Continuous Compounding

I feel there is something mathematically wrong with the way compound interest is defined today. We say “5% per annum, semi-annually compounded”. If I have money invested, mathematically speaking, it should get compounded all the time, not just in fixed intervals.

I would like to define the term “absolute percentage” – the annual interest rate at which the money must grow all the time in order to reach the same amount as it does using normal interest rate calculation. Let me explain what that means.

If I invest amount ‘p’ for period ‘t’ years, at an ‘absolute’ interest rate of ‘rdash’, then,

a=p*e^(rdash*t/100)

where ‘e’ is a mathematical constant having value approximately 2.71828182845904.

This means, that amount ‘p’ will grow to amount ‘a’ in ‘t’ years if it compounds continuously.

Here, rdash is the absolute equivalent of rate r if
a=p*(1+r/100)^t

Here is a table that explains it. Try and understand, ok?

Gurbani Wallpaper

Attached below is a Gurbani wallpaper that I have created and intend to submit to SikhNet.com for inclusion in their wallpaper collection for downloads. It comes in six flavours, each slightly different – select the one that you like most.

The wallpaper is a composite: the pebbles background was photographed by me in Goa, the Gurmukhi text and meanings is computer graphics, but the Ik Onkar is not. The Ik Onkar is also a photograph taken in slowshutter, and with a flashlight that I moved by hand to make the shape.

TinuURL link to this entry: http://tinyurl.com/gwallpapers

Deh Shiva bar mohe

Prime Minister Manmohan Singh, first Indian Sikh prime minister is undergoing a confidence motion as I write this. He invoked a war prayer by Guru Gobind Singh Ji while introducing the motion. The meaning of the prayer is very well narrated here. I quote below the relevant section:

“Daahay shiva bur mohaay eaahay sub karman tay kabhuun na taruun
Na daruun aar saun jab jaayaay laruun nischaay kar apuni jeet karuun
Aar sikh ho apanay hi man ko eah laluch ho gun tau uchuruun
Jab aav ki audh nidhan banaay aut hi run main tab jhonnj maruun”

Shiva, God Almighty
Pray do confer
A blessing on me
From Pious deeds
I should not flee

And in a battle
There shouldn’t occur
Any fear in me
Determined I may spur
Myself to victory

And Pray Almighty
Let my mind gather
A lesson for me
A craving to utter

When the end is nigh
Let me then stir
Myself to ecstasy
And enter
The battlefield and die

In the prayer, “Shiva” stands for God Almighty, who is the Creator, the Preserver and the Destroyer. (Once you have decided Dr Jekyll and Mr Hyde are one and the same person, you can refer to him by any of those names.) Same goes for “Ram”, which literally means One who is Omnipresent.

An explanation in my own words: God, please grant that I may never back out from the path of good deeds. If I have to go to war and fight (towards the good cause), that I may be the victor. That I may have only one greed in my mind, which is for the utterance of Your Bounties. When the end of my life is near, that I may die on the battle-field fighting the enemy.

I wish the Akali leaders would support the Sikh Prime Minister. Issuing an Edict would be taking a political matter too much into the religious domain. All the best Mr.Prime Minister 🙂

QR Codes

I came across QR codes recently. QR stands for Quick response. The coded message looks something like this:

In Japan, they are printed on business cards so that you can take a photograph of the code with your mobile phone, and use special software (also in the phone) to decode it. It makes your life simpler so that you dont have to feed the business card information into your phone contact book manually. However they can be used for almost anything – on ads to store contact information etc.

The QR code shown above is my own web business card. It has my name, the names of my websites and my contact email ID. You can go to http://qrcode.kaywa.com/ to generate QR codes, and download an application to read them. Mobile phone applications are also available.

Why they attracted my attention was in connection to digital security: If you digitally sign a document using GPG for example, there is no way to reflect that on a printed version of the document. QR Codes present an easy way: include a QR code for a short summary of the document, digitally signed, into the document itself. To make it watertight, include a URL to the online version of the document, and a hash of the document. Makes sense?

The uses are endless: they can be added to ID cards, where on one side there is human-readable information, and on the other there is QR code, ready to be verified in case of suspected forgery, they can be added to marksheets digitally signed by the university – the list is endless. No softcopy of the marksheet needs to be provided is what makes this schema more interesting.

Here is a signed message from me:

No need to make them black and mundane – in fact you can superimpose your logo. The first reader to unravel the message in this QR Code will get a digitally signed certificate from me! My public key is here. Post in comments.

Raja Ravi Verma

There is an interesting folklore in India, where Raja Harishchandra, one of the ancestors of Lord Rama promised a saint a large sum of money. He had to sell off himself, his wife and his son in order to repay the debt of this saint. I came across a nice painting by Raja Ravi Verma depicting this. I did some digital improvements on the painting. Here it is:

Picnic Scene

The picture called Picnic Scene was created by Hardeep Singh when he was 11 years old. I am 29 today – cant imagine so much time has passed. What use did I put these 18 years to? The image is licensed under Creative Commons Non-commercial Attribute ShareAlike license.

Picnic Scene by

GIMP helped me create a very interesting perspective on the image – I have an association with the Globe that I have never quite understood:

Nice – isn’t it?

Welcome

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