Friday, 17 October 2014

Why Do People Hate Math??

There are three types of people in this world.............
the ones who LOVE math,
and the ones who absolutely HATE math .................aand the ones who probably dont give a crap.

Well, I belong to the first category. I LOVE math. It fascinates me. It is one of those subjects which can stretch your power of imagination, your thinking abilities to the maximum extent ..........and beyond. It is a super deep, super wide, super awesome, super beautiful ocean which if one gets to dive to, to swim in it, one wouldnt want to come back ever again!!!
(and no,...sharks wont eat you there. hehe)


but ALAS!!!!!!!!!!!

Very few people actually get to see its truie beauty.
and thus, they dont appreciate it.

Well, people who hate math, either suck at it, or think that its absolutely pointless.
I wont blame those who are bad at math and thus they hate it. If I was bad at something , I would hate it. (i was not happy with Dota2 as at start i was very bad at it, and being called a noob is not pleasant).

But those people who think who think its pointless, i dont think they have even tried to understand Math. Just dismissing a subject because you THINK its useless does not make it actually useless.......... and does not make you right.

Whom to blame???
The school?
The teachers?
The Parents?
The education system?
The student himself??????

We cant blame anyone specifically.
I was lucky enough to have very good math teachers during my junior classes.
But there are schools, were the teachers know absolutely nothing about the true, inner, abstract nature of the subject, and just support rote learning.

Math will be a super huge pain in the neck if one tries rote learning.

In Math, one surely needs patience. One teeny weeny mistake can lead to disastrous results. And yes, this can be frustrating.
The whole point of Math just for getting the correct answer is what drives people away from Math.

"
-Why do we learn Math?
-To pass exams.
- What is the point of it?
-To get good marks so that you wont fail exams.
"

NOPE!! This should not be the system. But sadly, this is the system.
If there was a system, where a problem was given and it was left to the student do think about the algorithm, to devise a method not just getting the correct answer, the scenario would have been much different.
When one studies, one should not just focus upon getting the answer. The real achievement doesn't lie at the end.

The true adventure, the true lesson lies in the path you have taken, not your destiny

Now,
in the current society, if a student is good at Math, he is SMART!. When a student is good at math, he becomes more confident of himself.
But on the other hand, if someone is terrible at Math, he is tagged as "not so smart" or more harshly "stupid".He starts to lose confidence over himself. He gets conscious. When he seems himself fail in something that others succeed in, he gets frustrated. angry. he starts hating the subject.

If someone is bad at math......is he stupid??? ABSOLUTELY NOT!!!!!!!!!!!!!!!!!!!!

"We are all smart. Telling yourself you are dumb is and excuse. Others telling you that you are dumb is discrimination. get over it"


One more factor is that the way of teaching, the textbooks are a bit drab and boring.
(I'll be frank, i think that except for Political Science, EVERY school textbook from which I had to learn was monotonous and boring. I loved the cartoons in the political science textbook)

Its all about how one is introduced to the word of Math.
I had taken an online course by Prof Jim Fowler and Prof Bart Snapp and Oh My God!!! it was SUPERB!!!!!! People went absolutely crazy over it!!
What was the topic?? Calculus
yes
the same topic which is a NIGHTMARE for many, and people who are ready to poke their eyes out and eat 20 year old rotten ham sandwich lying in a pig pen rather than solve calculus problem.

What was the difference??
the way it was taught. The format of the course. The emphasis on understanding rather than solving and of course...........the touch of craziness and humour.


When one looks at Mathematics ,
one should not see just plain old boring numbers.
It should not just about finding "x"
Its not just about getting marks.
Its not about just forcing yourself through the subject.

Its all about understanding, deciphering, breaking down and appreciating the numbers, the real beauty, the abstract nature, the unimaginable vast ocean.


The real beauty is that, Math doesnt have any limits.
Nothing can stop you from thinking weird wacky unimaginable stuff.
There are no limits to your imagination.

Math is like art. It lies in the eyes and the minds of the artist..

If you dont like Mathematics, its okay, leave it. Just dont hate it. Not only math, dont hate ANY subject.

 Every topic, every subject is beautiful in its own way.
Its just how you look at it.

Peace Out!!!



Friday, 15 August 2014

Ridiculously large numbers,Graham's Number, Infinite and beyond!!!!!

We humans are curious about everything, we want to reach the limits of everything.
We are never satisfied until we reach the thresh hold, our thirst is never satiated.
When we see something good, we want something better. When we have a lot of things, we crave for more. Something like in the case of money.
We we see something is big, we want to see something bigger. There came the empire state building, then the twin towers then Bhurj Khalifa. Probably there are plans to build something bigger.

The same is with numbers!
There was ten, hundred, thousand, million, billion, trillion, zillions squillions and somethingelsions.

Do we stop there???  NNNNOOOOOOPPPPPPEEEEE!!!!!!!!!!!!!!

Lets check out some insanely large numbers.........................and by insane.............
I MEAN INSANE!!!

The Googol:-

A Googol is defined as 10^100 = 10,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000

Its 1 followed by a HUNDRED zeroes. Thats equal to ten thousand trillion trillion  trillion  trillion  trillion  trillion trillion trillion. Thats a lot!!

The Googolplex:-
The googolplex= 10^googolplex = 10^(10^100)
Thats 1 followed by ten thousand trillion trillion  trillion  trillion  trillion  trillion trillion trillion ZEROES!!
Thats a VERY BIG number.

Skewe's number :-
In 1933, Stanley Skewes used the number 10101034 (= 10^10^10^34) in a proof involving prime numbers. G. H. Hardy said it was "the largest number which has ever served any definite purpose in mathematics".

But this number doesnt hold the record...................

Guys

Welcome To

*drum roll*

THE GRAHAMS NUMBER!!!!!!!!!!!!!!!!!!!!!!!!!!!!

what? think im exaggerating??? pfffffffffffffffffffffft.
If u dont know about grahams number, u have absolutely NO idea how big it is. NOPE!

Note:- Serious Math Ahead!!!

first, lets see whats the arrow notation.

3\uparrow3 = 3^3=27

3 \uparrow \uparrow 3 =  3 \uparrow (3 \uparrow 3) =  3^(3^3)=3^27= 7625597484987................yup, one small teeny little arrow made the value BLOW UP!!!!

3 \uparrow \uparrow \uparrow 3 =   3 \uparrow \uparrow (3 \uparrow \uparrow 3) =  3\uparrow \uparrow 7625597484987    which is UNBELIEVABLY LARGE!!!!!!!!!!!! SO large that  its digits wont even fit in the universe.

is this the grahams number?? hohoho........nope..........nowhere near...........

let  3^^^^3= G1

G1 = 3^^^^3
G2 = 3^...(G1 arrows)...^3
G3 = 3^...(G2 arrows)...^3
G4 = 3^...(G3 arrows)...^3
G5 = 3^...(G4 arrows)...^3
G6 = 3^...(G5 arrows)...^3
G7 = 3^...(G6 arrows)...^3
G8 = 3^...(G7 arrows)...^3
G9 = 3^...(G8 arrows)...^3
G10 = 3^...(G9 arrows)...^3
G11 = 3^...(G10 arrows)...^3
G12 = 3^...(G11 arrows)...^3
G13 = 3^...(G12 arrows)...^3
G14 = 3^...(G13 arrows)...^3
G15 = 3^...(G14 arrows)...^3
G16 = 3^...(G15 arrows)...^3
G17 = 3^...(G16 arrows)...^3
G18 = 3^...(G17 arrows)...^3
G19 = 3^...(G18 arrows)...^3
G20 = 3^...(G19 arrows)...^3
G21 = 3^...(G20 arrows)...^3
G22 = 3^...(G21 arrows)...^3
G23 = 3^...(G22 arrows)...^3
G24 = 3^...(G23 arrows)...^3
G25 = 3^...(G24 arrows)...^3
G26 = 3^...(G25 arrows)...^3
G27 = 3^...(G26 arrows)...^3
G28 = 3^...(G27 arrows)...^3
G29 = 3^...(G28 arrows)...^3
G30 = 3^...(G29 arrows)...^3
G31 = 3^...(G30 arrows)...^3
G32 = 3^...(G31 arrows)...^3
G33 = 3^...(G32 arrows)...^3
G34 = 3^...(G33 arrows)...^3
G35 = 3^...(G34 arrows)...^3
G36 = 3^...(G35 arrows)...^3
G37 = 3^...(G36 arrows)...^3
G38 = 3^...(G37 arrows)...^3
G39 = 3^...(G38 arrows)...^3
G40 = 3^...(G39 arrows)...^3
G41 = 3^...(G40 arrows)...^3
G42 = 3^...(G41 arrows)...^3
G43 = 3^...(G42 arrows)...^3
G44 = 3^...(G43 arrows)...^3
G45 = 3^...(G44 arrows)...^3
G46 = 3^...(G45 arrows)...^3
G47 = 3^...(G46 arrows)...^3
G48 = 3^...(G47 arrows)...^3
G49 = 3^...(G48 arrows)...^3
G50 = 3^...(G49 arrows)...^3
G51 = 3^...(G50 arrows)...^3
G52 = 3^...(G51 arrows)...^3
G53 = 3^...(G52 arrows)...^3
G54 = 3^...(G53 arrows)...^3
G55 = 3^...(G54 arrows)...^3
G56 = 3^...(G55 arrows)...^3
G57 = 3^...(G56 arrows)...^3
G58 = 3^...(G57 arrows)...^3
G59 = 3^...(G58 arrows)...^3
G60 = 3^...(G59 arrows)...^3
G61 = 3^...(G60 arrows)...^3
G62 = 3^...(G61 arrows)...^3
G63 = 3^...(G62 arrows)...^3
G64 = 3^...(G63 arrows)...^3    (source 
http://www.susans.org/forums/index.php?topic=99242.0)

G64 is grahams number!!!!!!!!!!!!! Phew!!!!!!!!!!!!!!!!

its something like this


Source- WIkipedia



Dont worry................my mind nearly imploded trying to comprehend this.
This is UNBELIEVABLY huge.

THIS IS ABSOLUTELY VERY CRAZILY RIDICULOUSLY 

INSANELY MIND NUMBINGLY HUGE!!!!!!!!!!!


and you know what??
this was ACTAULLY used in a serious mathematical proof........... ( ~OO__OO~ )


*splurge* was that ur brain???? ahhhh, i wont blame you, thinking about this will almost turn your brain into a blackhole
(having a blackhole in a brain is not pleasant :P )

so now lets go to infinity............


INFINITY:-

Grahams number is HUGE

is it near infinity?? is it infinity?????

no.......
the interesting thing is that, Grahams number is as near to infinity as zero is.
everyone is at the same distance from infinity.

Infinity is NOT a number.
Never ever treat is as a number.
Why isnt a number???
if it was a number.......
infinity + 1= infinity
infinity + 0= infinity
therefore 1=0
yaaay!!! i just proved something that literally obliterates the foundation of math!!!!!
nope, infinity is not a number!


Infinity is an idea! its just an idea about endlessness.
Infinity is unfathomable, depths unknown, and would never be known.

As John Green said, some infinities are bigger than the others.
There are infinities inside infinities.
But they are infinite.
No limits
No bounds
No ends
Just endless.


Sunday, 10 August 2014

Fermi Problems

I thought this will be my first post just because of one reason...................... THIS GUY IS AWESOME!!!!!!

I mean, he is like one of the golden nuggets, one of the rare assets Science could have. Fermi problems give us a glimpse on how brilliant this person was.

Fermi sitting on a chair, using a piece of paper, a pencil , and his brain could calculate stuff like the circumference of the Earth,  what is the weight of the air above lake superior, how many hair are their on a human head, how many molecules are there in a standard classroom, how many piano tumers are there in Chicago and............

*deep breath*                                                                                                                                       How many atoms of your great^n-grandfather who lived about 2000 years ago do you ingest with each meal ............... wait WHAT!!!!!! O_O                                                                                                                                                                                                                                                                                          
yup, thats the wonder of approximations. Lets dive into some of them..........



Q How many Jelly Beans fit in a one Liter Jar?

First, what will the size of a normal bean be? 
We can think of a jelly bean as a small cylinder, 2 cm long and 1.5 cm  long

If we fill the whole bottle with jelly beans. the complete jar wont be filled, and there will be some air spaces left. So we can assume that about 80% of the bottle is filled.

what is the volume of a single Jelly Bean?
Volume of 1 Jelly Bean = h(pi)(d/2)^2  where h=2cm is the height of the cylinder and d=1.5 is the diameter
thus volume= = 2cm * 3.14* (1.5cm/2)^2 = 3.53 cubic cm

The number of jellybeans in a one liter jar is Volume of the Jar/Volume of one bean
((8/10) x 1000 cubic centimeters)/(3.53 cubic cm)= 227 jelly beans

Voila! you can check this too! the answer may not be exact, but it will be very near to this!

Q How many piano tuners are there in Chicago???

The question seems very absurd at first and impossible to answer, but hey.............there is a solution to everything!!!

Each individual may not own pianos for their own. A Piano is like a family property, a family will have one piano.

Lets take the number of families in Chicago to be 2,000,000. (its crowded out there)
Of course, every family will not have a piano. we can assume that one out of 5 families have a piano.
Thus the number of pianos is  400,000

Suppose a piano tuner can tune 5 pianos a day, and supposing the number of working days is 200, he can tune 1000 pianos a year.

Frankly speaking, i dont know how much time it takes, till a piano needs tuning. I assume it to be five year.
So in one year, 400,000/5= 80,000 pianos need tuning.

Thus the number of piano tuners is 50,000/1000= 80 piano tuners in the city.


Q How many kernels of popcorn will it take to fill a classroom?

WE can assume that in a cubic inch, there will be nearly 4 popcorn kernels.

 There are 12*12*12 inch cubes in a cubic foot. This value is near 1500. Thus there are 1500*4= 6000 kernels in a cubic foot..

A standard classroom can be taken as 70 feet long and 40 feet wide and nearly 10 feet high.
So the volume of the classroom will be  28000 cubic foot.

Thus the number of kernels in a standard classroom is
28000*6000= 168,000,000.  Phew! thats a LOT!

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You might be thinking that they answers may be waaaay off the actual value as we are taking  huge approximations.
Even though the approximations seem random, the answer is near to the actual values.
The approximation will be of the same order of magnitude as that of the actual answer.

so why does this happen??
in simple words, the errors tend to cancel each other.
The over approximations and the under approximations cancel each other, thus the answer tends to be near the actual value.

During a testing of the nuclear bomb, Fermi was sitting in a lab, near to the bomb site.
When the bomb exploded, he started dropping small pieces of paper to the ground.
When the shock-wave arrived, the small pieces got displaced.

Then on the back of an envelope, he calculated the strength of the bomb to be 10 kilo tonnes, which is quite close to the actual value!!!!!

Thats how  brilliant this method was!!!!!!!!