Sample Copy. Not for Distribution.the cosmos. Information seems to be the driving force behind the physical structure of the universe. It appears to solve the big scientific questions

Sample Copy. Not for Distribution.

i

Information Theory

of The Cosmos


ii

Publishing-in-support-of,

EDUCREATION PUBLISHING

RZ 94, Sector - 6, Dwarka, New Delhi - 110075 Shubham Vihar, Mangla, Bilaspur, Chhattisgarh - 495001

Website: www.educreation.in

________________________________________________________________

© Copyright, 2018, Raghunath Tiruvaipati

All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form by any means, electronic, mechanical, magnetic, optical, chemical, manual, photocopying, recording or otherwise, without the prior written consent of its writer.

ISBN: 978-1-5457-1880-3

Price: ` 1,614.00

The opinions/ contents expressed in this book are solely of the authors and do not represent the opinions/ standings/ thoughts of Educreation or the Editors . The book is released by using the services of self-publishing house.

Printed in India


iii

Information Theory

of The Cosmos How The New Science of Information Changes Our

Understanding And Perception of The Universe

Raghunath Tiruvaipati

EDUCREATION PUBLISHING (Since 2011)

www.educreation.in


iv


v

To My Mother

And Father


vi

Content List

Sr. No. Content Page

Prologue vii

1. Cryptography 1

2. Thermodynamics 12

3. Information theory 19

4. Genetic Code 40

5. Cosmology 133

6. Life on Earth 165

7. Astronomy 225

8. Relativity 272

9. Quantum Computing 297

10. Quantum Entanglement & Quantum

Tunneling

307

Epilogue 321


vii

Prologue ______________________________________________________

Information theory is a relatively new paradigm even though

scientific research about it began in 1948 itself. it is synthesized

from information revolution which is the greatest technological

advancement in the 21st century. Computers , hard drives and

internet have revolutionized the world. In 20th century itself,

Communications technology has advanced from wired to wire-

less. Computers and communication technology are only tiny

aspects of the information theory that we are going to talk

about in this book. It deals not only with the way that machines

like computers, cell-phones work , but also with objects on the

scale from quantum level such as electron, photons, atoms

etc.. to astronomical level such as planets, suns, galaxies ,

black holes and the universe itself. Its rules determine the life

course of the universe and the entire cosmos as well.

Information theory took birth or rather uncovered in the 20th

century which has changed the world dramatically.

Information theory spans across thermo dynamics, theory

of relativity , quantum mechanics, genetics, cosmology,

astronomy and quantum computing. So I will touch upon all of

these topics in this book.

Thermo dynamics - which explains about the working of

engines, exchange of heat energy and motion of atoms is an

information theory.

Theory of relativity – which explains about the large

objects moving at extremely high speeds (almost at speed of

light) and the influence on them by gravity is also an

information theory.

Quantum mechanics – which explains about the domain of

atoms and sub-atomic particles is also an information theory.

Genetics – genes are literally information-carrying bio-devices. So genetics is also an information theory. We will discuss it later.

Astronomy – all the galaxies, stars, planets contain a huge

amount of information in the form of electromagnetic waves.

And through these waves, they influence with each other. So

astronomy is also a information theory.


viii

Information is much more than what we assume about it

(that is, simply some content) and co-relates all the above

mentioned theories together.

Information theory changes our perception of the world

radically because information is not something that is non-

objective. Everything in the universe is constructed from

information. So it is a rather important aspect of energy and

matter. It is physical and can be quantized and measured which

is contrary to our usual thinking. It is influenced by several

physical laws which prescribe how it can be manipulated,

transferred, copied, erased or destroyed. And everything in the

universe must accord to the laws of the information theory.

As a result of the information theory, communications and

computers have been transformed in a huge way. The laws of

the information theory influences not only the data in a

computer (data - bits and bytes which are ultimately the

electrical voltage),but also codes and communication channels.

They govern the way how the sub-atomic particles (electrons,

quarks,etc..) behave . Even life obeys these laws and so does

the entire universe.

Everything in the universe including life-forms on our earth

are bundled with information. The DNA molecule in the living

beings contains a huge amount of information in the form of

genes which works like a blue print for the construction of the

organism. Our body and mind processes trillions of bits of

information each second unconsciously. Every particle , be it a

photon, or an electron or a quark or an atom, is teeming with

information in the form of spin, charge, size, electron

configuration and weight which can be processed and

transformed in energy transactions (chemical reactions). All the

stars and galaxies in the universe are emitting information in

the form of electro-magnetic waves which is spreading all over

the cosmos.

Information seems to be the driving force behind the

physical structure of the universe. It appears to solve the big

scientific questions such as the origin of life, the black holes,

the relativity theory and the quantum mechanics. The

information theory is leading to a way to answer some of the

most profound issues about the universe in the scientific

community.

*****


Information Theory of the Cosmos

1

Cryptography ______________________________________________________

Information should be transferred from place to place or from

person to person in a secure way. The most ancient way to

secure information is to use cryptography in the form of codes

and ciphers. They must be secure enough so that when

somebody taps the message, they must not be able to make it

out.

Even though cryptography has been in place since time

immemorial, the codes and ciphers were not secure enough.

Somebody who has a little bit of knowledge about ciphers can

break the encrypted message. Yet, people had to rely on these

weak codes and ciphers to communicate sensitive information.

Regardless of how well the information is encrypted, there is a

chance for it to decrypted as it is passing from place to place.

In the digital world, information is communicated in bits. To a

sniffer, every bit is very much tangible and susceptible.

As said earlier, information is very much real and solid just

as other properties of a particle. We can not see the spin,

charge and electronic configuration of an atom directly but they

are real. Similarly information is equally real. It can be

quantized, evaluated and tampered with. Information has to

travel physically from sender to receiver just like any other

physical object. It can travel through a telephone line or a cable

or wireless mechanism. Of course there is quantum

entanglement in which two particles are entangled with each

other over incredibly vast distance and still communicate with

each other instantly. But the mechanism behind it is yet to be

found out by the physicists.

Because information is a real entity, it can be displaced or

sniffed through just like any other thing. But information must

be propagated from place to place and from person to person

to be of any value.

Now a days, encryption technology has advanced so much.

A cryptographer has to design the cipher such that the

information passes from the sender to the receiver without

anybody sniffing that information in-between. The information



2

essence of the encrypted message should not be perceived by

anybody. Similarly, a decrypter tries to make out information

from a random mixture of letter and symbols. He can break the

encrypted message if the cipher is weak.

That the information is tangible and quantized is the main

principle of the information theory. The science of cryptography

will give an idea how information is tangible and how it must be

propagated from place to place. One of the most important

properties of information is its redundancy. If you grasp

redundancy ,you can know why information is real and tangible.

When we receive an information, for example something

like ―this rose is beautiful‖, what is happening is that your brain

is taking a series of words in the visual cortex and processing

them to get the meaning of the message. when you read

something on a paper, what is happening is you are receiving a

series of symbols and try to grasp the meaning of that

message. Your brain receives a set of symbols that say ―this

rose is beautiful‖ in the visual cortex and processes those

symbols until its meaning is understood. All this happens at the

sub-conscious level. This sub-conscious process is vital to our

ability to use language. Redundancy is makes a message easy

to grasp.

When a sentence is distorted , we can still decipher it. That

is because of redundancy. Every sentence in any language is

quite redundant and has more information than you need to

make out its meaning. For example, take the sentence ―j-st s—

th-s‖ . it is quite distorted because all the vowels in the

sentence are removed. How ever we can still decipher it and

extract its meaning.

Redundancy is very useful. It allows for a sentence to be

understood easily even if the sentence is distorted somewhat.

Syntax and lexicographic rules create redundancy in all

languages. When your are amidst a crowd, It is redundancy

that helps us understand words spoken by others. Our brains

unconsciously processes the words according to lexicographic

rules.

Let us discuss the information redundancy in terms of

computer science , communication theory and we will also

discuss the enigma machine and the turing machine , two

famous machines in history used for breaking the cryptgrams.

In computer science, information redundancy adds extra

information to tolerate communication faults. Mainly two kinds

of codes are used for fault tolerance : error detecting codes &



3

error correcting codes. These codes are used mostly in

communication channels and computing science. Code of length

n is a set of n-tuples satisfying some well-defined set of rules.

Binary codes use only 0 and 1.

From the ―Mathematical theory of information‖ by

C.E.Shannon, the definition of information is as follows:

Definition1: information is the minimum number of bits,

necessary to encode the subject message.

Definition2: information is the length of the shortest possible

code, used to transport the message.

Example1: a report about rainfall , indicating weather there is

rainfall or no rainfall alternatives, has information of 1 bit

Rainfall code

Yes 1

No 0

Example2: information about a measurement scale- a more

detailed one answering two simple yes/no questions: is it tall or

short? And is it smooth or rough? The information content of

the below table is 2 bits.

Tall? Smooth? code

Yes Yes 11

Yes No 10

No Yes 01

No No 00

If the message is longer than is necessary, that means if it

is longer than information of the message, the code contains

redundancy. It is the 2-logarithm of the quotient between the

code length and the information of the message.

Redundancy=log2 (code length / information)

Redundancy can never be negative. It can be zero. when

the code is as short as it can be (Code length is identical to the



4

INFORMATION, which is seldom the case). It is 1.0, when the

code length is 2 x

INFORMATION. The REDUNDANCY present in different

messages is eventually a compromise between

efficiency concerns and security issues. Example:

Measurement scale code

Tall & smooth TS

Tall & rough TR

Short & smooth SS

Short & rough SR

The INFORMATION did not change and still amounts to 2

bits. The code length however increased from 2 to 16 bits.The

REDUNDANCY of this code is log2(16/2) = log2(8) = 3.

Error detection and correction is one of the main concerns

while transmitting information and it is characterized by the

number of bits that can be corrected.

Double-bit detecting code can detect two single-bit errors

Single-bit detecting code can detect one single-bit error.

There is something called Hamming distance which gives

the measure of error detection/correction capabilities of a code.

HAMMING DISTANCE

Hamming distance is the number of bit positions in which two

n-tuples differ.



5

Code distance

Code distance is the minimum Hamming distance between any

two distinct codewords.

Information and redundancy complement each other. When you deprive all the redundancy from a message, the left over is the information. Compression programs take this factor into account when downsizing the files.

The efficiency of a compression program is determined by

the percentage of redundancy that it removes from the file. No

matter how efficient the program is, there will be some data

that is at the heart of the message. This chunk of information

has to pass from sender to receiver.

Often cryptographers try to remove as much redundancy

as possible. If he designs a good cipher, the message will be

encrypted efficiently and it can be deciphered only by the

intended recipient. Anybody who sniffs at the packet of



6

information while it is passing from sender to receiver will not

be able to make out the meaning of it. Often cipher exposes

data because of redundancy.

The Enigma machine is a piece of hardware invented by a

german and used by britain‘s code breakers as a way of

deciphering german signals traffic during second world war.

A Turing machine is a hypothetical machine thought of by

the mathematician Alan Turing in 1936. Despite its simplicity,

the machine can simulate ANY computer algorithm, no matter

how complicated it is!

Above is a very simple representation of a Turing machine.

It consists of an infinitely-long tape which acts like the memory

in a typical computer, or any other form of data storage. The

squares on the tape are usually blank at the start and can be

written with symbols. In this case, the machine can only

process the symbols 0 and 1 and " " (blank), and is thus said to

be a 3-symbol Turing machine.

At any one time, the machine has a head which is

positioned over one of the squares on the tape. With this head,

the machine can perform three very basic operations:

Read the symbol on the square under the head.

Edit the symbol by writing a new symbol or erasing it.

Move the tape left of right by one square so that the

machine can read and edit the symbol on a neighbouring

square.

A simple demonstration

As a trivial example to demonstrate these operations, let's try

printing the symbols "1 1 0" on an initially blank tape:

First, we write a 1 on the square under the head:

Next, we move the tape left by one square:



7

Now, write a 1 on the new square under the head:

We then move the tape left by one square again:

Finally, write a 0 and that's it!

A simple program

With the symbols "1 1 0" printed on the tape, let's attempt to

convert the 1s to 0s and vice versa. This is called bit inversion,

since 1s and 0s are bits in binary. This can be done by passing

the following instructions to the Turing machine, utilising the

machine's reading capabilities to decide its subsequent

operations on its own. These instructions make up a simple

program.

Symbol read Write instruction Move instruction

Blank None None

0 Write 1 Move tape to the right

1 Write 0 Move tape to the right

The machine will first read the symbol under the head,

write a new symbol accordingly, then move the tape left or

right as instructed, before repeating the read-write-move

sequence again.

Let's see what this program does to our tape from the

previous end point of the instructions:


Get Complete Book At Educreation Store

www.educreation.in



Documents

Sample Copy. Not for Distribution.the cosmos. Information seems to be the driving force behind the physical structure of the universe. It appears to solve the big scientific questions