Newton - A "Relative" of Einstein

While answering the query of a school kid recently pertaining to the Law of gravitation, I started thinking a bit more about Newtons laws of motion. One thing led to another and a thought experiment now seems to suggest to me that Newton may have unknowingly laid down the foundation for the Special Theory of Relativy in some sense. This is a very crude comparison in some senses but nevertheless it seems interesting (well to me atleast :-))
Here is what I have come up with.
We all know that Newtons law says that F=ma i.e The force is equal to the product of the mass and the acceleration of a body. Viewed in terms of an objects relation to the force of gravity, this also leads to the definition of "Weight" which is w = mg and here g being the acceleration due to gravity.
In essense thus, the acceleration of a body can be thought of as contributing to its weight. Acceleration on the other hand implies an addition of energy to the system. Thus, adding energy to a body by accelerating it in some sense increases the weight of the body and hence necessitates addition of higher amounts of energy to maintain the acceleration. This is also refelected by the Inertia of Motion exhibited by a body.
Looking at this from a different viewpoint, it appears that the addition of energy to a system and trying to increase its acceleration will in some respect manifest as an increased weight of the system. (E=mc2.. wink :-) )
So the next logical qusestion would be what the limiting condition is i.e how much energy can be added to the system so that its weight (mass) becomes so large that no amount of energy can accelerate it further. What Einstein found is this limit and gave us the exact relation between mass and energy.

Chaos Theory - One dimension Logistic map (Excel)

Chaos Theory - Pretty interesting stuff and somehow very profound. It is yet another of those mathematical models which goes against the very grain of mathematics itself (well the 19th century view of mathematics to be precise).
Mathematics has always been regarded as the holiest of the scientific subjects owing to its inherent properties of being testable, predictable and deterministic. It was natural to assume that if something could be described mathematically then there would remain no surprises and it made perfect sense. Then maths got complicated!
1) Probability Theory - Here, after rigorous mathematical somersaults all you would end up with is the probability of the occurrence of an event not a certainty. Though it can be argued that it does limit the range of possible outcomes and hence is deterministic in some sense.
2) Quantum Theory - My favorite ! The uncertainty principle virtually guarantees that no matter what instrument is used it is impossible to determine the position and momentum simultaneously. Then of course there is the "Measurement problem" the mention of which will send shivers down any Physicists spine. To put it bluntly, if you set up an experiment to measure something like a Photon as a particle then you will detect it as a particle. An experiment set up to detect it as a wave will detect it as a wave. Funny isnt it? :-)
Well thats how the collapsible wave function of gauge boson behaves..deal with it. So essentially here mathematics has determined that you cannot determine.
3) Chaos Theory - Perhaps the most counter intuitive of all theories. Seemingly innocuous linear equations display behavior that is very surprising. I was trying to model the one dimension logistic map equation which is incidentally one of the good example of deterministic chaos. This equation is also very intriguing because this has wide uses in fields as diverse as ecology! ( Population Growth model) . In essence this equation has a very high dependency on the initial conditions and the behavior changes drastically with changes in initial conditions.
The linked spreadsheet has the equation embedded and plots a graph of 200 points based on the input value of the scaling parameter k ( Sheet: Input, Cell: A8). I have put down the ranges of k that induces different behavior from the same equation. Have fun trying it out for yourselves.
Also, Wolframs Mathematica has done a better job of modeling this equation so if you want to try out a widget which allows a greater control of parameters as well as a mean square minimized error then please refer the Wolfram Demonstration Project

And to think, our universe Probably started from Chaotic conditions on a scale that necessitates the existence of Quantum effects.

If God exists he must be ROFLing now.. couldnt have made it more puzzling. :-)

FIFA 2010 - Mathematical modeling

After having sleep deprived myself for more than two weeks, I decided to try and take out some suspense from this World Cup :-)
The following is my analysis of the next round and predicted winners, the metric used was the normalized linear combination of the goals scored for and against a team. Lets see how things turn out.

Are we getting smarter?

I guess everyone would have noticed that kids nowadays on an average seem much more intelligent. This might not appear very surprising but I got thinking about this phenomena a bit more and it seems that there might be more then what meets the eye.
It is a well known fact that the rate of evolution in humans is 10 to 100 times the average long term rate. You might be surprised to know that 10,000 years ago no human had blue eyes but now the gene OCA2 has emerged and so we do. The mundane (and perhaps logical) explanation for this phenomenon is that the population explosion that mankind has experienced provided for a lot opportunities for mutations to creep in. That plus the added challenges of post industrial life may have contributed to this accelerated rate of evolution.

From this viewpoint it seems natural to assume that generation next will be better equipped to deal with the challenges that we now face and indeed we do see this happening in the animal kingdom as well. However, can this phenomena alone explain this growth in intellect? Rats, ants, rabbits, mosquitoes even, all propagate at rates much higher than humans but I am yet to see a rat that can understand calculus (not that I have tried teaching it to one :-)). Cockroaches have a few million years of lead on us but they havent done much beyond survival yet. There seems to something else driving our evolution that cannot be explained away by physical processes.

Here is my hypothesis:

Before I present it I think I need to point out a surprising form of memory called "Flatworm memory". In an experiment conducted in in 1953, Dr James McConell made a few worms get through a maze and then he killed them and fed them to a second batch of worms. These made it through the maze faster than all the control groups. The same experiment has been repeated with goldfish, rats and canaries with similar results. An injection of RNA seems to induce the same result. So, this cannibalistic experiment seems to point out that somehow memory is being absorbed and hence knowledge is being passed on by the act of digestion.

Maybe humans also transmit information in some way to their surroundings. If we assume that mankind as a whole is connected to a hypothetical meta physical universe that holds the consciousness of the species itself then things start getting interesting. Knowledge acquired by prior generations get accumulated in this "cloud" and any new sentient being that can tap into it instantly inherits this vast expanse of knowledge. This can explain why people are getting smarter. Yes, we have the internet and news travels fast but that is information. Knowledge is a different ball game. It is the ability to interpret information and God knows that the internet does anything but help that cause. Looking at major religions we can draw similarities between many stories and all seem to have a similar theme. Is this coincidence because during ancient times it was not possible for stories to circle the globe rapidly or is it something else? Here for example is a list of the similarities between Jesus and Krishna.
This is not mere speculation, the Global Consciousness Project has been running for over 10 years gathering data and analyzing correlations between random numbers and for many major events they have noticed a significant deviation. This is being speculated to be the result of a global consciousness that can actually have physical and measurable effects. Surprised?

Maybe there is more than just our appearance and genetics that makes us HUMAN. Certainly a tantalizing prospect.

Unprovoked Thoughts

Unprovoked Thoughts


The rising sun, desperate heat
The thought of sweet rain.
Randomness of pure thought
A smile, a laugh and pain.

Memories, dreams, hopes
Fleeting glimpses of a time past;
Fear, regret, plans and tears
How long will it all last?

Some things frozen in time:
Small joys, bigger smiles
Friends standing forever
Roads walked alone for miles.

Dreams that turned to life
Unrealized reality that taints.
Ah! Randomness of thought
What a canvas it paints!

Antithesis of Anectdotal Evidence

I dedicate this article to the old and senseless sayings that have been thrown my way since I remember.

To start off with, I got this recently from someone saying that repetition is always boring and change is always welcome. Hmm.... and I think to myself that over the last two years Katrina's skirt has remained at the same length and I havent heard so much as a peep from anyone??

Anyways, I had this idea of trying to have a conversation with myself using as many idioms as I could think of and each conveying the opposite of the other. So here is how it went.. the theme being me trying to convince myself to open a Demat account

Me: You should make hay while the sun shines
Myself: But shouldn't I look before I leap
Me: All I am saying is you should start now, Rome was not built in a day
Myself: But shouldn't I do as the Romans do when only in Rome
Me: No, doesn't matter. All roads lead to Rome anyway and Time and Tide wait for none
Myself: But I think its better to be safe than sorry
Me: Action speaks louder than words
Myself: But You know a fool and his money are quickly parted
Me: But A rolling stone gathers no moss.
Myself: All that glitters is not gold
Me: A stitch in time saves nine
Myself: Beggars can't be choosers
Me: A man's got to do what a man's got to do
IRENE: Wise men argue cases, fools decide them
???????????????.....

Not to mention a saying that has always had me confused. A watched ketttle never boils. What??

The specific of water is 4.186 joule/gram °C. So under standard temperature and pressure it is always possible to calculate the amount of heat needed to boil water and that can be equated to the time taken given a knowledge of the heat source. Till date I haven't come across an equation that factors in "watching" and its relation to the time taken but surprisingly I have heard this adage a lot.

Well, let me end it here with a quick note. You shouldn't believe everything you hear :-)

SDLC - Bollywood style

Software Development Life Cycle.. as most would call it. However, typically some vendor organizations adhere to the more popular version.. (Sab Dhakkano ko Lagao Chunna)
:-)
Anyways, I was wondering that if a developer could relate each of the stages of SDLC to a Bollywood song then what would they be. Here is what I came up with based on my personal experiences

1) Requirement Gathering:
Choli kai pichay kya hai?Choli kai pichay? Ku Ku ku ku....

2)Design:
Na bole tum na mainay kuch kaha, kaha...

3) Implementation:
Sathi haat badhana. Ek ekala thak jayega, mil kar boj uthana.Sathi haath badhana..

4) Testing:
Yehhhhh Kya hua, kaisay hua, kyon hua. Woh choddo yeh na socho...

5) Deploy:
Raat ka nasha abhi, aankh sai gaya nahi...

6) Maintenance:
Hum hongay kamyiab, hum hongay kamiyab ek din, ek din..


Adieu!
Thoughts welcome