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
62.2LengthFword
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 OUT861311111111111621111112111111
RATHER DRAMATICALLY THE OTHER DAY41111111151111111111161111111111111R R R R4 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 2THA112
THE 1 1 1ANT3 1 3ERS1 1 2MOT1 1 2HER222
THA 1 1 2
HEN1 1 3ERS1 1 2TH_
1 1 3AN_312
HE_ 2 2 1REV1 1 5ERS1 1 2MOT1 1 2AND311
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 letterF04.75F14.03F23.32F33.1