Wednesday, October 8, 2014

Blog Post #97 - Aliens - 0/0,QED and Golbach conjecture - Cool Math without equations/calculations

Most of time we get confused between Math and Calculation. Let me begin by saying 

Math is not calculations!

Of course not arithmetic nor algebra nor calculus. 

Math is the medium humans use to communicate other than Language.

Think about it - everything you read or see has either numbers or letters (alphanumeric!) along with some cryptic characters !,;' .: 

Arithmetic by itself is beautiful in fact that there are only 10 numbers  0 1 2 3 4 5 6 7 8 and 9 which make up every single number on earth ,moon and in mars.(Just to brag that humans have reached moon and mars).


What will the aliens talk other than alien language ?

MATH!

For most of us ,no wonder MATH sounds like Alien language!

In spacecraft Pioneer 10 which was launched by NASA in 1972 and Pioneer 11 spacecraft in 1973 humans placed the following image.
Look closely what do you see?








If you are like me you would have seen 
  1. Hyperfine transition of neutral hydrogen
  1. Figures of a man and a woman
  1. Relative position of the Sun to the center of the Galaxy and 14 pulsars
  1. Solar System
  1. Silhouette of the spacecraft

I am sure you didn't notice or know what 1,3,4 and 5 meant!
Learn about the message here 
In short we want to let them know about Hydrogen, Man and Women, Where is sun and what is our solar system - where earth is located and what is the size of humans compared to this spacecraft.
Notice the lack of language !- only pictures and numbers. Notice the arrow from the 3rd circle saying we are coming from earth which is 3rd closest planet from Sun.

Pretty lame? 


Why don't you comment on how you will communicate with aliens in the 
comment section below or in facebook what you will communicate to the aliens and how ?

(Married men are not allowed to answer this question as they have been practicing and perfecting this task in their daily communication with their wife!)



In 1977 NASA sent Voyager 1 with Voyager Golden Record
This is a present from a small, distant world, a token of our sounds, our science, our images, our music, our thoughts and our feelings. We are attempting to survive our time so we may live into yours.
  — U.S. president Jimmy Carter
The contents of the record were selected for NASA by a committee chaired by Carl Sagan of Cornell University. Sagan and his associates assembled 116 images and a variety of natural sounds, such as those made by surf, wind, thunder and animals (including the songs of birds and whales). To this they added musical selections from different cultures and eras, spoken greetings in 55 ancient and modern languages, and printed messages from US president Jimmy Carter and U.N. Secretary-General Kurt Waldheim.

The collection of images includes many photographs and diagrams both in black and white and color. The first images are of scientific interest, showing mathematical and physical quantities, the Solar System and its planets, DNA, and human anatomy and reproduction.

The musical selection is also varied, featuring artists such as Bach, Mozart, Beethoven, Stravinsky, Guan Pinghu, Blind Willie Johnson, Chuck Berry, Kesarbai Kerkar and Valya Balkanska. 

The pulsar map and hydrogen molecule diagram are shared in common with the Pioneer plaque.

The 116 images are encoded in analogue form and composed of 512 vertical lines. The remainder of the record is audio, designed to be played at 16⅔ revolutions per minute.
From Wikipedia 


Can you believe  we sent the Phonograph disc which is a physical disc which looks like the following to the aliens and hoped they will play it?

A teenager or a kid today won't know what is a floppy disk let alone these round discs which looks like supersized cds or dvds!



To play it the aliens will need something like this. (picture below)
We should be sending usb stick or put in the cloud!  (this is 2014 and this is hi-tech .. what will some one comment in 50 years from now?)



No wonder we are still waiting to hear from the aliens!!!

Now turning our attention from aliens to the alien language of math - 


What is 0/0 or  0^0 (zero raised to the zeroth power)?

Number 2 is the first and only even number that is prime number !
We had discussed earlier if 0 and 1 are prime!
Do you know Prime Numbers - God may not play dice with the universe, but something strange is going on with the prime numbers #primenumbers


While there are issues with 1 and 0 being prime we have a confusion when it comes to 0/0
same number/same number = 1
0/any number = 0
Any number/0 = infinity
So which rule should be apply?
What about 0 to the power of 0
0 to any positive power is 0, so 0 to the power 0 should be 0.
But any positive number to the power 0 is 1, so 0 to the power 0 should be 1.
We can't have it both ways.


Underlying this argument is the same idea as was used in the attempt to define 0 divided by 0.
Consider a to the power b and ask what happens as a and b both approach 0. Depending on the precise way this happens the power may assume any value in the limit.

We will never stop discussing about zero!


Here is my previous post on Zero - answer to both the questions asked above is 'undefined!' Dah!
- When I was learning math I always had to accept some things as facts - remember! we all did. These were called - Axiom!. These were self evident. Kind of saying - you already know this stuff!
Theorems were then proved LHS = RHS (Left Hand Side = Right Hand Side) and concluded with QED.  - which expanded to quod erat demonstrandum meaning hence proved.
We proved so many theorems that was already proved. Most of the time we were looking to finish the proof as quickly as possible.
Let's try to prove this


 Every even integer greater than 2 can be expressed as the sum of two primes.

This is called  Golbach conjecture

4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
...
100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53

Golbach (from Russia) has formed this conclusion - any even number can be represented as addition of prime numbers.

While solving for x ask Y (Why!)

is a quote I heard in a ted talk from Arthur Benjamin - A performance of "Mathemagic"
Here is the link
It is sad that we look a problem , then assume - ok these are the variables and where is my equation?
If I substitute these variables in that equation I have solved Math (Physics, Chemistry ,economics or any field - every field on earth which requires Math.

we never stop and ask a silly question like question variations of phytogoras therem like what is in Fermat's conjecture 

(remember once you read and understand the word conjecture you will see it everywhere!. Believe me now I see it everywhere! Google is using my keywords and facebook is using it to show me all things conjecture in all websites I visit. I hate paying privacy as a cost to use google to search and facebook to communicate with my friends!)


Fermat's last theorem was proved after 300 years by Andrew Wiles from princeton.

 x^n+y^n=z^n,





where xyz, and n are integers, has no nonzero solutions for n>2 has come to be known as Fermat's Last Theorem. 
To learn about Fermat's last theorem and the story of how this was solved after 300 years read this blog


Reading Books - Every Day a Friday: How to Be Happier 7 Days a Week , TED Talks and Fermat's last theorem

Math is magic! 

Keep Mathing(is there a word like that?)
Sivakumar Manikanteswaran





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