Ball Park-ing ! :)

Hi pa !! :-)


HOW have you been...?

Well, yester-night,  me stayed over with my dear friends (Amod & Vijay)...since the weather (& my health! :-( My Fever...! :) !) was not very good...!

But we slept at dunno...bout 3 am or so purr-haps...!!! :)

Not fer werk...(we'd have dozed off sooner if it was jussst our stupid werk! In fact, we did some good progress on our work first...)

But...discussing & doodling on a problem I had preposed while I was in the UK to my friends...
 

I asked my friends again if we could...try to see what is the MAX size of a smaller ball that will fit in the space left when a Bigger ball rests in a cubical enclosure..

[NOTE that this could be a standard, "solved" problem elsewhere in Mathematics, but looking up too much of already "done" stuff, is what usually try to avoid...since it might (& does!) influence our "original" thoughts. Whatever we get should be our own "flowering"...]

• ...initially, it was bout packing circles ( 2 Dimensions)...
• ...then, I took it 'higher'...to 3 Dimensions...!!
• ....and there. started the FUN! Because it is NOT easy to imagine 3-D spatial relationships...We 3 friends were like 3 Blind POETS/MEN trying to describe the proverbial ELEPHANT, gesturing, doodling, & doing our best to get a "handle" on our intuitive "grasp" of what could really happen in different scenarios...! Our heads got scrambled when we realized that in a 3-D cube, the "space" available at the CORNER is MORE compared to that at the meeting of just 2 faces...!!

Walking deeper based on some great li'l insights that my friend Amod stumbled upon, we were able to "break-ice, make in-roads" & slowly began to see some beautiful results.
 

We also began wondering HOW amazing the patterns are in Nature...in multiple-dimensions [right frem ZERO to THREE...it also got me back to wondering...as to what exactly is "space"..."dimensions", etc...! Hmmm...]..!! :)

I could DREAM of OLL sorts of NUMBERS n EQUATIONS n maddening PATTERNS jumping out o' nowhere & asserting their existence(?!?) to me..!!
And I went on "venting" them out to my dear friends, who were more than willing to listen, & even contribute to oLL that....!!

In the end, it was deeep into the night (or MORNING!? :P ) when we "fainted" & "slipped" into the valley of Sleeeep...

I used our 2D result that we got thanks to the work by Amod, & intuitively guessed the pattern fer 3-D...
We could even "verify" it experimentally, but our fatigued, stressed, THINKING Minds could NOT find the equation Formally, TRY as WE MIGHT...!!! :-(

AND I woke up EARLY in the MORNING, n sat Listening to SONGS....without THINKING about it, & LO & BEHOLD..!!!!!
I suddenly "got" the way to find the equation fer the 3D case that we were SO desperately TRYING to "derive"!  ["The 'EUREKA' PHENOMENON" :-) ]

Anyways, Don't think that OLL we did was some crazy doodling in our scrap-books, & write some "imaginary" equations & symbols...!!
The beautiful lit'l patterns we discovered have kept us animated n all awake....!!!! <3 :)

I enclose below few pics of some Mathematica-l  "doodles" I did immediately yester-night in order to "visualize" & "verify" our Mathematical results. :)
And I must say, I'm pleased as punch with them all! :)
[Coz these drawings are "driven" by the mad doodling n equations we friends scribbled all night...!! :P :) And the results just made us smile with joy !!  

The Very Spirit of SCIENCE...! <3 --Prediction("Guesses"), Observation/Experimentation, and Refinement of the Prediction/Guess...! :) ]

Click below on the pics to see clearly:

SCENARIO --> 001

[2D-Case...2 circles against the axes...! :)]  

 

And now fer the 2 scenarios for pa(r/c)king "balls"....! :P :)

SCENARIO --> 002

[Pa(r/c)king "on the Edge"]

SCENARIO --> 003

[Pa(r/c)king in the Corner] 

 

At-LAST, we could say, Ball-e Ball-e [fer the un-initiated, this is an oft-used phrase used in Punjabi songs which are known fer their peppy music..!]...!! :P

...Or...should i call it "BALL-PARK-ing" ?!?! ;-) 

LOL..!!!

TC, n Keep Smilin'....

Love n Best Wishes,
The boy in "rags"

 

Planet (H)eart(H)

Poe-tic Lie-scents ! :)

Thanks to a funny article shared by my friend Roopa D'Almeida about pony-tails & an equation describing them, I suddenly had this hunch to scribble a couple of lines modeled on the famous (& one of my favourites, fer its ability to create 'atmosphere' with words!) poems of Edgar Allan Poe, "The Raven".

Without much ado, I present to you the work below (please click on the image to see/read better!)

Note:

Another peculiar thing fer my dear friends to observe is the 'dimensions' of the 'FRAME' in which I have 'composed' this; the white image originally is of the size 1034 X 639 pixels. 

Why..??

Any guesses..?


Yes !!!


The ratio 1034/639 approaches the value of 1.618, the Golden Ratio-'Phi'...

At-least some food fer thought, in my "Phi-night" existence...?!?!

Hope this poem makes you smile...fer a while pa..!??!

Liked it..!?!?

Ok then...give me a High-Phi...!!! :-)

[Incidentally, the pun was on High-Five, and Phi plays a vital role in all things five sided, from the Pentagon to the Star-shape...Hmmm.....! :)]

Love & Best Wishes,

 

the boy in "rags". . .

Planet Earth

Hmmmm...!!

Well..here it is..below...my version of the He(ART)...! :)
How is it..!??!? (Look @ the shine on it..!!! )

















And if you are curious, well, the figure above was made by drawing many nested HEART-Curves...one inside the other...(like the layers of Onion--Allium cepa..! :) )...

And each of such layer is given as below...




















...this is done by a parametric-set of equations that I crazily obtained by pure, sheer Serendipity, and Stubborn-ness in terms of tweaking various parameters with a MAD Hope against OLL rhyme or reason...!! :)
[Note : (a,b,c) = (3,2,2) ]

There then, is it NOT better than the "blunt" Cardioid ? What do you reckon..? ;)

I think I should call it Ugare's Heart..!??! ;-)

Truly..when we are (B/M)AD-ly in LOVE...we tend to get some immensely beautiful things...!! :)

And even Science, has to forgo ALL Logic, and plunge madly, with Intuition and Hope, to uncover new (de)-Lights..!!!??


Love & Cheers !

The boy in "rags"


++++++++++++++++++++++++
Wherever you go, go with ALL your HEART.
:~ Confucius
++++++++++++++++++++++++

Un-Lightenment..! :-/

Science (f)-or Pseudo-science. . .


Thanks to Microsoft 's research project code-named Project-Tuva, (which is actually a nice way of attracting people to try out their new web-app runtime/platform SilverLight ..!), I was watching the first of the Messenger Series Lectures on the Character of Physical Law delivered at Cornell University by none other than one of the MOST brilliant theoretical physicists, & one of the most original thinkers of recent times--- Richard Feynman...!!

After explaining the Law of Gravitation in a way that ONLY he can do, he paused & went into the applications of the law...

I quote below the excerpt of his lecture verbatim...

-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o
"The only applications [of the gravitational law] I could think of were,

first, in some geophysical prospecting,

in predicting the tides;

nowadays, more modernly, in working out the motions of the satellites and the planet probes, and so on, that we send up–

and also, modernly, (his head bows down..he smiles wryly...)
to calculate the predictions of the planets' positions, which have great utility for astrologers to publish their predictions and horoscopes in the magazines.

That’s the strange world we live in, . . .

that all the advances and understanding . . .

are used. . .

ONLY to continue the NON-sense which has existed for 2,000 years...!"

-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o

Oh My !!!

You MUST truly hear this LAST sentence in the Lecture I say...!
( The intonation, everything shows how agitated he feels..!)

SUCH Pain...Such wry humour, Such ANGST...such helpless frustration & shame...was/is ALL so evident in his ever smiling face when he said/says this...!!

In fact, for a very short-while, his always-effervescent face almost becomes grim...!

Needless to say, it HURTS to see Science again being made to Work for Pseudo-Science, which ONLY serves to mis-Guide our lives, rather than Enlighten & Guide us from the Depths of our Ignorance...!

Hmmmmmm...

Anyway, thanks to Mr.Bill Gates for his initiative of buying these gems of thought & sharing them with the rest of the world...

Now...
"I just hope we EVOLVE soon to become Better, Wiser, truly SAP-ient species...like Trees" :-raghu.ugare

With Lots of Love, & HOPE & Best Wishes fer U(s). . .

The boy in "rags"


Planet (H)eart(h). . .
-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o
Now, fer some light-hearted humour on Parents' view of what kids learn @ school..!

-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o

Still "eclipsed" in Darkness..!!? :-( Wake UP..! :)

Hi pa...!! :)

Well, I began seeing the snaps of today's Solar Eclipse that was very nicely visible from Northern parts of India..

I am attaching pics of the same herewith...[courtesy :- The Times of India]

Such a SHAME indeed that, we people still abhor/cower-at Nature's grand shows like these...!

Just see the snaps I say..!! :)

So beautiful and rare a phenomenon in deed..!!

It is so strange ( & downright silly & sometimes tragic too !!) that we people still hold those poor, lovely celestial bodies responsible for our failures, successes, health, wealth, conditions,etc & we go to the extent of even allowing their positions to decide &/or determine our jobs, our houses, or even our life-partners...!!

I really do NOT agree with this...!!!

I bet even Wild animals are more prudent in this aspect..!!

As the great scientist, my dear Carl Sagan lamented...
"Almost EVERY newspaper in the world carries an Astrology column/section, but almost none of them have something devoted to Astronomy."

I really wish we wake up & really "open-our" eyes...our Mind's Eyes...which are STILL "eclipsed" by centuries of dogmas, & blind-beliefs..

With lots of Love & (Sun/De-)Light..!!

The boy in "rags"


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