my belief on Astrology.

Now, a question arises in our mind, as to how far that interpreted information would be correct. I myself, am not sure to answer this question, but this is definitely worth to give a thought. Accroding to Hindu Mythology, there is a short story on the chances of a true astrologer's report, which I would share with you tomorrow.

Until then, I would be working on some non-homogeneous differential equations, as I have an exam scheduled on Friday, the 15th.

Let peace prevail in this world.

--

Sun

Astrology & Mathematics - 1

Hey folks,

How was ur day? Its my time now to start filling this space, and pour some new content into this blog. has been working on nth-order linear differential equations today, and it's quite a wonderful experience. More to come in the next few days. Today, I was planning to talk to about Astrology. I have had a small time experience of making some astrological calculations under 2 people.

1) A Hindu priest 

2) A Free Thinker & a Research Scientist in Chemical Engineering

After working under them, I felt the experience as a "coin". The same content with two different faces.

------------

The library would close in 2 more mins, would continue tomorrow.

Let peace prevail in this world.

--

Sun

The week Ahead - Proxy#2

Hope you all had a wonderful weekend. Mine was pretty relaxing. Watched a couple of movies, and cooked fo some time. I felt to write something in a lighter vein today. So, I thought may be planning the next week posts would be a good idea. I would start discussing my views about astrology and its efficiency in depicting future, the next week. The role Mathematics plays in Astrology, and may be something interesting might turn up.

I wish you to participate more actively, and we can have a lively discussion here, rather than me talking continuously. Looking forward to spend quality time in the next week.

Good night and a warm welcome to Monday!!

Let peace prevail in this world.

--

Sun

Glossary

This place would define some of the terms I frequently use in discussions.

1. IB Time ( Idle Brain Time) is defined as "the time during which you are involved in an activity of any form(working/studying etc.), however, you are not willing to do anything and just want to pass the time by any unproductive activity like clicking refresh tab in your orkut/facebook profile, calling your friends and telling them that you are bored to death, thinking about the mistakes you made or lost oppurtunites in past and many such activities which just result in nothing except scrolling the time domain in universe".


Shall update it as soon as I use another wierd term. :)

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Sun

Activity Area

Activity 1:

Open a note pad and start writing a list of all animals you know, their habits, features and compare them with that of humans'. This would help you understand the behaviour of nature, on which I would write later.

Just as a lion roar would control the entire forest, our motives control our entire lives. Hence it is very important to identify our motive in every action and verify it with our conscience.

For more details regarding the background of this activity, click here.

Activity 2:
 
Open your note pad, and based on all your experiences so far, write what do you feel as the purpose of life, and what have you done so far to achieve that purpose.

This activity would tickle your neurons in brain to generate some thoughts which provide you a wonderful experience. Donot forget to share those experiences with me. In the mean time, I would be giving some thought on those questions.

For more details regarding the background of this activity, click here.
 
 
Shall update this space, as soon as the next activity is posted.

2 New Areas

Hello people,

I am just adding 2 new posts Glossary & Activity Area which are completely dedicated to the new terms, which by a chance would be coined by me for usage in this blog, and the activities I reccomend. I feel that would help readers get a quick glance of them, rather than searching the entire blog. Shall update this space soon.

Let peace prevail in this world

--

Sun

Complex Numbers & Dreams - 2

Hello everybody,

Finally, entered the weekend. Last 2 days I had been busy solving some non-linear ODE stuff, which was really tiring. Ofcourse, I am still learning how to solve them, apart from checking the stability of the solution obtained. It was a wonderful experience. I had plotted some graphs depicting the behaviour of solutions on slight perturbation. They were awesome. Also, the solution turned out to be right, so I felt very happy.

Coming back to our discussion on vanishing imaginary numbers, I understood a fact after solving the problem. Any mathematical system which is real, no matter what happens in the intermediate steps, bears real solutions. The imaginary numbers encountered are just an illusion, however, would lead us to real solution if we continue our work. Some times, they do leave their impression on the resulting solution. Like for example, whenever a system has solutions in the form Sine and Cosine summation series, there is a high probbality that the system is complex ( similarly, if the system is of polynomial, chances are high for repeated roots ).

I somehow felt this process analogous to the dreams, which we experience. They are imaginary, but often do we cacth glimpses of images, which would repeat in our real life, and that phenomena is better known as Deja Vu, the feeling in ourselves which tells us that we have encountered that situation before ( just as some of the imaginary roots leave their impression on solution ), some of our dreams leave an impression of what's going to happen. What does this mean??  

Is our destiny pre-defined?? Just as we retrieve, images stored in a folder; can we retrieve some information from future, and take a look at it?? (or) Is it that we program our future and these images generated by our subconscious mind, are just snapshots of what situation we have dragged ourselves in?? 

What information do these dreams generate?? What is its source?? What does it suggest to us?? Is this what we call Sixth-Sense?? Can we control the source to generate the dreams we like?? Or are we just like the variables executed in a computer program??

Is Destiny already created?? (or) Is it what we create for ourselves?? Can the future be predicted?? How far does astrology succeed in predicting whats going to happen?? Are we controlling this world?? (or) Are we under any control?? Are the situations in our life programmed in a particular fashion?? (or) Are they random?? Whats happening around us??

** Is Destiny different from God?? (or) Is it that they are same and would be called with different names by people with different perspectives?? Who is God?? 

All the questions are just canonical forms of one question which cannot be put in words, as its abstract, however trying to fit that sense in words, it would lead us to the question which has been bothering me a lot since many years.:

"Is this Universe Probablistic or Deterministic ??"

OOOOOOOOOOOOOPSSS!!

Where did we start and where are we now?? Is it so complex as the problems in Complex Numbers?? Is this stuff related to mathematics at all??  Question to be discussed in the coming days.

 

Wow!! thats a lot for today. I owe you a lot for patiently sharing my thoughts. I believe that it would be wonderful if you work on the following activity, which is highly recommended by me in your IB Time ( You would find the definition of IB Time here in this post).

Activity 2:

Open your note pad, and based on all your experiences so far, write what do you feel as the purpose of life, and what have you done so far to achieve that purpose.

This activity would tickle your neurons in brain to generate some thoughts which provide you a wonderful experience. Donot forget to share those experiences with me. In the mean time, I would be giving some thought on those questions.

I would leave at this point. Enjoy your weekend.

Let peace prevail in this world.

--

Sun

Disclaimer:

** I am no theist/atheist//non-theist. I am just a traveller in my mind, wandering around in my thoughts, trying to find out the relation between the concepts of Destiny and God, which take me a step further in finding out the truth. The truth which might reveal the purpose of this life, which I am interested in. So, join me in this journey. Journey for the search of truth, which I call Life.

Just one word - "Hectic" - Proxy#1

Good Evening people,

Hope you had a wonderful day. Mine was pretty hectic, with all the non-linear ODE's and complex eigen values, and tiresome algebra, which aggrevated the decay-rate of gray cells exponentially, for today. I felt like picking up sleep immediately, however, under any circumstances, I donot want P(E) < 1. ( P(E) is defined  here )

I need to rejuvenate those cells now. Sound sleep for about 7 hours might help me.

Thats for today :)

Let peace prevail in this world.

--

Sun 

Complex Numbers & Dreams - 1

Good evening people,

Today was a bit different from the other days. I got some time to fill this space pretty early, and I want to talk about Complex Numbers. The title of this post might sound goofy, but I had been thiking over this for the past couple of years. As a matter of fact, Complex Numbers were born after the discovery of the imaginary number  -- sqrt(-1) denoted as "i".

These numbers cannot be represented on the normal x,y co-ordinate plane, and yes these have the imaginary part, just as we do have imaginations. Couple of days ago, I was solving a linear ODE system using matrices. Normally when the eigen values of such systems are calculated they turn out to be distinct, which would facilitate the method to discover the eigen vetors and solve the problem. However, for that particular system, the eigen values turned out to be complex numbers in some particular cases. However, the given physical system was not imaginary. Hope you are following me...Let me rephrase my sentences. I was solving the equations of a reactor which is physically existing and running perfectly, however I encountered imaginary values, as I tried to solve those equations. Technically, this should not happen  as the given system is real.

Nevertheless, I tried to solve the problem with the obtained imaginary numbers, and thanks to De Moivre for his wonderful theorem, {exp(it) = cost + isint}, which converts these complex numbers to trigonometric functions. After that step, the usual Gaussian Elimination, finally me the result which was surprisingly a real value. I was full of joy after solving the problem, but....

What happened to the imaginary eigen value numbers?

Why were they eliminated at the end??

How would that happen???

Doesnt it look similar to the dreams which vanish as soon as we wake up from sleep??  Are dreams really imaginary??  or  imaginarily real??

These questions were born in my mind, and I guess you would have the same questions in your mind too...

I would take a leave here today, and would talk about it tomorrow, as i got some Non-Linear ODE stuff to work on right now. Hope you would share your thoughts on this post.

See you people tommorow.

Let peace prevail in this world.

--

Sun.

  

Functions & Life - 2

Hello Everyone,

It is 2345hrs right now, I want to sleep badly, however, before that I would just like to share some words with you.:) Yesterday's post might look crazy but thats the way I feel about life. I started learning about the concept called "Sets" when I was about 10 years, in the mathematics course of 6th grade. After that in the next grade, I had learnt about "Relations", and the list follows. Now when I look back, I feel that those concepts are much more important than what we use them for. They teach us something else too.

A Relation can be termed as a Function only under certain condtions, in a similar fashion, any personal relation in real life would be functioning properly only under certain situations (when proper amount of time, money and interest is invested). Similarly, there would be specific Limits to any function, as we do have in any real situation in life. Identifying the limits is one of the most important aspects in the analysis of a function, which is quite analogous to real life, where it would always be better to identify our limits under any situation and behave accordingly.  

1. I curse my poor memory, as I forgot the name of a theorem which states that any function can be expressed as a sum of series of sine and cosine terms. As we all are well aware of the behaviour these famous trigonometric functions. They are periodic fluctuations (ups and downs).

Doesn't this seem like something???

2. We all know that life is a repeated cycle with up's and down's; infact only change is constant in life. There would be high times and low times in all of our lives' which neither stay forever nor conclude at once.

Now I get close to make a point here. Doesn't 1 & 2 seem similar??  I was surprised when this thought arouse in my mind. It was quite fascinating. It was then that I believed there something else to mathematics, which I should start to understand. From then, I started relating everything in mathematics to life, and I find it wonderful. Apart from that, I also had some analogies between the concepts of mathematics and science which can be realted to life.

I want to type more, but its 0020hrs right now, and I got to catch sleep. See you people tomorrow.

Let peace prevail in this world

--

Sun

Functions & Life - 1

Hello everyone,

A tiring day. Started with a "Molecular Simulation" class and a couple of classes on "Jordan Blocks" & "Stability of Roots"; finally, some work on matrices ended my day. Today, I would start writing about my experiences working with functions and how they can be related to our life.

Sets --> Relations --> Functions --> Differential & Integral Calculus --> Difference Equations.

The above order represents the hierarchial order of courses taught in Mathematics. All of us are well aware of sets, and these simple concepts form the base of Calculus. Sets containing ordered pairs can forRelations, which lead to Functions under some special conditions(injective, bijective or surjective), and these Functions act as bridge to enter Calculus, which is one of the most wonderful inventions in  history of mankind.

Now, whenever I start thinking about functions, (as you know there can be an infinite number of functions written with various combinations of variables, constants and numbers), I just think of them as our fellow people. In life, we can find various kinds of people with different mentalities, habits, personalities, disorders, behaviours, likes, dislikes, and many other features, which is quite analogous to various types of functions which can be increasing, decreasing, constant, fluctuating, oscillating, continuous, discrete, even, odd, exponential, logarithmic, special functions(just like some very very special people in this world).

Also, it would be quite amazing to observe the fact that, all of us have high and low times in our lives (well, atleast most of us) which is quite similar to a function which has maximum and minimum at some point in its course. Well, some functions are monotonically decreasing, while others are quite opposite, similar to people who had always been succesful and some other who always taste failure.

Another fact which would quite interest us is that similar to how the behaviour of a function can be studied with the help of calculus (i.e. analyse its growth rate, identify maxima and minima, etc.), the behaviour of a person can be studied with the help of Psychology (which analyses the cause of a person's action under certain circumstances). Apart from that, just as we can change the behaviour of any function by manipulating its variables or constants, or interchanging the variables, the behaviour of humans can be changed by Hypnotism.

I guess my words seem sensible to you :). I always look at everyone in this world as a function, which has been pre-defined, and the way anyone behaves is due to that intrinsic function (i.e. the inherent qualities which was attained and developed from birth). One more analogy, would be that, there are a lot of time-dependent functions, which change their nature with respect to time, and it is a fact that we all change with time.

I strongly believe that every subject we learn is related to other, and all of them teach us how to live. I would like to write some more, but I my function for today needs to find constant rest with respect to time for the next 6 hours in the time domain. So, I would bid adieu and would come with many other ideas tomorrow.

Let peace prevail in this world

--

Sun