Thinking wide Vs thinking deep

This is a post after a long time. I have been very busy lately including a trip to visit my family. You might say I was vacationing but then I find my vacations so much busy - because I am meeting my family after a year and there are just so many things to do - lot of travel, socializing, eating :), catching up etc. Contrast this with my life here - simple : Goto office, work and be back home for TV at most including some exercising in between.

That was just to update you about my whereabouts. I have been again reading lot of theory CS (and well yes relativity too :)) and I was thinking of what kind of thinking is really necessary in different aspects of life. I could come up with classifying thinking into two broad categories - thinking wide and thinking deep. Thinking wide is being able to come up with ideas - lots of them inspired by different walks and some maybe even not effective to the problem at hand. Thinking deep means being able to drill down into any one idea - this requires lot of analytical skills and knowledge etc. I thinking I am good at the latter (in the domain I find interesting). Generally thinking deep also requires thinking wide to an extent but the new ideas you generate/consider are from a small domain. Creativity is the ability to be able to think wide and be able to have the intuition to see what ideas are good. Research requires creativity and the ability to drill down into an idea and convert it into a solution.

A Resolve

Dear all,
so much has gone past so soon. I decided to understand the deepest of theories, the General Theory of Relativity. I think it will give me peace to know the mind of God. I have always always wanted to understand it. Why? Because to me it seems like a profound theory in itself examining the most fundamental of assumptions about our daily experience. Also it came out not trying to explain something but trying to reconcile the fundamental understanding about the nature of space-time as found from Special theory with Gravitation. And out came the equations of the General Theory. Another of my dreams from a long time has been to understand Quantum Theory (or to convince myself that I understand it, since no one really understands QT). But that I will keep for a later time. I found some really nice lecture on GTR which employs Mathematics not beyond what I know. I will try to understand it now. But how do I force myself? Readers of this blog, at least the interested ones, I am going to try to explain what I read in the simplest of words, as I read along, to you. Of course this is not going to be easy for you to understand unless you remember your mathematics. But please readers remind me if I am slowing down or tell me if I am covering too much in one day/week. I will try to be regular. So day 1 will be tomorrow (procrastinating today!).
For those who never heard about relativity - The theory of relativity was formulated by Einstein based on a very well experimentally 'confirmed' assumption - the speed of light is constant in all intertial frames of reference. Based on this single assumption Einstein proved that our notions of space-time are incorrect. The most surprising of those conclusions is that the concept of 'Simultaneity' (for example : You and your roommate are reading this blog at the SAME TIME) is RELATIVE i.e. to a different user this statement might not be true!. When Einstein tried to use his understanding in the framework of Gravity he came up with the General Theory which basically explains Gravitation not as a REAL force but merely an 'illusion' created by curvature (this is a deep mathematical concept) of the four dimensional fabric of space-time. What mathematics led him to conclude this? What was the intuition behind all this .. the blog entries will try to explore all this as well as the mathematical equations which came out of the powerful insight of Einstein. Without the power of equations it is said to be pretty much impossible to understand the GTR.

So dear readers .. buckle up for the ride .. and brush up your knowledge of mathematics :) Vector spaces, Geometry (differential) and the Calculus! Watch out for the next post ...

The truth?

Many a wise men have often said that they search for the truth. However a strange fear has engulfed me since I really thought seriously about it. What if there is really NO truth? Ok, let me try define truth. First of all the issue is the attachment of a boolean value to a certain question (is this entity X true) according to a certain answering mechanism (for Computer scientists that would be an ALGORITHM!). IF all people who are able to answer the question attach the boolean YES to the question - we say it is TRUTH, OR, IF by logical reasoning alone one is able to answer the question to YES we would say it is truth. So for the wise men, the question is which one among one of several possibilities about whatever they are looking for is true. A basic quality of truth is the following. If entity X logically negates entity Y or is mutually exclusive with Y, both X and Y cannot be true.

So, first of all wise people - here are the faults in your reasoning.

(a) Suppose two of those theories about the question you have out to be true. Then none is truly true :). This is also called breaking of consistency in Mathematical systems.
(b) What if, there is really NO way to answer if something is true? And this is called not having completeness in Mathematical systems.
(c) while (a) and (b) are attacks on TRUTH from a mathematical standpoint lets come to more physical issues - what if, different reference frames provide different answers to the issue under concern. This, by far, is my greatest fear about the very nature of TRUTH.

Sadly, no powerful enough mathematical system is both consistent and complete so inside the boundaries of a mathematical system there is really nothing called TRUTH - defining TRUTH to be all true statements - if there is we cant know it hence the wise should stop their quest!.

While with the physical world, TRUTH is subject to reference frames itself. How can we ever establish the TRUTH even if we had to choose among one of several possible theories? Eventually we would come down to some equations confirming the validity of that in all frames .. but coming down to equations is actually simplifying the problem to a Mathematical system in which the TRUTH is impossible to find? Maybe I am saying something wrong there but I guess I am stepping into the regions of Mathematics, Physics and Philosophy and because none of them is my domain I have the right to make such foolish mistakes :)

Then, I believe that indeed there is NO TRUTH. But our best effort can only be something fortified by the power of a Mathematical framework - an IF-THEN guard : IF THEN . Even with such a framework we cannot hope to find the truth in that system but at least we can work in a consistent subset of the system.

Now at the end of this rant, I seem to have forgotten the very issue which seemed to have caused this! I guess it was something to do with my searching to know the truth of some matter .. and I now realize that none of my rant above actually disproves that for a certain specific matter the truth cannot be known .. hmmm .. well but what if the judging of truth is a subjective feeling ? Then what is true to you, can be false to me .. truth may be relative .. damn .. I give up

A strange story

A strange story I know - of love or hatred I know not. Love without hatred is impossible and vice-versa at least till you remain in the shackles of the great Illusion of the material world (please refer to the Gita for this!). Love and hatred are then just two feelings of material nature and it is impossible for one to exist without the other - just like action and reaction. When you love, you reserve the place for hatred somewhere in your heart (albeit for a different object at a different time) and when you hate you must fill it by love in order to live (and the human heart searches desperately for love). Those who say that they only love everything are LyInG (unless they are free of the Matrix - Illusion - Maya whatever you want to call it). What does it take to turn love to hatred and vice-versa ? - that catalytic agent is called TRUST. And thus one is caught in this vicious cycle of love-hatred-need_for_love->love-hatred-need_for_love->love endlessly till one realizes that TRUST itself is the culprit. For Trust by itself comes from expectations and assumptions .. attachments to the fruits of actions thus directly prodding the great Illusion (hencforth we call it GI). Can anybody except Neo get away with taking direct panga (hindi slang) with GI?

Let go ...

And whats the bitterest and sweetest of all philosophies - To let go. Well, this is so general that it is pointless to demean it by giving specific examples or maybe I am just too lazy to find one (sometimes being very lazy may pay in the long run - just a side remark!). A mystique that I am, philosophy from the Gita has always been something that I am awed at ... and this one is just one small lesson stolen from there. Detachment from what one does ... is difficult and bitter and yet everything is sweet if such is achieved. It is hard and hardest it is indeed of all normal human activity, but sweet are the consequences ....

Whats the motivation?

This is a post after a long long time! I guess I was (and probably still am) in the so called "blogger burnout" period. But today I felt I had to blog about what keeps me running during those long runs. Inspite of myself being through the long runs (19, 20, 22.4) miles, I am touched by stories of my Asha friend's completing their marathons (Maui and Chicago). Some of us still have the SF/SV to do by the end of this month. I have often wondered myself what keeps me going on? Is it the bagels after the race (no kidding here!) or is it just that I am too strong and this is all trivial or is it just the feeling that I have to get done with it now that I have come so far .. or is it something else? While I do not discount in partial any of the reasons I gave above (except that the second just vanishes after mile 16!!) the real reason is the love to see how far one can go ... its almost like indulging with your mind :) These marathon runs are a test not only of body fitness but also the determination of the mind! Many times I have had to fight pain for few miles and the sweet thought of finishing it strong seems to help mask it in the mind. So do I still know the answer of what keeps me going on? Its probably so complicated and with multiple small thoughts/feelings contributing to it that I will never know ..

Knoppix

Dont start googling on Knoppix: thats the very main topic of discussion here and you will soon be getting to know it. This post is a continuation from the last one. After my installation of Windows XP and the desktop version of Fedora Core 4, I realized that I had to resize my windows NTFS partition. The only safe well known softwares for available for this were expensive - Partition Magic I think is the most well known. The demo version of these softwares just simulate : they dont actually modify anything (and of course I learnt this frustrating fact after I tried it out). I came to know that there is a ntfsresize program for Linux that can resize NTFS partitions from your Linux installation on the same disk. So I installed ntfsprogs (the package that contains ntfsresize) and ran it from Fedora - it sure did work and resized my /dev/hda1 to 8GB but then Windows seemed to have lost track of the remaining space. The trick was to create another NTFS partition on the remaining space. I think fdisk could you used to do that but I was slightly scared of doing that since it meant deleting the windows partition and recreating and so on .. Then I came to know that there is a Linux variant (free of course) of the well known partition magic - its called QTParted. I downloaded that and tried to install it only to now realize that I did not even have gcc on my machine! Damn - I had installed the desktop version instead of a custom Fedora installation .. since I hadnt really installed anything on Linux yet so I reinstalled Fedora, custom this time, and went ahead with QTParted. But it was not to be so simple after all .. soon I ran into several dependancy problems - X includes not found (fixed), libXext not found (gave up on this) ... I realized that it was too tiring .. a new google search revealed that there is a Linux called Knoppix Linux that has QTparted built into its Live CD. I immediately downloaded it and booted from it .. Aha, what a nice experience it was! Knoppix immediately mounted my /dev/hda1. QTParted found it pretty easily too. But one has to unmount the partition before modifying it. I figured that out in 5-6 minutes. After that it was a piece of cake .. QTParted resized it and I created a new NTFS partition on the freed space. I then restarted the machine to check if Windows was alright still!
The logo appeared fine and then I came to chkdsk (ntfsresize schedules a chkdsk automatically if it touches your NTFS partition). With each step my heart jumped as if Windows would throw some fatal error .. but lo and behold! everything went perfectly fine ... a final restart led to Windows XP without any problems at all. And all was done.
Well, I still need to fix some things - like Wireless networking on Fedora and also some error in the filesystem driver (I have no idea what that error is!), but at the end of it all I concluded that Knoppix RULEZ. Just have a copy whenever you have to do any installs, repartitioning etc. Forget Partition Magic and the like ... and anyway if Windows XP disk management will someday include partition resizing nobody is ever going to use Partition Magic :)

Laptop reborn!

Last week I finally got some time to fix my laptop. Earlier, using the Sony recovery console I had restored the laptop to its factory installed configuration (of course without having prepared the recovery disks). But even then it had the same problem of slow start and screeching(!) sound while the disks rotated. Then, last week the laptop refused to boot after 50 attempts. I then declared it officially dead. Found time to buy a new 60GB 5400 RPM Western Digital Notebook HDD, which came to $120 after taxes, and installed it in the laptop. Then I installed Windows XP on it. Unfortunately I did not make an extended partition, although I left 7GB for Fedora Core 4. After I had spent some hours installing various softwares on it, as well as completed the installation of the desktop version of Fedora Core 4, I thought of resizing the /dev/hda1 to have a data partition for Windows ... and realized after few minutes that there was no free software available to do that. I could have again installed Windows but instead I decided to go around it and solve the problem .... stay tuned how I managed to do that!!