I never had book reading on the top of my priority list. But ya, have had a few small stints with books. Highly inspired by a very close friend of mine, recently i have started looking beyond Chetan Bhagat for books to read.
So the first book i took a task to read is "Fermat's last theorm". Its the best fiction story you may be able to lay your hands on. Just kiddin, it has nothing to do with fiction. Its all truth may be a little myth but no fiction for sure. Its all about mathematics.Wait dont be scared,its not complicated mathematical proofs. I am not going to write the proof of some complex mathematical equation here nor am i capable enough to do so :P.
Anyways what mainly it teaches us is that "Everything is Maths".But what i learnt mainly from a first few pages is...not everything thats looks intuitive is correct. A small example for the same would be..If there are 23 men in a room. What are the %age chances that 2 people will share same birthdate?
So going by intuition first.....there are 365 days in a year, ok ok it can be 366 also. We have 23 people. So to share same birthday among 365 days for 23 people ,probability seem very low.At most a 10% chance.
Now lets see the right answer if you havent calculated by now. It will come out to be slightly greater than 50%. Amazed?? If the group size is increased to around 30 the chances are almost 100%. Doesnt sound right?? This is COUNTER INTUITION.
How many group of 2 can we make out of 23 people?? Those many groups and 365 days....does it sound right now?? :)
PS- My first blog. Just wanted to start by writing on a topic which i found interesting. Not everyone is excited by Mathematics so apologies to those who find it boring.
Update: On popular demand here is the solution to above question :P, atleast i think so that this is the solution :D.
It should be 1 - ((365C23)/(365)^23)== .50729 approx.
7 comments:
My intution was that it will be about some complex phenomenon but "COUNTER INTUTION" ;)....
It is simple, interesting....and explains, what could have been difficult in a very easy manner!!!
well done chinki
ps: i have read this book :)
Nice blog sir ..
good start .. adding you to my feeds ...
Hope to see more .. :)
yaar the blog is nice for appetizer but i could not find the the formula for the birthday puzzle.
is it 23C2/365C2 ??
hmm..tyical chinki(shobhit) blogs...gg dude!
Kya baat hai chinki .. blog suru kar di tune apni....
book padh liya ki nahin :D
Mein ne apne feed mein tere ko add kar liya ..
Hi Shobhit,
Good one dude, kept me engrossed for a long time :P.
"Everything is Maths" - well if you refine the statement, it boils down to "EVERYTHING IS NUMBERS". Well i guess you can define anything in terms of numbers, if not a subjective definition, it actually gives you a logic of how and why it happened.
In fact, there was a serial in AXN titled "NUMBERS", with a very interesting concept.....it said that any crime or the next move of any criminal can be traced by an equation.
I am not sure about Fermat's Last theorem, but he certainly has a "Little Theorem" and it is really a worthy read ;-).
Talking of counter intuition, lets first define what counter intuition means.
"A counter intuitive proposition is one that does not seem likely to be true when assessed using intuition or gut feelings." Now try to define the same thing with the example of NUMBERS. That would be easy with the birthday problem.
If you want to think in terms of physics : Think of the property of light - Is is a WAVE or LIGHT ? What we do now is accept it to have both the properties and use it to solve tough physics questions :-). Never really gave it a "counter" thought ;-).
Now, let us take one more example of numbers involved.
Is 0.999999... = 1 ?
Well let me show a proof :-
1 = 9 / 9
=> 1 = 9 x 1/9
= 9 x 0.1111....
= 0.9999....
=>1 = 0.9999.....
Is this a case of Counter Intuition ?
Socha hai........socha nahitoh socho abhi :-).
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