How much information does a language have?

• Shanon, C. Prediction and Entropy of Printed English, Bell System Technical Journal, 1951

Motivation/Skills

RedundancyThe redundancy of ordinary English, not

considering statistical structure over greater distances than about eight letters, is roughly 50%. This means that when we write

En_ _ _sh ha_f o_ w_ _t w_ w_ _te i_ dete_ _ _ _e_ b_ t_e str_ct_r_ _ f _ _ _ lang_ _ _ _ a_d H_ _f i_ c_os_n fre_ _ _

Redundancy =1-H/Hmax

Entropy

How much information is produced on average

for each letter

i

ii ppH log

27

1

logi

ii ppH

‘L’Evêqe en effet est très streect: le clergé, de temps en temps, se permet de révéler ses préférences envers des

‘événements’ frenchement débreedés, mets l’évêqe hème qe ses fêtes respectent des règles sévères et les

trensgresser, c’est fréqemment reesqer de se fère relegger’.

Saisi par l'inspiration, il composa illico un lai, qui, suivant la tradition du Canticum Canticorum Salomonis,

magnifiait l'illuminant corps d'Anastasia : Ton corps, un grand galion où j'irai au long-cours, un sloop, un brigantin tanguant sous mon roulis, Ton front, un fort dont j'irai à

l'assaut, un bastion, un glacis qui fondra sous l'aquilon du transport qui m'agit,

>

0.131E0.105T0.082A0.08O

0.071N0.068R0.063I0.061S0.053H0.038D0.034L0.029F0.028C0.025M0.025U0.02G0.02Y0.02P

0.015W0.014B0.009V0.004K0.002X0.001J0.001Q8E-04Z

13.4EnglishS

01.4SpanishS

How much information is obtained by adding one

letter?

ji

ii jbpLogjbp,

2 ),(),(

S E

i

ii bpLogbp )()( 2 NF

E

NN FLimH

0.131E

0.105T

0.082A

0.002X0.001J0.001Q8E-04Z

SE

FnBits per letter

F04.75

F14.03

F23.32

F33.1

3 order

IN NO IST LAT WHEY CRATICT FROURE BIRS GROCID PONDENOME OF

DEMONSTURES OF THE REPTAGIN IS REGOACTIONA OF CRE.

#WordProbability

1The.071

2of.034

3and.03

Vocabulary size (no. lemmas)

%of content in OEC

Example lemmas

10 25% the, of, and, to, that, have

100 50% from, because, go, me, our, well, way

1000 75% girl, win, decide, huge, difficult, series

7000 90% tackle, peak, crude, purely, dude, modest

50,000 95% saboteur, autocracy, calyx, conformist

>1,000,000 99% laggardly, endobenthic, pomological

#WordProbability

1The.071

2of.034

3and.03

Zipf’s Law

82.11wordF

nPn

1.

11

nnP 1

8727

1

n

nP

62.2Length

Fword

Is English trying to warn us?

992-995 America ensure oil opportunity

2629-2634 bush admit specifically agents smell denied

16047-16048 arafat unhealthy

#WordProbability

1The.071

2of.034

3and.03

How to continue?

Aoccdrnig to rseearch at an Elingsh uinervtisy, it deosn't

mttaer in waht oredr the ltteers in a wrod are, the

olny iprmoatnt tihng is that the frist and lsat ltteer is at the rghit pclae. The rset can be a toatl mses and you can

sitll raed it wouthit a porbelm. Tihs is bcuseae we do not raed ervey lteter by

it slef but the wrod as a wlohe.

Revealing the statistic of the language

• Q….. 2034 words start with q

• ….q 8 words finish with q

….q …. Ira0q q0.1

Revealing the statistic of the language

THERE IS NO REVERSE ON A MOT0RCYCLE

1115112112111511711121321227111141111131

FRlEND 0F MINE FOUND THIS OUT

861311111111111621111112111111

RATHER DRAMATICALLY THE OTHER DAY

41111111151111111111161111111111111R R R R

4 1 1 1

# of times guessedPosition of the guessed letter

What is the probability to find the number 1 in the third position?

THE 1 1 1REV1 1 5ERS1 1 2MOT1 1 2THA

112

THE 1 1 1ANT3 1 3ERS1 1 2MOT1 1 2HER

222

THA 1 1 2

HEN1 1 3ERS1 1 2TH_

1 1 3AN_

312

HE_ 2 2 1REV1 1 5ERS1 1 2MOT1 1 2AND

311

11...

11 ),,...,(Nii

NNi jiipq

21

),,( 2131

ii

jiipq

LASCUProbability to find the number I in

the place N

21

),,( 2132

ii

jiipq

BoundsTHERE IS NO REVERSE ON A

MOT0RCYCLE

F0 (all the letter have the

same probability)

F1(each letter has its own

probability)

F2(correlation of two letters)

1115112112111511711121321227111141111131

F0 (all the numbers have the

same probability)

F1(each number has its own

probability)

F2(correlation of two

numbers) FN

27

1i

Ni

Ni Logqq

Bounds

27

1i

Ni

NiN LogqqF

27

11 )()(

iN

Ni

Ni FiLogqqi

Entropy

4

47

17

13

3

1

5

3

4

47

17

13

1.3

1.3

1.3

1.3

4

.47

.17

.13

0.013

0.013

0.013

0.013

41q

42q

444 ii LogqqF

27

1

41

4 )(i

ii Logiqqi

Bounds

Redundancy ~ 75%

FnBits per letter

F04.75

F14.03

F23.32

F33.1