Frequenz F Definition Essay

The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Iraqi mathematician Al-Kindi (c. 801–873 AD), who formally developed the method (the ciphers breakable by this technique go back at least to the Caesar cipher invented by Julius Caesar, so this method could have been explored in classical times).

Letter frequency analysis gained additional importance in Europe with the development of movable type in 1450 AD, where one must estimate the amount of type required for each letterform, as evidenced by the variations in letter compartment size in typographer's type cases.

Linguists use letter frequency analysis as a rudimentary technique for language identification, where it's particularly effective as an indication of whether an unknown writing system is alphabetic, syllablic, or ideographic. For example, the Japanese Hiragana syllabary contains 46 distinct characters, which is more than most phonetic alphabets, e.g. the Hawaiian alphabet which has a mere 13 letters, or English which has 26.

No exact letter frequency distribution underlies a given language, since all writers write slightly differently. However, most languages have a characteristic distribution which is strongly apparent in longer texts. Even language changes as extreme as from old English to modern English (regarded as mutually unintelligible) show strong trends in related letter frequencies: over a small sample of Biblical passages, from most frequent to least frequent, enaid sorhm tgþlwu (æ)cfy ðbpxz of old English compares to eotha sinrd luymw fgcbp kvjqxz of modern English, with the most extreme differences concerning letterforms not shared.[1]

Linotype machines for the English language assumed the letter order, from most to least common, to be etaoin shrdlu cmfwyp vbgkjq xz based on the experience and custom of manual compositors. The equivalent for the French language was elaoin sdrétu cmfhyp vbgwqj xz.

Modern International Morse code (generally believed to have been developed by Alfred Vail based on English-language letter frequencies of the 1830s) encodes the most frequent letters with the shortest symbols; arranging the Morse alphabet into groups of letters that require equal amounts of time to transmit, and then sorting these groups in increasing order, yields e it san hurdm wgvlfbk opxcz jyq. Similar ideas are used in modern data-compression techniques such as Huffman coding.

Letter frequency was used by other telegraph systems, such as the Murray Code.

Introduction[edit]

Letter frequencies, like word frequencies, tend to vary, both by writer and by subject. One cannot write an essay about x-rays without using frequent Xs, and the essay will have an idiosyncratic letter frequency if the essay is about the frequent use of x-rays to treat zebras in Qatar. Different authors have habits which can be reflected in their use of letters. Hemingway's writing style, for example, is visibly different from Faulkner's. Letter, bigram, trigram, word frequencies, word length, and sentence length can be calculated for specific authors, and used to prove or disprove authorship of texts, even for authors whose styles are not so divergent.

Accurate average letter frequencies can only be gleaned by analyzing a large amount of representative text. With the availability of modern computing and collections of large text corpora, such calculations are easily made. Examples can be drawn from a variety of sources (press reporting, religious texts, scientific texts and general fiction) and there are differences especially for general fiction with the position of 'h' and 'i', with H becoming more common.

Herbert S. Zim, in his classic introductory cryptography text "Codes and Secret Writing", gives the English letter frequency sequence as "ETAON RISHD LFCMU GYPWB VKJXQ Z", the most common letter pairs as "TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO", and the most common doubled letters as "LL EE SS OO TT FF RR NN PP CC".[2]

Also, to note that different dialects of a language will also affect a letter's frequency. For example, an author in the United States would produce something in which the letter 'z' is more common than an author in the United Kingdom writing on the same topic: words like "analyze", "apologize", and "recognize" contain the letter in American English, whereas the same words are spelled "analyse", "apologise", and "recognise" in British English. This would highly affect the frequency of the letter 'z' as it is a rarely used letter elsewhere in the English language.[3]

The "top twelve" letters constitute about 80% of the total usage. The "top eight" letters constitute about 65% of the total usage. Letter frequency as a function of rank can be fitted well by several rank functions, with the two-parameter Cocho/Beta rank function being the best.[4] Another rank function with no adjustable free parameter also fits the letter frequency distribution reasonably well[5] (the same function has been used to fit the amino acid frequency in protein sequences.[6]) A spy using the VIC cipher or some other cipher based on a straddling checkerboard typically uses a mnemonic such as "a sin to err" (dropping the second "r")[7][8] or "at one sir"[9] to remember the top eight characters.

The use of letter frequencies and frequency analysis plays a fundamental role in cryptograms and several word puzzle games, including Hangman, Scrabble and the television game show Wheel of Fortune. One of the earliest descriptions in classical literature of applying the knowledge of English letter frequency to solving a cryptogram is found in E.A. Poe's famous story The Gold-Bug, where the method is successfully applied to decipher a message instructing on the whereabouts of a treasure hidden by Captain Kidd.[10]

Letter frequencies had a strong effect on the design of some keyboard layouts. The most frequent letters are on the bottom row of the Blickensderfer typewriter, and the home row of the Dvorak Simplified Keyboard.

Relative frequencies of letters in the English language[edit]

There are three ways to count letter frequency that result in very different charts for common letters. The first method, used in the chart below, is to count letter frequency in root words of a dictionary. The second is to include all word variants when counting, such as "abstracts", "abstracted" and "abstracting" and not just the root word of "abstract". This system results in letters like "s" appearing much more frequently, such as when counting letters from lists of the most used English words on the Internet. A final variant is to count letters based on their frequency of use in actual texts, resulting in certain letter combinations like "th" becoming more common due to the frequent use of common words like "the". Absolute usage frequency measures like this are used when creating keyboard layouts or letter frequencies in old fashioned printing presses.

An analysis of entries in the Concise Oxford dictionary, ignoring frequency of word use, gives an order of "EARIOTNSLCUDPMHGBFYWKVXZJQ".[11]

The letter-frequency table below is taken from Pavel Mička's website, which cites Robert Lewand's Cryptological Mathematics.[12]

LetterRelative frequency in the English language
a8.167%8.167

 

b1.492%1.492

 

c2.782%2.782

 

d4.253%4.253

 

e12.702%12.702

 

f2.228%2.228

 

g2.015%2.015

 

h6.094%6.094

 

i6.966%6.966

 

j0.153%0.153

 

k0.772%0.772

 

l4.025%4.025

 

m2.406%2.406

 

n6.749%6.749

 

o7.507%7.507

 

p1.929%1.929

 

q0.095%0.095

 

r5.987%5.987

 

s6.327%6.327

 

t9.056%9.056

 

u2.758%2.758

 

v0.978%0.978

 

w2.360%2.36

 

x0.150%0.15

 

y1.974%1.974

 

z0.074%0.074

 

According to Lewand, arranged from most to least common in appearance, the letters are: etaoinshrdlcumwfgypbvkjxqz Lewand's ordering differs slightly from others, such as Cornell University Math Explorer's Project, which produced a table after measuring 40,000 words.[13]

In English, the space is slightly more frequent than the top letter (e)[14] and the non-alphabetic characters (digits, punctuation, etc.) collectively occupy the fourth position (having already included the space) between t and a.[15]

Relative frequencies of the first letters of a word in the English language[edit]

The frequency of the first letters of words or names is helpful in pre-assigning space in physical files and indexes.[16] Given 26 filing cabinet drawers, rather than a 1:1 assignment of one drawer to one letter of the alphabet, it is often useful to use a more equal-frequency-letter code by assigning several low-frequency letters to the same drawer (often one drawer is labeled VWXYZ), and to split up the most-frequent initial letters — S, A, and C - into several drawers (often 6 drawers Aa-An, Ao-Az, Ca-Cj, Ck-Cz, Sa-Si, Sj-Sz). The same system is used in some multi-volume works such as some encyclopedias. Cutter numbers, another mapping of names to a more equal-frequency code, are used in some libraries.

Both the overall letter distribution and the word-initial letter distribution approximately match the Zipf distribution and even more closely match the Yule distribution.[17]

Often the frequency distribution of the first digit in each datum is significantly different from the overall frequency of all the digits in a set of numeric data—see Benford's law for details.

An analysis by Peter Norvig on Google Books data determined, among other things, the frequency of first letters of English words:[18]

LetterRelative frequency as the first letter of an English word
a11.682%11.682

 

b4.434%4.434

 

c5.238%5.238

 

d3.174%3.174

 

e2.799%2.799

 

f4.027%4.027

 

g1.642%1.642

 

h4.200%4.2

 

i7.294%7.294

 

j0.511%0.511

 

k0.456%0.456

 

l2.415%2.415

 

m3.826%3.826

 

n2.284%2.284

 

o7.631%7.631

 

p4.319%4.319

 

q0.222%0.222

 

r2.826%2.826

 

s6.686%6.686

 

t15.978%15.978

 

u1.183%1.183

 

v0.824%0.824

 

w5.497%5.497

 

x0.045%0.045

 

y0.763%0.763

 

z0.045%0.045

 

Relative frequencies of letters in other languages[edit]

LetterEnglishFrench[19]German[20]Spanish[21]Portuguese[22]Esperanto[23]Italian[24]Turkish[25]Swedish[26]Polish[27]Dutch[28]Danish[29]Icelandic[30]Finnish[31]Czech
a8.167%7.636%6.516%11.525%14.634%12.117%11.745%12.920%9.383%10.503%7.486%6.025%10.110%12.217%8.421%
b1.492%0.901%1.886%2.215%1.043%0.980%0.927%2.844%1.535%1.740%1.584%2.000%1.043%0.281%0.822%
c2.782%3.260%2.732%4.019%3.882%0.776%4.501%1.463%1.486%3.895%1.242%0.565%00.281%0.740%
d4.253%3.669%5.076%5.010%4.992%3.044%3.736%5.206%4.702%3.725%5.933%5.858%1.575%1.043%3.475%
e12.702%14.715%16.396%12.181%12.570%8.995%11.792%9.912%10.149%7.352%18.91%15.453%6.418%7.968%7.562%
f2.228%1.066%1.656%0.692%1.023%1.037%1.153%0.461%2.027%0.143%0.805%2.406%3.013%0.194%0.084%
g2.015%0.866%3.009%1.768%1.303%1.171%1.644%1.253%2.862%1.731%3.403%4.077%4.241%0.392%0.092%
h6.094%0.737%4.577%0.703%0.781%0.384%0.636%1.212%2.090%1.015%2.380%1.621%1.871%1.851%1.356%
i6.966%7.529%6.550%6.247%6.186%10.012%10.143%9.600%*5.817%8.328%6.499%6.000%7.578%10.817%6.073%
j0.153%0.613%0.268%0.493%0.397%3.501%0.011%0.034%0.614%1.836%1.46%0.730%1.144%2.042%1.433%
k0.772%0.049%1.417%0.011%0.015%4.163%0.009%5.683%3.140%2.753%2.248%3.395%3.314%4.973%2.894%
l4.025%5.456%3.437%4.967%2.779%6.104%6.510%5.922%5.275%2.564%3.568%5.229%4.532%5.761%3.802%
m2.406%2.968%2.534%3.157%4.738%2.994%2.512%3.752%3.471%2.515%2.213%3.237%4.041%3.202%2.446%
n6.749%7.095%9.776%6.712%4.446%7.955%6.883%7.987%8.542%6.237%10.032%7.240%7.711%8.826%6.468%
o7.507%5.796%2.594%8.683%9.735%8.779%9.832%2.976%4.482%6.667%6.063%4.636%2.166%5.614%6.695%
p1.929%2.521%0.670%2.510%2.523%2.755%3.056%0.886%1.839%2.445%1.57%1.756%0.789%1.842%1.906%
q0.095%1.362%0.018%0.877%1.204%00.505%00.020%00.009%0.007%00.013%0.001%
r5.987%6.693%7.003%6.871%6.530%5.914%6.367%7.722%8.431%5.243%6.411%8.956%8.581%2.872%4.799%
s6.327%7.948%7.270%7.977%6.805%6.092%4.981%3.014%6.590%5.224%3.73%5.805%5.630%7.862%5.212%
t9.056%7.244%6.154%4.632%4.336%5.276%5.623%3.314%7.691%2.475%6.79%6.862%4.953%8.750%5.727%
u2.758%6.311%4.166%2.927%3.639%3.183%3.011%3.235%1.919%2.062%1.99%1.979%4.562%5.008%2.160%
v0.978%1.838%0.846%1.138%1.575%1.904%2.097%0.959%2.415%0.012%2.85%2.332%2.437%2.250%5.344%
w2.360%0.074%1.921%0.017%0.037%00.033%00.142%5.813%1.52%0.069%00.094%0.016%
x0.150%0.427%0.034%0.215%0.253%00.003%00.159%0.004%0.036%0.028%0.046%0.031%0.027%
y1.974%0.128%0.039%1.008%0.006%00.020%3.336%0.708%3.206%0.035%0.698%0.900%1.745%1.043%
z0.074%0.326%1.134%0.467%0.470%0.494%1.181%1.500%0.070%4.852%1.39%0.034%00.051%1.503%
à00.486%000.072%00.635%00000000
â00.051%000.562%0~0%00000000
á0000.502%0.118%00000001.799%00.867%
å000000001.338%001.190%00.003%0
ä000.578%000001.797%00003.577%0
ã00000.733%0000000000
ą0000000000.699%00000
æ000000000000.872%0.867%00
œ00.018%0000000000000
ç00.085%000.530%001.156%0000000
ĉ000000.657%000000000
ć0000000000.743%00000
č000000000000000.462%
ď000000000000000.015%
ð0000000000004.393%00
è00.271%00000.263%00000000
é01.504%00.433%0.337%00000000.647%00.633%
ê00.218%000.450%0~0%00000000
ë00.008%0000000000000
ę0000000001.035%00000
ě000000000000001.222%
ĝ000000.691%000000000
ğ00000001.125%0000000
ĥ000000.022%000000000
î00.045%0000~0%00000000
ì000000(0.030%)00000000
í0000.725%0.132%00.030%000001.570%01.643%
ï00.005%0000000000000
ı00000005.114%*0000000
ĵ000000.055%000000000
ł0000000002.109%00000
ñ0000.311%00000000000
ń0000000000.362%00000
ň000000000000000.007%
ò0000000.002%00000000
ö000.443%00000.777%1.305%0000.777%0.444%0
ô00.023%000.635%0~0%00000000
ó0000.827%0.296%0~0%001.141%000.994%00.024%
õ00000.040%0000000000
ø000000000000.939%000
ř000000000000000.380%
ŝ000000.385%000000000
ş00000001.780%0000000
ś0000000000.814%00000
š000000000000000.688%
ß000.307%000000000000
ť000000000000000.006%
þ0000000000001.455%00
ù00.058%0000(0.166%)00000000
ú0000.168%0.207%00.166%000000.613%00.045%
û00.060%0000~0%00000000
ŭ000000.520%000000000
ü000.995%0.012%0.026%001.854%0000000
ů000000000000000.204%
ý0000000000000.228%00.995%
ź0000000000.078%00000
ż0000000000.706%00000
ž000000000000000.721%

*See Dotted and dotless I.

The figure below illustrates the frequency distributions of the 26 most common Latin letters across some languages. All of these languages use a similar 25+ character alphabet.

Based on these tables, the 'etaoin shrdlu'-equivalent results for each language is as follows:

  • French: 'esait nruol'; (Indo-European: Romance; traditionally, 'esartinulop' is used, in part for its ease of pronunciation[32])
  • Spanish: 'eaosr nidlt'; (Indo-European: Romance)
  • Portuguese: 'aeosr idmnt' (Indo-European: Romance)
  • Italian: 'eaion lrtsc'; (Indo-European: Romance)
  • Esperanto: 'aieon lsrtk' (artificial language – influenced by Indo-European languages, Romance, Germanic mostly)
  • German: 'enisr atdhu'; (Indo-European: Germanic)
  • Swedish: 'eanrt sildo'; (Indo-European: Germanic)
  • Turkish: 'aeinr lkdım'; (Turkic)
  • Dutch: 'enati rodsl'; (Indo-European: Germanic)[28]
  • Polish: 'aieon wrszc'; (Indo-European: Slavic)
  • Danish: 'ernta idslo'; (Indo-European: Germanic)
  • Icelandic: 'arnie stulð'; (Indo-European: Germanic)
  • Finnish: 'ainte slouk'; (Uralic: Finnic)
  • Czech: 'aeoni tvsrl'; (Indo-European: Slavic)

See also[edit]

References[edit]

  1. ^Moreno, Marsha Lynn (Spring 2005). "Frequency Analysis in Light of Language Innovation"(PDF). Math UCSD. Retrieved 19 February 2015. 
  2. ^Zim, Herbert Spencer. (1961). Codes & Secret Writing: Authorized Abridgement. Scholastic Book Services. OCLC 317853773. 
  3. ^http://www.oxforddictionaries.com/words/british-and-american-spelling
  4. ^Li, Wentian; Miramontes, Pedro (2011). "Fitting ranked English and Spanish letter frequency distribution in US and Mexican presidential speeches". Journal of Quantitative Linguistics. 18 (4): 359. doi:10.1080/09296174.2011.608606. 
  5. ^Gusein-Zade, S.M. (1988). "Frequency distribution of letters in the Russian language". Probl. Peredachi Inf. 24 (4): 102–7. 
  6. ^Gamow, George; Ycas, Martynas (1955). "Statistical correlation of protein and ribonucleic acid composition"(PDF). Proc. Natl. Acad. Sci. 41 (12): 1011–19. doi:10.1073/pnas.41.12.1011. PMC 528190. PMID 16589789. 
  7. ^Friedrich L. Bauer. "Decrypted Secrets: Methods and Maxims of Cryptology". 2006. p. 57.
  8. ^Greg Goebel. "The Rise Of Field Ciphers: straddling checkerboard ciphers" 2009.
  9. ^Dirk Rijmenants. "One-time Pad"
  10. ^Poe, Edgar Allan. "The works of Edgar Allan Poe in five volumes". Project Gutenberg. 
  11. ^"What is the frequency of the letters of the alphabet in English?". Oxford Dictionary. Oxford University Press. Retrieved 29 December 2012. 
  12. ^Mička, Pavel. "Letter frequency (English)". Algoritmy.net. 
  13. ^"Frequency Table". cornell.edu. 
  14. ^"Statistical Distributions of English Text". data-compression.com. Archived from the original on 2017-09-18. 
  15. ^Lee, E. Stewart. "Essays about Computer Security"(PDF). University of Cambridge Computer Laboratory. p. 181. 
  16. ^Herbert Marvin Ohlman. "Subject-Word Letter Frequencies with Applications to Superimposed Coding". [1] Proceedings of the International Conference on Scientific Information (1959).
  17. ^Hemlata Pande and H. S. Dhami. "Mathematical Modelling of Occurrence of Letters and Word’s Initials in Texts of Hindi Language".
  18. ^English Letter Frequency Counts: Mayzner Revisited
  19. ^"CorpusDeThomasTempé". Archived from the original on 2007-09-30. Retrieved 2007-06-15. 
  20. ^Beutelspacher, Albrecht (2005). Kryptologie (7 ed.). Wiesbaden: Vieweg. p. 10. ISBN 3-8348-0014-7. 
  21. ^Pratt, Fletcher (1942). Secret and Urgent: the Story of Codes and Ciphers. Garden City, N.Y.: Blue Ribbon Books. pp. 254–5. OCLC 795065. 
  22. ^"Frequência da ocorrência de letras no Português". Retrieved 2009-06-16. 
  23. ^"La Oftecoj de la Esperantaj Literoj". Retrieved 2007-09-14. 
  24. ^Singh, Simon; Galli, Stefano (1999). Codici e Segreti (in Italian). Milano: Rizzoli. ISBN 978-8-817-86213-4. OCLC 535461359. 
  25. ^Sefik Ilkin Serengil, Murat Akin. "Attacking Turkish Texts Encrypted by Homophonic Cipher" Proceedings of the 10th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications, pp.123-126, Cambridge, UK, February 20–22, 2011.
  26. ^"Practical Cryptography". Retrieved 2013-10-30. 
  27. ^Wstęp do kryptologii, counting [space] 17.2%, [dot point] 0.9%, [comma] 0.9% and [semicolon] 0.5%
  28. ^ ab"Letterfrequenties". Genootschap OnzeTaal. Retrieved 2009-05-17. 
  29. ^"Practical Cryptography". Retrieved 2013-10-24. 
  30. ^"Practical Cryptography". Retrieved 2013-10-24. 
  31. ^"Practical Cryptography". Retrieved 2013-10-24. 
  32. ^Perec, Georges; Alphabets; Éditions Galilée, 1976
Notes

Some useful tables for single letter, digram, trigram, tetragram, and pentagram frequencies based on 20,000 words that take into account word-length and letter-position combinations for words 3 to 7 letters in length. The references are as follows:

  1. Mayzner, M.S.; Tresselt, M.E. (1965). "Tables of single-letter and digram frequency counts for various word-length and letter-position combinations". Psychonomic Monograph Supplements. 1 (2): 13–32. OCLC 639975358. 
  2. Mayzner, M.S.; Tresselt, M.E.;Wolin, B.< R.< (1965). "Tables of trigram frequency counts for various word-length and letter-position combinations". Psychonomic Monograph Supplements. 1 (3): 33–78. 
  3. Mayzner, M.S.; Tresselt, M.E.;Woliin, B.< R,.. (1965). "Tables of tetragram frequency counts for various word-length and letter-position combinations". Psychonomic Monograph Supplements. 1 (4): 79–143. 
  4. Mayzner, M.S.; Tresselt, M.E.Wolin, B,.< R.> (1965). "Tables of pentagram frequency counts for various word-length and letter-position combinations". Psychonomic Monograph Supplements. 1 (5): 144–190. 

External links[edit]

Relative frequencies of letters in text.
Relative frequencies ordered by frequency.

To write a definition essay, you’ll need to define a word that:

  1. has a complex meaning
  2. is disputable (could mean different things to different people)

It wouldn't be wise to choose a word like "cat" for a definition essay. The word, "cat" has a pretty simple meaning, so we'll have trouble writing an entire essay about it.  Similarly, not many people disagree over the definition of the word "cat," which means our definition will be short and ordinary.

What about choosing to define the word, “family”?  Let’s check it out!

  • Does it have a complex meaning? Yes, I could discuss the different types of families that exist in my community.
  • Is the word disputable?  Yes, I could explain that even though the other women on my sports team aren't blood relatives, they are a kind of family.
  • Optional:  Could I discuss the word's origin in a meaningful way?  Yes, look up the word’s origin in the Oxford English Dictionary for additional essay ideas!

Sample Paper

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