(Sorry...Yet Another one..!! :)) )
My friend Kiran reminded me that today's the Birth-anniversary of the great Gauss---& that reminded me to share this CRAZY piece of mail that I had scribbled to my junior friends...!!
Wanted to share it...! :)
Hope you too feel inspired...?
Love,
Mor(e)on rags
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hi,
Here is a small mail i wrote to MANY people ( but to WHICH i got VERy Little..or NO response !! :-( As Always !! ) about which i would like to know your opinion..!!
I honestly feel that it is ONE of the CRAZIESt mails that ANY Human would ever compose...(with So many Colours, Energy, & Restlesness...!!! )...
And Yet, i Strongly believe that...it( i.e., this mail that i'd written...) shows the TRUE Essence of WHAT it is to INNOVATE...!!! Allva ?!?!
[ allva = Kannada for "isn't it ??" Sorry..! Can't keep my "Native language" from popping out..!! It always has a High priority you see...! ;-)]
What do U feel...?? ( about the incident..& also..well...my CRAZY writing...!!?!? ;) )
Please DO let me know...ONLY if/WHEN u feel like doing...!!
Ok ....Let me Shut up now...!!
THANKS ....Have a great day..& weekend...& X-mas vacations..!!
"r a g h u"
Planet Earth
raghu.ugare@gmail.com
From: Raghu Ugare
To: Raghu M Ugare
Sent: Tuesday, July 11, 2006 1:14 PM
Subject: Something Crazy Raghu wanted to Share with You Today...!!
[
Note :
if
( if _u _have_one( ) && U_have_NOT_Already_Given_It_
{
Could_U_Pleeze_give_me_Ur_
}
BECAUSE,
I don't want---
(1) ---To Pollute your Official In-box with the kind of mails like below ...
as well as,
(2)---My colorful, dear babies(mails!!) to be Deleted one day (b'coz u r changing ur m/c...or..u r "cleaning out UNWANTED files"...!!
because my Mails are NEVER mere Forwards...somehow i prepare such mails ..adding bit by bit whenever i'm free(Late at Night or Early in the Morning !)
...almost like making an Ocean by using an Ink-filler....drop by Drop..!! :-)
]
Something Crazy Raghu wanted to Share with You Today...!!
{
Ha ha ! You are free to read it either way u want !!
Something-Crazy, Raghu wanted to share with You...!
or
Something , Crazy-Raghu wanted to share with You...!
Both Are True !! So, you will Be right in Both the cases...!
NOW, that's what i call a Win-Win Situation...! :-)
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hi !!
I..don't KNOW WHY...but...I suddenly "felt like sharing" an interesting lit'l anecdote with you...!
{
And WHENEVER that happens....i feel it VERY hard to (and ALmost IMPOSSIBLE!!) suppress such ideas/thoughts within Me...!! :-(
i..i...MUSSST share it with someone...a friend..a colleague..or ....Believe it or NOT...even an Imaginary person..!
But I'm soo Lucky to have some friends WHo are Kind enough to lend a patient ear to my Crazy ideas/feelings....!
Anyway, Please Ignore it if u are busy... or not interested in it...ok??
Thank U !!
}
In elementary school, the great GERMAN Mathematician C.F.Gauss was a very naughty boy (but a very precocious one too!).
One day, his teacher ( some say it was one Mr.J.G.Buttner ) came up with an idea to keep his pupils occupied... and asked ALL of them to calculate the sum 1+ 2+3+ .....+ 100=?
[or say, 1+2+3+.......+1000 ??]
The teacher had perhaps imagined that THIS would keep the unruly crowd of children busy for an hour or so...
But lit'l Gauss just shocked the teacher ( & his classmates too ! ) by showing him the answer ( the correct one too ! umm...i think it's 5050...?!?) in a few moments...!!!
Even at THAT tender age...Gauss looked at the given problem in a way No One Had ever Looked at it Before...
{
I don't want to bore u with the details..but if u r interested (How can ppl NOT be interested in my babies(mails!)?!?!)...please see at the end of the mail...
Don't Worry......i'll try to make it As Interesting As Possible..or rather i must say,
"As Interesting (& Simple) As ONLY i Can..!??! Ha ha !! ;-)
Hope u appreciate it & are Inspired by it...!!?!?!
}
Like Everybody else, perhaps, He too scribbled it down...BUT He ALONE thought about it in a highly Original way ( read as"CRAZY/Stupid way" for his friends/teachers back then ! )...
That is Why Nature immediately blessed him with a Flash of Great Mathematical insight, which showed him a pattern...and the Key to the problem...!!
I just remembered this anecdote now, b'coz i felt many a time we too ( Atleast me ! ) are STUCK with some problem..absolutely in a dead-stop...with no apparent way out...
But suddenly, out of no where...comes a magical idea...a blinding flash of insight...a Beautiful pattern is discovered...and...voila !!
I suddenly realize with Immense Joy that i have discovered a Wonderful new Pattern, rule, equation, algorithm, POem, Word, etc....!!!
Such moments happen with me occasionally...when i am sitting in the Bus, or walking home ALONE very late at night on a deserted street near our B'lore room...
or when i take a stroll on the terrace looking at the stars...or...when i go walking in a jungle, looking at the trees & birds...
in short, WHEN i AM NOT thinking Deliberately on the Problem that WAS on my Mind...!!
[
Oops!!
First of all, I seriously doubt if i have any Mind at all to "store" any Problem ...i'm too stupid & ignorant...So, i must apologize for using the phrase "on My Mind"... !! :)
Sorry !
If at ALL i do have a Mind...then, it is FULL to the brim....with...with....
]
Anyway, where was I ???
Haan, all i wanted to convey by this mail was that i somehow feel...(Like Sooooo many others have done in the PAst !)....
that there's a Special component inside the Human Mind...which is INCREDIBLY more Powerful compared to the NOrmal, Logical/Rational thinking part...
...it is capable of providing us with Amazing Intuitive Insights...of showing us Beautiful Hidden Patterns
...allowing us to make discoveries On our own ( may not be Of our own !!
To be Honest, I myself have stumbled upon Mathematical discoveries, which i later realized to be 2000, 3000 years old..right from the Greeks...!!!
i hope ( & wish rather !!) that i'll shortly make a TRULY "BRAND NEW" Discovery...I ALready have sooo many "candidates" for That....in fact, just the day-before-Yesterday...sitting in a home-bound bus...i have discovered some MORE new things regarding Prime Numbers....perhaps, Unproved ( or Unprovable ??!) Conjectures....or Theorems, if they can be proved one day...!!!!
But i've not shared them with the Outer World...perhaps due to my shyness..or my Supreme Confidence---in my Stupidity...!! ;-) :-( Let us C...!! )
....
....But....
...but....we....have to "LET that Happen"....and Not stifle the Child in Us by saying things like "Duh ! What A Crazy idea i got this morning !! I must've Gone mad !!" to ourselves....!!
Remember that....umm..that...
... ALL Innovation is Craziness to begin with...
...ALL Great Ideas from Great People are often laughed Upon....!!
[
But it Does take Courage to really Follow ur Crazy ideas/dreams...like Archimedes (supposedly?!)did running in the buff,
screaming "Eureka! Eureka!"...!
But...I for one, AM Never Afraid to Follow my HEART...Whatever may Happen ...!!
[
Even if it turns out to be a Wild-Goose Chase IN THE END...I'll laugh at Myself & say :
"Well ! That was a Beautiful Goose indeed ! I learnt some Bird-Watching !!;-) " --my kind of Optimism !!
]
I'll Never LET Go of the Dreams of my Heart...!!
And then, i'll just "Let Go" of my self..in pursuing them...!!
]
Hmmm...!!
Well then, Let Us see !
Where ALL this Leads Me..?!?!!
[
Beautiful lit'l couplet i say !
It uses a poetic element called "Slant Rhyme"...where words do NOT rhyme exactly...but still provide a "sense" of rhyming...
like for example, "feel/need", "soon/fool"...etc...!!
Oh !! Sorry ! I must've been a Poetry professor hundreds of years ago(?!?!)...don't know WHY i'm soo steeped in Poetry nowadays...?!?!
]
Take Care & have a great day....And Please....NEVER Cramp your Heart....and Never Stifle the Child in You !!!
Thanks for "listeniing" to Me...!
Love & Best Wishes,
"r a g h u"
Planet Earth...
~~~~~~~~~~~~~~~~~~~~~~~~~
* "Even the Truth requires 2 people...one to say it, and one to listen... "
:- Anon.
*" At the touch of Love, Everyone becomes a Poet."
:- Plato
~~~~~~~~~~~~~~~~~~~~~~~~~
[
LAST but NOT the Least....How can RAGHU forget "the Beauty of figures...!?!?" ;-)
[
ha ha! P(F)un intended !! ;-)
See?
Perhaps, I'm the First ( & the Last too?!?!) person to crack a pun (& hence poke fun !) on the word pun itself...!! ;-)
]
OOps ! Had almost forgotten...! But i NEVER ( or Seldom!) Forget my Promises...!!
As promised, here's my simplified explanation of HOW Gauss "FIGURED it out "...!
[Ha ha ! What a Clever piece of Figur-ative writing...! Sometimes, i feel i should be in the field of Creative Writing....!! ;-) ]
First, He saw that it was a pretty tough problem....
S = 1 + 2 + 3 + .......................+ 100 = ?
He imagined something like :
S = 1 + 2 + 3 + ......................+ 98 + 99 + 100 = ?
"Ummmm.......Gotcha !!", He said !
( My Guess ! He must have uttered something in German...like ..say, "Wunderbar !!"...ha ha !! :-) )
Do u see a pattern above ...?!?!
U see,
Add the pairs of numbers at the extremes...& continue the process inwards...He saw a Peculiar thing ...
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
4 + 97 = 101
:
:
and so on...
Clearly, lit'l Gauss saw that there were 50 such pairs of numbers , summing to 101
Therefore, he figured out that
S = 50 X 101 = 5050
(
A paltry Multiplication, from the Initial Monster of a Sum..!!
What a Beauty !!!!
In fact, i too have exclaimed "Wunderbar!" {"Wonderful" in Deutsch} in my HEART whenever I FEEEEL what He must have felt ...!!! :-)
Exhilarating stuff indeed...!!
Just toooo Beautiful....! :)
)
Later on...his lit'l discovery became a formula to find the sum of the first 'n' nos...
S(1 to n) = [n X (n+1)] / 2
(In Gauss' case, the 50 is actually, 100/2...hope u got it..! )
Hope U Liked this Baby of mIne...
PLEASE Excuse me if there are (M!)any Mistakes/typos in it...i can't do touch-typing too...!
People usually have Absolutely NO IDEA as to HOW much of Labour (--Pain) goes ino producing a "baby" like THIS one !! ;-)
(
There you go..!
There's My naughty word-play again..!! ;-)
Sorry...
I just Can't HELP it..!!
So...you please HELP yourself to some more..!! ;)
)
]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
How do you explain when the number of numbers is odd?
ReplyDeleteThe example you showed works fine when the numbers are even.
1 + 2 + 3 + 4 -> 1+4 + 2+3 -> 5 * 2 = 10
How about
1 + 2 + 3 + 4 + 5 ???
Beautiful.
ReplyDeleteI am actually missing your 'babies' nowadays. I assume you got little busy :)
Sorry people, had NOT seen these comments, since I was LOST in Scotland this last weekend..!
ReplyDelete@vijayananth, thanks pa..!
Yeah...have not been THAT 'prolific' these days..! [Though the desire to deliver a lot, is there..!! ;)]
@mmh, well...thanks for this doubt indeed..! :)
I saw this comment on my iPhone just as I was going to sleep & in my dream I saw what was happpening..!! :)
If 'n' is Odd, then we have 1 element LEFT alone in the middle...we need to stretch it out into 2 similar ones..!! :P
1+2+3 is like
2 times of ( 1+3 and 2+2 which is the same value 4 ). Thus 1+2+3 = 2*(4) = 8 MINUS 2(the extra element) i.e., 8-2 = 6
Similarly, 1+2+3+4+5 is like
1+5, 2+4, and 3+3 ( 3 pairs summing to 6 ), thus equalling 3*6 MINUS 3 = 18-3 = 15.
Interestingly,
1+2+3+4+5+6+7, will have 4 pairs, with the middle '4' cloned as I explained..!
Thus the sum will be (4*8 - 4) = 28 (?!)
Hence, when the number of elements is ODD...
SUM = Num_of_pairs*(Sum_of_Extreme_elements-1)
where 'Num_of_pairs' is the number of pairs...(counting the middle element too!)
Note that this analogy only gave the basis for deriving the formulae for Sums...WHO knows if Gauss would have been able to spot the pattern if he had been asked to find the sum from 1 to say 101..???
{Even then, the extreme elements just go on adding upto 102...till we reach the middle...Beautiful..!! :) }