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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