Chaos, Communication and Consciousness Module PH19510 Lecture 16 Revision.

Chaos, Communication and ConsciousnessModule PH19510

Lecture 16

Revision

Past Exam Papers

www.aber.ac.uk & follow links:Learning & TeachingPast Exam Papers IMAPSPhysicsExaminations 2007Semester1PH19510

Communications in pre-history

First Communications from pre-history to early manExpressions (1,000,000 BC)Gestures & Body LanguageEarly Spoken language (100,000 BC)First cave paintings (30,000 BC)

Analogue & Digital Information

Analogue InformationAny value between limitsMost ‘real world’ quantities are analogueTemperature, pressure, light intensity etc

Digital InformationOnly discrete values possibleNumbers, Letters, other abstractionsBinary

Noise Margin

Why Binary ?

Noise is endemic in circuits Freedom from noise process information faithfully

0

1Output Device

0

1

Input Device

Codes to Transmit Information

Alphabets - 26 characters Number systems - biunary -- hexagesimal Semaphore

Hand signalling with flags – 26 charactersChappe Tower – 92 symbols, pairs = 8,464

codes Morse – 2 symbols, variable length codes Binary – On/Off

Jean-Maurice-Émile Baudot

1874 Multiplexing printing telegraph system

Up to 4 telegraph channels on single wire

Time Division Multiplexing

5 bit code

Baudot codeBin Hex Dec LTRS FIGS Bin Hex Dec LTRS FIGS

00011 03 3 A - 10111 17 23 Q 1

11001 19 25 B ? 01010 0A 10 R 4

01110 0E 14 C : 00101 05 5 S '

01001 09 9 D $ 10000 10 16 T 5

00001 01 1 E 3 00111 07 7 U 7

01101 0D 13 F ! 11110 1E 30 V ;

11010 1A 26 G & 10011 13 19 W 2

10100 14 20 H # 11101 1D 29 X /

00110 06 6 I 8 10101 15 21 Y 6

01011 0B 11 J <BELL> 10001 11 17 Z "

01111 0F 15 K ( 01000 08 8 <CR> <CR>

10010 12 18 L ) 00010 02 2 <LF> <LF>

11100 1C 28 M . 00100 04 4 <SP> <SP>

01100 0C 12 N , 11111 1F 31 <LTRS> <LTRS>

11000 18 24 O 9 11011 1B 27 <FIGS> <FIGS>

10110 16 22 P 0 00000 00 0 [..unused..]

Pulse code Modulation (PCM)

Sample analogue signal

n-bits 2n levels Quantisation

Noise

Quantisation Noise

PCM Audio Sampling

Rate and number of levels dependent on quality

fsample = 2 x fsignal Speech 8-bit (256 levels) 8kHz CD quality 16-bit (65,536 levels) 44kHz

Many signals down one wire

MultiplexingTime divisionFrequency Division

Time Division Multiplexing (TDM)

First used on telegraph Interleave messages Synchronised clocks Digital Signals

F U D i n a r i v s v e t e r L u s aF i r s t uU n i v e r sD a v e L a

Time

Frequency Division Multiplexing

Speech Signal Modulate 60Khz

Carrier Put many signals

along 1 wire. Separate in frequency

space

60Hz - 64kHz 64kHz - 68kHz

60kHz 64Hz f

f68Khz - 72kHz 72kHz - 76kHz

…

300kHz 4kHz f

The Thermionic ValveThe Diode 1904 J.Fleming Heated filament

Cathode

Electrons liberated If Anode is +ve

Electrons attracted Current Flows

One way device Anode –ve No Flow

Diode

Anode (+ve)

Cathode (-ve)

The Thermionic ValveThe Triode 1907 Lee DeForest Grid between

Cathode & Anode -ve voltage on grid

repels electrons Control of anode

current 1911 Amplification

Anode (+ve)

Cathode (-ve)

Grid

The Cathode Ray Tube (CRT)

Heater

Cathode

Control Grid

AnodesFluorescent

Screen

Focus Coil Deflection

Coils

NPN Bipolar Junction Transistor

Emitter at ground +ve voltage on collector Collector-Base reverse

biased no current Apply +ve voltage on

base Electrons pulled from

emitter into base Collector base depletion

region shrinks many electrons flow

from Emitter to Collector Amplification

n

n

p

Collector

Base

Emitter

1965 - Moore’s Law

Certain minimum cost per component

Complexity doubles every year

Technology drives chip sizes down

Number of components on chipC

ost

/ c

om

pon

en

t

Fixed costs dominate,(sawing, packaging, handling etc)

Yield goes down above certain critical point

Minimum cost/component

Moore’s law over 30 years

Cryptography and Cryptanalysis

Keeping information secret Steganography

Hide the message Cryptography

Obscure the message Cryptanalysis

Undo someone else’s cryptography

Substitution Cipher

Algorithm substitute letters Key cipher alphabet

A I Q P F C WO H J T N U

L B M E V S G Z D X K Y R

Simple cipher alphabet based of pairs of letters

a t t a c k t h e c a s t l e a t d a w n

L K K L S T K D P S L C K A P L K H L G Y

Plain Text

Cipher Text

Cryptanalysis - Code breaking

Al-Kindi 800 – 873 AD Analysis of text

frequency of letters double letters (ee, oo, mm, tt …) adjacent letters single letter words common words

The Enigma Machine

Patented 1921 by Arthur Scherbius

Used in WWII Plugboard

fixed substitution Rotors

substitutionchanges every

character

Plugboard

Rotors

Impact of Computers on Cryptography Pros

Computer can mimic any machine (Turing) Ability to perform complicated encryption easily Working with binary numbers rather than letters,

closer to mathematical process Cons

Cryptanalysis eased Try many keys quickly Computer data tends to have fixed form known

plaintext attacks

Alice, Bob and Eve

Alice wants to send a secret message to Bob

Eve is eavesdropping

Public Key cryptography in use

2 prime numbers p and q Public key N = p × q

Easy to multiply number Difficult to factor Make N > 10308

Chaos – Making a New Science

James Gleick Vintage ISBN

0-749-38606-1

£8.99 http://www.around.com

What is Chaos ?

Not randomness Chaos is

deterministic – follows basic rule or equationextremely sensitive to initial conditionsmakes long term predictions useless

Phase Space

Mathematical map of all possibilities in a system

Eg Simple Pendulum Plot x vs dx/dt Damped Pendulum

Point Attractor Undamped Pendulum

Limit cycle attractor

Damped Pendulum – Point Attractor

velo

cit

y

position

Undamped Pendulum – Limit Cycle Attractor

The ‘Strange’ Attractor

Edward Lorentz From study of weather

patterns Simulation of convection

in 3D Simple as possible with

non-linear terms left in. Aperiodic – doesn’t repeat

The Lorenz Attractor

bzxydt

dz ,xzyrx

dt

dy ,xy

dt

dx

What are Fractals ?

"Clouds are not spheres, coastlines are not circles, bark is not smooth, nor does lightning travel in straight lines" - B.B. Mandelbrot

Fractals are rough or fragmented geometric shapes that can be subdivided into parts, each of which is exactly, or statistically a reduced-size copy of the whole : self-similarity

Dimensions of Objects

Consider objects in 1,2,3 dimensions

Reduce length of ruler by factor, r

Quantity increases by N = rD

Take logs:

D is dimension

D = 1 D = 2 D = 3

r = 2

r = 3

N = 2

N = 3

N = 4

N = 9

N = 8

N = 27

r

ND

log

log

using a ruler of length L (green) - total length = 3L

using a ruler of length 3

L (red) - total length = 4L

using a ruler of length 9

L (blue) - total length =

3L16

To find the fractal dimension, either plot a graph of log(total length) against log(ruler length) - the gradient is (1-D)

Or 26134rND .)log()log(loglog

Fractal Dimension of Koch Snowflake

Past Exam Papers

www.aber.ac.uk & follow links:Learning & TeachingPast Exam Papers IMAPSPhysicsExaminations 2007Semester1PH19510

Review of Course

Communications Communications in pre-history Development of language, writing and counting Telegraph, telephones, television Codes to transmit information Modulation and multiplexing Encryption to hide information

Chaos Simple chaotic system Fractals