Randomness_001

Coins...Fer a Change...!! :)


Was feeling 'lost'...and then decided to pay ettention to my thoughts....

I was thinking randomly...a lot about random numbers... 
(Hmmmm....i've not yet stopped...nor will I ever...hahaha!)

You can't imagine the MAGICAL things that lurk behind a seemingly RANDOM Universe....!

As one of my thoughts encouraged me to do, I took out a coin...& flipped it...(yeah...Cricket -match coin-TOSS! :P )...

And as it turns out...fer a few tosses, it appeared to be biased towards HEADS or TAILS...

[Out of 10 chances...7 will be heads, or even 8 or 9 will be tails...!]

But then, I imagined....
WHAT if...what if I extend this tossing OVER & OVER & OVER egain....& egain..!?!?

In the short-term...we may feel the Universe/God is biased...but over a Loooong term...there is JUSTICE..n EQUALITY (of Probability..)..?? :P

So armed with this thought...and tonnes of emptiness....i sat blinking before my monitor....waiting....fer the magic to happen...

And happen it did...!!

Before long, between my work....I had whipped up a couple of lines to show me graphically the results of 1,000 coin tosses...to help me 'see'...

And the results...are (t)here fer YOU to see...! :)

• n(heads)  = 504 
• n(tails)    = 496

{ Click on the picture below !} 

Moral: EVEN a state of ORDER has CHAOS & Randomness underneath...! :) 
It is just amazing HOW a seemingly random set of events...can aggregate and 'appear' to be 'orderly' to our Mind/Brain...! 


Is it not pa..? :)


Phew..! :)

Love & Best Wishes,

The boy in "rags"

Five elements !!

Phew..!!!

At-last, I have been able to "write out" this GEM, and thankfully, this time, not in a notebook in my scribbly hand-writing...!! :)

Please take a moment...to Behold the Beauty Below...:)
(Oh...nice alliteration there! :) Hmmm... :))

[ And Click it if you like..! ;-) ]

Like the five cosmic elements of the Greeks, or the ancient Indian system of seeing the Cosmos as being composed of Pancha-bhoothas (ಪಂಚಭೂತಗಳು--see this link), this lit'l equation, also known as Euler's Identity, somehow manages to unite 5 lovely "elements" in one place..!

(a) Euler's number e,


(b) a mystical element i (square root of -1) frem the Complex World..(like Ether..?? :) ),


(c) Unity (1),


(d) Nothingness (Zero--0 ), and


(e) To top it all, a Pi, the transcendental number that makes the World & so many more things (go) ROUND ! :P

Really, an awe-inspiring beauty indeed..!!

  

Love & Best Wishes,

The moron in 'raghu',{Planet Earth} 

{

PS: How nice that even 'raghu' & "moron" have 5 (a Prime!!) characters apiece in them...! :) 

}

An in(cr)edible recipe_Part_001 <3 :)

Hi pa..!!

Please Listen to Me...at-least one time...!?!

{ Time is running out..!! Hope you ARE listening...!? :-/ Hmmm.. :-( }

I just want you to do something fer me, & I promise YOU to show you something so incredible..!!!! :)

If I give you a +ve integer, 'n' to start with, you should go on giving me the smallest integer that is a multiple of (n-1) such that it is greater than or equal to 'n', STORE the result, & go on till you reach n=2, at which point the result does NOT change...

Okay..? :) 

JUST do that, and I shall show you a MAGICAL new thingy...!! :)
But don't stop...continue with this value 6 & the value 3 as your new 'n'...
i.e.., 6 gives way to 3-1=2*3=6 (n-1 is now 2)
and now, you can verify that considering n=2 , the answer remains the same =  6

Hence, given n=4 the final answer should be 6.
i.e.., 6 gives way to 3-1=2*3=6 (n-1 is now 2)
and now, you can verify that considering n=2 , the answer remains the same =  6
Hence, given n=4 the final answer should be 6.
Hence, given n=4 the final answer should be 6.
Or...to take another example, given n=5, the answer should be 10
{5-->8(by 4)-->9(by 3)-->10(by 2)-->10(by 1)-->STOP}

E.g., fer n=4, u start, & first come up with 6 (temporary result) by considering (n-1)=3

Or....given n=10, the answer should be 34. 

HOW..?

Here's HOW...

{10-->18(by 9)-->24(by 8)-->28(by 7)-->30(by 6)-->30(by 5)-->32(by 4)-->33(by 3)-->34(by 2)-->34(by 1)-->STOP}

So LET us imagine this PROCESS of generating the ANSWER, given a +ve integer 'n' input...as a Black-box...!

In Mathematical terms...let me call it a Function 'f' mapping an input 'n' (+ve integer) to some other +ve integer.

Thus, we have, 

f(1)=1,

f(4)=6,

f(5)=10,

f(10)=34

:

:

and so on...

[Can u write a simple function or manually build a table like this..for different values of +ve integers..?]

AHEM..!!

JUSST keep this function in mind...be READY..!!

For WHAT I shall unveil to YOU...is going to be one amazing surprise...!!!!!

I Promise..!!!!

(To be continued. . .)

[
PS: 

Not that I want to keep you waiting...no way...I myself can't wait...!! 

As I have said, Time is running out...& i have to SHARE soo many beautiful thingies..!!

It's just that I may have to spend some more energy/focus on R&D...! :)

I shall try & come up with a 'black-box' (function) of my own & try to graph some results...which shall be a fitting tribute to this incredible thingy we're going to witness..!

Am sure you shall agree...SOOON....!! ;) :)

Get Ready...to be SURPRISED...!!!

]

Baffling Beauty

Bamboo-zled..! <3


I won't say much.
I don't have to.
I...can't actually. 


Just click on the below image...read, imagine & wonder...!


No one knows, how these plants communicate to each other...truly baffling, isn't it..?


Love,
the moron in rags
------

Patterns in Nature...! :)

Hi pa..!
 
During the seemingly lazy Easter-weekend, I was completely bowled over by a gem of a short-movie inspired by the occurrence of numbers, & geometrical patterns in NATURE....made by a Spanish graphic-designer and "3D-artisan" named Cristóbal Vila...
 
The movie so elegantly depicts the beautiful manifestations of  :
 
1) The Fibonacci series & the (logarithmic) spiral,
2) The Golden ratio & the (related) Golden angle, and
3) The Delaunay Triangulation, & the Voronoi tessellations/tilings...
 
Before you feel overwhelmed &/or bored by all the esoteric stuff I just mentioned, 

I urge you to please take some time off...to watch the movie with your dear friends...and let me know..
 
The movie is -- Nature By Numbers, & it is available at :- http://vimeo.com/9953368
 
And a separate link to  Cristóbal Vila's personal site, which has a lucidly illustrated text on the mathematical theory behind the movie is :- http://www.etereaestudios.com/docs_html/nbyn_htm/about_index.htm
 
Kudos to you Cristóbal Vila..!! :) That is absolutely brilliant in deed..!

That's all fer now...

I shall look forward to hearing frem YOU...regarding how you liked this little gem, & also about the phenomena there in...(like the Sunflower heads, and most amazing of all fer me, even the seemingly random patterns on the Wings of a Dragon Fly being nothing but Voronoi tilings...!! )


Phew....!!!!!!!!!!.... :)

Love & Best wishes,

 

The boy in rags...

Planet E-art-h

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

And now, fer a funny pic...courtesy "BC" by Hart..
Keep Smiling...! :) 

The Beautiful Droste Effect !!

(yet) Another disturbance frem me...! :)

Today, in the afternoon, I was just chatting with my friends Adarsh & Shilpa, regarding an interesting drawing that Adarsh had made in his notebook, & our talk somehow veered towards recursively self-referential (or self-inclusive rather..??) diagrams...! :)

And I suddenly remembered the world-renowned brand of Chocolates frem Holland that I had once taken home...& also a very interesting effect that is named after the brand...

If & when free/interested, please check out the so-called Droste Effect..!

Many people have come up with innovative ways of 'transforming' images suitably to bring in this effect.

A very interesting article discussing about an algorithm for doing the same, can be found here!

And in general, if you're drawn to some incredible works of art that achieve the seemingly impossible, you simply cannot afford to miss on the works of the great Dutch illusionist painter-- M.C.Escher

And for a nice article demonstrating the use of one of my favourite softwares-- Mathematica,for transforming a very cute snap of 2 children into one exhibitng the Droste Effect, please do jump to this hyper-link..!

Hope you enjoy(ed) knowing/appreciating this lit'l beautiful phenomenon..?? :)

{ I agree it's a bit dizzying too...but that's how it feels when you taste something maddening...addictive...when you fall in love too..!?? ;-) }

Anyways, take care, keep smiling & keep sharing...! :)...

With Lots of Love & Chocolates...!

[Alright! If not chocolates always...at-least chocolaty love..?!? ;) :) hahaha]

The boy in rags

Planet (H)Eart(h)

-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-

" I do not use drugs. I am drugs ! "

- Salvador Dali, the great surrealist painter 

A Loving Heart...LOST...!! :'(

 

Hi pa..!

February 24,2010---yet another lonely night, and I stumbled upon a lovely lit'l documentary on TV with sheer serendipity, that ended up affecting me deeply !

It is a heart-warmingly true-story of a beautiful being "reaching out" beyond its world and be-friending a human-being...almost like an alien being initiating a dialogue voluntarily & be-friending us !

 

What a GifT indeed..!

(

This happens so often, but we almost always take it for granted..
In fact, we have become numb to even Miracles ! 
We take miracles for granted--so, perhaps, we no longer deserve them, or can NO longer "spot them" too..!? :(

)

I simply felt both so touched by the LOVE, unconditional TRUST and miraculous bond of love and friendship extended to us humans by an Orca, or a Killer-Whale called "Luna", & also felt extremely ashamed and SAD to see HOW we (Morons) LOST him ferever...!! :-(

 

[

The term Killer-whale is a slight misnomer ; 

it's not a whale per se but the largest member of the Dolphin family--Orcinus orca to be precise...! Please see this link for info...

]

Truly, we humans know nothing about cherishing & maintaining bonds of Love & Trust...!! We sever them at the slightest hint of discomfort or adversity, or if we see any kind of benefits in doing so...! :(

 

We can even feign Love & Friendship fer our selfish needs/means...!! :-/

Our cunning, calculating, selfish minds (=LOGIC) have overtaken our simple, trusting hearts...! :(

Sigh...!!

Anyways, here is the link for the award-winning, full-documentary-movie that will be released soon all over the world...

http://www.mountainsidefilms.com/savingluna/

I sincerely hope we all get to 

...see it, 

FEEL it, 

& 

be changed by it--

...at-least a bit...!

Unfortunately, ALL the media attention, the awards, our money, our science & technology, the gadgets, & our medical advances put together.., can NOT bring back that precious lit'l Life again...to cheer up the few individuals who knew HOW beautiful it was...! :-(

It just takes a few moments of unscrupulous madness to WIPE off a beautiful little LIFE from the face of the EARTH, irreversibly...!

Hmmmm...

 

May dear Luna (means the MOON, i believe)  "Swim in Peace"...among the stars...floating playfully...far far away from all the human vice...! :)

 

And as the parting quote in the documentary so aptly put it, we people need to accept & understand the fact..that---

" A life does NOT have to be human to be GREAT...! "

Hmmmmm...

With (Prayers fer){1,∞} Love and Best wishes fer beings which/who deserve but don't get it..

The boy in "rags"..
Planet (H)eart(H)...